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Gain18*(2*4^t-8^t)>0 for0max(2^60*N^5,2^(2*H)) avoiding every finitely compiled denominator/rank witness. All QQ matrices and relative SOURCE projectors compiled before choice." + }, + "all_in_fixed_primitive_fee": { + "F": "48*(q+2)^(32*(N+1)^2)*(A(N)+2)^8", + "actual_cost": "F times positive maximum of the retained stream/route/normalizer/completed-backend constants, fixed anew at each finite level. No primitive has cost0 or a claimed universal cost1.", + "parking": "4*(B_N+C_N) positive FIELD passes per child plus initialization/teardown, with C_N<=48*A(N); F dominates their products.", + "bad_classes": "<=32*N^2 ordinary calls charged separately by the retained moment/cover argument." + }, + "stock": { + "reserve": "[B_N*|GL_N(F_q)|*q^(N^2*(w-1))]^D*S_completed_backend", + "D": "floor(log_N ceil(e/w))+1", + "borrowed_digits": "D*(N^2*(w-1)+ceil(log_q(B_N*|GL_N(F_q)|)))+ceil(log_q S_completed_backend)+1 =O_new(w loge)", + "ownership": "All48whole owned banks for EVERY compiled instance, including suspended ones, get distinct tags; full entry/exit CLEAR charged. No ancestor region is swept or external zero stock assumed." + }, + "eventual_threshold": { + "K_j": "At least16 times sum of F*positive retained primitive constants, reserve/adapter bounds and already frozen backend constant completed at all widths by finite fallback.", + "eta_j": "min(rho-a_j,1-rho-a_j,a_j-b_j)>0", + "e_j": "Fresh integer dominating E_backend^(ceil(2/rho)), borrow threshold, ceil((32*K_j/eta_j)^(ceil(8/eta_j)))+2^(ceil(8/eta_j)).", + "scope": "Constructive finite threshold schema under retained native/compiler/ROW/precision/tape premises. Winning uniform program and decimal threshold are not materialized." + } + }, + "strict_margin_range": { + "C_min": "3505778525569/1000000000000000", + "C_max": "351/100000", + "gamma_upper_bound": [ + "6031406080566339495160720508178211184606898117319925700025/6277101735386680763835789423207666416102355444464034512896", + "6031406080566339495160720508178211184606898117319926058445/6277101735386680763835789423207666416102355444464034512896" + ], + "delta_upper_bound": [ + "1458447552782909211096574548458045751249710606795352542499/1569275433846670190958947355801916604025588861116008628224", + "729223776391454605548287274229022875624855303397676296049/784637716923335095479473677900958302012794430558004314112" + ], + "rank_mass_tails": [ + 753, + 25440, + 73752, + 76776, + 80736, + 89916, + 90996, + 90996, + 31524, + 31524, + 31524, + 31524, + 31524, + 31524, + 37740, + 31080, + 31080, + 31080, + 31080, + 31080, + 31080, + 40404, + 30636, + 30636, + 30636, + 30636, + 30636, + 30636, + 43068, + 30192, + 30192, + 30192, + 30192, + 30192, + 30192, + 45732, + 29748, + 29748, + 29748, + 29748, + 29748, + 29748, + 48396, + 29304, + 29304, + 29304, + 29304, + 29304, + 29304, + 51060, + 28860, + 28860, + 28860, + 28860, + 28860, + 28860, + 53724, + 28416, + 28416, + 28416, + 28416, + 28416, + 28416, + 42402, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 0 + ], + "tensor_reserve_controls": { + "8": 1024, + "39": 1024, + "48": 2048, + "96": 4096, + "192": 8192, + "384": 16384 + }, + "claim": "Under the retained framework, every ordinary saving strictly below this invoice raw crossing is attainable with fresh finite margins. 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"owner": 11036, + "stage": 31, + "begin": 377399, + "end": 399055 + }, + { + "owner": 11037, + "stage": 31, + "begin": 377458, + "end": 399056 + }, + { + "owner": 11038, + "stage": 31, + "begin": 377517, + "end": 399057 + }, + { + "owner": 11039, + "stage": 31, + "begin": 377577, + "end": 399058 + }, + { + "owner": 11040, + "stage": 31, + "begin": 377636, + "end": 399059 + }, + { + "owner": 11041, + "stage": 31, + "begin": 377696, + "end": 399060 + }, + { + "owner": 11042, + "stage": 31, + "begin": 377753, + "end": 399061 + }, + { + "owner": 11024, + "stage": 31, + "begin": 391517, + "end": 399062 + }, + { + "owner": 11025, + "stage": 31, + "begin": 391101, + "end": 399063 + }, + { + "owner": 11026, + "stage": 31, + "begin": 391110, + "end": 399064 + }, + { + "owner": 11027, + "stage": 31, + "begin": 391020, + "end": 399065 + }, + { + "owner": 11028, + "stage": 31, + "begin": 391004, + "end": 399066 + }, + { + "owner": 11029, + "stage": 31, + "begin": 391210, + "end": 399067 + }, + { + "owner": 11043, + "stage": 31, + "begin": 391064, + "end": 399068 + }, + { + "owner": 11044, + "stage": 31, + "begin": 391473, + "end": 399069 + }, + { + "owner": 11045, + "stage": 31, + "begin": 391380, + "end": 399070 + }, + { + "owner": 11033, + "stage": 32, + "begin": 414266, + "end": 414974 + }, + { + "owner": 11046, + "stage": 32, + "begin": 414285, + "end": 414983 + }, + { + "owner": 11068, + "stage": 32, + "begin": 414274, + "end": 414987 + }, + { + "owner": 11052, + "stage": 32, + "begin": 414281, + "end": 414991 + }, + { + "owner": 11022, + "stage": 32, + "begin": 414269, + "end": 414995 + }, + { + "owner": 11066, + "stage": 32, + "begin": 414373, + "end": 415002 + }, + { + "owner": 11064, + "stage": 32, + "begin": 414384, + "end": 415005 + }, + { + "owner": 11032, + "stage": 32, + "begin": 414346, + "end": 415007 + }, + { + "owner": 11047, + "stage": 32, + "begin": 414403, + "end": 415016 + }, + { + "owner": 11051, + "stage": 32, + "begin": 414395, + "end": 415021 + }, + { + "owner": 11050, + "stage": 32, + "begin": 414408, + "end": 415026 + }, + { + "owner": 11062, + "stage": 32, + "begin": 414514, + "end": 415042 + }, + { + "owner": 11049, + "stage": 32, + "begin": 414498, + "end": 415045 + }, + { + "owner": 11060, + "stage": 32, + "begin": 414503, + "end": 415048 + }, + { + "owner": 11053, + "stage": 32, + "begin": 414521, + "end": 415053 + }, + { + "owner": 11030, + "stage": 32, + "begin": 414541, + "end": 415063 + }, + { + "owner": 11031, + "stage": 32, + "begin": 414574, + "end": 415068 + }, + { + "owner": 11054, + "stage": 32, + "begin": 414556, + "end": 415083 + }, + { + "owner": 11056, + "stage": 32, + "begin": 414563, + "end": 415086 + }, + { + "owner": 11058, + "stage": 32, + "begin": 414546, + "end": 415090 + }, + { + "owner": 11048, + "stage": 32, + "begin": 414570, + "end": 415093 + }, + { + "owner": 11069, + "stage": 32, + "begin": 414277, + "end": 417591 + }, + { + "owner": 11067, + "stage": 32, + "begin": 414376, + "end": 417743 + }, + { + "owner": 11065, + "stage": 32, + "begin": 414387, + "end": 417748 + }, + { + "owner": 11061, + "stage": 32, + "begin": 414506, + "end": 417922 + }, + { + "owner": 11063, + "stage": 32, + "begin": 414517, + "end": 417938 + }, + { + "owner": 11059, + "stage": 32, + "begin": 414549, + "end": 418029 + }, + { + "owner": 11057, + "stage": 32, + "begin": 414566, + "end": 418034 + }, + { + "owner": 11055, + "stage": 32, + "begin": 414559, + "end": 418049 + }, + { + "owner": 11023, + "stage": 32, + "begin": 414510, + "end": 418085 + }, + { + "owner": 11034, + "stage": 32, + "begin": 399532, + "end": 421304 + }, + { + "owner": 11035, + "stage": 32, + "begin": 399589, + "end": 421305 + }, + { + "owner": 11036, + "stage": 32, + "begin": 399650, + "end": 421306 + }, + { + "owner": 11037, + "stage": 32, + "begin": 399709, + "end": 421307 + }, + { + "owner": 11038, + "stage": 32, + "begin": 399768, + "end": 421308 + }, + { + "owner": 11039, + "stage": 32, + "begin": 399828, + "end": 421309 + }, + { + "owner": 11040, + "stage": 32, + "begin": 399887, + "end": 421310 + }, + { + "owner": 11041, + "stage": 32, + "begin": 399947, + "end": 421311 + }, + { + "owner": 11042, + "stage": 32, + "begin": 400004, + "end": 421312 + }, + { + "owner": 11024, + "stage": 32, + "begin": 413768, + "end": 421313 + }, + { + "owner": 11025, + "stage": 32, + "begin": 413352, + "end": 421314 + }, + { + "owner": 11026, + "stage": 32, + "begin": 413361, + "end": 421315 + }, + { + "owner": 11027, + "stage": 32, + "begin": 413271, + "end": 421316 + }, + { + "owner": 11028, + "stage": 32, + "begin": 413255, + "end": 421317 + }, + { + "owner": 11029, + "stage": 32, + "begin": 413461, + "end": 421318 + }, + { + "owner": 11043, + "stage": 32, + "begin": 413315, + "end": 421319 + }, + { + "owner": 11044, + "stage": 32, + "begin": 413724, + "end": 421320 + }, + { + "owner": 11045, + "stage": 32, + "begin": 413631, + "end": 421321 + } +] diff --git a/research/g20-helper-split/PROOF.md b/research/g20-helper-split/PROOF.md new file mode 100644 index 0000000000..1253292326 --- /dev/null +++ b/research/g20-helper-split/PROOF.md @@ -0,0 +1,153 @@ +# The G20 split and its complete bill + +## 1. Exact source and cut + +Use the PR5671 word at31bd16e74c3833a9fb25dca17a0f00fa9046325c. +All normalized values are linear over F2. QUERY changes the physical +frame and leaves the normalized row unchanged. ADD uses one actual +common frame. Each owned ERASE removes its arbitrary input column. + +Immediately after event14875, fields19,465,466 and665 have frame508. +This frame has dimension4. Let A be the complete scalar prefix and B +its suffix, with all684 entry and output columns. Define + + a = e19^T + e465^T, b = e465 + e466 + e665, + c = e465^T, d = e297 + e465. + +The executable check proves aA=c, Bb=d and ab=cd=1. Both boundary +vectors use retained helpers with entrance frame1 of dimension8 and +exit frame0. No main or owned input occurs in c. No main or owned +output occurs in d. These are exact row identities, not point samples. + +The helper basis G is the single ADD297,465. Its row465 is c and +Gd=e465. The cut basis J is + + ADD465,19; ADD466,465; ADD665,465. + +Its row465 is a and Jb=e465. Each operation is its own inverse over F2; +the inverse program uses reverse order. All basis operations use one +physical frame. Their exact matrices need no recursive call. + +Apply G inverse at the input. Run the source prefix and apply J. +Field465 now contains the independent old helper coordinate. Keep it +as an early output at frame508. New independent input684 starts at +frame508. Substitute it for role465 in J inverse, the full source +suffix and the final G. Give field684 final frame0. Every other output +has its source endpoint. The new program has eight more ADDs. + +For helper vector h and successor input z, the suffix state changes +by b(z-c h). Its helper output is h+d(z-c h). The final basis gives +G h+e465(z-c h). Thus the old independent coordinate has already +returned at frame508, and the successor independently returns at0. +No helper is assumed zero. The early output stays public and live. +No new owned field, COPY or CLEAR is needed. + +## 2. Physical action and target normalization + +For each actual frame U, let D_U denote its source bit coframe operator. +The physical value of a normalized row is the corresponding D_U image. +Every common-frame ADD commutes with D_U. Nested source query frames +satisfy the exact rational projector identities. This induction applies +to arbitrary functions and every positive tensor width under the +retained native contract. It is not restricted to the two finite address +moduli used as controls. + +The new targets are D_508 D_1 and D_0 D_508. Their residual ranks are4 +and4. The first uses the complement of frame508; the second uses +frame508 itself. `MATCHER.json` contains the actual rational forward +basis and inverse. Both matrix products are the identity, and the +frame and complement are orthogonal. The complete fee includes both +directions and both paired address halves:5,472 new coefficient terms +and72 new route passes over all36 targets. Their positive fixed fees +enter the finite ordinary bound. + +All685 independent local columns are checked in forward and separate +adjoint replays. Each includes arbitrary dirty owned inputs. A dynamic +bit iterator covers the new public column684; the inherited iterator +was bounded by the old field count. The complete frame induction and +source formulas, rather than finite point samples alone, supply the +all-function claim. + +## 3. How far the cut strategy was taken + +At every cut and physical common-frame bank, group helpers by their +entrance and exit frames. The cut frame must lie strictly between both +boundary frames. The current domain requires a helper in that group +as the physical pivot. Other public fields and existing owned fields +may occur in the cut bank. + +For each group, remove its input columns from A's bank rows and its +output rows from B's bank columns. Compute the two exact kernels. +Their vectors give a and b with aA=c and Bb=d supported on the group. +A candidate needs both ab=1 and cd=1. The second test excludes empty +owned coordinates that carry no independent helper input. + +The search tests each left kernel basis vector and each sum of two +basis vectors. This suffices for existence of a left vector for which +both right-side linear functionals are nonzero: if no basis vector +works, choose one on which the first functional is nonzero and one +on which the second is nonzero. Each other's functional is then zero, +so their sum works. For two nonzero right linear functionals, either +they agree or their pair is surjective onto F2 squared. The code +constructs a right vector with both values one in each case. + +Every touched bank is checked after each event; unchanged banks have +unchanged matrices. Exact tuples remove duplicate contexts. The source +has7,412 distinct contexts and six basis witnesses at the two frames. +The4+4 split gives more concave credit than7+1 for0 0, 0>i&1] +def need(c,m): + if not c:raise ValueError(m) +def replay(w): + n=len(w['start']);rows=[1<>p&d>>p&1),p));actual=st[p];av=sum(1<>s&1:b^=1<>p&1): + j=bits(a)[0] + add(p,j);add(j,p);add(p,j) + for i in bits(a^rows[p]): + # After the swap, original coordinate i may occupy the swapped role. + q=next(q for q,row in rows.items()if row==1<>p&1,'Basis row formed') + for i in bits(b^(1<=660),W[2+len(pivots):]));need(N==11022,'Independent successor inputs included') + values=[1<0,'Positive rank');source.append({'event':len(events),'prefix_sha256':prefix.hexdigest(),'owner':d,'version':versions[d],'epoch':epochs[d],'rank':k,'detail':detail,'RAW_hex':hex(values[d]),'function_identity':'Exact literal program prefix plus current owner/epoch/version and actual geometric source job; RAW bitmap is extra evidence, not a claim of purity.'});paid[k]+=1;versions[d]+=1;emit(['QUERY',d,k,detail]) + def swap(d,s,why):add(d,s,why);add(s,d,why);add(d,s,why) + def boundary(program,why): + for op,d,s in program: + for p in range(111): + if op=='ADD':add(compact[d*111+p],compact[s*111+p],why) + else:need(op=='SWAP','Controller opcode');swap(compact[d*111+p],compact[s*111+p],why) + boundary(controller['boundaries']['right_program'],'RIGHT_BOUNDARY') + thick=controller['invoice']['thick_stages'];stage_index={s:i for i,s in enumerate(thick)} + for event in controller['physical_events']: + op=event[0] + if op=='LOCAL': + _,stage,pair,rev=event;x,y=2*pair,2*pair+1 + if rev:x,y=y,x + helper=3552+436*stage_index[stage] + def owner(r): + if r==684:return 11004+stage_index[stage] + if r==658:return center + if r==659:return shadow + if r in pivotwork:return pivotwork[r] + if r in snapshotwork:return snapshotwork[r] + return compact[(x if r<111 else y)*111+r%111]if r<222 else compact[helper+r-222] + sx=[values[owner(i)]for i in range(111)];sy=[values[owner(111+i)]for i in range(111)];helpers=[r for r in range(222,658)if r not in pivotwork]+[684];before={r:values[owner(r)]for r in helpers} + if stage: + for bank in(x,y): + for p in range(111):emit(['PAID_PORT_ROUTE',stage,compact[bank*111+p],p,'ENTRY']) + start=len(events);lp=Counter();st=local['start'][:];livebegin={} + for ix,e in enumerate(local['records']): + typ,d=e[:2];gd=owner(d) + if typ=='ERASE': + erase(gd,['LOCAL',stage,ix],e[2]);st[d]=e[2] + if gd in livebegin:episodes.append({'owner':gd,'stage':stage,'begin':livebegin.pop(gd),'end':len(events)-1}) + elif typ=='INIT':need(values[gd]==0,'Whole zero INIT');st[d]=e[2];emit(['OWNED_ZERO_HEADER',gd,e[2],stage]) + elif typ=='ADD': + s,f=e[2:];need(st[d]==st[s]==f,'Actual instantiated coframe') + if gd in W and gd not in livebegin:livebegin[gd]=len(events) + add(gd,owner(s),['LOCAL',stage,f,ix]) + elif typ in('Q','ZERO_Q'): + a,b,k=e[2:];need(st[d]==a,'Current instantiated query frame');st[d]=b + if typ=='Q':query(gd,k,['LOCAL_INVERSE',stage,a,b,ix]);lp[k]+=1 + else:need(values[gd]==0,'Zero only free query');emit(['WHOLE_ZERO_FRAME',gd,a,b,k,stage]) + else:raise ValueError('Local opcode '+typ) + need(not livebegin and st==local['final'],'No live local owned state at return') + need(all(values[owner(i)]==sx[i]and values[owner(111+i)]==sy[i]^sx[i]for i in range(111)),'All retained main RAW inputs') + need(all(values[owner(r)]==before[r]for r in helpers)and all(values[w]==0 for w in W),'All415 independent retained helper inputs and48owned returns') + need(lp==Counter(read(R/'LOCAL-RESULT.json')['stats']['paid'])or lp==Counter({int(k):v for k,v in read(R/'LOCAL-RESULT.json')['stats']['paid'].items()}),'Actual local query count') + calls.append({'stage':stage,'pair':pair,'source_bank':x,'target_bank':y,'old_direction_inverse':rev,'new_direction_inverse':True,'helper_old_owner_begin':helper,'core_begin':start,'core_end':len(events),'owned_global_indices':W,'retained_helper_count':415,'paid':dict(lp)}) + if stage: + for bank in(x,y): + for p in range(111):emit(['PAID_PORT_ROUTE',stage,compact[bank*111+p],p,'RETURN']) + elif op=='QUERY_SHEAR': + _,stage,pair,rev=event;x,y=2*pair,2*pair+1 + if rev:x,y=y,x + for p in range(111): + src,dst=compact[x*111+p],compact[y*111+p];need(values[center]==0,'Clean thin scratch');v=versions[src];begin=len(events);add(center,src,['THIN_COPY',stage,p]);query(center,1,['THIN',stage,p]);add(dst,center,['THIN_DELIVER',stage,p]);need(versions[src]==v,'Thin immutable SOURCE');erase(center,['THIN',stage,p]);episodes.append({'owner':center,'stage':stage,'kind':'THIN','begin':begin,'end':len(events)-1}) + elif op=='IDLE': + _,pair,stages=event;k=7*len(stages) + for bank in(2*pair,2*pair+1): + for p in range(111):query(compact[bank*111+p],k,['WHOLE_IDLE',stages,p]) + elif op=='ADD': + for p in range(111):add(compact[event[1]*111+p],compact[event[2]*111+p],'BRIDGE') + else: + need(op=='SWAP','Known controller event') + for p in range(111):swap(compact[event[1]*111+p],compact[event[2]*111+p],'FINAL_SWAP') + boundary(controller['boundaries']['left_program'],'LEFT_BOUNDARY') + for d in W:erase(d,'GLOBAL_EXIT_TEARDOWN') + need(values==[1<0,"Exact tensor contraction margin") + cover=F(1,10**14);L.need(2**60*cover>256,"Paid regular cover and prime guard") + c1=uniform-cover;backend=F(L.read(L.R/'prior/ORDINARY-RESULT.json')['admitted']) + grid=10**15 + for level in result['finite_backend_levels']: + a=F(99,100)*c1+F(1,100)*backend + numerator=-((-a.numerator*grid)//a.denominator)-1;b=F(numerator,grid) + L.need(backend=1024 and v%1024==0 and 256*v>=4*v*64,'Explicit tensor count envelope') + return{'status':'PASS_POSITIVE_NEW_FINITE_FEE_AND_STOCK_SCHEMA','base_counts':{'raw_records':raw,'new_matcher_coefficient_terms':matcher_terms,'all_XOR_CLEAR_INIT_zeroheader_passes':scans,'parent_parking_FIELD_passes':park,'internal_and_wholejob_routes':routes,'coarse_primitive_count_with_dimension_work':base,'strict_upper':2**64,'all_owned_allocated':owned,'owned_productive_credit':0}, + 'fixed_tensor_unit':{'v':v,'K':'2^'+str(256*v),'meaning':'Bounds fixed integer ranks, all role/round/operation inventories after tensoring, charged target completion and charged paid splitting.'}, + 'finite_compiler':{'N':'2^'+str(H1),'J(n)':'(n+1)^4*K^(4*n+4)','A(1)':'K^4','A(n)':'(J(n)+2)^4*(A(n-1)+2)^(4*n+8)','counts':'Productive roles B_N, paid leaves P_N, instances and primitive descriptions <=A(N). Each compiled instance gets48distinct owned banks; C_N<=48*A(N). Denominator replication product <=A(n-1)^(n-1).'}, + 'height_prime':{'base_height_bits':1024,'T':'(2*N+2)^4*(A(N)+2)^2','H':'1026*4^(T+1)','q':'Choose odd prime q>max(2^60*N^5,2^(2*H)) avoiding every finitely compiled denominator/rank witness. All QQ matrices and relative SOURCE projectors compiled before choice.'}, + 'all_in_fixed_primitive_fee':{'F':'48*(q+2)^(32*(N+1)^2)*(A(N)+2)^8','actual_cost':'F times positive maximum of the retained stream/route/normalizer/completed-backend constants, fixed anew at each finite level. No primitive has cost0 or a claimed universal cost1.','parking':'4*(B_N+C_N) positive FIELD passes per child plus initialization/teardown, with C_N<=48*A(N); F dominates their products.','bad_classes':'<=32*N^2 ordinary calls charged separately by the retained moment/cover argument.'}, + 'stock':{'reserve':'[B_N*|GL_N(F_q)|*q^(N^2*(w-1))]^D*S_completed_backend','D':'floor(log_N ceil(e/w))+1','borrowed_digits':'D*(N^2*(w-1)+ceil(log_q(B_N*|GL_N(F_q)|)))+ceil(log_q S_completed_backend)+1 =O_new(w loge)','ownership':'All48whole owned banks for EVERY compiled instance, including suspended ones, get distinct tags; full entry/exit CLEAR charged. No ancestor region is swept or external zero stock assumed.'}, + 'eventual_threshold':{'K_j':'At least16 times sum of F*positive retained primitive constants, reserve/adapter bounds and already frozen backend constant completed at all widths by finite fallback.','eta_j':'min(rho-a_j,1-rho-a_j,a_j-b_j)>0','e_j':'Fresh integer dominating E_backend^(ceil(2/rho)), borrow threshold, ceil((32*K_j/eta_j)^(ceil(8/eta_j)))+2^(ceil(8/eta_j)).','scope':'Constructive finite threshold schema under retained native/compiler/ROW/precision/tape premises. Winning uniform program and decimal threshold are not materialized.'}} +def run(): + invoice=L.read(R/'INVOICE.json');glob=L.read(R/'GLOBAL-RESULT.json');P={int(k):v for k,v in invoice['paid'].items()};T={int(k):v for k,v in invoice['targets'].items()} + need(sum(T.values())==11022 and sum(P.values())==56223 and T.get(4,0)==36 and T[8]==7434 and P.get(7,0)==0,'Actual complete new target/paid bill') + E=load('nine_credited_interval',S/'ordinary-certificate/inputs/credited_intervals.py');I=load('nine_independent_series',S/'ordinary-certificate/inputs/separate_series.py') + tested=F('.00350741073843');uniform=F('.00350741073842');cover_gap=F(1,10**14);rho=F(1,100);reserve=F(1,2**48);v=tensor_degree(reserve);t=1-tested;u=F(1,5) + target=E.moment(T,t);paid=E.moment(P,t);alpha=E.divide(paid,target);gamma=E.divide(E.moment(P,t+u),E.mul(E.power(17,u),target));delta=E.divide((F(11022*18),)*2,E.mul(E.power(17,tested),target)) + need(alpha[1]<1-reserve and gamma[1]0 if sign>0 else margin[1]<0,'Independent root sign '+label);cross[label]={'saving':c,'margin':margin} + need(F(31,32)**1280 and 17**64<18**63 and max(T)<256,'Charged completion, separation and ambient') + z=1-uniform;z0=(t+z)/2;gap=z0-t;h=F(1,64);H0,H1=compiler_cutoffs(tested,uniform,v) + need(H0>=8*v and H0*h*gap>gap*(5+8*h)*v+1+8*v*(1-z0)and H1*(z-z0)>H0*(1-z0),'Fresh finite integer compiler thresholds') + C1=uniform-cover_gap;need(F(2**60)*cover_gap>256,'Cover/bad-prime gap') + backend=F(L.read(R/'prior/ORDINARY-RESULT.json')['admitted']);old=backend;levels=[] + for j in range(1,6): + a=(1-rho)*C1+rho*backend;b=below_grid(a,10**15);need(backendold,'New complete ordinary component saving') + cmin=F(L.read(R/'prior/ORDINARY-RESULT.json')['admitted']);cmax=F('.00351') + worst_target=E.moment(T,1-cmax) + worst_gamma=E.divide(E.moment(P,1-cmin+u),E.mul(E.power(17,u),worst_target)) + worst_delta=E.divide((F(11022*18),)*2,E.mul(E.power(17,cmin),worst_target)) + need(worst_gamma[1]=a)-sum(k*n for k,n in P.items() if k>=a) for a in range(1,129)] + need(min(tails)>=0 and tails[0]==753,'Strict first-moment monotonicity from rank-mass tails') + range_certificate={'C_min':cmin,'C_max':cmax,'gamma_upper_bound':worst_gamma,'delta_upper_bound':worst_delta, + 'rank_mass_tails':tails,'tensor_reserve_controls':controls(), + 'claim':'Under the retained framework, every ordinary saving strictly below this invoice raw crossing is attainable with fresh finite margins. This is not a global optimality claim.'} + + result={'status':'PASS_CONDITIONAL_G20_HELPER_SPLIT_ORDINARY_FIVE_FINITE_LEVELS','invoice':invoice,'params':{'tested':tested,'uniform':uniform,'cover_gap':cover_gap,'rho':rho,'v':v,'alpha_gap':reserve,'grid_denominator':10**15,'prime_multiplier':2**60,'cutoff':17,'floor':18,'u':u},'raw_crossing_independent_exact':cross,'tail':{'alpha':alpha,'gamma':gamma,'delta':delta,'normalized_surplus':surplus,'H0':H0,'H1':H1},'C1':C1,'finite_backend_levels':levels,'admitted':backend,'comparator':old,'relative_gain':backend/old-1,'relative_gain_percent':100*(backend/old-1),'uniform_signed_invoice_improvement':'Relative to PR5671: Pnew=Pold; Tnew-Told=36H4-18H8. Gain18*(2*4^t-8^t)>0 for00 for0max(2^60*N^5,2^(2*H)) avoiding every finitely compiled denominator/rank witness. All QQ matrices and relative SOURCE projectors compiled before choice." + }, + "all_in_fixed_primitive_fee": { + "F": "48*(q+2)^(32*(N+1)^2)*(A(N)+2)^8", + "actual_cost": "F times positive maximum of the retained stream/route/normalizer/completed-backend constants, fixed anew at each finite level. No primitive has cost0 or a claimed universal cost1.", + "parking": "4*(B_N+C_N) positive FIELD passes per child plus initialization/teardown, with C_N<=48*A(N); F dominates their products.", + "bad_classes": "<=32*N^2 ordinary calls charged separately by the retained moment/cover argument." + }, + "stock": { + "reserve": "[B_N*|GL_N(F_q)|*q^(N^2*(w-1))]^D*S_completed_backend", + "D": "floor(log_N ceil(e/w))+1", + "borrowed_digits": "D*(N^2*(w-1)+ceil(log_q(B_N*|GL_N(F_q)|)))+ceil(log_q S_completed_backend)+1 =O_new(w loge)", + "ownership": "All48whole owned banks for EVERY compiled instance, including suspended ones, get distinct tags; full entry/exit CLEAR charged. No ancestor region is swept or external zero stock assumed." + }, + "eventual_threshold": { + "K_j": "At least16 times sum of F*positive retained primitive constants, reserve/adapter bounds and already frozen backend constant completed at all widths by finite fallback.", + "eta_j": "min(rho-a_j,1-rho-a_j,a_j-b_j)>0", + "e_j": "Fresh integer dominating E_backend^(ceil(2/rho)), borrow threshold, ceil((32*K_j/eta_j)^(ceil(8/eta_j)))+2^(ceil(8/eta_j)).", + "scope": "Constructive finite threshold schema under retained native/compiler/ROW/precision/tape premises. Winning uniform program and decimal threshold are not materialized." + } + }, + "strict_margin_range": { + "C_min": "3497804579519/1000000000000000", + "C_max": "351/100000", + "gamma_upper_bound": [ + "6031553312937429052053920596336788169151139422077357308513/6277101735386680763835789423207666416102355444464034512896", + "753944164117178631506740074542098521143892427759669708369/784637716923335095479473677900958302012794430558004314112" + ], + "delta_upper_bound": [ + "5687894767170268958822245021550810577848310158991834291/6129982163463555433433388108601236734474956488734408704", + "728050530197794426729247362758503753964583700350954814007/784637716923335095479473677900958302012794430558004314112" + ], + "rank_mass_tails": [ + 753, + 25440, + 73752, + 76776, + 80880, + 90060, + 91140, + 91140, + 31524, + 31524, + 31524, + 31524, + 31524, + 31524, + 37740, + 31080, + 31080, + 31080, + 31080, + 31080, + 31080, + 40404, + 30636, + 30636, + 30636, + 30636, + 30636, + 30636, + 43068, + 30192, + 30192, + 30192, + 30192, + 30192, + 30192, + 45732, + 29748, + 29748, + 29748, + 29748, + 29748, + 29748, + 48396, + 29304, + 29304, + 29304, + 29304, + 29304, + 29304, + 51060, + 28860, + 28860, + 28860, + 28860, + 28860, + 28860, + 53724, + 28416, + 28416, + 28416, + 28416, + 28416, + 28416, + 42402, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 0 + ], + "tensor_reserve_controls": { + "8": 1024, + "39": 1024, + "48": 2048, + "96": 4096, + "192": 8192, + "384": 16384 + }, + "claim": "Under the retained framework, every ordinary saving strictly below this invoice raw crossing is attainable with fresh finite margins. This is not a global optimality claim." + }, + "whole_kappa": null, + "assumptions": "Same retained native/allcolumn arbitraryinput/ROW/spectator, mixed-target finite compiler, completed ordinary fallback, precision and fixed-tape contracts as PR4760/4814; no full theorem verification claimed." +} diff --git a/research/g20-helper-split/prior/PROOF.md b/research/g20-helper-split/prior/PROOF.md new file mode 100644 index 0000000000..e584778c8b --- /dev/null +++ b/research/g20-helper-split/prior/PROOF.md @@ -0,0 +1,89 @@ +# Source-bound late binding and complete admission + +## 1. Exact source and causal identity + +Pin Dugongue PR5665 at `3cbf1765c9b680ca0a257de9c79f2bc51cce59fa` and the completed PR5667 word at `e9f3375fc06f639285f4fbca44c3280831f84318`. The literal forward source is `research/bit-g20-nine-owned-relations/vendor/g20/provider/data/FORWARD.json.gz` at `5e0052ca0aa3036a3afa8b0438927377c8d97d53`. The runtime uses the inverse word. All consumed files have byte hashes and original source paths. + +The retained endpoint is independent of each full helper entrance. Before a helper's first outward read, its old prefix has the form `h=Lh0+b(x)`, with L invertible, and cannot affect any other current field. To assign a current value v at that cut, choose the counterfactual old entrance `h0=L^-1(v-b(x))`. The runtime does not compute that value. It writes v at the actual shared frame and follows the old suffix. The retained outputs stay equal to their old endpoint. Its old independent helper target must be removed. + +For several cuts, process their first outward reads in chronological order. A helper not yet read cannot affect an earlier binding. The counterfactual entrances can therefore be chosen successively. This is the causal theorem in the frozen proposal; no simultaneous inverse system is assumed. + +## 2. Actual emitted cuts + +The chosen helpers are 223, 319, 331, 344, 371, 375, 484, 501 and 551. The replay checks all nine forward source rows against the literal bytes. Each has one unobserved rank-one query, destination-only prefix additions, and a first read in a three-addition receiver block at a shared rank-seven frame. The three donors are distinct from the other newly retired helpers. + +At global entry, clear each now-owned helper, including its arbitrary dirty entrance. Omit its unobserved prefix. In its three-addition block, perform the other two additions first. While the helper is zero, acquire the actual shared frame. Execute `h += y` and retain `y += h`. Characteristic two makes the whole receiver zero. The old rank-seven query is replaced by its known-zero header transition. Every other suffix instruction remains. Clear each retired output at its old final frame. + +The copy is the literal old pointwise common-frame operation. The native replay checks the actual frame at each ADD. This does not infer matching from scalar equality across two charts. The full native/ROW premise is retained. No productive receiver input is erased: its current information enters the owned helper and the exact suffix preserves its final endpoint. + +The old word's 39 owned fields and these nine distinct retired fields give 48. The word has 636 retained original fields and 684 total entry columns. The scalar and native tests include every column. Physical fixtures use two odd address moduli and the written causal identity is valid on the complete payload module. The source physical main and helper endpoint involutions supply both orientations; destructive clears are not reversed to construct an inverse. + +## 3. Exhausted first-read model + +The model permits one retained full rank-eight helper, deletion of its unobserved invertible unary/destination-only prefix, reordering within its contiguous common-frame receiver ADD block, binding at its last ADD, and omission of the receiver's next write only when that write is a paid native query. No changed suffix, additional receiver assignment, block of helpers, or new native operation belongs to this screen. + +All 423 initially retained full helpers are examined. Helper 413 has a next receiver write outside the model. The remaining 422 candidates comprise nine positive cuts and 413 negative cuts. Their rank-balance counts are `{-7:111,-6:17,-4:180,-2:95,-1:10,0:9}`. The zero-balance cases are exactly the nine `(1,7)->8` splits. + +For a negative case, the sum of removed paid ranks is at most seven. If `07^100`. Thus none improves the signed moment in that interval. The nine chosen cases improve it by strict concavity. Their blocks are disjoint and their joint word passes exact replay. After installing them, all 414 remaining helpers are checked again: 413 negative cases and the same one case outside the model remain. A separate incidence-list method reproduces both complete scans. + +This proves completion of this bounded model, not a global optimum. Changed first readers, block binding, continuation changes or other words require a new screen. + +## 4. Complete caller and paid profile + +Use the same p16/a7 eighteen-call controller. Remove exactly the old global target owners for the nine new helpers in each call. The previous thirteen retired helper owners remain removed. There are 396 retired global originals in total, 11,004 retained original owners, and 48 owned global fields. Each suspended compiled instance later receives a distinct 48-field reserve. + +The full caller checks all retained main and helper outputs and all arbitrary dirty owned columns. Every query has a source descriptor with its exact event, prefix digest, version, epoch, owner and geometric job. Every local use returns all owned fields to zero. The full controller's physical main polynomial check is retained. The separate stream check recounts all queries, targets and ownership boundaries. + +The complete paid histogram is + +``` +{1:24687,2:24156,3:1008,4:1026,5:1836,6:180, + 14:444,21:444,28:444,35:444,42:444,49:444,56:444,63:222} +``` + +The productive histogram is + +``` +{8:7452,15:444,22:444,29:444,36:444,43:444,50:444, + 57:444,64:222,127:222} +``` + +There are 56,223 paid queries and rank surplus 753. Relative to PR5667 the exact moment gain is `162(1+7^(1-C)-8^(1-C))>0`. Relative to PR5512, the prior partial retirements, snapshots and refinements remain present. No lost helper is still credited. + +The global word has 443,094 events: 375,330 ADDs, 3,489 owned CLEARs, 56,223 queries, 324 zero-frame changes, 180 owned zero headers and 7,548 routes. There are 2,529 owned payload episodes. Its stream SHA256 is `5071bc74d8ca909ed0fee2fcd86a955e6448385d5a4f2b57e4e92d53710b2b67`. + +## 5. Fresh strict finite ordinary admission + +Let P and T denote these complete inventories. Two rational-series engines certify the raw crossing in `(.00350577852560,.00350577852564)`. Use tested saving `C=.00350577852559`, uniform saving `U=.00350577852558`, reserve `r=2^-48`, tensor power `v=2048`, and `u=1/5`. They prove + +`P_(1-C)/T_(1-C)<1-r`, + +`P_(1-C+u)/(17^u*T_(1-C))<31/32`, + +`11004*18/(17^C*T_(1-C))<19/20`. + +The exact tensor contraction is `1/(1+vr)+4*2^(-v/32)<1`. The source separation and ambient-rank guards remain. The strict finite compiler rules from PR5667 give `H0=748015044649435137` and `H1=524475016069298931558990496030`. Their inequalities are checked independently. + +The new positive arithmetic majorant uses 517 bits, below the fresh 1024-bit base envelope. All explicit matcher coefficients are included. The base primitive bound is 952,834,512,981: 379,419 scalar/clear/header passes, 2,485,506,384 parent-parking passes, 14,796 routes, all 443,094 records, dimension work for 56,223 queries, and 5,472 frame-506 matcher coefficient terms. These are positive finite counts, not measured runtime. + +Retain the explicit finite recurrences in `prior/PROOF.md`, with `K=2^524288`, `N=2^H1`, and the new 48-field reserve for each compiled instance. Choose fresh coefficients, ranks and denominators before a prime `q>max(2^60*N^5,2^(2H))` avoiding the finite bad-prime set. The fixed primitive multiplier is now `48*(q+2)^(32*(N+1)^2)*(A(N)+2)^8`, multiplied by the positive maximum of all retained and new primitive costs. Owned initialization, full return, parking, routes and normalizers are paid. + +Take cover loss `10^-14`, paid by the exact guard `2^60*10^-14>256`. Thus `L=.00350577852557`. Start from completed backend `b0=.003497804579519`. At each of five levels let `a=.99L+.01b` and set `b=(ceil(10^15*a)-1)/10^15`. The exact admitted sequence is + +``` +.003505698786109 +.003505777728175 +.003505778517596 +.003505778525490 +.003505778525569 +``` + +All adapter, stock, coefficient and rounding gaps are strict. Each backend call uses a completed earlier finite level. Fresh positive constants and eventual thresholds are specified in ORDINARY-RESULT.json. No self-fallback or obsolete owned reserve is used. + +Uniform compiler-tail guards and rank-mass-tail monotonicity are freshly checked on `[b0,.00351]`. Therefore the strict-margin theorem in `prior/PROOF.md` applies: every strict ordinary saving below this invoice's unique crossing is attained with fresh finite parameters. This does not attain the crossing or prove global optimality. The displayed certificate is within 7.1e-14 of the upper bound. + +## 6. Verification and limitations + +Normal and optimized registered commands authenticate all frozen inputs before import, rebuild all artifacts in a fresh copy, and compare exact outputs. Global CPU timing is excluded from deterministic comparison. The two complete domain scans agree. Missing bindings, dirty entry, final return, stale epoch and target-debit controls reject. Finite modular fixtures, written all-input identities and the inherited all-width framework remain separate kinds of evidence. + +Native all-width realization, ROW/spectators, mixed-target compilation, ordinary normalizers/backends, owned erasure/stock, precision/fixed-tape execution and analytic recovery remain premises. The enormous uniform word and rounded multiplier are not materialized. A whole multiplication kappa still needs a compatible Gaussian supplier and outer assembly. No selected change, human mathematical acceptance or formal-kernel proof is claimed. diff --git a/research/g20-helper-split/prior/WORD.json.gz b/research/g20-helper-split/prior/WORD.json.gz new file mode 100644 index 0000000000..784e699ff2 Binary files /dev/null and b/research/g20-helper-split/prior/WORD.json.gz differ diff --git a/research/g20-helper-split/prior/global_retirement.py b/research/g20-helper-split/prior/global_retirement.py new file mode 100644 index 0000000000..3a1a7c07a4 --- /dev/null +++ b/research/g20-helper-split/prior/global_retirement.py @@ -0,0 +1,113 @@ +"""Literal p16/a7 caller with twenty-two retired helper targets and forty-eight owned fields. + +Adapted from ai-nanachi PR5512 global_relations.py. The four retirements +are Dugongue PR5629. Dugongue PR5639 gives two snapshot fusions; this +version adds the third and reuses the zero centre. Implementation by Ali Romman with OpenAI Codex assistance. +Apache-2.0; retain the source notices. + +Retains G20 native controller/geometry; uses the independently checked reverse +physical involution at each full call. No old helper target is given to owned work. +""" +from pathlib import Path +from collections import Counter +from hashlib import sha256 +from time import process_time +import gzip,json,importlib.util,sys +sys.path.insert(0,str(Path(__file__).resolve().parent)) +import integration as L +R=L.R;S=L.S +def need(c,m): + if not c:raise ValueError(m) +def read(p):return L.read(p) +def put(n,x):L.put(n,x) +def run(): + clock=process_time();controller=read(S/'inputs/CONTROLLER.json');base,frames,_=L.source();local=read(R/'WORD.json.gz');owned=local['owned'];pivots=sorted(x for x in owned if x<658);need(pivots==sorted(L.RETIRED),'Exact twenty-two retired helper owners') + oldcalls=read(S/'provider/data/CALLS.json');retired={c['helper_owner_begin']+p-222 for c in oldcalls for p in pivots};retained=[i for i in range(11400)if i not in retired];compact={x:i for i,x in enumerate(retained)};N=len(retained);W=list(range(N,N+len(owned)));center,shadow=W[:2];pivotwork=dict(zip(pivots,W[2:2+len(pivots)]));snapshotwork=dict(zip(sorted(r for r in owned if r>=660),W[2+len(pivots):]));need(N==11004,'New retained original count') + values=[1<0,'Positive rank');source.append({'event':len(events),'prefix_sha256':prefix.hexdigest(),'owner':d,'version':versions[d],'epoch':epochs[d],'rank':k,'detail':detail,'RAW_hex':hex(values[d]),'function_identity':'Exact literal program prefix plus current owner/epoch/version and actual geometric source job; RAW bitmap is extra evidence, not a claim of purity.'});paid[k]+=1;versions[d]+=1;emit(['QUERY',d,k,detail]) + def swap(d,s,why):add(d,s,why);add(s,d,why);add(d,s,why) + def boundary(program,why): + for op,d,s in program: + for p in range(111): + if op=='ADD':add(compact[d*111+p],compact[s*111+p],why) + else:need(op=='SWAP','Controller opcode');swap(compact[d*111+p],compact[s*111+p],why) + boundary(controller['boundaries']['right_program'],'RIGHT_BOUNDARY') + thick=controller['invoice']['thick_stages'];stage_index={s:i for i,s in enumerate(thick)} + for event in controller['physical_events']: + op=event[0] + if op=='LOCAL': + _,stage,pair,rev=event;x,y=2*pair,2*pair+1 + if rev:x,y=y,x + helper=3552+436*stage_index[stage] + def owner(r): + if r==658:return center + if r==659:return shadow + if r in pivotwork:return pivotwork[r] + if r in snapshotwork:return snapshotwork[r] + return compact[(x if r<111 else y)*111+r%111]if r<222 else compact[helper+r-222] + sx=[values[owner(i)]for i in range(111)];sy=[values[owner(111+i)]for i in range(111)];helpers=[r for r in range(222,658)if r not in pivotwork];before={r:values[owner(r)]for r in helpers} + if stage: + for bank in(x,y): + for p in range(111):emit(['PAID_PORT_ROUTE',stage,compact[bank*111+p],p,'ENTRY']) + start=len(events);lp=Counter();st=local['start'][:];livebegin={} + for ix,e in enumerate(local['records']): + typ,d=e[:2];gd=owner(d) + if typ=='ERASE': + erase(gd,['LOCAL',stage,ix],e[2]);st[d]=e[2] + if gd in livebegin:episodes.append({'owner':gd,'stage':stage,'begin':livebegin.pop(gd),'end':len(events)-1}) + elif typ=='INIT':need(values[gd]==0,'Whole zero INIT');st[d]=e[2];emit(['OWNED_ZERO_HEADER',gd,e[2],stage]) + elif typ=='ADD': + s,f=e[2:];need(st[d]==st[s]==f,'Actual instantiated coframe') + if gd in W and gd not in livebegin:livebegin[gd]=len(events) + add(gd,owner(s),['LOCAL',stage,f,ix]) + elif typ in('Q','ZERO_Q'): + a,b,k=e[2:];need(st[d]==a,'Current instantiated query frame');st[d]=b + if typ=='Q':query(gd,k,['LOCAL_INVERSE',stage,a,b,ix]);lp[k]+=1 + else:need(values[gd]==0,'Zero only free query');emit(['WHOLE_ZERO_FRAME',gd,a,b,k,stage]) + else:raise ValueError('Local opcode '+typ) + need(not livebegin and st==local['final'],'No live local owned state at return') + need(all(values[owner(i)]==sx[i]and values[owner(111+i)]==sy[i]^sx[i]for i in range(111)),'All retained main RAW inputs') + need(all(values[owner(r)]==before[r]for r in helpers)and all(values[w]==0 for w in W),'All414 independent retained helper inputs and48owned returns') + need(lp==Counter(read(R/'LOCAL-RESULT.json')['stats']['paid'])or lp==Counter({int(k):v for k,v in read(R/'LOCAL-RESULT.json')['stats']['paid'].items()}),'Actual local query count') + calls.append({'stage':stage,'pair':pair,'source_bank':x,'target_bank':y,'old_direction_inverse':rev,'new_direction_inverse':True,'helper_old_owner_begin':helper,'core_begin':start,'core_end':len(events),'owned_global_indices':W,'retained_helper_count':414,'paid':dict(lp)}) + if stage: + for bank in(x,y): + for p in range(111):emit(['PAID_PORT_ROUTE',stage,compact[bank*111+p],p,'RETURN']) + elif op=='QUERY_SHEAR': + _,stage,pair,rev=event;x,y=2*pair,2*pair+1 + if rev:x,y=y,x + for p in range(111): + src,dst=compact[x*111+p],compact[y*111+p];need(values[center]==0,'Clean thin scratch');v=versions[src];begin=len(events);add(center,src,['THIN_COPY',stage,p]);query(center,1,['THIN',stage,p]);add(dst,center,['THIN_DELIVER',stage,p]);need(versions[src]==v,'Thin immutable SOURCE');erase(center,['THIN',stage,p]);episodes.append({'owner':center,'stage':stage,'kind':'THIN','begin':begin,'end':len(events)-1}) + elif op=='IDLE': + _,pair,stages=event;k=7*len(stages) + for bank in(2*pair,2*pair+1): + for p in range(111):query(compact[bank*111+p],k,['WHOLE_IDLE',stages,p]) + elif op=='ADD': + for p in range(111):add(compact[event[1]*111+p],compact[event[2]*111+p],'BRIDGE') + else: + need(op=='SWAP','Known controller event') + for p in range(111):swap(compact[event[1]*111+p],compact[event[2]*111+p],'FINAL_SWAP') + boundary(controller['boundaries']['left_program'],'LEFT_BOUNDARY') + for d in W:erase(d,'GLOBAL_EXIT_TEARDOWN') + need(values==[1<=end),None) + if nxt is None or nxt[0]!='Q':reconstructed[h]=('next receiver write is not a paid query',None) + else:reconstructed[h]=(None,sum(prefix[h])+nxt[4]-8) + report=L.read(L.R/'CUTS.json');actual={c['helper']:(c.get('rejected'),c.get('rank_balance')) for c in report[report_key]} + L.need(actual==reconstructed and len(actual)==len(helpers),'Separate complete first-read domain') + positive={h for h,(why,rank) in actual.items() if rank==0} + L.need(positive==set(expected_positive),'Separate profitable set') + L.need(all(rank is None or rank<=0 for why,rank in actual.values()) and 8**99>7**100,'Separate full interval sign screen') + L.need(actual[523][1]<0 and actual[488][1]<0 and actual[342][1]<0,'Hot-helper choices are not eligible gains') + return dict(helpers=len(actual),profitable=len(positive),negative=sum(rank is not None and rank<0 for why,rank in actual.values()),outside_model=sum(why is not None for why,rank in actual.values())) + + +def pricing(): + I=L.load("refinement_second_series",L.S/"ordinary-certificate/inputs/separate_series.py") + invoice=L.read(L.R/"INVOICE.json");result=L.read(L.R/"ORDINARY-RESULT.json");glob=L.read(L.R/"GLOBAL-RESULT.json") + paid,target=({int(k):v for k,v in invoice[name].items()} for name in ["paid","targets"]) + c,uniform,reserve=F(".00350577852559"),F(".00350577852558"),F(1,2**48) + denominator=I.moment(target,1-c) + alpha=I.div(I.moment(paid,1-c),denominator) + gamma=I.div(I.moment(paid,1-c+F(1,5)),I.mul(I.power(17,F(1,5)),denominator)) + delta=I.div((F(11004*18),)*2,I.mul(I.power(17,c),denominator)) + L.need(alpha[1]<1-reserve and gamma[1]0,"Exact tensor contraction margin") + cover=F(1,10**14);L.need(2**60*cover>256,"Paid regular cover and prime guard") + c1=uniform-cover;backend=F(L.read(L.R/'prior/ORDINARY-RESULT.json')['admitted']) + grid=10**15 + for level in result['finite_backend_levels']: + a=F(99,100)*c1+F(1,100)*backend + numerator=-((-a.numerator*grid)//a.denominator)-1;b=F(numerator,grid) + L.need(backend7. Integer exponent comparison avoids logs. + need(8**99>7**100,'All negative-rank candidates lose throughout stated interval') + return out,positive + + +def construct(old): + allcuts,cuts=census(old,LATE);es=old['records'];skip=set();replacements={};zero=set();frames=old['start'][:] + for c in sorted(cuts,key=lambda c:c['cut']): + h,y,f=c['helper'],c['receiver'],c['frame'];lo,hi=c['block'];block=es[lo:hi] + need(len(block)==3 and sum(e[2]==h for e in block)==1,'Literal three-donor cut') + need(all(e[2] not in LATE-{h} for e in block),'Other cut donors remain retained') + need(not set(range(lo,hi))&skip,'Disjoint reordered blocks') + skip.update(c['removed_prefix_events']);skip.update(range(lo,hi));zero.add(c['zero_query']) + replacements[lo]=[e[:] for e in block if e[2]!=h]+[['INIT',h,f],['ADD',h,y,f],['ADD',y,h,f]] + result=[['ERASE',h,old['start'][h]] for h in sorted(LATE)] + for i,e in enumerate(es): + if i in replacements:result.extend(replacements[i]) + if i in skip:continue + result.append(['ZERO_Q']+e[1:] if i in zero else e[:]) + result.extend([['ERASE',h,old['final'][h]] for h in sorted(LATE)]) + return dict(old,records=result,owned=sorted(set(old['owned'])|LATE)),allcuts,cuts + + +def source_rows(cuts): + forward=read(R/'FORWARD.json.gz')['records'] + rows=[(185,371,599,9660,8562,8568,8565),(183,344,597,9637,8548,8552,8549), + (177,484,591,9742,8506,8510,8507),(172,319,586,9618,8471,8476,8473), + (171,331,585,9627,8464,8469,8466),(157,375,571,9662,8366,8370,8367), + (133,551,547,9792,8198,8204,8201),(120,501,534,9753,8107,8113,8110), + (114,223,528,9546,8065,8071,8068)] + evidence=[] + for y,h,f,terminal,main,first,nxt in rows: + need(forward[first]==['ADD',y,h,f],'Literal proposal first read') + need(forward[terminal]==['Q',h,f,1,1] and forward[main]==['Q',y,0,f,7], 'Literal removed queries') + refs=[(i,e) for i,e in enumerate(forward) if e[1]==h or e[0]=='ADD' and e[2]==h] + need(all(e[1]==h for i,e in refs if i>first),'No earlier inverse outgoing read') + need([e for i,e in refs if i>first and e[0]=='Q']==[forward[terminal]],'Only one unobserved native query') + need(forward[nxt][0]=='Q' and forward[nxt][1]==h and forward[nxt][3:]==[f,1],'Retained suffix query') + evidence.append(dict(helper=h,receiver=y,frame=f,terminal=terminal,main=main,first_read=first,next_query=nxt)) + need({r['helper'] for r in evidence}=={r['helper']for r in cuts},'Proposal and executed census agree') + return evidence + + +def run(): + import native + old=read(R/'prior/WORD.json.gz');word,allcuts,cuts=construct(old);base,frames,_=source() + source_evidence=source_rows(cuts) + result=native.replay(base,frames,word['records'],set(word['owned'])) + physical=[native.replay(base,frames,word['records'],set(word['owned']),m) for m in (101,101**2)] + need(result['paid']=={1:1279,2:1342,3:56,4:57,5:102,6:10},'Exact paid complement removal') + need(len(word['owned'])==48 and result['retained_originals']==636,'Actual required owned reserve') + m=matcher(frames,word);controls=[] + for c in cuts: + bad=[e[:]for e in word['records']];op=['ADD',c['helper'],c['receiver'],c['frame']];bad.pop(bad.index(op)) + try:native.replay(base,frames,bad,set(word['owned']),101) + except ValueError:controls.append('missing_binding_'+str(c['helper'])) + else:raise ValueError('Missing binding accepted') + for label,op in [('dirty_entrance',['ERASE',371,old['start'][371]]),('missing_return',['ERASE',371,old['final'][371]])]: + bad=[e[:]for e in word['records']];bad.pop(bad.index(op)) + try:native.replay(base,frames,bad,set(word['owned']),101) + except ValueError:controls.append(label) + else:raise ValueError('Owned control accepted') + after,_=census(word,set());put('WORD.json.gz',word);put('CUTS.json',dict(all_candidates=allcuts,selected=cuts,after_candidates=after,proposal_source_rows=source_evidence)) + data=dict(status='PASS_G20_LATE_BINDING_NATIVE_ALL684_COLUMNS',stats=result,native_moduli=[v['native_modulus']for v in physical], + matcher=m,candidate_helpers=len(allcuts),profitable_cuts=len(cuts),rejected_controls=controls, + canonical_word_sha256=sha256(json.dumps(word['records'],separators=(',',':')).encode()).hexdigest()) + put('LOCAL-RESULT.json',data);return data + + +if __name__=='__main__':print(json.dumps(run(),indent=2)) diff --git a/research/g20-helper-split/prior/native.py b/research/g20-helper-split/prior/native.py new file mode 100644 index 0000000000..da98fc6e40 --- /dev/null +++ b/research/g20-helper-split/prior/native.py @@ -0,0 +1,50 @@ +"""Native replay adapted from ai-nanachi PR5512 for twenty-six extra addressable fields and forty-eight owned banks. + +All source geometry and coframe checks are retained. Ali Romman with +substantial OpenAI Codex assistance. Apache-2.0. +""" +from collections import Counter +import integration as B +Geometry=B.SOURCE.Geometry +need=B.need +bitids=B.SOURCE.bitids +N=658 +def replay(base,frames,program,owned,modulus=None): + width=max(N+2,max(owned)+1);extra=width-N + geom=Geometry(frames);st=base['final']+[None]*extra;rows=[1<=1024 and v%1024==0 and 256*v>=4*v*64,'Explicit tensor count envelope') + return{'status':'PASS_POSITIVE_NEW_FINITE_FEE_AND_STOCK_SCHEMA','base_counts':{'raw_records':raw,'new_matcher_coefficient_terms':matcher_terms,'all_XOR_CLEAR_INIT_zeroheader_passes':scans,'parent_parking_FIELD_passes':park,'internal_and_wholejob_routes':routes,'coarse_primitive_count_with_dimension_work':base,'strict_upper':2**64,'all_owned_allocated':owned,'owned_productive_credit':0}, + 'fixed_tensor_unit':{'v':v,'K':'2^'+str(256*v),'meaning':'Bounds fixed integer ranks, all role/round/operation inventories after tensoring, charged target completion and charged paid splitting.'}, + 'finite_compiler':{'N':'2^'+str(H1),'J(n)':'(n+1)^4*K^(4*n+4)','A(1)':'K^4','A(n)':'(J(n)+2)^4*(A(n-1)+2)^(4*n+8)','counts':'Productive roles B_N, paid leaves P_N, instances and primitive descriptions <=A(N). Each compiled instance gets48distinct owned banks; C_N<=48*A(N). Denominator replication product <=A(n-1)^(n-1).'}, + 'height_prime':{'base_height_bits':1024,'T':'(2*N+2)^4*(A(N)+2)^2','H':'1026*4^(T+1)','q':'Choose odd prime q>max(2^60*N^5,2^(2*H)) avoiding every finitely compiled denominator/rank witness. All QQ matrices and relative SOURCE projectors compiled before choice.'}, + 'all_in_fixed_primitive_fee':{'F':'48*(q+2)^(32*(N+1)^2)*(A(N)+2)^8','actual_cost':'F times positive maximum of the retained stream/route/normalizer/completed-backend constants, fixed anew at each finite level. No primitive has cost0 or a claimed universal cost1.','parking':'4*(B_N+C_N) positive FIELD passes per child plus initialization/teardown, with C_N<=48*A(N); F dominates their products.','bad_classes':'<=32*N^2 ordinary calls charged separately by the retained moment/cover argument.'}, + 'stock':{'reserve':'[B_N*|GL_N(F_q)|*q^(N^2*(w-1))]^D*S_completed_backend','D':'floor(log_N ceil(e/w))+1','borrowed_digits':'D*(N^2*(w-1)+ceil(log_q(B_N*|GL_N(F_q)|)))+ceil(log_q S_completed_backend)+1 =O_new(w loge)','ownership':'All48whole owned banks for EVERY compiled instance, including suspended ones, get distinct tags; full entry/exit CLEAR charged. No ancestor region is swept or external zero stock assumed.'}, + 'eventual_threshold':{'K_j':'At least16 times sum of F*positive retained primitive constants, reserve/adapter bounds and already frozen backend constant completed at all widths by finite fallback.','eta_j':'min(rho-a_j,1-rho-a_j,a_j-b_j)>0','e_j':'Fresh integer dominating E_backend^(ceil(2/rho)), borrow threshold, ceil((32*K_j/eta_j)^(ceil(8/eta_j)))+2^(ceil(8/eta_j)).','scope':'Constructive finite threshold schema under retained native/compiler/ROW/precision/tape premises. Winning uniform program and decimal threshold are not materialized.'}} +def run(): + invoice=L.read(R/'INVOICE.json');glob=L.read(R/'GLOBAL-RESULT.json');P={int(k):v for k,v in invoice['paid'].items()};T={int(k):v for k,v in invoice['targets'].items()} + need(sum(T.values())==11004 and sum(P.values())==56223 and T.get(4,0)==0 and T[8]==7452 and P.get(7,0)==0,'Actual complete new target/paid bill') + E=load('nine_credited_interval',S/'ordinary-certificate/inputs/credited_intervals.py');I=load('nine_independent_series',S/'ordinary-certificate/inputs/separate_series.py') + tested=F('.00350577852559');uniform=F('.00350577852558');cover_gap=F(1,10**14);rho=F(1,100);reserve=F(1,2**48);v=tensor_degree(reserve);t=1-tested;u=F(1,5) + target=E.moment(T,t);paid=E.moment(P,t);alpha=E.divide(paid,target);gamma=E.divide(E.moment(P,t+u),E.mul(E.power(17,u),target));delta=E.divide((F(11004*18),)*2,E.mul(E.power(17,tested),target)) + need(alpha[1]<1-reserve and gamma[1]0 if sign>0 else margin[1]<0,'Independent root sign '+label);cross[label]={'saving':c,'margin':margin} + need(F(31,32)**1280 and 17**64<18**63 and max(T)<256,'Charged completion, separation and ambient') + z=1-uniform;z0=(t+z)/2;gap=z0-t;h=F(1,64);H0,H1=compiler_cutoffs(tested,uniform,v) + need(H0>=8*v and H0*h*gap>gap*(5+8*h)*v+1+8*v*(1-z0)and H1*(z-z0)>H0*(1-z0),'Fresh finite integer compiler thresholds') + C1=uniform-cover_gap;need(F(2**60)*cover_gap>256,'Cover/bad-prime gap') + backend=F(L.read(R/'prior/ORDINARY-RESULT.json')['admitted']);old=backend;levels=[] + for j in range(1,6): + a=(1-rho)*C1+rho*backend;b=below_grid(a,10**15);need(backendold,'New complete ordinary component saving') + cmin=F(L.read(R/'prior/ORDINARY-RESULT.json')['admitted']);cmax=F('.00351') + worst_target=E.moment(T,1-cmax) + worst_gamma=E.divide(E.moment(P,1-cmin+u),E.mul(E.power(17,u),worst_target)) + worst_delta=E.divide((F(11004*18),)*2,E.mul(E.power(17,cmin),worst_target)) + need(worst_gamma[1]=a)-sum(k*n for k,n in P.items() if k>=a) for a in range(1,129)] + need(min(tails)>=0 and tails[0]==753,'Strict first-moment monotonicity from rank-mass tails') + range_certificate={'C_min':cmin,'C_max':cmax,'gamma_upper_bound':worst_gamma,'delta_upper_bound':worst_delta, + 'rank_mass_tails':tails,'tensor_reserve_controls':controls(), + 'claim':'Under the retained framework, every ordinary saving strictly below this invoice raw crossing is attainable with fresh finite margins. This is not a global optimality claim.'} + + result={'status':'PASS_CONDITIONAL_G20_LATE_BINDING_ORDINARY_FIVE_FINITE_LEVELS','invoice':invoice,'params':{'tested':tested,'uniform':uniform,'cover_gap':cover_gap,'rho':rho,'v':v,'alpha_gap':reserve,'grid_denominator':10**15,'prime_multiplier':2**60,'cutoff':17,'floor':18,'u':u},'raw_crossing_independent_exact':cross,'tail':{'alpha':alpha,'gamma':gamma,'delta':delta,'normalized_surplus':surplus,'H0':H0,'H1':H1},'C1':C1,'finite_backend_levels':levels,'admitted':backend,'comparator':old,'relative_gain':backend/old-1,'relative_gain_percent':100*(backend/old-1),'uniform_signed_invoice_improvement':'Relative to PR5667: Pnew-Pold=-162H1-162H7; Tnew-Told=-162H8. Gain162*(1+7^t-8^t)>0 for00 for0max(2^60*N^5,2^(2*H)) avoiding every finitely compiled denominator/rank witness. All QQ matrices and relative SOURCE projectors compiled before choice." + }, + "all_in_fixed_primitive_fee": { + "F": "39*(q+2)^(32*(N+1)^2)*(A(N)+2)^8", + "actual_cost": "F times positive maximum of the retained stream/route/normalizer/completed-backend constants, fixed anew at each finite level. No primitive has cost0 or a claimed universal cost1.", + "parking": "4*(B_N+C_N) positive FIELD passes per child plus initialization/teardown, with C_N<=39*A(N); F dominates their products.", + "bad_classes": "<=32*N^2 ordinary calls charged separately by the retained moment/cover argument." + }, + "stock": { + "reserve": "[B_N*|GL_N(F_q)|*q^(N^2*(w-1))]^D*S_completed_backend", + "D": "floor(log_N ceil(e/w))+1", + "borrowed_digits": "D*(N^2*(w-1)+ceil(log_q(B_N*|GL_N(F_q)|)))+ceil(log_q S_completed_backend)+1 =O_new(w loge)", + "ownership": "All39whole owned banks for EVERY compiled instance, including suspended ones, get distinct tags; full entry/exit CLEAR charged. No ancestor region is swept or external zero stock assumed." + }, + "eventual_threshold": { + "K_j": "At least16 times sum of F*positive retained primitive constants, reserve/adapter bounds and already frozen backend constant completed at all widths by finite fallback.", + "eta_j": "min(rho-a_j,1-rho-a_j,a_j-b_j)>0", + "e_j": "Fresh integer dominating E_backend^(ceil(2/rho)), borrow threshold, ceil((32*K_j/eta_j)^(ceil(8/eta_j)))+2^(ceil(8/eta_j)).", + "scope": "Constructive finite threshold schema under retained native/compiler/ROW/precision/tape premises. Winning uniform program and decimal threshold are not materialized." + } + }, + "strict_margin_range": { + "C_min": "3488579527/1000000000000", + "C_max": "7/2000", + "gamma_upper_bound": [ + "6025568896714756734468836454965751300051243342029676225321/6277101735386680763835789423207666416102355444464034512896", + "6025568896714756734468836454965751300051243342029676585589/6277101735386680763835789423207666416102355444464034512896" + ], + "delta_upper_bound": [ + "1468586668696254738094063705789482730484248156263639265257/1569275433846670190958947355801916604025588861116008628224", + "91786666793515921130878981611842670655265509766477457219/98079714615416886934934209737619787751599303819750539264" + ], + "rank_mass_tails": [ + 753, + 25602, + 73914, + 76938, + 81042, + 90222, + 91302, + 92436, + 31524, + 31524, + 31524, + 31524, + 31524, + 31524, + 37740, + 31080, + 31080, + 31080, + 31080, + 31080, + 31080, + 40404, + 30636, + 30636, + 30636, + 30636, + 30636, + 30636, + 43068, + 30192, + 30192, + 30192, + 30192, + 30192, + 30192, + 45732, + 29748, + 29748, + 29748, + 29748, + 29748, + 29748, + 48396, + 29304, + 29304, + 29304, + 29304, + 29304, + 29304, + 51060, + 28860, + 28860, + 28860, + 28860, + 28860, + 28860, + 53724, + 28416, + 28416, + 28416, + 28416, + 28416, + 28416, + 42402, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 28194, + 0 + ], + "tensor_reserve_controls": { + "8": 1024, + "39": 1024, + "48": 2048, + "96": 4096, + "192": 8192, + "384": 16384 + }, + "claim": "Under the retained framework, every ordinary saving strictly below this invoice raw crossing is attainable with fresh finite margins. This is not a global optimality claim." + }, + "whole_kappa": null, + "assumptions": "Same retained native/allcolumn arbitraryinput/ROW/spectator, mixed-target finite compiler, completed ordinary fallback, precision and fixed-tape contracts as PR4760/4814; no full theorem verification claimed." +} diff --git a/research/g20-helper-split/prior/prior/PROOF.md b/research/g20-helper-split/prior/prior/PROOF.md new file mode 100644 index 0000000000..dd110d2e48 --- /dev/null +++ b/research/g20-helper-split/prior/prior/PROOF.md @@ -0,0 +1,167 @@ +# Complete caller, finite admission and strict-margin theorem + +## 1. Construction and exact source boundary + +Use the literal word from PR5662 at `e0f9b0bbcb14f3cbc47433c7f7770a9aaa35b029`. Its bytes are retained as both `audited/WORD.json.gz` and the published `WORD.json.gz`. The source proof is Dugongue PR5657 at `2f091bc3b656ed85d26cf44b7fc84c28fb510273`. Its fourteen windows not already in the completed PR5653 baseline add six protected-reader fusions and eight paid SOURCE refinements. Helper 444 and the earlier retirements and snapshots remain credited predecessor work. + +The local word has 645 independent original fields and 39 owned fields. All 684 entry columns are included, with arbitrary initial owned values. Every ADD has distinct operands at the same actual frame. Each query is checked at its current frame and actual residual rank. Only whole zero owned fields receive a free frame change. Every owned field is zero on return. + +The new local paid inventory is `{1:1288,2:1342,3:56,4:57,5:102,6:10,7:9}`. Exact native replay uses the retained geometric implementation, with two odd address moduli. The separate adjoint uses different address points. These checks support the exact source join and the rational projector identities from PR5662. The retained all-width/native hypotheses are not inferred from the finite modular fixtures. + +## 2. Frame-506 matcher and finite cost + +For frame 506, the columns of W are the source basis B transposed, followed by its orthogonal complement A transposed. The new replay reconstructs these columns from the frozen frame file and checks both products with the supplied inverse. Orthogonality makes + +`W diag(I_4,0) W^-1 = P_506`. + +Applied to both paired address halves, these ordinary basis maps conjugate the standard rank-four involution to the required residual. The denominator is 4; an odd address prime can satisfy the new denominator condition. The original `1 -> 506` request has the complementary residual, so literal reuse of that oriented request is not asserted. + +There are four occurrences per local word and eighteen local calls. The two matrices contain 38 nonzero coefficients. Both paired halves therefore contribute `72*2*38=5472` coefficient terms. This quantity is added to the complete positive finite primitive-count bound. The remaining finite cost includes the actual whole maps, both routing directions, arithmetic on the fixed coefficients, and the positive normalizer implementation constants. It is covered by the retained finite ordinary matcher framework, not a unit-cost dense address primitive. + +## 3. Complete chronological caller + +Install the local word in the retained p16/a7 controller. The exact thirteen retired helper IDs are the nine owned relations and the four prior partial retirements. Every retained original owner has a distinct global index. The 39 owned global fields have no productive target credit and are cleared at global entry and exit. Every suspended compiled instance later receives its own reserve; the local reuse does not imply one global bank shared by simultaneous instances. + +The emitter rebuilds every local query, thin query, whole idle query, bridge, boundary, owned operation and route. The source descriptors bind the event index, complete prefix digest, owner, epoch, version, current symbolic data and geometric job. A second implementation consumes the emitted stream and reconstructs these fields. A stale epoch is rejected. + +All 11,166 original symbolic inputs return at the prescribed endpoint, while all 39 arbitrary owned entry columns are annihilated. The retained physical main-controller polynomial check also passes. There are 446,604 events, 56,547 paid queries and 2,367 payload episodes. The positive precision majorant has 516 bits. Every local return closes its live owned episodes before another call uses the bank. + +The complete paid histogram is + +``` +{1:24849,2:24156,3:1008,4:1026,5:1836,6:180,7:162, + 14:444,21:444,28:444,35:444,42:444,49:444,56:444,63:222} +``` + +The complete productive histogram is + +``` +{8:7614,15:444,22:444,29:444,36:444,43:444,50:444, + 57:444,64:222,127:222} +``` + +The 72 rank-four target debits from the prior retirements remain. There are 11,166 productive fields and rank surplus 753. Relative to PR5653, the paid delta is `-252H1-252H3+252H4` and targets do not change. Thus the moment gain is `252(1+3^t-4^t)>0` for `0max(2^60 N^5,2^(2H))` + +that avoids all finite compiled denominator and rank-witness primes. This is a fresh choice. The fixed primitive multiplier + +`39(q+2)^(32(N+1)^2)(A(N)+2)^8` + +is multiplied by the positive maximum needed for the retained primitives, the new forward/inverse matcher operations and the completed preceding backend. It includes parent parking, normalizers, routes, initialization and teardown. The source owned-stock and eventual-threshold constructions use the new 39-bank reserve and fresh constants. No old seventeen-bank reserve or cancellation-growth bound is reused. + +Choose cover loss `epsilon=10^-14`. The exact guard `2^60 epsilon>256` pays the source regular-cover and bad-prime terms. The ordinary limiting saving after this loss is + +`L=U-epsilon=.00349780457952`. + +The source full fixed-tape, precision, ordinary cover and normalizer premises are retained here. The large constants are fixed before the final input size grows. They are not discarded because the asymptotic saving is positive. + +## 6. Five finite ordinary levels + +Start from the completed PR5653 backend `b0=.003488579527`. With `rho=1/100` and `Q=10^15`, define + +`a_j=(1-rho)L+rho b_(j-1)`, + +`b_j=(ceil(Q a_j)-1)/Q`. + +This strict lower grid also works when `Q a_j` is an integer. The five completed savings are + +``` +.003497712328994 +.003497803657014 +.003497804570294 +.003497804579427 +.003497804579519 +``` + +Every level has strict adapter, stock and rounding gaps. Each ordinary backend call reduces the finite level; each native recursive call reduces the atom count. No self-fallback occurs. At each level choose a fresh coefficient and eventual threshold from its positive primitive and reserve constants, as specified in ORDINARY-RESULT.json. The ordinary result is conditional on the same retained source framework as its predecessor. + +## 7. Arbitrarily small strict losses for this fixed invoice + +Let `b0` be the prior completed saving and let `c_star` be the raw crossing of the new invoice. The verifier checks every rank-mass tail. Summation by parts shows the signed moment is strictly decreasing on `[b0,.0035]`: `x^(-C) log x` is increasing there. Thus its zero is unique. + +The certificate also proves tail guards uniformly on this entire interval. A conservative numerator uses the paid moment at `b0`; a conservative target denominator uses the target moment at `.0035`. For the completion denominator, use `17^b0` and that same target lower bound. Both resulting rational upper bounds remain below `31/32` and `19/20`. + +Fix a rational requested ordinary saving `B` with `b0B`. Increase the fixed prime multiplier to exceed `256/epsilon`. These changes only enlarge finite constants and eventual thresholds under the retained framework. + +Choose an integer grid denominator Q with + +`1/(Q(1-rho))= L-rho^j(L-b0)-(1-rho^j)/(Q(1-rho))`. + +Hence some finite level satisfies `b_j>B`. Stop there, with fresh positive coefficients, owned reserves and thresholds at every level. For `B<=b0`, the prior completed algorithm suffices. This proves that every strict ordinary saving below `c_star` is attainable under the retained framework. + +This theorem does not make the raw crossing itself admissible, remove a strict inequality, prove a globally optimal BIT algorithm, or improve a Gaussian caller automatically. It shows that this fixed invoice has no additional fixed asymptotic loss from the finite choices in the certificate. + +## 8. Verification boundary + +The registered normal and optimized commands rebuild all scientific outputs in isolated temporary copies. Input authentication occurs before imports of retained engines. Local scalar/native checks, a separate physical adjoint, the complete chronological stream, target debits, independent moment intervals, positive fees, fresh cutoffs and all five backend levels pass. The audited word is retained byte-for-byte. + +The framework assumptions remain: arbitrary-function/all-column native operators, ROW and spectator behavior, constructive mixed-target compilation, ordinary normalizers and completed backends, owned erasure/stock, precision, fixed-tape and analytic contracts. The uniform word and enormous threshold are algorithm-defined, not executed. A complete multiplication kappa requires a compatible Gaussian/outer caller. No selected-frontier change, independent human review or formal-kernel acceptance is claimed. diff --git a/research/g20-helper-split/prior/prior/WORD.json.gz b/research/g20-helper-split/prior/prior/WORD.json.gz new file mode 100644 index 0000000000..976059558e Binary files /dev/null and b/research/g20-helper-split/prior/prior/WORD.json.gz differ diff --git a/research/g20-helper-split/prior/prior/audited/RESULT.json b/research/g20-helper-split/prior/prior/audited/RESULT.json new file mode 100644 index 0000000000..9a4d76fc36 --- /dev/null +++ b/research/g20-helper-split/prior/prior/audited/RESULT.json @@ -0,0 +1,669 @@ +{ + "all_input_columns": 684, + "changed_old_events": 102, + "controller_paid": { + "1": 24849, + "2": 24156, + "3": 1008, + "4": 1026, + "5": 1836, + "6": 180, + "7": 162, + "14": 444, + "21": 444, + "28": 444, + "35": 444, + "42": 444, + "49": 444, + "56": 444, + "63": 222 + }, + "controller_targets": { + "8": 7614, + "15": 444, + "22": 444, + "29": 444, + "36": 444, + "43": 444, + "50": 444, + "57": 444, + "64": 222, + "127": 222 + }, + "controls": [ + "changed_residual_matcher", + "source_version_233", + "source_version_358", + "source_version_385", + "source_version_297", + "source_version_271", + "source_version_360", + "source_version_241", + "source_version_340", + "source_version_319", + "source_version_357", + "source_version_381", + "source_version_368", + "source_version_365", + "source_version_352", + "missing_snapshot", + "missing_refinement", + "missing_teardown", + "retained_helper_erasure", + "recipient_injection_removed" + ], + "delta_from_5653": { + "1": -14, + "3": -14, + "4": 14 + }, + "local_paid": { + "1": 1288, + "2": 1342, + "3": 56, + "4": 57, + "5": 102, + "6": 10, + "7": 9 + }, + "matcher": { + "common_denominator": 4, + "forward": [ + [ + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "1", + "0", + "-1", + "0", + "0" + ], + [ + "0", + "0", + "1", + "1", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "1" + ], + [ + "2", + "0", + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "2", + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "-1", + "0", + "0", + "0", + "0", + "1" + ] + ], + "forward_norm": "3", + "frame": 506, + "inverse": [ + [ + "0", + "-1/4", + "-1/4", + "0", + "1/4", + "1/2", + "0", + "-1/4" + ], + [ + "0", + "-1/4", + "-1/4", + "0", + "1/4", + "0", + "1/2", + "-1/4" + ], + [ + "0", + "0", + "0", + "0", + "1/2", + "0", + "0", + "-1/2" + ], + [ + "0", + "1/2", + "1/2", + "0", + "-1/2", + "0", + "0", + "1/2" + ], + [ + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "-1/2", + "1/2", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1/2", + "0", + "0", + "1/2" + ] + ], + "inverse_norm": "2", + "max_numerator_bits": 2, + "nonzero_coefficients": 38, + "physical_tape_price_supplied": false, + "rank": 4 + }, + "new_kappa": false, + "new_query_types": [ + [ + 7, + 0, + 1 + ], + [ + 24, + 0, + 1 + ], + [ + 37, + 0, + 1 + ], + [ + 65, + 0, + 1 + ], + [ + 76, + 0, + 1 + ], + [ + 115, + 11, + 1 + ], + [ + 116, + 56, + 1 + ], + [ + 117, + 48, + 1 + ], + [ + 130, + 74, + 1 + ], + [ + 132, + 63, + 1 + ], + [ + 162, + 68, + 1 + ], + [ + 163, + 67, + 1 + ], + [ + 191, + 62, + 1 + ], + [ + 506, + 0, + 4 + ], + [ + 506, + 115, + 2 + ], + [ + 506, + 116, + 2 + ], + [ + 506, + 117, + 2 + ], + [ + 507, + 0, + 4 + ], + [ + 507, + 130, + 2 + ], + [ + 507, + 132, + 2 + ], + [ + 508, + 0, + 4 + ], + [ + 508, + 162, + 2 + ], + [ + 508, + 163, + 2 + ], + [ + 509, + 0, + 4 + ], + [ + 509, + 191, + 2 + ] + ], + "new_residual_orientation": [ + [ + 506, + 0, + 4 + ] + ], + "operation_counts": { + "ADD": 19043, + "ERASE": 78, + "INIT": 1, + "Q": 2864, + "ZERO_Q": 9 + }, + "owned": 39, + "paid_queries": 56547, + "rank_surplus": 753, + "raw_crossing": [ + "58683422957/16777216000000", + "117366845917/33554432000000" + ], + "retained_helper444": true, + "retained_local_originals": 645, + "source_independent": true, + "status": "PASS_G20_SOURCE_REFINEMENT_AUDIT", + "test_C": "3497/1000000", + "test_moment": [ + "171920889810167927/1000000000000000000", + "21490111226270991/125000000000000000" + ], + "windows": [ + { + "cold": 2845, + "h": 233, + "hqs": [ + 2870, + 6298 + ], + "inj": 2871, + "kind": "upper", + "l": 7, + "p": 114, + "proper": 3338, + "r": 242, + "rq": 3337, + "sq1": 3333, + "sq2": 7333, + "u": 506, + "x": 5 + }, + { + "cold": 2815, + "h": 358, + "hqs": [ + 3096, + 6334 + ], + "inj": 3097, + "kind": "upper", + "l": 64, + "p": 129, + "proper": 3433, + "r": 354, + "rq": 3432, + "sq1": 3448, + "sq2": 7374, + "u": 507, + "x": 62 + }, + { + "cold": 2761, + "h": 385, + "hqs": [ + 3146, + 6351 + ], + "inj": 3147, + "kind": "upper", + "l": 76, + "p": 160, + "proper": 3624, + "r": 401, + "rq": 3623, + 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"l": 68, + "p": 162, + "proper": 3644, + "r": 347, + "sq": 7471, + "u": 508, + "x": 66 + }, + { + "cold": 2753, + "h": 365, + "hqs": [ + 3110, + 3648, + 6367 + ], + "independent_source": 66, + "inj": 3111, + "kind": "refined", + "l": 67, + "p": 163, + "proper": 3649, + "r": 369, + "sq": 7477, + "u": 508, + "x": 65 + }, + { + "cold": 2711, + "h": 352, + "hqs": [ + 3088, + 3800, + 6376 + ], + "independent_source": 50, + "inj": 3089, + "kind": "refined", + "l": 62, + "p": 191, + "proper": 3801, + "r": 330, + "sq": 7567, + "u": 509, + "x": 60 + } + ] +} diff --git a/research/g20-helper-split/prior/prior/global_retirement.py b/research/g20-helper-split/prior/prior/global_retirement.py new file mode 100644 index 0000000000..95a0e0c392 --- /dev/null +++ b/research/g20-helper-split/prior/prior/global_retirement.py @@ -0,0 +1,112 @@ +"""Literal p16/a7 caller with thirteen retired helper targets and thirty-nine owned fields. + +Adapted from ai-nanachi PR5512 global_relations.py. The four retirements +are Dugongue PR5629. Dugongue PR5639 gives two snapshot fusions; this +version adds the third and reuses the zero centre. Implementation by Ali Romman with OpenAI Codex assistance. +Apache-2.0; retain the source notices. + +Retains G20 native controller/geometry; uses the independently checked reverse +physical involution at each full call. No old helper target is given to owned work. +""" +from pathlib import Path +from collections import Counter +from hashlib import sha256 +from time import process_time +import gzip,json,importlib.util,sys +sys.path.insert(0,str(Path(__file__).resolve().parent)) +import integration as L +R=L.R;S=L.S +def need(c,m): + if not c:raise ValueError(m) +def read(p):return L.read(p) +def put(n,x):L.put(n,x) +def run(): + clock=process_time();controller=read(S/'inputs/CONTROLLER.json');base,frames,_=L.source();local=read(R/'WORD.json.gz');owned=local['owned'];pivots=sorted(x for x in owned if x<658);need(pivots==[462,463,466,468]+list(range(469,478)),'Exact thirteen retired helper owners') + oldcalls=read(S/'provider/data/CALLS.json');retired={c['helper_owner_begin']+p-222 for c in oldcalls for p in pivots};retained=[i for i in range(11400)if i not in retired];compact={x:i for i,x in enumerate(retained)};N=len(retained);W=list(range(N,N+len(owned)));center,shadow=W[:2];pivotwork=dict(zip(pivots,W[2:15]));snapshotwork=dict(zip(sorted(r for r in owned if r>=660),W[15:]));need(N==11166,'New retained original count') + values=[1<0,'Positive rank');source.append({'event':len(events),'prefix_sha256':prefix.hexdigest(),'owner':d,'version':versions[d],'epoch':epochs[d],'rank':k,'detail':detail,'RAW_hex':hex(values[d]),'function_identity':'Exact literal program prefix plus current owner/epoch/version and actual geometric source job; RAW bitmap is extra evidence, not a claim of purity.'});paid[k]+=1;versions[d]+=1;emit(['QUERY',d,k,detail]) + def swap(d,s,why):add(d,s,why);add(s,d,why);add(d,s,why) + def boundary(program,why): + for op,d,s in program: + for p in range(111): + if op=='ADD':add(compact[d*111+p],compact[s*111+p],why) + else:need(op=='SWAP','Controller opcode');swap(compact[d*111+p],compact[s*111+p],why) + boundary(controller['boundaries']['right_program'],'RIGHT_BOUNDARY') + thick=controller['invoice']['thick_stages'];stage_index={s:i for i,s in enumerate(thick)} + for event in controller['physical_events']: + op=event[0] + if op=='LOCAL': + _,stage,pair,rev=event;x,y=2*pair,2*pair+1 + if rev:x,y=y,x + helper=3552+436*stage_index[stage] + def owner(r): + if r==658:return center + if r==659:return shadow + if r in pivotwork:return pivotwork[r] + if r in snapshotwork:return snapshotwork[r] + return compact[(x if r<111 else y)*111+r%111]if r<222 else compact[helper+r-222] + sx=[values[owner(i)]for i in range(111)];sy=[values[owner(111+i)]for i in range(111)];helpers=[r for r in range(222,658)if r not in pivotwork];before={r:values[owner(r)]for r in helpers} + if stage: + for bank in(x,y): + for p in range(111):emit(['PAID_PORT_ROUTE',stage,compact[bank*111+p],p,'ENTRY']) + start=len(events);lp=Counter();st=local['start'][:];livebegin={} + for ix,e in enumerate(local['records']): + typ,d=e[:2];gd=owner(d) + if typ=='ERASE': + erase(gd,['LOCAL',stage,ix],e[2]);st[d]=e[2] + if gd in livebegin:episodes.append({'owner':gd,'stage':stage,'begin':livebegin.pop(gd),'end':len(events)-1}) + elif typ=='INIT':need(values[gd]==0,'Whole zero INIT');st[d]=e[2];emit(['OWNED_ZERO_HEADER',gd,e[2],stage]) + elif typ=='ADD': + s,f=e[2:];need(st[d]==st[s]==f,'Actual instantiated coframe') + if gd in W and gd not in livebegin:livebegin[gd]=len(events) + add(gd,owner(s),['LOCAL',stage,f,ix]) + elif typ in('Q','ZERO_Q'): + a,b,k=e[2:];need(st[d]==a,'Current instantiated query frame');st[d]=b + if typ=='Q':query(gd,k,['LOCAL_INVERSE',stage,a,b,ix]);lp[k]+=1 + else:need(values[gd]==0,'Zero only free query');emit(['WHOLE_ZERO_FRAME',gd,a,b,k,stage]) + else:raise ValueError('Local opcode '+typ) + need(not livebegin and st==local['final'],'No live local owned state at return') + need(all(values[owner(i)]==sx[i]and values[owner(111+i)]==sy[i]^sx[i]for i in range(111)),'All retained main RAW inputs') + need(all(values[owner(r)]==before[r]for r in helpers)and all(values[w]==0 for w in W),'All423 independent retained helper inputs and39owned returns') + need(lp==Counter(read(R/'LOCAL-RESULT.json')['stats']['paid'])or lp==Counter({int(k):v for k,v in read(R/'LOCAL-RESULT.json')['stats']['paid'].items()}),'Actual local query count') + calls.append({'stage':stage,'pair':pair,'source_bank':x,'target_bank':y,'old_direction_inverse':rev,'new_direction_inverse':True,'helper_old_owner_begin':helper,'core_begin':start,'core_end':len(events),'owned_global_indices':W,'retained_helper_count':423,'paid':dict(lp)}) + if stage: + for bank in(x,y): + for p in range(111):emit(['PAID_PORT_ROUTE',stage,compact[bank*111+p],p,'RETURN']) + elif op=='QUERY_SHEAR': + _,stage,pair,rev=event;x,y=2*pair,2*pair+1 + if rev:x,y=y,x + for p in range(111): + src,dst=compact[x*111+p],compact[y*111+p];need(values[center]==0,'Clean thin scratch');v=versions[src];begin=len(events);add(center,src,['THIN_COPY',stage,p]);query(center,1,['THIN',stage,p]);add(dst,center,['THIN_DELIVER',stage,p]);need(versions[src]==v,'Thin immutable SOURCE');erase(center,['THIN',stage,p]);episodes.append({'owner':center,'stage':stage,'kind':'THIN','begin':begin,'end':len(events)-1}) + elif op=='IDLE': + _,pair,stages=event;k=7*len(stages) + for bank in(2*pair,2*pair+1): + for p in range(111):query(compact[bank*111+p],k,['WHOLE_IDLE',stages,p]) + elif op=='ADD': + for p in range(111):add(compact[event[1]*111+p],compact[event[2]*111+p],'BRIDGE') + else: + need(op=='SWAP','Known controller event') + for p in range(111):swap(compact[event[1]*111+p],compact[event[2]*111+p],'FINAL_SWAP') + boundary(controller['boundaries']['left_program'],'LEFT_BOUNDARY') + for d in W:erase(d,'GLOBAL_EXIT_TEARDOWN') + need(values==[1<0,"Exact tensor contraction margin") + cover=F(1,10**14);L.need(2**60*cover>256,"Paid regular cover and prime guard") + c1=uniform-cover;backend=F(L.read(L.R/'predecessor/ORDINARY-RESULT.json')['admitted']) + grid=10**15 + for level in result['finite_backend_levels']: + a=F(99,100)*c1+F(1,100)*backend + numerator=-((-a.numerator*grid)//a.denominator)-1;b=F(numerator,grid) + L.need(backend=1024 and v%1024==0 and 256*v>=4*v*64,'Explicit tensor count envelope') + return{'status':'PASS_POSITIVE_NEW_FINITE_FEE_AND_STOCK_SCHEMA','base_counts':{'raw_records':raw,'new_matcher_coefficient_terms':matcher_terms,'all_XOR_CLEAR_INIT_zeroheader_passes':scans,'parent_parking_FIELD_passes':park,'internal_and_wholejob_routes':routes,'coarse_primitive_count_with_dimension_work':base,'strict_upper':2**64,'all_owned_allocated':owned,'owned_productive_credit':0}, + 'fixed_tensor_unit':{'v':v,'K':'2^'+str(256*v),'meaning':'Bounds fixed integer ranks, all role/round/operation inventories after tensoring, charged target completion and charged paid splitting.'}, + 'finite_compiler':{'N':'2^'+str(H1),'J(n)':'(n+1)^4*K^(4*n+4)','A(1)':'K^4','A(n)':'(J(n)+2)^4*(A(n-1)+2)^(4*n+8)','counts':'Productive roles B_N, paid leaves P_N, instances and primitive descriptions <=A(N). Each compiled instance gets39distinct owned banks; C_N<=39*A(N). Denominator replication product <=A(n-1)^(n-1).'}, + 'height_prime':{'base_height_bits':1024,'T':'(2*N+2)^4*(A(N)+2)^2','H':'1026*4^(T+1)','q':'Choose odd prime q>max(2^60*N^5,2^(2*H)) avoiding every finitely compiled denominator/rank witness. All QQ matrices and relative SOURCE projectors compiled before choice.'}, + 'all_in_fixed_primitive_fee':{'F':'39*(q+2)^(32*(N+1)^2)*(A(N)+2)^8','actual_cost':'F times positive maximum of the retained stream/route/normalizer/completed-backend constants, fixed anew at each finite level. No primitive has cost0 or a claimed universal cost1.','parking':'4*(B_N+C_N) positive FIELD passes per child plus initialization/teardown, with C_N<=39*A(N); F dominates their products.','bad_classes':'<=32*N^2 ordinary calls charged separately by the retained moment/cover argument.'}, + 'stock':{'reserve':'[B_N*|GL_N(F_q)|*q^(N^2*(w-1))]^D*S_completed_backend','D':'floor(log_N ceil(e/w))+1','borrowed_digits':'D*(N^2*(w-1)+ceil(log_q(B_N*|GL_N(F_q)|)))+ceil(log_q S_completed_backend)+1 =O_new(w loge)','ownership':'All39whole owned banks for EVERY compiled instance, including suspended ones, get distinct tags; full entry/exit CLEAR charged. No ancestor region is swept or external zero stock assumed.'}, + 'eventual_threshold':{'K_j':'At least16 times sum of F*positive retained primitive constants, reserve/adapter bounds and already frozen backend constant completed at all widths by finite fallback.','eta_j':'min(rho-a_j,1-rho-a_j,a_j-b_j)>0','e_j':'Fresh integer dominating E_backend^(ceil(2/rho)), borrow threshold, ceil((32*K_j/eta_j)^(ceil(8/eta_j)))+2^(ceil(8/eta_j)).','scope':'Constructive finite threshold schema under retained native/compiler/ROW/precision/tape premises. Winning uniform program and decimal threshold are not materialized.'}} +def run(): + invoice=L.read(R/'INVOICE.json');glob=L.read(R/'GLOBAL-RESULT.json');P={int(k):v for k,v in invoice['paid'].items()};T={int(k):v for k,v in invoice['targets'].items()} + need(sum(T.values())==11166 and sum(P.values())==56547 and T.get(4,0)==0 and T[8]==7614 and P[7]==162,'Actual complete new target/paid bill') + E=load('nine_credited_interval',S/'ordinary-certificate/inputs/credited_intervals.py');I=load('nine_independent_series',S/'ordinary-certificate/inputs/separate_series.py') + tested=F('.00349780457954');uniform=F('.00349780457953');cover_gap=F(1,10**14);rho=F(1,100);reserve=F(1,2**48);v=tensor_degree(reserve);t=1-tested;u=F(1,5) + target=E.moment(T,t);paid=E.moment(P,t);alpha=E.divide(paid,target);gamma=E.divide(E.moment(P,t+u),E.mul(E.power(17,u),target));delta=E.divide((F(11166*18),)*2,E.mul(E.power(17,tested),target)) + need(alpha[1]<1-reserve and gamma[1]0 if sign>0 else margin[1]<0,'Independent root sign '+label);cross[label]={'saving':c,'margin':margin} + need(F(31,32)**1280 and 17**64<18**63 and max(T)<256,'Charged completion, separation and ambient') + z=1-uniform;z0=(t+z)/2;gap=z0-t;h=F(1,64);H0,H1=compiler_cutoffs(tested,uniform,v) + need(H0>=8*v and H0*h*gap>gap*(5+8*h)*v+1+8*v*(1-z0)and H1*(z-z0)>H0*(1-z0),'Fresh finite integer compiler thresholds') + C1=uniform-cover_gap;need(F(2**60)*cover_gap>256,'Cover/bad-prime gap') + backend=F(L.read(R/'predecessor/ORDINARY-RESULT.json')['admitted']);old=backend;levels=[] + for j in range(1,6): + a=(1-rho)*C1+rho*backend;b=below_grid(a,10**15);need(backendold,'New complete ordinary component saving') + cmin=F(L.read(R/'predecessor/ORDINARY-RESULT.json')['admitted']);cmax=F('.0035') + worst_target=E.moment(T,1-cmax) + worst_gamma=E.divide(E.moment(P,1-cmin+u),E.mul(E.power(17,u),worst_target)) + worst_delta=E.divide((F(11166*18),)*2,E.mul(E.power(17,cmin),worst_target)) + need(worst_gamma[1]=a)-sum(k*n for k,n in P.items() if k>=a) for a in range(1,129)] + need(min(tails)>=0 and tails[0]==753,'Strict first-moment monotonicity from rank-mass tails') + range_certificate={'C_min':cmin,'C_max':cmax,'gamma_upper_bound':worst_gamma,'delta_upper_bound':worst_delta, + 'rank_mass_tails':tails,'tensor_reserve_controls':controls(), + 'claim':'Under the retained framework, every ordinary saving strictly below this invoice raw crossing is attainable with fresh finite margins. This is not a global optimality claim.'} + + result={'status':'PASS_CONDITIONAL_G20_REFINEMENT_ORDINARY_FIVE_FINITE_LEVELS','invoice':invoice,'params':{'tested':tested,'uniform':uniform,'cover_gap':cover_gap,'rho':rho,'v':v,'alpha_gap':reserve,'grid_denominator':10**15,'prime_multiplier':2**60,'cutoff':17,'floor':18,'u':u},'raw_crossing_independent_exact':cross,'tail':{'alpha':alpha,'gamma':gamma,'delta':delta,'normalized_surplus':surplus,'H0':H0,'H1':H1},'C1':C1,'finite_backend_levels':levels,'admitted':backend,'comparator':old,'relative_gain':backend/old-1,'relative_gain_percent':100*(backend/old-1),'uniform_signed_invoice_improvement':'Relative to PR5653: Pnew-Pold=-252H1-252H3+252H4; targets unchanged. Gain252*(1+3^t-4^t)>0 for00 for0max(2^45*N^5,2^(2*H)) avoiding every finitely compiled denominator/rank witness. All QQ matrices and relative SOURCE projectors compiled before choice." + }, + "all_in_fixed_primitive_fee": { + "F": "(q+2)^(32*(N+1)^2)*(A(N)+2)^8", + "actual_cost": "F times positive maximum of the retained stream/route/normalizer/completed-backend constants, fixed anew at each finite level. No primitive has cost0 or a claimed universal cost1.", + "parking": "4*(B_N+C_N) positive FIELD passes per child plus initialization/teardown, with C_N<=11*A(N); F dominates their products.", + "bad_classes": "<=32*N^2 ordinary calls charged separately by the retained moment/cover argument." + }, + "stock": { + "reserve": "[B_N*|GL_N(F_q)|*q^(N^2*(w-1))]^D*S_completed_backend", + "D": "floor(log_N ceil(e/w))+1", + "borrowed_digits": "D*(N^2*(w-1)+ceil(log_q(B_N*|GL_N(F_q)|)))+ceil(log_q S_completed_backend)+1 =O_new(w loge)", + "ownership": "All11whole owned banks for EVERY compiled instance, including suspended ones, get distinct tags; full entry/exit CLEAR charged. No ancestor region is swept or external zero stock assumed." + }, + "eventual_threshold": { + "K_j": "At least16 times sum of F*positive retained primitive constants, reserve/adapter bounds and already frozen backend constant completed at all widths by finite fallback.", + "eta_j": "min(rho-a_j,1-rho-a_j,a_j-b_j)>0", + "e_j": "Fresh integer dominating E_backend^(ceil(2/rho)), borrow threshold, ceil((32*K_j/eta_j)^(ceil(8/eta_j)))+2^(ceil(8/eta_j)).", + "scope": "Constructive finite threshold schema under retained native/compiler/ROW/precision/tape premises. Winning uniform program and decimal threshold are not materialized." + } + }, + "whole_kappa": null, + "assumptions": "Same retained native/allcolumn arbitraryinput/ROW/spectator, mixed-target finite compiler, completed ordinary fallback, precision and fixed-tape contracts as PR4760/4814; no full theorem verification claimed." +} diff --git a/research/g20-helper-split/prior/prior/source/PROOF.md b/research/g20-helper-split/prior/prior/source/PROOF.md new file mode 100644 index 0000000000..951ce90c64 --- /dev/null +++ b/research/g20-helper-split/prior/prior/source/PROOF.md @@ -0,0 +1,278 @@ +# G20 partial helpers with nine owned relations + +The admitted conditional ordinary BIT saving is + + 435496247 / 125000000000 = 0.003483969976. + +The comparator is the completed PR4814 supplier +1737729/500000000 = 0.003475458. The relative increase is exactly +1063997/434432250, or 2127994/8688645 percent (about 0.24491667%). +This is a BIT component result. No complete multiplication coefficient or +selected result is changed. All native, arbitrary-function/all-column, +ROW/spectator, mixed-target finite compiler, ordinary fallback, precision +and fixed-tape hypotheses retained by PR4760/PR4814 remain hypotheses. + +## Sources, ownership and credit + +The two-transport source word is due to DreamingOfClouds (PR589), following +eumemic's 111-port construction (PR555) and their credited predecessors. +Cinna Davis / 1337isnot1337 supplies the query-thinned controller, physical +port/ROW interface and delayed-cover bridge. The productive helper +restriction and finite ordinary bootstrap follow our PR4760 and PR4814. +The finite bootstrap is prior work of rohanarun (PR185/199/204), not a new +general compiler theorem. The unchanged exact interval engine credits zxv +and Jacob Alan Sussman's mixed-target recursion; its source notices remain. + +Ali Romman's PR5421, head +295b00764305694b3c510d3b0bebc2ab024a7809, supplies the nine-owned-relation +method. We rederive it on a different actual word: the previously private +G20 partial436/capture-shadow producer. Its complete frozen source and +proof are included unchanged under vendor/g20, together with its public +predecessor source pins. It was not a previously published or externally +approved mathematical result. The nine pivots here are 469 through 477, +not the pivots in PR5421. Public5421 has 661 original fields; our source +has 658 and retains its four partial-rank4 helper jobs. These contracts +are not substituted for one another. Substantial OpenAI Codex assistance +was used. New work is Apache-2.0; vendor notices remain unchanged. + +VENDOR-PINS.json records the exact immutable closure. Old absolute paths +inside historical provenance are descriptive; no executable in the new +scientific package reads a workspace path or network service. + +## 1. The actual G20 word and changed premise + +The source has 111 X fields, 111 Y fields, 436 arbitrary helper fields, +one owned rank7 capture centre (658), and one owned shadow (659). Its +productive helper targets are 432 rank8 and four rank4 jobs. Its complete +local paid profile is + + P0={1:1318,2:1342,3:77,4:40,5:102,6:10,7:18}. + +G20's positive-fee shadow window replaces [1,3,3] by [3,4] at the actual +helper464/SOURCE0 interaction. The frozen proof describes both directions, +the fresh rank4 matcher and the paid shadow's exact lifetime. The new +verifier does not merely trust the profile: it checks every instruction +of the emitted inverse, every current FRAME, proper nested residual and +common-FRAME XOR. The exact frame induction proves arbitrary-function +correctness; finite q101 and q101^2 sparse controls exercise every one of +the 660 distinct entry symbols. The integer majorant bounds cancellation +free growth; it is not an integer-valued endpoint identity. + +This construction changes the initial-data contract by retiring nine +independent helper targets and owning those fields. It does not reopen +the closed unchanged-word QUERY-fusion or wrong-FRAME cache censuses. +No surviving arbitrary original is cleared or presumed zero. + +## 2. Nine paid owned relations + +Replay the actual G20 inverse in scalar F2 symbols and record the current +SOURCE row at every one of its nine COPY entries. Gaussian elimination +using helper columns gives nine independent rows. Each reduced row has +exactly its own pivot among {469,...,477}; its other terms are X fields +0,...,110. Every term has the actual full8 entrance FRAME1, and each pivot +has a complete full8 target (birth FRAME0, exit FRAME1). None is one of +the four partial helpers 462,463,466,468. + +Own the nine pivots. At entry, erase each entire owned payload and XOR +the other terms of its relation into it at FRAME1. These 523 pointwise +XORs are paid. They set all nine recorded COPY forms to zero while +preserving the 649 independent retained fields. The capture centre and +shadow also receive paid whole-payload entry erasures; arbitrary DIRTY +entry values in all eleven owned fields therefore have no output effect. + +Chronological exact replay shows nine rank1 QUERYs occur on whole zero +fields and all nine rank7 COPY values are zero. Only these eighteen +charged jobs disappear. A free zero FRAME change requires the entire +symbolic function to be zero, not only its scalar bitmap. The centre is +kept zero with paid erasure/header operations; no immutable old SOURCE +ticket remains. The original shadow operations remain. At exit each +pivot receives a paid whole-payload erasure, and all eleven owned fields +return to their declared zero/end headers. + +The actual resulting profile and complete local operations are + + P1={1:1309,2:1342,3:77,4:40,5:102,6:10,7:9}, + 19595 XORs, 39 whole ERASEs, 1 zero INIT, 9 zero FRAME changes. + +All 660 independent RAW/DIRTY entry columns are checked: the retained +649-field map is (X,Y)->(X,Y+X), identity on the 427 retained helpers, +and every owned output is zero. Native controls include the complete +paired HEAD/TAIL function, not just the scalar rows. Missing initial +DIRTY erasure is rejected. Independent checks also reject a changed +relation and an unearned zero transition. + +## 3. Why the reverse body serves every thick caller + +Let P be an actual port rank1 projector, K=I-P and let D denote the +paired ADDRESS interchange, including the source's fixed bank reversal. +Exact rational checks give D_P^2=D_K^2=D_I^2=I and +D_I D_P=D_P D_I=D_K. These are ADDRESS compositions. Their induced data +permutations commute and have the same involution laws. + +With the two-field shear M over F2, both the original forward and inverse +physical endpoints are + + diag(D_I,D_K) M diag(D_P,I) + = diag(D_P,I) M diag(D_I,D_K) + = [[D_K,0],[D_I,D_K]]. + +The bottom-left term in its square is zero by characteristic two and +commutation. Each retained helper has physical endpoint D_U for its +actual full8 or partial4 projector U; D_U is also an involution. Owning +and restoring the nine retired helpers does not change any surviving +physical output. Thus the new inverse implementation realizes exactly +the previous physical thick-call operator in either direction. + +Every new thick core explicitly starts at base.final and ends at +base.start. These are its internal decomposition coframes. We do not +claim that they equal the old forward internal headers. The outer paid +rho15 entry/return is unchanged and conjugates the same physical operator, +so no additional unimplemented physical map is hidden in a header +relabeling. All 111 exact rho matrices and P/K complements are checked. +For multiplicity f tensor every projector/route with I_f and retain the +whole ROW and spectator coordinates. The identities remain exact under +the inherited streaming/native interface; different ports receive no +common free physical chart. + +## 4. Literal global word and full target debit + +The p16/a7 controller has eighteen thick calls and fifteen thin stages. +We instantiate the new body on its actual source/target banks, reuse +nine separately owned pivot arrays between calls, and keep the centre +and shadow separate. No erased helper remains an independent input. +The global domain has 11238 independent retained fields and eleven +owned arrays, with paid initialization, clear and teardown. Distinct +owned banks are reserved again for every compiled unit instance, +including suspended instances; they are never credited as DATA targets. + +The literal tape has 456232 events, canonical SHA256 +30f5f0cc16bb700465d05cafa04b6d15b86289721c84671a17cf41ecb2b86c4e. +It checks all 11249 independent RAW/DIRTY entry columns, all eighteen +exact mapped cores and owned returns. There are 1845 nonzero owned +payload episodes. Exact controller group-ring evaluation gives the +prescribed diagonal monomial on all 32 main bank inputs, including the +real scalar boundaries. Independent orthogonal stage factors and the +local arbitrary-function statement lift it to the complete function +operator. Source descriptors bind every actual prefix, owner, version, +epoch and geometric job; a RAW bitmap is only additional control data. + +The entire target inventory is + + T={4:72,8:7614,15:444,22:444,29:444,36:444, + 43:444,50:444,57:444,64:222,127:222}. + +The entire paid inventory is + + P={1:25227,2:24156,3:1386,4:720,5:1836,6:180,7:162, + 14:444,21:444,28:444,35:444,42:444,49:444,56:444,63:222}. + +There are 56997 paid QUERYs and rank surplus753. Relative to G20 this is +-162 H1 -162 H7 in paid jobs and -162 H8 in targets. All four partial +helpers per call remain credited exactly once. For any 00, by strict subadditivity. +No lost target, CLEAR, normalizer or consumer cost is treated as free. + +Every retained target descriptor has exactly its old matcher, port, +physical job, ROW routes and domain, with only a compact owner renaming. +MAIN projectors are the exact central P or I8 plus disjoint coordinate +stage projectors. All helper projectors are checked over Q. For each +actual projector U, U^2=U=U^T and the paired D_U is a symmetric ADDRESS +involution. Its induced FUNCTION permutation therefore satisfies +A^-1=A=A^T=A^-T. The whole target operator is their direct sum. The SAME +complete literal program, with eleven newly paid owned banks, supplies +forward, inverse, transpose and inverse-transpose under the identical +external domain. We never reverse or transpose a destructive erasure. +This is an operator statement, not a scalar-bit-transpose inference. + +## 5. Complete finite fees and compiler + +The new literal invoice counts 389118 XOR passes, 2389 whole owned CLEARs, +18 zero header acquisitions, 162 zero FRAME changes, and 7548 internal +paid port routes. Separate canonical whole-job routing is still 7248 +routes, including 144 partial-helper routes. Even the known zero-centre +header/clear steps and extra conservative initialization/teardown scans +are charged. Before each child, charge + + 4*(11238+11)*56997 = 2564637012 FIELD passes + +for parent parking, input/output, restore and head return. No ancestor +region is swept. Every fixed route and actual current SOURCE normalizer +also carries its positive retained primitive constant. A 1e9 raw-record +cap is not reused as an all-in machine coefficient. + +The new cancellation-free global envelope is 517 bits. The actual +rational base geometry has at most three-bit entries, and the retained +fixed base height bound1024 covers both. All old numerical rank/prime, +precision and tape thresholds are regenerated rather than reused. + +Use tested saving0.00348398, uniform saving0.00348397, tensor power1024, +cutoff17, floor18, and second-moment parameter1/5. Two unchanged rational +interval engines independently check the new complete P/T, including a +strict raw crossing in (0.0034839853304,0.0034839853305). With t=1-tested, + + alpha=P_t/T_t < 1-2^-39, + gamma=P_(t+1/5)/(17^(1/5)*T_t) <31/32, + delta=11238*18/(17^tested*T_t) <19/20. + +Complete every small target on the SAME owner at18^1024, and split every +paid job at17^1024 with all pieces charged. Both decay blocks raised to128 +are below1/16. The normalized contraction surplus is the positive +536870911/576460753377165312. Separation follows from17^64<18^63; +the minimum4 and maximum paid63 are not falsely compared directly. + +The fresh exact finite integer-compiler thresholds are + + H0=378121592832, H1=263473235277373441, N=2^H1. + +The source inequalities for h=1/64, z0 halfway between t and1-uniform +are checked exactly. They are rank-compiler thresholds, not old machine +thresholds. With K=2^262144, use + + J(n)=(n+1)^4*K^(4*n+4), A(1)=K^4, + A(n)=(J(n)+2)^4*(A(n-1)+2)^(4*n+8). + +These oversized finite integers bound productive roles, leaves, compiled +instances and primitive descriptions, including the denominator-clearer +product of smaller widths. Reserve C_N<=11*A(N) whole owned banks. +Let T_arith=(2N+2)^4*(A(N)+2)^2 and H=1026*4^(T_arith+1). +Choose an odd prime q>max(2^45*N^5,2^(2H)) avoiding all finitely compiled +denominators and rank witnesses. These choices precede the input width. +The positive multiplier + + F=(q+2)^(32*(N+1)^2)*(A(N)+2)^8 + +dominates the charged fixed scans, parking, low-type/carry normalizers and +routes in retained primitive invocations, multiplied by the positive +maximum retained primitive/backend constant. It is not a universal unit +machine cost. The inherited bad-class ordinary calls are charged in the +moment/cover argument. ORDINARY-RESULT.json records the corresponding +reserve, borrowed digits and explicit finite eventual-threshold schema. + +## 6. Three finite ordinary backends + +Use cover gap2^-36+10^-20 and atom fraction rho=1/100. The cover prime +inequality 2^45*gap>256 is checked. Begin with the already completed +PR4814 ordinary backend b0=1737729/500000000. At each j=1,2,3 freeze +the completed preceding algorithm, then compile + + a_j=(1-rho)*(uniform-cover_gap)+rho*b_(j-1), + b_j=floor(10^12*a_j)/10^12. + +No algorithm calls itself as its own atom backend. The adapter, stock, +rounding and improvement gaps are all positive. Newly fixed finite +constants and each completed all-width fallback determine a fresh +eventual threshold; the retained proof absorbs every positive coefficient +before taking the input-size limit. The result is b3=0.003483969976. +The astronomical winning uniform program, prime and decimal eventual +threshold are not expanded. This remains a conditional construction, +not a formal or complete multiplication-theorem verification. + +## Open next questions + +An independent universal audit of the retained native/ROW, precision, +fixed-tape and analytic recovery premises is still valuable. A feasible +first step is one caller-bound quantified interface, with explicit all-f +and spectator scope. The present finite checks do not close those +framework assumptions. Further scalar savings alone do not justify a +new exponent: any changed paid mechanism needs a fresh complete target, +ownership, whole-program and ordinary invoice. diff --git a/research/g20-helper-split/prior/prior/source/RECORD.json b/research/g20-helper-split/prior/prior/source/RECORD.json new file mode 100644 index 0000000000..501cdde1cc --- /dev/null +++ b/research/g20-helper-split/prior/prior/source/RECORD.json @@ -0,0 +1,20 @@ +{ + "schema_version": 1, + "status": "PROPOSED_CONDITIONAL_ORDINARY_BIT_003483969976", + "scientific_base": "32890bc5de034ab8fc93ac88ead7279a6a416d04", + "axis": "ordinary_BIT_saving", + "admitted": "435496247/125000000000", + "comparator_PR": 4814, + "comparator_head": "f56ae4533a7d97d782a2c596a33fe844cd051747", + "comparator": "1737729/500000000", + "relative_gain": "1063997/434432250", + "relative_gain_percent": "2127994/8688645", + "raw_paid_profile_changed": true, + "owned_productive_credit": 0, + "whole_kappa_changed": false, + "selected_global_kappa": "605457647/200000000000", + "maintainer_mathematical_review": "Pending", + "external_independent_reproduction": "Not claimed; separate internal AI audits.", + "hosted_CI": "Not yet observed for this proposed package.", + "publication": "Actual PR identity/head/time is recorded only after creation." +} diff --git a/research/g20-helper-split/prior/prior/source/WORD.json.gz b/research/g20-helper-split/prior/prior/source/WORD.json.gz new file mode 100644 index 0000000000..6ffe744d17 Binary files /dev/null and b/research/g20-helper-split/prior/prior/source/WORD.json.gz differ diff --git a/research/g20-helper-split/prior/prior/source/global_relations.py b/research/g20-helper-split/prior/prior/source/global_relations.py new file mode 100644 index 0000000000..aed289de8b --- /dev/null +++ b/research/g20-helper-split/prior/prior/source/global_relations.py @@ -0,0 +1,104 @@ +"""Literal p16/a7 caller with nine retired helper targets and shared owned work. + +Retains G20 native controller/geometry; uses the independently checked reverse +physical involution at each full call. No old helper target is given to owned work. +""" +from pathlib import Path +from collections import Counter +from hashlib import sha256 +from time import process_time +import gzip,json,importlib.util,sys +import local_relations as L +R=L.R;S=L.S +def need(c,m): + if not c:raise ValueError(m) +def read(p):return L.read(p) +def put(n,x):L.put(n,x) +def run(): + clock=process_time();controller=read(S/'inputs/CONTROLLER.json');base,frames,_=L.source();local=read(R/'WORD.json.gz');owned=local['owned'];pivots=owned[:-2];need(pivots==list(range(469,478)),'Exact retired helper owners') + oldcalls=read(S/'provider/data/CALLS.json');retired={c['helper_owner_begin']+p-222 for c in oldcalls for p in pivots};retained=[i for i in range(11400)if i not in retired];compact={x:i for i,x in enumerate(retained)};N=len(retained);W=list(range(N,N+11));center,shadow=W[:2];pivotwork=dict(zip(pivots,W[2:]));need(N==11238,'New retained original count') + values=[1<0,'Positive rank');source.append({'event':len(events),'prefix_sha256':prefix.hexdigest(),'owner':d,'version':versions[d],'epoch':epochs[d],'rank':k,'detail':detail,'RAW_hex':hex(values[d]),'function_identity':'Exact literal program prefix plus current owner/epoch/version and actual geometric source job; RAW bitmap is extra evidence, not a claim of purity.'});paid[k]+=1;versions[d]+=1;emit(['QUERY',d,k,detail]) + def swap(d,s,why):add(d,s,why);add(s,d,why);add(d,s,why) + def boundary(program,why): + for op,d,s in program: + for p in range(111): + if op=='ADD':add(compact[d*111+p],compact[s*111+p],why) + else:need(op=='SWAP','Controller opcode');swap(compact[d*111+p],compact[s*111+p],why) + boundary(controller['boundaries']['right_program'],'RIGHT_BOUNDARY') + thick=controller['invoice']['thick_stages'];stage_index={s:i for i,s in enumerate(thick)} + for event in controller['physical_events']: + op=event[0] + if op=='LOCAL': + _,stage,pair,rev=event;x,y=2*pair,2*pair+1 + if rev:x,y=y,x + helper=3552+436*stage_index[stage] + def owner(r): + if r==658:return center + if r==659:return shadow + if r in pivotwork:return pivotwork[r] + return compact[(x if r<111 else y)*111+r%111]if r<222 else compact[helper+r-222] + sx=[values[owner(i)]for i in range(111)];sy=[values[owner(111+i)]for i in range(111)];helpers=[r for r in range(222,658)if r not in pivotwork];before={r:values[owner(r)]for r in helpers} + if stage: + for bank in(x,y): + for p in range(111):emit(['PAID_PORT_ROUTE',stage,compact[bank*111+p],p,'ENTRY']) + start=len(events);lp=Counter();st=local['start'][:];livebegin={} + for ix,e in enumerate(local['records']): + typ,d=e[:2];gd=owner(d) + if typ=='ERASE': + erase(gd,['LOCAL',stage,ix],e[2]);st[d]=e[2] + if gd in livebegin:episodes.append({'owner':gd,'stage':stage,'begin':livebegin.pop(gd),'end':len(events)-1}) + elif typ=='INIT':need(values[gd]==0,'Whole zero INIT');st[d]=e[2];emit(['OWNED_ZERO_HEADER',gd,e[2],stage]) + elif typ=='ADD': + s,f=e[2:];need(st[d]==st[s]==f,'Actual instantiated coframe') + if gd in W and gd not in livebegin:livebegin[gd]=len(events) + add(gd,owner(s),['LOCAL',stage,f,ix]) + elif typ in('Q','ZERO_Q'): + a,b,k=e[2:];need(st[d]==a,'Current instantiated query frame');st[d]=b + if typ=='Q':query(gd,k,['LOCAL_INVERSE',stage,a,b,ix]);lp[k]+=1 + else:need(values[gd]==0,'Zero only free query');emit(['WHOLE_ZERO_FRAME',gd,a,b,k,stage]) + else:raise ValueError('Local opcode '+typ) + need(not livebegin and st==local['final'],'No live local owned state at return') + need(all(values[owner(i)]==sx[i]and values[owner(111+i)]==sy[i]^sx[i]for i in range(111)),'All retained main RAW inputs') + need(all(values[owner(r)]==before[r]for r in helpers)and all(values[w]==0 for w in W),'All427 independent retained helper inputs and11owned returns') + need(lp==Counter(read(R/'LOCAL-RESULT.json')['stats']['paid'])or lp==Counter({int(k):v for k,v in read(R/'LOCAL-RESULT.json')['stats']['paid'].items()}),'Actual local query count') + calls.append({'stage':stage,'pair':pair,'source_bank':x,'target_bank':y,'old_direction_inverse':rev,'new_direction_inverse':True,'helper_old_owner_begin':helper,'core_begin':start,'core_end':len(events),'owned_global_indices':W,'retained_helper_count':427,'paid':dict(lp)}) + if stage: + for bank in(x,y): + for p in range(111):emit(['PAID_PORT_ROUTE',stage,compact[bank*111+p],p,'RETURN']) + elif op=='QUERY_SHEAR': + _,stage,pair,rev=event;x,y=2*pair,2*pair+1 + if rev:x,y=y,x + for p in range(111): + src,dst=compact[x*111+p],compact[y*111+p];need(values[center]==0,'Clean thin scratch');v=versions[src];begin=len(events);add(center,src,['THIN_COPY',stage,p]);query(center,1,['THIN',stage,p]);add(dst,center,['THIN_DELIVER',stage,p]);need(versions[src]==v,'Thin immutable SOURCE');erase(center,['THIN',stage,p]);episodes.append({'owner':center,'stage':stage,'kind':'THIN','begin':begin,'end':len(events)-1}) + elif op=='IDLE': + _,pair,stages=event;k=7*len(stages) + for bank in(2*pair,2*pair+1): + for p in range(111):query(compact[bank*111+p],k,['WHOLE_IDLE',stages,p]) + elif op=='ADD': + for p in range(111):add(compact[event[1]*111+p],compact[event[2]*111+p],'BRIDGE') + else: + need(op=='SWAP','Known controller event') + for p in range(111):swap(compact[event[1]*111+p],compact[event[2]*111+p],'FINAL_SWAP') + boundary(controller['boundaries']['left_program'],'LEFT_BOUNDARY') + for d in W:erase(d,'GLOBAL_EXIT_TEARDOWN') + need(values==[1<>i&1] +def source():return read(S/'inputs/BASELINE-LOCAL.json.gz'),read(S/'inputs/FRAMES.json')['frames'],read(S/'provider/data/INVERSE.json.gz')['records'] +def relations(program): + rows=[1<>p&1:row^=v + h=row>>222;need(h,'New helper pivot');p=222+(h&-h).bit_length()-1 + for k in basis: + if basis[k]>>p&1:basis[k]^=row + basis[p]=row + need(len(basis)==9,'Nine independent relations') + pm=sum(1<

=4*v*64,'Explicit tensor count envelope') + return{'status':'PASS_POSITIVE_NEW_FINITE_FEE_AND_STOCK_SCHEMA','base_counts':{'raw_records':raw,'all_XOR_CLEAR_INIT_zeroheader_passes':scans,'parent_parking_FIELD_passes':park,'internal_and_wholejob_routes':routes,'coarse_primitive_count_with_dimension_work':base,'strict_upper':2**64,'all_owned_allocated':11,'owned_productive_credit':0}, + 'fixed_tensor_unit':{'v':v,'K':'2^262144','meaning':'Bounds fixed integer ranks, all role/round/operation inventories after tensoring, charged target completion and charged paid splitting.'}, + 'finite_compiler':{'N':'2^'+str(H1),'J(n)':'(n+1)^4*K^(4*n+4)','A(1)':'K^4','A(n)':'(J(n)+2)^4*(A(n-1)+2)^(4*n+8)','counts':'Productive roles B_N, paid leaves P_N, instances and primitive descriptions <=A(N). Each compiled instance gets11distinct owned banks; C_N<=11*A(N). Denominator replication product <=A(n-1)^(n-1).'}, + 'height_prime':{'base_height_bits':1024,'T':'(2*N+2)^4*(A(N)+2)^2','H':'1026*4^(T+1)','q':'Choose odd prime q>max(2^45*N^5,2^(2*H)) avoiding every finitely compiled denominator/rank witness. All QQ matrices and relative SOURCE projectors compiled before choice.'}, + 'all_in_fixed_primitive_fee':{'F':'(q+2)^(32*(N+1)^2)*(A(N)+2)^8','actual_cost':'F times positive maximum of the retained stream/route/normalizer/completed-backend constants, fixed anew at each finite level. No primitive has cost0 or a claimed universal cost1.','parking':'4*(B_N+C_N) positive FIELD passes per child plus initialization/teardown, with C_N<=11*A(N); F dominates their products.','bad_classes':'<=32*N^2 ordinary calls charged separately by the retained moment/cover argument.'}, + 'stock':{'reserve':'[B_N*|GL_N(F_q)|*q^(N^2*(w-1))]^D*S_completed_backend','D':'floor(log_N ceil(e/w))+1','borrowed_digits':'D*(N^2*(w-1)+ceil(log_q(B_N*|GL_N(F_q)|)))+ceil(log_q S_completed_backend)+1 =O_new(w loge)','ownership':'All11whole owned banks for EVERY compiled instance, including suspended ones, get distinct tags; full entry/exit CLEAR charged. No ancestor region is swept or external zero stock assumed.'}, + 'eventual_threshold':{'K_j':'At least16 times sum of F*positive retained primitive constants, reserve/adapter bounds and already frozen backend constant completed at all widths by finite fallback.','eta_j':'min(rho-a_j,1-rho-a_j,a_j-b_j)>0','e_j':'Fresh integer dominating E_backend^(ceil(2/rho)), borrow threshold, ceil((32*K_j/eta_j)^(ceil(8/eta_j)))+2^(ceil(8/eta_j)).','scope':'Constructive finite threshold schema under retained native/compiler/ROW/precision/tape premises. Winning uniform program and decimal threshold are not materialized.'}} +def run(): + invoice=L.read(R/'INVOICE.json');glob=L.read(R/'GLOBAL-RESULT.json');P={int(k):v for k,v in invoice['paid'].items()};T={int(k):v for k,v in invoice['targets'].items()} + need(sum(T.values())==11238 and sum(P.values())==56997 and T[4]==72 and T[8]==7614 and P[7]==162,'Actual complete new target/paid bill') + E=load('nine_credited_interval',S/'ordinary-certificate/inputs/credited_intervals.py');I=load('nine_independent_series',S/'ordinary-certificate/inputs/separate_series.py') + tested=F('.00348398');uniform=F('.00348397');cover_gap=F(1,2**36)+F(1,10**20);rho=F(1,100);reserve=F(1,2**39);v=1024;t=1-tested;u=F(1,5) + target=E.moment(T,t);paid=E.moment(P,t);alpha=E.divide(paid,target);gamma=E.divide(E.moment(P,t+u),E.mul(E.power(17,u),target));delta=E.divide((F(11238*18),)*2,E.mul(E.power(17,tested),target)) + need(alpha[1]<1-reserve and gamma[1]0 if sign>0 else margin[1]<0,'Independent root sign '+label);cross[label]={'saving':c,'margin':margin} + need(F(31,32)**1280 and 17**64<18**63 and max(T)<256,'Charged completion, separation and ambient') + z=1-uniform;z0=(t+z)/2;gap=z0-t;h=F(1,64);H0=ceil((gap*(5+8*h)*v+1+8*v*(1-z0))/(h*gap));H1=(H0*(1-z0)/(z-z0)).__floor__()+1 + need(H0>=8*v and H0*h*gap>=gap*(5+8*h)*v+1+8*v*(1-z0)and H1*(z-z0)>H0*(1-z0),'Fresh finite integer compiler thresholds') + C1=uniform-cover_gap;need(F(2**45)*cover_gap>256,'Cover/bad-prime gap') + backend=F(1737729,500000000);old=backend;levels=[] + for j in range(1,4): + a=(1-rho)*C1+rho*backend;b=F((a*10**12).__floor__(),10**12);need(backendF(1,1000),'New actual ordinary gain clears .1percent publication guard') + result={'status':'PASS_CONDITIONAL_G20_NINE_RELATIONS_ORDINARY_THREE_FINITE_LEVELS','invoice':invoice,'params':{'tested':tested,'uniform':uniform,'cover_gap':cover_gap,'rho':rho,'v':v,'alpha_gap':reserve,'cutoff':17,'floor':18,'u':u},'raw_crossing_independent_exact':cross,'tail':{'alpha':alpha,'gamma':gamma,'delta':delta,'normalized_surplus':surplus,'H0':H0,'H1':H1},'C1':C1,'finite_backend_levels':levels,'admitted':backend,'comparator':old,'relative_gain':backend/old-1,'relative_gain_percent':100*(backend/old-1),'qualifies_0_1_percent':True,'uniform_signed_invoice_improvement':'Pnew-Pold=-162H1-162H7; Tnew-Told=-162H8, gain162*(1+7^t-8^t)>0 for00 for0max(2^45*N^5,2^(2*H)) avoiding every finitely compiled denominator/rank witness. All QQ matrices and relative SOURCE projectors compiled before choice." + }, + "all_in_fixed_primitive_fee": { + "F": "(q+2)^(32*(N+1)^2)*(A(N)+2)^8", + "actual_cost": "F times positive maximum of the retained stream/route/normalizer/completed-backend constants, fixed anew at each finite level. No primitive has cost0 or a claimed universal cost1.", + "parking": "4*(B_N+C_N) positive FIELD passes per child plus initialization/teardown, with C_N<=15*A(N); F dominates their products.", + "bad_classes": "<=32*N^2 ordinary calls charged separately by the retained moment/cover argument." + }, + "stock": { + "reserve": "[B_N*|GL_N(F_q)|*q^(N^2*(w-1))]^D*S_completed_backend", + "D": "floor(log_N ceil(e/w))+1", + "borrowed_digits": "D*(N^2*(w-1)+ceil(log_q(B_N*|GL_N(F_q)|)))+ceil(log_q S_completed_backend)+1 =O_new(w loge)", + "ownership": "All15whole owned banks for EVERY compiled instance, including suspended ones, get distinct tags; full entry/exit CLEAR charged. No ancestor region is swept or external zero stock assumed." + }, + "eventual_threshold": { + "K_j": "At least16 times sum of F*positive retained primitive constants, reserve/adapter bounds and already frozen backend constant completed at all widths by finite fallback.", + "eta_j": "min(rho-a_j,1-rho-a_j,a_j-b_j)>0", + "e_j": "Fresh integer dominating E_backend^(ceil(2/rho)), borrow threshold, ceil((32*K_j/eta_j)^(ceil(8/eta_j)))+2^(ceil(8/eta_j)).", + "scope": "Constructive finite threshold schema under retained native/compiler/ROW/precision/tape premises. Winning uniform program and decimal threshold are not materialized." + } + }, + "whole_kappa": null, + "assumptions": "Same retained native/allcolumn arbitraryinput/ROW/spectator, mixed-target finite compiler, completed ordinary fallback, precision and fixed-tape contracts as PR4760/4814; no full theorem verification claimed." +} diff --git a/research/g20-helper-split/prior/prior/source/retirement-proof.md b/research/g20-helper-split/prior/prior/source/retirement-proof.md new file mode 100644 index 0000000000..3f1f05be62 --- /dev/null +++ b/research/g20-helper-split/prior/prior/source/retirement-proof.md @@ -0,0 +1,199 @@ +# Native G20 retirement and an ordinary BIT supplier + +The conditional ordinary BIT saving is `0.003486609089`. The source +PR5512 saving is `0.003483969976`. The exact increase is `0.000002639113`. +This result gives more BIT capacity for a future complete multiplication +construction. It does not increase the selected multiplication coefficient. +The complex component and its complete caller still require their own bill. + +## 1. Contract and attribution + +The native G20 word, geometry, controller, and ordinary framework are the +PR5512 construction of ai-nanachi. Its nine owned relations use Ali Romman's +PR5421. Dugongue's PR5629 identifies four further partial helpers that can +retire. The exact proposal and its source commit are in `proposal/` and +`INPUTS.json`. This package supplies an emitted word, its actual caller, +separate replay, and a new ordinary certificate for that proposal. + +The fixed native, arbitrary-function, all-column, ROW, spectator, finite +compiler, ordinary fallback, precision, and tape contracts of PR4760 and +PR4814 remain assumptions. The finite checks here do not prove those +contracts. Read `source/PROOF.md` and `source/NOTICE.md` for the retained +proof and full credit. The all-input argument below is conditional on the +same native coframe identities as that proof. + +## 2. Emit and retire four whole owned fields + +Make fields `462, 463, 466, 468` owned. Clear each complete field at entry. +Keep every source operation through its last nonzero source read. Those +source record indices are respectively `16202, 16206, 16160, 16139`. +The protected rank-four reads occur before these cuts and remain paid. +Clear each field immediately after its cut. Set its return frame at that +clear. Omit its later destination operations and reads of the resulting +whole zero. This removes four rank-three queries, four rank-one queries, +four other tail ADDs, and 32 cold zero reads per local call. + +The source invariant represents a field in frame F by one normalized +linear row in the independent input functions. ADD requires the same +coframe on both operands. A native query changes the coframe and keeps +that normalized row. Thus a zero normalized row is the zero function for +every native input width under the retained coframe identity. It is not +only a scalar zero at a sampled point. Specializing an owned input to +zero and then replaying these rows proves each omitted read is zero. +After the last nonzero read, a field has no effect on any retained output. +Its remaining return path can therefore be replaced by whole-field CLEAR. +No retained original input is cleared, and no live frame is renamed. + +The resulting local word has 645 retained original fields and 15 owned +fields. The 15 include the source centre, its shadow, the source nine +relations, and these four new helpers. Every owned entry can contain an +arbitrary dirty value; the entry CLEAR removes its complete column. +The output on each retained field is the same physical source map. The +owned outputs are all zero. The local paid histogram is + +```text +rank 1 2 3 4 5 6 7 +count 1305 1342 73 40 102 10 9 +``` + +The source exact rational coframe checks are retained. Forward native +replay tracks all 660 original and dirty columns over moduli 101 and +10201. A separate adjoint implementation uses other address points at +both moduli and checks all transpose columns. CLEAR has the total zero +linear extension; it is not inverted. These finite tests support the +coframe proof. They are not a substitute for its all-width assumptions. +Missing entry CLEAR, an early retirement, and retained-input erasure all +fail the verifier. + +## 3. Complete controller and target bill + +Install the new physical involution in all 18 G20 local calls. Share 15 +owned banks serially; all return zero between calls. Retire 234 original +helper targets: 18 copies of the source nine helpers and the new four. +The actual 11,166 retained originals stay independent. The caller also +includes its thin query shears, scalar boundaries, idles, bridges, return +routes, COPY, CLEAR, and private epochs. `GLOBAL.jsonl.gz` emits all +455,592 events. `SOURCE-DESCRIPTORS.json.gz` binds every one of the +56,853 queries to its chronological owner, epoch, version, normalized +row, and prefix hash. The row is extra evidence; it does not certify a +pure physical source without its native prefix. + +`independent.py` recounts these events and all targets from the source +owner table. It verifies the full identity on 11,166 original columns +and annihilation of all 15 dirty columns. A stale query epoch fails. +The positive envelope has 516 bits. No owned field has output credit. +The new bill relative to PR5512 is + +```text +P_new - P_old = -72 H1 -72 H3 +T_new - T_old = -72 H4 +``` + +For `t=1-C` in `(0,1)`, the exact target-minus-paid gain is +`72*(1+3^t-4^t)>0`. Strict subadditivity gives the sign. This proves a +positive gain for every such exponent, with the new target debit included. +The full histograms, not this difference alone, feed the ordinary compiler. + +## 4. New finite compiler and positive costs + +Use tested saving `0.003486609105`, uniform saving `0.003486609104`, +tensor power 1024, cutoff 17, floor 18, and second parameter `1/5`. +Two separate rational interval engines verify the full bill. The raw +crossing is in `(0.00348660910743, 0.00348660910744)`. With `t=1-tested`, +the exact intervals satisfy + +```text +alpha = P_t/T_t < 1-2^-39 + gamma = P_(t+1/5)/(17^(1/5)*T_t) < 31/32 + delta = 11166*18/(17^tested*T_t) < 19/20 +``` + +Complete each small target on the same owner at `18^1024`. Split every +paid job at `17^1024` and charge every piece. The two decay blocks to +power 128 are less than `1/16`. The normalized contraction surplus is +`536870911/576460753377165312`. The separation check is `17^64<18^63`. +The new integer thresholds are + +```text +H0 = 3783974628696064 +H1 = 26386480783217407411429377 +N = 2^H1 +``` + +These values satisfy the source inequalities with `h=1/64` and `z0` +halfway between `t` and `1-uniform`. The base precision envelope is less +than 1024 bits. The complete positive base count is `963540729957<2^64`. +It includes `4*(11166+15)*56853` field passes for parent parking, +all emitted scans, internal and whole-job routes, and dimension work. + +Set `K=2^262144`. Retain the source finite bounds + +```text +J(n)=(n+1)^4*K^(4*n+4) +A(1)=K^4 +A(n)=(J(n)+2)^4*(A(n-1)+2)^(4*n+8) +T_arith=(2*N+2)^4*(A(N)+2)^2 +H=1026*4^(T_arith+1) +``` + +Each compiled instance gets 15 distinct owned banks. This also applies +to suspended instances. Thus `C_N<=15*A(N)`. All entry and exit CLEAR +passes are charged. Choose an odd prime +`q>max(2^45*N^5,2^(2*H))` that avoids every compiled denominator and +rank witness. Choose it after the fixed matrices and before the input +width. The source positive multiplier +`F=(q+2)^(32*(N+1)^2)*(A(N)+2)^8` bounds primitive counts. Multiply it +by the positive maximum of the retained primitive and backend constants. +No primitive has zero cost or a claimed universal unit machine cost. + +`ORDINARY-RESULT.json` states the complete stock, borrowed-digit, prime, +and fresh eventual-threshold formulas. In particular, all owned banks +have separate tags, ancestor storage is preserved, and no external zero +stock is assumed. The retained bad-class calls are charged by the cover +argument. These finite but large choices meet the inherited compiler +schema. The winning uniform program and decimal threshold are not expanded. + +## 5. Four finite ordinary levels + +Let `g=2^-36+10^-20` and `rho=1/100`. The cover guard `2^45*g>256` +holds. Start with the completed source backend `b0=0.003483969976`. +At each level freeze the preceding completed algorithm, then set + +```text +a_j=(1-rho)*(uniform-g)+rho*b_(j-1) +b_j=floor(10^12*a_j)/10^12 +``` + +The four new admitted values are `0.003486582698`, `0.003486608825`, +`0.003486609086`, and **`0.003486609089`**. Every improvement, adapter, +stock, and rounding gap is positive. Each level gets new finite constants +and a fresh threshold from its completed all-width fallback. No level +calls itself as its atom backend. A fifth level has the same admitted +value on this decimal grid, so it adds no useful result here. + +## 6. Check the immediate extension strategy + +Before freezing the word, `extensions.py` checks 1,174 further cohorts. +These include every one of the 423 possible single additions, all complete +pure-helper supports at source reads or queries, and the whole eligible +helper set. Each cohort contains the chosen four. The emitter constructs +each specialized word and counts all additional removed paid queries. +Every extra owner debits one rank-eight target per local call. For +`0<=C<=1/100`, the sum of removed ranks is already less than the lower +bound on that target debit. Since `r^(1-C)<=r`, none of these cohorts +can improve the chosen bill. This is a bound for the declared finite +census. It does not exclude other subsets or a changed reconstruction +program. Its purpose is to test the next step in this constructive +strategy before presenting a small local gain as the end of the search. + +## Open next questions + +Can a priced reconstruction change a later nonzero helper read and retire +more of its return path? First emit that changed native continuation, +then debit all lost targets and replay its complete caller. The current +cohort census does not answer this question. A higher complete kappa also +requires a compatible complex supplier and a complete paired bill. + +Prepared by Ali Romman with substantial OpenAI Codex assistance. New work +is Apache-2.0. 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a/research/g20-helper-split/prior/prior/source/vendor/g20/ordinary-certificate/inputs/credited_intervals.py b/research/g20-helper-split/prior/prior/source/vendor/g20/ordinary-certificate/inputs/credited_intervals.py new file mode 100644 index 0000000000..4b24a50961 --- /dev/null +++ b/research/g20-helper-split/prior/prior/source/vendor/g20/ordinary-certificate/inputs/credited_intervals.py @@ -0,0 +1,421 @@ +#!/usr/bin/env python3 +"""Higher-moment strictification and a polynomial-logarithm compiler bound. + +New arithmetic is independent of predecessor interval code. The unchanged +invoice replay and two outer ledgers are credited, byte-pinned oracles. +zxv with substantial OpenAI Codex assistance. Apache-2.0. +""" +import argparse +import ast +from collections import Counter +from contextlib import redirect_stdout +from fractions import Fraction as Q +from functools import lru_cache +from hashlib import sha256, sha1 +import io +import json +from pathlib import Path + +HERE = Path(__file__).resolve().parent +GRID = 2**192 +C = Q('0.00268648') +KAPPA = Q('0.00268647') +T = {5:420, 6:270, 7:840, 8:1395, 9:3195, + 25:448, 41:448, 57:448, 121:224} +P = {1:37305, 2:10695, 3:3360, 4:1530, 5:300, + 8:1464, 16:448, 32:448, 48:448} + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def down(x): + return Q((x*GRID).__floor__(), GRID) + + +def up(x): + return Q(-((-x*GRID).__floor__()), GRID) + + +def rounded(lo, hi): + return down(lo), up(hi) + + +def mul(a, b): + products = [x*y for x in a for y in b] + return rounded(min(products), max(products)) + + +def scale(a, x): + return mul(a, (x, x)) + + +def divide(a, b): + need(b[0] > 0, 'positive interval denominator') + return mul(a, rounded(1/b[1], 1/b[0])) + + +@lru_cache(None) +def log_bounds(n): + """Exact atanh series, binary reduction; round only the final interval.""" + need(isinstance(n, int) and n >= 1, 'positive integer logarithm') + + def series(x): + u = (x-1)/(x+1) + term, total = u, Q(0) + for j in range(80): + total += 2*term/(2*j+1) + term *= u*u + tail = 2*term/(161*(1-u*u)) + return total, total+tail + + k = n.bit_length()-1 + a, b = series(Q(2)) + c, d = series(Q(n, 2**k)) + return rounded(k*a+c, k*b+d) + + +def exp_point(x): + """Outward fixed-point Taylor enclosure, with binary scaling/squaring.""" + need(abs(x) < 16, 'bounded exponential argument') + if x < 0: + a, b = exp_point(-x) + return rounded(1/b, 1/a) + divisions = 0 + while x > Q(1, 2): + x /= 2 + divisions += 1 + term = total = (Q(1), Q(1)) + for j in range(1, 65): + term = scale(term, x/j) + total = rounded(total[0]+term[0], total[1]+term[1]) + following = scale(term, x/65) + # Every remaining ratio is <= 1/132. Twice the next term is safe. + result = rounded(total[0], total[1]+2*following[1]) + for _ in range(divisions): + result = mul(result, result) + return result + + +def exp_interval(a): + return exp_point(a[0])[0], exp_point(a[1])[1] + + +@lru_cache(None) +def power(n, exponent): + return exp_interval(scale(log_bounds(n), exponent)) + + +def moment(histogram, exponent): + low = high = Q(0) + for n, count in histogram.items(): + a, b = power(n, exponent) + low += count*a + high += count*b + return rounded(low, high) + + +def display(a): + unit = 10**30 + + def fixed(n): + sign = '-' if n < 0 else '' + s = str(abs(n)).rjust(31, '0') + return sign+s[:-30]+'.'+s[-30:] + + return {'lower': fixed((a[0]*unit).__floor__()), + 'upper': fixed(-((-a[1]*unit).__floor__()))} + + +def encoded(x): + if isinstance(x, Q): + return str(x) + if isinstance(x, dict): + return {str(k): encoded(v) for k, v in x.items()} + if isinstance(x, (list, tuple)): + return [encoded(v) for v in x] + return x + + +def source_environment(path): + env = {'__file__': str(path), '__name__': 'pinned_source_oracle'} + exec(compile(path.read_bytes(), str(path), 'exec'), env) + return env + + +def authenticate(): + result = {} + for row in json.loads((HERE/'VENDOR.json').read_text())['files']: + path = HERE/'vendor'/Path(row['path']).relative_to( + 'research/higher-moment-strictification/vendor') + digest = sha256(path.read_bytes()).hexdigest() + need(digest == row['sha256'], 'changed source: '+row['path']) + raw = path.read_bytes() + need(sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest() + == row['git_blob'], 'changed Git source blob') + result[row['path']] = digest + return result + + +def invoice_oracle(): + """Run #4426 unchanged, rebinding only its two file-location globals.""" + path = HERE/'vendor/invoice-review/verify.py' + env = source_environment(path) + env.update(ROOT=path.parent, PHASES='DATA-PHASES.json') + output = io.StringIO() + with redirect_stdout(output): + env['main']() + result = json.loads(output.getvalue()) + need(result['status'] == 'PASS_PR4416_INVOICE_REBUILD', 'source invoice oracle') + need({int(k): v for k, v in result['targets'].items()} == T + and {int(k): v for k, v in result['paid'].items()} == P, + 'exact literal-word invoice') + return result + + +def tail_certificate(v=150, cutoff=10, floor=15, u=Q(3, 10)): + t = 1-C + need(v >= 1 and 1 < cutoff < floor < 121, 'strict finite ranks') + need(t+u >= 1, 'tail moment exponent at least one') + target, paid = moment(T, t), moment(P, t) + alpha = divide(paid, target) + gamma = divide(moment(P, t+u), mul(power(cutoff, u), target)) + delta = divide((Q(sum(T.values())*floor),)*2, + mul(power(cutoff, C), target)) + limits = (1-Q(1, 10**8), Q(181, 200), Q(439, 500)) + for name, bounds, limit in zip(('alpha', 'gamma', 'delta'), + (alpha, gamma, delta), limits): + need(0 < bounds[0] <= bounds[1] < limit < 1, name+' certified limit') + a, g, d = limits + bound = 1/(1+v*(1-a))+2*g**v+2*d**v + need(bound < 1, 'complete charged normalized moment') + old_gamma = divide((Q(sum(k*n for k, n in P.items())),)*2, + mul(power(cutoff, C), target)) + old_lower = alpha[0]**v+2*old_gamma[0]**v + need(old_lower > 1, 'rank-one-tail estimate fails at this tensor power') + return {'tensor_power': v, 'cutoff_base': cutoff, 'floor_base': floor, + 'paid_moment_exponent': t+u, 'tail_offset_u': u, + 'tested_saving': C, 'alpha': display(alpha), 'gamma': display(gamma), + 'delta': display(delta), 'rational_upper_limits': limits, + 'normalized_paid_upper': bound, 'strict_moment_gap': display((1-bound,)*2), + 'old_rank_one_gamma': display(old_gamma), + 'old_rank_one_bound_lower': display((old_lower, old_lower)), + 'ambient': '121^'+str(v), 'minimum_target': str(floor)+'^'+str(v), + 'maximum_paid': str(cutoff)+'^'+str(v), + 'productive_fields_before_uniform_compiler': '7688^'+str(v), + 'rank_one_surplus': '131723^'+str(v)+'-131115^'+str(v), + 'materialized_product_or_uniform_word': False} + + +def uniform_rank(v): + t, p, theta = 1-C, 13, Q(6, 7) + gap = (C-KAPPA)/7 + uniform_saving = C-gap + need(10**7 < 15**6, 'theta upper bound') + need(2*(10**v)**7 <= (121**v)**6, 'shifted logarithm inequality') + eta = scale(exp_interval(scale(log_bounds(121), -v*C)), t) + need(eta[0] > theta**p, 'exit contraction below complement capacity') + base = exp_interval(scale(log_bounds(121), v*C)) + need(base[1] < 2**p, 'entire ordinary base range fits') + # Integer grid: gap*H is integral, avoiding enormous rational powers. + step = gap.denominator + need(gap.numerator == 1, 'chosen rational gap grid') + + def passes(j): + H = step*j + return (H+1)**p < 2**j + + lo, hi = 1, 2 + while not passes(hi): + lo, hi = hi, 2*hi + while hi-lo > 1: + mid = (lo+hi)//2 + if passes(mid): + hi = mid + else: + lo = mid + H = step*hi + need(H > 7*v and passes(hi) and not passes(hi-1), 'final integer comparison') + need(eta[1] < theta**(p-1), 'one smaller logarithmic power fails') + return {'t': t, 'uniform_saving': uniform_saving, 'gap': gap, + 'logarithm_power': p, 'theta_upper': theta, 'eta': display(eta), + 'eta_minus_theta_to_p': display((eta[0]-theta**p, eta[1]-theta**p)), + 'm_to_saving': display(base), 'H': H, 'N': '2^'+str(H), + 'integer_test': {'left_base': H+1, 'left_exponent': p, + 'right_base': 2, 'right_exponent': hi}, + 'grid_step': step, 'previous_grid_point_rejected': True, + 'smaller_logarithmic_power_rejected': True} + + +def power_majorant_comparison(v, uniform_saving): + """Retain #4416's older power proof, changing only the new unit's ranks.""" + t, z, h = 1-C, 1-uniform_saving, Q(1, 7) + z0 = (t+z)/2 + delta = z0-t + B, debt = (4+7*h)*v, 1+7*v*(1-z0) + ratio = (delta*B+debt)/(h*delta) + H0 = -((-ratio.numerator)//ratio.denominator) + ratio = H0*(1-z0)/(z-z0) + H1 = ratio.numerator//ratio.denominator+1 + need(H0 >= 7*v and H0*h*delta >= delta*B+debt, 'power majorant threshold') + need((H0-1)*h*delta < delta*B+debt, 'previous power threshold rejected') + need(H1*(z-z0) > H0*(1-z0) >= (H1-1)*(z-z0), + 'strict power-majorant comparison and previous-rank control') + return {'H0': H0, 'H1': H1, 'N': '2^'+str(H1), 'theta_upper': 1-h, + 'scope': 'Tail transformation alone, retaining the older power majorant.'} + + +def outer_ledger(uniform_saving): + d = (C-KAPPA)/7 + params = {'kappa': KAPPA, 'tested_saving': C, + 'complex_uniform_saving': uniform_saving, 'b': KAPPA+5*d, + 'a': KAPPA+4*d, 'q': KAPPA+3*d, 'bit_saving': Q('0.0027'), + 'epsilon': 1-d, 'beta': 1-3*d, 'r0': d/10, + 'stop': d, 'layout': d, 'd': d} + env = source_environment(HERE/'vendor/outer_endpoint.py') + row = env['ledger'](params) + need(len(row['strict_checks']) == 54 and len(row['functional_checks']) == 3, + 'complete first outer ledger') + need(all(v > 0 for group in ('strict_checks', 'functional_checks') + for v in row[group].values()), 'all outer predicates') + frozen = json.loads((HERE/'vendor/p7-RESULT.json').read_text())['endpoint']['outer'] + need(encoded(row) == frozen, 'unchanged full p7 endpoint ledger') + parsed = ast.parse((HERE/'vendor/check_ledger.py').read_bytes()) + function = next(n for n in parsed.body + if isinstance(n, ast.FunctionDef) and n.name == 'ledger') + constants = [n for n in parsed.body if isinstance(n, ast.Assign) + and any(isinstance(t, ast.Name) and t.id.startswith('KAPPA_') + for t in n.targets)] + eps, beta, q, a = (params[k] for k in ('epsilon', 'beta', 'q', 'a')) + grid = 10**10 + backoff = Q((eps*q*grid).__floor__(), grid)-KAPPA + need(backoff > 0, 'strict derived oracle grid backoff') + oracle = {'Q': Q, 'R0': params['r0'], 'ZETA': Q(1, 10**8), + 'SLACK': d, 'STOP': d, 'FLOOR': grid, 'BACKOFF': backoff, + 'EPS': eps, 'BETA': beta, 'THETA_POWER': Q(2), + 'HALO_POWER': 48, 'CORE_POWER': 128, 'STRASSEN_TAU': Q(45, 16), + 'b': params['b'], 'q': q, 'a': a, 'bit': params['bit_saving'], + 'online': Q('0.001730970419199163702738'), + 'old': Q('0.001730970419199163702738')} + code = ast.fix_missing_locations(ast.Module(body=constants+[function], type_ignores=[])) + exec(compile(code, 'pinned 63-predicate ledger', 'exec'), oracle) + second = oracle['ledger']('higher_moment_smaller_ranks') + need(second['kappa'] == KAPPA and second['margins'] == row['margins'], + 'all nine rows match both ledgers') + need(len(second['strict_checks']) == 63 and + all(v > 0 for v in second['strict_checks'].values()), 'all 63 legacy predicates') + controls = {} + for name, updates in [('closed_epsilon', {'epsilon': Q(1)}), + ('missing_layout', {'layout': Q(0)}), + ('unfunded_kappa', {'kappa': C}), + ('closed_uniform_gap', {'complex_uniform_saving': params['b']}), + ('insufficient_BIT', {'bit_saving': Q('0.0023')})]: + bad = env['ledger'](dict(params, **updates)) + failed = sorted(k for k, v in bad['strict_checks'].items() if v <= 0) + need(failed, 'outer control rejected: '+name) + controls[name] = failed + for name, options in [('old_per_axis_scan', {'old_scan': True}), + ('group_equals_dimension', {'beta_': eps})]: + bad = oracle['ledger']('reject_'+name, **options) + failed = sorted(k for k, v in bad['strict_checks'].items() if v <= 0) + need(failed, 'legacy control rejected: '+name) + controls[name] = failed + return {'ledger': row, 'legacy_63_checks': second['strict_checks'], + 'legacy_grid': grid, 'legacy_backoff': backoff, + 'minimum_margin_minus_kappa': min(row['margins'].values())-KAPPA, + 'rejected_controls': controls} + + +def finite_controls(): + def tensor(histogram): + out = Counter() + for k, n in histogram.items(): + for h, b in histogram.items(): + out[k*h] += n*b + return out + + def split(histogram, cutoff): + out = Counter() + for k, n in histogram.items(): + q, r = divmod(k, cutoff) + out[cutoff] += q*n + if r: + out[r] += n + return +out + + target, paid = tensor({2:1, 5:1}), tensor({1:2, 4:1}) + padded, completion = Counter(), Counter() + for k, n in target.items(): + padded[max(k, 9)] += n + if k < 9: + completion[9-k] += n + final = split(paid+completion, 4) + mass = lambda x: sum(k*n for k, n in x.items()) + need(mass(padded)-mass(final) == 7**2-6**2 == 13, 'exact paid padding mass') + need(min(padded) > max(final), 'exact toy separation') + need(final == Counter({1:5, 4:9}), 'literal toy expanded inventory') + # t=1/2, sigma=3/4, R=100, J=1 refutes a sublinear tail extension. + invalid = power(100, Q(1, 2))[1]+2*power(100, Q(3, 4))[1] + need(invalid < 100, 'sublinear upper-tail moment cannot bound splitting') + return {'toy_targets': padded, 'toy_paid': final, 'rank_one_surplus': 13, + 'sublinear_tail_counterexample': {'R': 100, 'J': 1, 't': '1/2', + 'sigma': '3/4', 'actual_charge': 100, + 'invalid_upper': display((invalid, invalid))}} + + +def verify(): + sources = authenticate() + invoice = invoice_oracle() + tail = tail_certificate() + rank = uniform_rank(tail['tensor_power']) + endpoint = outer_ledger(rank['uniform_saving']) + controls = finite_controls() + rejected = [] + for name, updates, expected in [ + ('too_short_product', {'v': 100}, 'complete charged normalized moment'), + ('sublinear_tail', {'u': C/2}, 'tail moment exponent at least one'), + ('lost_separation', {'floor': 10}, 'strict finite ranks'), + ]: + try: + tail_certificate(**updates) + except ValueError as error: + need(str(error) == expected, 'wrong rejection: '+name) + rejected.append({'mutation': name, 'failed_at': str(error)}) + else: + raise ValueError('accepted mutation: '+name) + old = json.loads((HERE/'vendor/p7-RESULT.json').read_text())['endpoint']['compiler'] + return encoded({'schema': 'higher-moment-native-strictification/1', + 'status': 'PASS_HIGHER_MOMENT_STRICTIFICATION', 'kappa': KAPPA, + 'invoice_oracle': invoice, 'strictification': tail, + 'uniform_rank': rank, 'outer': endpoint, + 'tail_only_power_majorant': power_majorant_comparison( + tail['tensor_power'], rank['uniform_saving']), + 'finite_controls': controls, 'rejected_mutations': rejected, + 'predecessor_H': old['H1'], + 'rank_exponent_reduction_factor': Q(old['H1'], rank['H']), + 'tensor_power_reduction_factor': Q(6240, tail['tensor_power']), + 'source_sha256': sources, + 'verifier_sha256': sha256(Path(__file__).read_bytes()).hexdigest(), + 'scope': 'Conditional charged transformation and finite compiler rank. Native all-column, physical, analytic, precision, storage, fixed-tape and recovery premises remain inherited. No new kappa, selected frontier or practical word.'}) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--out', type=Path) + args = parser.parse_args() + result = verify() + if args.out: + need(not args.out.exists(), 'new output path required') + args.out.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + need(json.loads((HERE/'RESULT.json').read_text()) == result, 'changed saved receipt') + print(json.dumps({'status': result['status'], 'tensor_power': result['strictification']['tensor_power'], + 'uniform_rank': result['uniform_rank']['N'], + 'strict_moment_gap': result['strictification']['strict_moment_gap'], + 'kappa': result['kappa']})) + + +if __name__ == '__main__': + main() diff --git a/research/g20-helper-split/prior/prior/source/vendor/g20/ordinary-certificate/inputs/separate_series.py b/research/g20-helper-split/prior/prior/source/vendor/g20/ordinary-certificate/inputs/separate_series.py new file mode 100644 index 0000000000..7c68264455 --- /dev/null +++ b/research/g20-helper-split/prior/prior/source/vendor/g20/ordinary-certificate/inputs/separate_series.py @@ -0,0 +1,32 @@ +"""Independent positive-series rational intervals, no external numeric library.""" +from fractions import Fraction as F +from functools import lru_cache +S=10**40 +def need(c,m): + if not c:raise ValueError(m) +def floor(q):return q.numerator//q.denominator +def ceil(q):return -((-q.numerator)//q.denominator) +def grid(lo,hi):return F(floor(lo*S),S),F(ceil(hi*S),S) +def logratio(z,n=60): + need(0<=z<=F(1,3),'Reduced log domain');s=F(0);p=z + for j in range(n):s+=2*p/(2*j+1);p*=z*z + return s,s+2*p/((2*n+1)*(1-z*z)) +LN2=logratio(F(1,3)) +@lru_cache(None) +def logbound(x): + if x==1:return F(0),F(0) + k=x.bit_length()-1;a,b=logratio(F(x-2**k,x+2**k));return grid(a+k*LN2[0],b+k*LN2[1]) +@lru_cache(None) +def expbound(y): + need(0<=y<7,'Bounded exp');s=p=F(1);n=90 + for j in range(1,n+1):p=p*y/j;s+=p + return grid(s,s+(p*y/(n+1))/(1-y/(n+2))) +@lru_cache(None) +def power(x,t): + if x==1:return F(1),F(1) + a,b=logbound(x);a,b=grid(t*a,t*b);return expbound(a)[0],expbound(b)[1] +def moment(profile,t): + vv=[(n,power(k,t))for k,n in profile.items()];return sum(n*v[0]for n,v in vv),sum(n*v[1]for n,v in vv) +def mul(a,b):return a[0]*b[0],a[1]*b[1] +def div(a,b):return a[0]/b[1],a[1]/b[0] +def interval(a):return {'lower':str(a[0]),'upper':str(a[1]),'display':float(sum(a)/2)} diff --git a/research/g20-helper-split/prior/prior/source/vendor/g20/provider/build_global.py b/research/g20-helper-split/prior/prior/source/vendor/g20/provider/build_global.py new file mode 100644 index 0000000000..adb6e21ec7 --- /dev/null +++ b/research/g20-helper-split/prior/prior/source/vendor/g20/provider/build_global.py @@ -0,0 +1,125 @@ +"""Materialize the exact G23 stream and separate current-source descriptors.""" +from pathlib import Path +from collections import Counter +from hashlib import sha256 +from datetime import datetime,timezone +from time import process_time +import gzip,json +from local_ir import N as LN,EXPECTED,need +HERE=Path(__file__).resolve().parent;ROOT=HERE.parent;INPUT=ROOT/'inputs';DATA=HERE/'data';N=11400;V=111 +def read(p):return json.loads(gzip.decompress(p.read_bytes()))if p.suffix=='.gz'else json.loads(p.read_bytes()) +def put(p,x):p.write_text(json.dumps(x,indent=2)+'\n',encoding='utf-8') +def xor(a,b): + out=a.copy() + for k,v in b.items(): + out[k]=out.get(k,0)^v + if not out[k]:del out[k] + return out +def shift(a,s):return{k^s:v for k,v in a.items()} +def physical_main(controller): + rows=[{0:1<=658 else((x if r>1).bit_count()]+=V + need(streamhash.hexdigest()==expected['expanded_event_sha256']and eventno==expected['expanded_event_count'],'ExactG23literalstreamnotanewunboundvariant') + need(paid==Counter({int(k):v for k,v in expected['paid'].items()})and targets==Counter({int(k):v for k,v in expected['targets'].items()})and len(changed_requests)==18,'ExactG23invoiceandfreshrank4requests') + need(peak.bit_length()==expected['cancellation_free_majorant_bits']and str(peak)==expected['cancellation_free_majorant'],'Actual newmajorantfullyregenerated') + need(len(calls)==18 and len(episodes)==1845 and privatepeak==2,'Allownedepisodesandmaximumcoexistence') + result={'status':'MATERIALIZED_EXACT_G23_ALL11400_RAW','at_utc':datetime.now(timezone.utc).isoformat(),'originals':N,'private_allocated':2,'private_peak':privatepeak,'private_episodes':len(episodes),'calls':18,'expanded_event_count':eventno,'expanded_event_sha256':streamhash.hexdigest(),'global_gzip_sha256':sha256((DATA/'GLOBAL.jsonl.gz').read_bytes()).hexdigest(),'SOURCE_descriptor_count':source_count,'SOURCE_descriptors_sha256':sourcehash.hexdigest(),'paid':dict(sorted(paid.items())),'targets':dict(sorted(targets.items())),'rank_surplus':sum(k*v for k,v in targets.items())-sum(k*v for k,v in paid.items()),'operation_counts':dict(counts),'majorant_bits':peak.bit_length(),'majorant':str(peak),'newbound':None,'CPU_seconds':process_time()-clock} + put(DATA/'GLOBAL-RESULT.json',result);put(DATA/'CALLS.json',calls);put(DATA/'PRIVATE-EPISODES.json',episodes);put(DATA/'NEW-RANK4-REQUESTS.json',changed_requests);put(DATA/'MAIN-PHYSICAL-COEFFICIENTS.json',mainrows);put(DATA/'INVOICE.json',{'paid':result['paid'],'targets':result['targets'],'originals':N,'private_output_credit':0,'QUERYs':sum(paid.values()),'rawrank_surplus':result['rank_surplus'],'rawprice_reference':'inputs/G23-RAW-PRICE.json only, notordinarysaving','ordinary_tail_bootstrap_status':'Pendingseparatecertificatewithfreshfees/constants; old4760/4814unchanged'}) + print(json.dumps({k:result[k]for k in('status','expanded_event_count','expanded_event_sha256','SOURCE_descriptor_count','private_episodes','majorant_bits','CPU_seconds')})) +if __name__=='__main__':main() diff --git a/research/g20-helper-split/prior/prior/source/vendor/g20/provider/data/CALLS.json b/research/g20-helper-split/prior/prior/source/vendor/g20/provider/data/CALLS.json new file mode 100644 index 0000000000..d61a37a481 --- /dev/null +++ b/research/g20-helper-split/prior/prior/source/vendor/g20/provider/data/CALLS.json @@ -0,0 +1,488 @@ +[ + { + "stage": 0, + "pair": 0, + "inverse": false, + "helper_owner_begin": 3552, + "source_bank": 0, + "target_bank": 1, + "core_begin": 6549, + "core_end": 28539, + "profile": { + "1": 1318, + "3": 77, + "2": 1342, + "4": 40, + "5": 102, + "7": 18, + "6": 10 + }, + "owned_global_indices": [ + 11400, + 11401 + ], + "original_helper_jobs": { + "4": 4, + "8": 432 + } + }, + { + "stage": 1, + "pair": 0, + "inverse": true, + "helper_owner_begin": 3988, + "source_bank": 1, + "target_bank": 0, + "core_begin": 28761, + "core_end": 50973, + "profile": { + "1": 1318, + "2": 1342, + "4": 40, + "5": 102, + "7": 18, + "6": 10, + "3": 77 + }, + "owned_global_indices": [ + 11400, + 11401 + ], + "original_helper_jobs": { + "4": 4, + "8": 432 + } + }, + { + "stage": 3, + "pair": 1, + "inverse": true, + "helper_owner_begin": 4424, + "source_bank": 3, + "target_bank": 2, + "core_begin": 52305, + "core_end": 74517, + "profile": { + "1": 1318, + "2": 1342, + "4": 40, + "5": 102, + "7": 18, + "6": 10, + "3": 77 + }, + "owned_global_indices": [ + 11400, + 11401 + ], + "original_helper_jobs": { + "4": 4, + "8": 432 + } + }, + { + "stage": 5, + "pair": 2, + "inverse": true, + "helper_owner_begin": 4860, + "source_bank": 5, + "target_bank": 4, + "core_begin": 75849, + "core_end": 98061, + "profile": { + "1": 1318, + "2": 1342, + "4": 40, + "5": 102, + "7": 18, + "6": 10, + "3": 77 + }, + "owned_global_indices": [ + 11400, + 11401 + ], + "original_helper_jobs": { + "4": 4, + "8": 432 + } + }, + { + "stage": 7, + "pair": 3, + "inverse": true, + "helper_owner_begin": 5296, + "source_bank": 7, + "target_bank": 6, + "core_begin": 99393, + 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"route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11319, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11320, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11321, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11322, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11323, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11324, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11325, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11326, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11327, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11328, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11329, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11330, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11331, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11332, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11333, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11334, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11335, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11336, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11337, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11338, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11339, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11340, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11341, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11342, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11343, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11344, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11345, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11346, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11347, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11348, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11349, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11350, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11351, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11352, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11353, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11354, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11355, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11356, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11357, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11358, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11359, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11360, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11361, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11362, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11363, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11364, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11365, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11366, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11367, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11368, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11369, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11370, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11371, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11372, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11373, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11374, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11375, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11376, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11377, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11378, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11379, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11380, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11381, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11382, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11383, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11384, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11385, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11386, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11387, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11388, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11389, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11390, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11391, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11392, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11393, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11394, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11395, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11396, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11397, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11398, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + }, + { + "original_owner": 11399, + "rank": 8, + "matcher": "IDENTITY_FULL8", + "native_frame": 1, + "route_pair_required_in_generic_job_matching": false + } +] diff --git a/research/g20-helper-split/prior/prior/source/vendor/g20/provider/local_ir.py b/research/g20-helper-split/prior/prior/source/vendor/g20/provider/local_ir.py new file mode 100644 index 0000000000..2edfa7018d --- /dev/null +++ b/research/g20-helper-split/prior/prior/source/vendor/g20/provider/local_ir.py @@ -0,0 +1,130 @@ +"""Local physical ARRAY IR and exact types; portable standard library only.""" +from collections import Counter +from fractions import Fraction as F +from functools import lru_cache +from math import gcd + +N=658;OWNED=(658,659);EXPECTED={1:1318,2:1342,3:77,4:40,5:102,6:10,7:18} +def need(c,m): + if not c:raise ValueError(m) +def transpose_rows(a,n=N):return [sum(((r>>j)&1)<=1024 and v%1024==0,'strict compiler inputs') + t,z=1-tested,1-uniform;z0=(t+z)/2;gap=z0-t;h=F(1,64) + rhs=gap*(5+8*h)*v+1+8*v*(1-z0) + h0=(rhs/(h*gap)).__floor__()+1 + h1=(h0*(1-z0)/(z-z0)).__floor__()+1 + need(h0>=8*v and h0*h*gap>rhs and h1*(z-z0)>h0*(1-z0),'strict finite cutoffs') + return h0,h1 + + +def below_grid(value,denominator): + need(isinstance(denominator,int) and denominator>0,'positive grid denominator') + out=F(-((-value.numerator*denominator)//value.denominator)-1,denominator) + need(0F(4,2**(v//32)),'positive exact contraction') + degrees[str(k)]=v + for value in (F(7,1000),F(701,100000),F(699,100000)): + need(below_grid(value,1000) (219/100) C. + +**Proof.** The identity + + log((1+x)/(1-x)) = 2 sum_(j>=0) x^(2j+1)/(2j+1) + +follows by integrating the geometric series on a compact subinterval of (-1,1). Positive truncation and a geometric tail at x=1/3 give + + 56/81 < log 2 < 25/36, + 69/100 < log 2 < 7/10. + +At x=1/2, retain three terms and bound every remaining denominator below by seven. This gives + + log 3 < 1+1/12+1/80+1/336 < 11/10. + +For C in the stated interval, exp(-u) >= 1-u and the positivity of the logarithms imply + + g'(C) + =4^(1-C) log 4 -3^(1-C) log 3 + >=4 log 4 -4C(log 4)^2 -3 log 3 + >111/50 -(196/25)C + >=111/50 -(196/25)(351/100000) + >219/100. + +Since g(0)=0, integration proves the claim. These are rational comparison bounds for logarithms, not decimal root calculations. QED. + +**Lemma 1b.** On the same interval 0(11/4)C. + +**Proof.** Keeping the first two terms of the log-2 expansion and bounding every remaining denominator below by five gives + + log 2<56/81+1/540<347/500. + +The integral for log(1-x) gives log(1-x)<-x-x^2/2 for 0=1-u on the positive term and 7^(1-C)<7 on the negative term yields + + j'(C)=8^(1-C) log 8-7^(1-C) log 7 + >291/100-(882/25)C + >=291/100-(882/25)(351/100000)>11/4. + +Since j(0)=0, integration proves the claim. The comparisons are explicit rational inequalities, not a numerical price calculation. QED. + +## 3. Rank-mass dominance proves convexity of the old moment + +**Lemma 2.** For every cutoff u, the old productive rank mass above u is at least the old paid rank mass above u: + + sum_(k>=u) T_k k >= sum_(r>=u) P_r r. + +Consequently F is convex on [0,351/100000], and for C>=C_L in that interval, + + dF/dC > -217000. + +**Proof.** The complete old rank-mass surplus is 753, as recorded by PR5512. For u<=4, no productive rank has yet been removed; deleting paid ranks can only improve the surplus. For 48, all low paid jobs and both low productive ranks are absent. Pair each remaining paid rank 14,21,28,35,42,49,56 with the productive rank one higher, with the same multiplicity 444. Pair paid rank 63 with productive rank 64, each of multiplicity 222. Each target in a pair has greater rank and rank mass, so its weighted tail dominates at every cutoff. The additional 222 productive rank-127 jobs only increase the tail. This proves dominance without evaluating a fractional moment. + +For 0<=C<=351/100000 the function + + h_C(x)=x^(-C)(log x)^2 + +is nonnegative and nondecreasing on [1,127], since + + h_C'(x)=x^(-C-1) log x (2-C log x)>=0. + +Here log 127<5 follows from 127<2^7 and log 2<7/10 in Lemma 1. Integrating h_C' against the nonnegative rank-mass tails yields + + d^2F/dC^2 + =sum_k T_k k h_C(k)-sum_r P_r r h_C(r)>=0. + +Thus F is convex. Because F(0)=753 and F(C_L)>0, convexity bounds its derivative at and to the right of C_L below by the secant slope: + + dF/dC >= (F(C_L)-753)/C_L > -753/C_L > -217000. + +The last inequality follows from C_L>0.00348 and 217000*0.00348>753. QED. + +This dominance argument uses the complete old inventories, not a claimed monotonic relation between isolated query ranks. It is the additional analytical mechanism that avoids a very weak absolute derivative bound. + +## 4. An explicitly funded test and both tail contractions + +Set + + C_test=0.003504, + U=0.0035035, + B=0.003503. + +**Theorem 3.** The actual changed complete profile has F_new(C_test)>1/32. All three source compiler ratios are strictly below one there. + +**Proof of the first moment.** The retained endpoint has C_L>0.0034839. The convexity/secant estimate of Lemma 2 gives + + F(C_test)>-217000*(0.003504-0.0034839)>-437/100. + +Lemmas 1 and 1b and an exact rational comparison give + + 378 g(C_test)+162 j(C_test) + >[378*(219/100)+162*(11/4)]*(3504/1000000) + >89/20. + +Consequently + + F_new(C_test)>89/20-437/100=2/25>1/32. + +The productive moment is below 2^21, so + + alpha_new(C_test)<1-2^-26. + +This is a proved strict moment above 0.0035 for the complete changed native word, not an optimistic isolated deletion. + +**Proof of the tails.** At C0 let t0=1-C0 and s0=t0+1/5. As in the predecessor analytical admission, 7/67/2 and 4^s0<16/3. The full paid second-moment change is + + P_new,s0-P_old,s0 + =18[-21(1+3^s0)+17*4^s0]-162(1+7^s0)<0. + +The last negative term charges exactly the nine extra local retirements. The productive t0-moment loss is + + 72*4^t0+162*8^t0<288+1296=1584. + +Using C0<1/100 and log 8<21/10, + + 8^t0=8 exp(-C0 log 8)>8[1-(1/100)(21/10)]>7. + +Hence the old productive moment T0 exceeds 7614*7>53000. The new independent count is W_new=W-72-162=11004. The old strict guards imply + + gamma_new(C0)<(31/32)T0/(T0-1584)<999/1000, + delta_new(C0)<(19/20)T0/(T0-1584)<999/1000. + +Both expressions decrease in T0. Substituting 53000 and multiplying positive denominators proves the final rational inequalities. No removed target or completion term is omitted. + +Let epsilon=C_test-C0. Its exact value is positive and below 21/1000000. Since log 127<5, + + epsilon log 127<1/8000, + 127^epsilon<1/(1-1/8000). + +The paid moment decreases as C increases, every productive rank is at most 127 and the 17^C completion denominator increases. Thus this factor bounds either tail ratio's possible growth. Both tail ratios at C_test are bounded by the rational + + theta=(999/1000)/(1-1/8000)=7992/7999<1. + +This proves the complete first- and higher-moment admission guards. QED. + +## 5. Fresh finite compiler constants and owned stock + +The following is a conditional use of the same constructive native, all-column, mixed-target batching, fixed-tape, precision and ordinary-cover framework as PR5512. It does not prove those inherited physical hypotheses anew. + +Put a=1-2^-26. Choose v to be the first positive multiple of 1024 satisfying + + a^v +4 theta^v <1/2. + +This is a finite integer definition, not an executed search. The source chronological product completes each small target on its SAME independent owner at 18^v and splits each paid job at 17^v. Their charged contraction is at most the displayed expression. The source separation guard is 17^64<18^63; the ambient bound remains 127<256. + +Set + + t=1-C_test, z=1-U, z0=(t+z)/2, + h=1/64, d0=z0-t, + R0=d0*(5+8h)*v+1+8v*(1-z0), + H0=8192v+ceil(R0/(h*d0))+1, + H1=floor(H0*(1-z0)/(z-z0))+1, + N=2^H1. + +Then d0>0 and the inherited guards hold directly: + + H0>=8192, + H0*h*d0>R0, + H1*(z-z0)>H0*(1-z0). + +The source constructive integer batching gives a finite independent-row unit with leaf-to-row ratio below N^(1-U). + +For explicit replacement finite majorants, let R be one plus the sum of the complete finite record, matching-step, role-incidence, descriptor, paid/target-job and owned-field counts, and the encoded bit lengths of every fixed coefficient, numerator, denominator, matching matrix entry and native descriptor in the changed base word. In particular R dominates coefficient and matcher heights as well as counts. This is the length of its specified finite encoded construction, not a mathematical census run here. Define + + D0=2^((R+1024)^4), + K=2^(4v(R+1024)^4), + J(n)=(n+1)^4 K^(4n+4), + A(1)=K^4, + A(n)=(J(n)+2)^4 (A(n-1)+2)^(4n+8). + +The source description/height induction with these enlarged base constants bounds rows, leaves, suspended instances and fixed descriptions. Reserve at most 49 A(N) owned arrays, distinct for simultaneous instances. No owned field is counted as an independent row. The earlier forty-, twenty-four-, seventeen- and eleven-array reserves are not reused. + +Put + + T_arith=(2N+2)^4 (A(N)+2)^2, + H=(D0+2) 4^(T_arith+1). + +Choose an odd prime q greater than max(2^45 N^5,2^(2H)) avoiding the finitely many compiled denominator and rank-witness primes. Every new H4 geometry is one of the source's actual frames 506 through 509, with its supplied two-sided matcher; geometry 507 is the original G20 helper-464 shadow matcher. Both fixed routing directions and all matching constants are charged. + +A conservative multiplier in retained primitive invocations is + + F=49(D0+1)^4 (q+2)^(32(N+1)^2) (A(N)+2)^8. + +Multiply it by the positive maximum retained primitive/backend coefficient when bounding machine time. It includes the new snapshots, late bindings, delayed reader copies, clears, source preservation, head returns, parking and routes. The unexecuted counterfactual helper entrances are correctness parameters, not runtime states or new arithmetic primitives; coefficient and precision bounds cover the actual finite program. No new unit-cost dense address primitive, Word RAM substitution or old cancellation-growth bound is assumed. These are finite constants fixed before the final input size grows; the source eventual-threshold proof absorbs them at a fresh threshold. + +## 6. Acyclic ordinary completion + +Use the retained whole-cover loss + + epsilon_cover=2^-36+10^-20, + L=U-epsilon_cover. + +The prime guard 2^45 epsilon_cover>256 is immediate. Also epsilon_cover<10^-9 and U-B=5*10^-7, so L>B+4*10^-7. This cover loss is not discarded. The source regular-cover/bad-class costs, whole-row matcher and borrowed-stock proof are retained with the new reserve and constants. + +Start from the completed PR4814 backend b0=1737729/500000000. Put rho=1/100 and Q=10^12. Freeze successive completed algorithms by + + a_j=(1-rho)L+rho*b_(j-1), + b_j=(ceil(Q a_j)-1)/Q. + +The strict lower grid gives 0B. If none of the first five suffice, the elementary recurrence bound gives + + b_6 >= L-rho^6(L-b0)-(1-rho^6)/(Q(1-rho)) + > L-3*10^-12 >B. + +Thus at most six finite levels suffice, without evaluating any b_j numerically. For each level let K_j be at least sixteen times the sum of its F-scaled positive retained primitive constants, its new reserve/adapter/stock bounds and the frozen completed preceding-backend coefficient. Enlarge it to include any additional finite base description. With + + eta_j=min(rho-a_j,1-rho-a_j,a_j-b_j)>0, + +enlarge its eventual threshold to dominate + + ceil((32K_j/eta_j)^(ceil(8/eta_j)))+2^(ceil(8/eta_j)), + +the previous backend threshold to power ceil(2/rho), and all finite base/stock thresholds. The standard source logarithm bound absorbs the positive coefficients. All borrowed arrays and digits are restored before their parent resumes. The resulting completed ordinary algorithm supports the weaker exact saving B. + +## 7. Conclusion and attribution + +Under the retained native/physical, constructive compiler, ordinary-cover/backend, precision, fixed-tape and analytic framework premises, this actual complete BIT word admits ordinary saving B=0.003503. In particular it supplies a component saving strictly above 0.0035. The old predecessor interval is used as retained evidence; no new numerical root or optimization is claimed. + +This does not prove whole multiplication κ ≥ 0.0035. A compatible complete funded Gaussian supplier and the actual outer assembly are still required. The result here closes the requested BIT component threshold, not those separate obligations. + +Retain ai-nanachi PR5512; Ali Romman PR5421; compact436/PR4326 and PR4760/PR4814; DreamingOfClouds PR589; eumemic PR555; Cinna Davis's native/ROW/controller/cover lineage; rohanarun PR185/PR199/PR204; zxv and Jacob Alan Sussman's compiler, mixed-target and precision work; all source notices; and the prior four-retirement/two-snapshot proofs. New text is Apache-2.0, with substantial OpenAI Codex assistance. The offline source pin is `5e0052ca0aa3036a3afa8b0438927377c8d97d53`. + diff --git a/research/g20-helper-split/prior/proposal/assembly.md b/research/g20-helper-split/prior/proposal/assembly.md new file mode 100644 index 0000000000..354166e186 --- /dev/null +++ b/research/g20-helper-split/prior/proposal/assembly.md @@ -0,0 +1,95 @@ +# Complete deferred-input BIT inventory and Gaussian scope + +Dugongue, with substantial OpenAI Codex assistance. This is an informal mathematical assembly from retained local sources. The new complete BIT construction admits conditional ordinary saving 0.003503. It does not by itself prove whole multiplication κ ≥ 0.0035. + +## 1. The new mechanism + +[bit.md](bit.md) retires nine full helper inputs by binding them at their actual first outgoing reads. Each helper's old unobserved inverse prefix consists of destination-only cleanup and exactly one H1 query. Omit that prefix, preserve all other fields, and assign the helper by the actual ordinary common-frame COPY immediately before the old ADD into a main receiver. The receiver becomes the whole zero function, so its old H7 query is omitted with a paid zero-header transition. + +The runtime never computes an inverse helper entrance. Such an entrance exists uniquely because the omitted prefix is affine and invertible in that helper input. Every retained old endpoint is independent of that input. This gives the correctness proof for arbitrary main and surviving helper payloads. Nine bindings compose causally because no still-unbound helper has been read into an earlier binding. + +The precise target loss is one H8 per retirement. All nine target debits are included. No independent main input is cleared: its current value is copied into the newly owned helper and the retained suffix restores the prescribed main output. Every newly owned field is initialized and returned zero. + +## 2. Retained predecessor chain + +The included [partial-retirement.md](partial-retirement.md) proves four target-debited partial-helper retirements. [snapshot-fusion.md](snapshot-fusion.md) proves two target-preserving full-helper fusions. + +[predecessor-protected-reader.md](predecessor-protected-reader.md) proves seven additional full-helper fusions, six with an actual cold/proper reader cancellation. [predecessor-source-refinement.md](predecessor-source-refinement.md) proves eight more, explicitly paying to refine SOURCE H3 through the helper's exact required rank-two frame and reserving both snapshots. + +These notes retain their intermediate inventories. The final inventory is the one below. Their transformations are valid for arbitrary helper/recipient baselines, so they remain valid after the new bindings. In particular the changes involving fields 319, 344 and 375 occur in the retained suffix of the corresponding new binding. The previous nine COPY-pivot preparations depend only on SOURCE entrance values, so their zero arguments retain their exact scope. + +## 3. Exact local and whole profiles + +Relative to PR5512, the full local transformation has + + delta P_local=-30 H1-21 H3+17 H4-9 H7, + delta T_local=-4 H4-9 H8. + +The final local paid inventory is + + {1:1279,2:1342,3:56,4:57,5:102,6:10}. + +All local H7 calls are now removed. There are 222 arbitrary main fields and 414 arbitrary full helpers. There are 49 owned local arrays: the original eleven, four previously retired partial fields, twenty-five SOURCE snapshots from the earlier fusions/refinements, and nine newly retired full helpers. No owned field is an independent target. + +The complete eighteen-call controller has + + P_new={1:24687,2:24156,3:1008,4:1026,5:1836,6:180, + 14:444,21:444,28:444,35:444,42:444, + 49:444,56:444,63:222}, + + T_new={8:7452,15:444,22:444,29:444,36:444, + 43:444,50:444,57:444,64:222,127:222}. + +Equivalently, + + P_new=P_5512-540 H1-378 H3+306 H4-162 H7, + T_new=T_5512-72 H4-162 H8. + +The independent original count is 11004. The 162 removed H8 targets are the nine genuinely retired full inputs in eighteen distinct helper cohorts. The earlier 72 removed H4 targets are the four partial inputs in those same distinct invocations. The high-rank paid/target inventories, all thin calls, idle jobs, scalar bridges, port routes, matchers and complete ROW/spectator domain are retained. + +All 49 owned slots are reserved anew for simultaneous suspended instances. Reuse between completed sequential local calls does not authorize sharing a live bank. All ordinary initialization, copies, zero-header changes, clears, physical matchers, parent parking and return routes are charged in fresh finite constants. + +## 4. Exact moment and threshold + +For signed moment F(C)=sum T_k k^(1-C)-sum P_r r^(1-C), write + + g(C)=1+3^(1-C)-4^(1-C), + j(C)=1+7^(1-C)-8^(1-C). + +The complete change is exactly + + F_new(C)-F_5512(C)=378 g(C)+162 j(C)>0 (00.0035. + +This closes the requested BIT component threshold within that conditional framework. It is not a new proof of the inherited framework itself, an optimized root or a claim of literature-wide best status. + +## 5. Gaussian positive constructions and their price + +[consumer.md](consumer.md) gives independent causal/matcher-explicit support for the BIT bindings and a zero-extra-child changed D25 provider. Literal swaps borrow sixteen arbitrary selected receivers before the actual native prefix and restore them after the complete-cover barrier. The provider costs the original p8 and has an explicit extra selected-to-ordinary receiver block Kz. Its caller composition keeps every K2B1 term. No cancellation between different routed stages is asserted without an actual identity. + +[gaussian.md](gaussian.md) gives a full dimension-coframe specialization of the original unrestricted free-group source: assign all native logical generators identity, emit actual identity warps, and compile every specified changed child. It constructs the required complementary main boundary normalizers and prices helpers from their actual input/output coframes. A completely priced illustrative path improves, but it has not been bound to an actual profitable source cohort. + +[gaussian-latebinding.md](gaussian-latebinding.md) extends retirement to complex coefficients, with the required sign and actual ordinary inverse matching. It gives complete block constructions and exact target-debited concavity gains. No profitable Gaussian first-read cohort is supplied. In particular, a read of SOURCE into a helper cannot be treated as a write into SOURCE, and an original main field cannot be retired as an auxiliary helper. + +These are explicit algorithms with stated endpoints and prices. They do not provide a complete funded Gaussian supplier at saving 0.0035. None of their isolated or illustrative savings is inserted into the BIT invoice. + +## 6. Whole multiplication claim and evidence + +The ordinary BIT component now exceeds 0.0035. Whole multiplication κ ≥ 0.0035 is still unproved because the compatible profitable Gaussian supplier and complete outer assembly have not been supplied. No selected frontier is changed. + +All proofs are informal and received separate worker mathematical review. Source records were read locally as text at `5e0052ca0aa3036a3afa8b0438927377c8d97d53`. Stored old interval/certificate statements are predecessor evidence. No mathematical computation, numerical pricing, source replay, solver, Lean run, web search or remote PR refresh was performed. Publication byte checks do not constitute mathematical verification. + +## Credit + +BIT: ai-nanachi PR5512; Ali Romman PR5421; compact436/PR4326 and productive-helper/ordinary PR4760/PR4814; DreamingOfClouds PR589; eumemic PR555; Cinna Davis's SOURCE/ROW/controller/cover work; rohanarun PR185/PR199/PR204; zxv and Jacob Alan Sussman's mixed-target, compiler and precision lineage; the G20 helper-464 shadow; and the retained four-retirement and SOURCE-fusion/refinement proofs. + +Gaussian: Cao Yifan PR4610; Cinna Davis PR4690/PR4672 and PR4694/PR4698; phase PR4710; native caller PR4713 with PR4630/PR4635; Dillon Amburgey PR5402; Chris R / Clear1nsight PR5407/PR5413; Ali Romman PR5383/PR5398; DaysSky; Nick Petalas; Ryanson Jonathan; zxv; Jacob Alan Sussman; Dugongue; and all retained native Clifford, scalar, stock, precision and analytic notices. Centre services retain their lane authors and PR3133/PR3148/PR2588/PR2226. No owning PR is invented where retained notes do not name one. + +Prepared for Dugongue with substantial OpenAI Codex assistance from one coordinator and three workers. New text is Apache-2.0; predecessor attribution and licenses remain authoritative. No formal verification or independent human acceptance is claimed. diff --git a/research/g20-helper-split/prior/proposal/bit.md b/research/g20-helper-split/prior/proposal/bit.md new file mode 100644 index 0000000000..c05404f549 --- /dev/null +++ b/research/g20-helper-split/prior/proposal/bit.md @@ -0,0 +1,121 @@ +# Nine late-bound helper retirements remove the remaining rank-7 main queries + +## Result and exact scope + +The retained G20 inverse word admits nine additional, fully charged helper retirements. Each retirement removes one paid rank-1 helper query and one paid rank-7 main query, and debits one productive rank-8 helper target. The mechanism is late binding at an actual common frame, rather than a free conversion of a main input into a helper's entrance chart. + +Relative to the twenty-one-improvement predecessor, the complete 18-call change is + +`ΔP = −162 H₁ −162 H₇`, `ΔT = −162 H₈`. + +Writing `j(C)=1+7^(1−C)−8^(1−C)`, its exact signed-moment improvement is `162 j(C)>0` for every `00, since x^t is strictly subadditive on positive x. The other two donors in each listed triple are not among these nine chosen helpers. Later dependencies between bound helpers are permitted by the chronological proof. Actual no-earlier-reader claims remain the literal source facts recorded in bit.md, not consequences of the abstract lemma alone. + +All new erasures are on newly owned fields. A suspended recursive instance reserves its own owned slots until return. The proof does not reverse erasures to manufacture a reciprocal physical program: both orientations still use the retained predecessor's explicit physical endpoint identity as stated in bit.md. + +## 3. An actual zero-extra-child D25 service + +Use the supplied joined (s,t)=(0,2) service in `research/centre-code-services`. Before its separate late reader query, the actual complete-cover native prefix has physical map + + (F1 x,F1 z,F1 q_R y) + -> (F2 x,F2 z,F2 q_R[y+(E2x)_R]). + +SOURCE x has 112 fields. Selected receiver z has sixteen fields, and ordinary receiver y has ninety-six. All these original inputs are arbitrary. The 416 outside fields stay fixed. F1 and F2 are the actual completed seventeen- and twenty-five-axis FULL frames, and q_R denotes the actual port-dependent hole operators. Its native profile is + + p8 = 1392 H1 + 64 H2 + 48 H3 + 16 H8. + +Let J insert a sixteen-field bank into the corresponding selected SOURCE slots, let D select those slots, and write Π=I-JD. At both physical cuts SOURCE and selected receivers have the same FULL frame. + +**Theorem C3.** Swap the sixteen selected SOURCE fields with the matching selected receiver fields before this prefix, and swap them back after its complete regular cover. Then run the original late reader query on restored SOURCE. The resulting physical endpoint is + + (F1 x,F1 z,F1 q_R y) + -> (F2 x,F2[z+Bx],F2 q_R[y+Cx+Kz]), + +where B=L0E2, C=(E2Π)_R and K=(E2J)_R. All 416 outside values are unchanged. The native profile is exactly p8; only finite ordinary swap costs have been added. No new owned field is needed. + +**Proof.** After the first swaps SOURCE is Πx+Jz and selected receiver is Dx. Arbitrary-input correctness of the actual prefix gives ordinary response (E2[Πx+Jz])_R, while SOURCE and selected contents stay unchanged and both advance from F1 to F2. The second swaps restore exactly x and z. The original late query therefore reads the original x, adds L0E2x to selected z, restores SOURCE and leaves ordinary receivers unchanged. Expansion gives the displayed endpoint. All swaps are admitted ordinary operations on actual common FULL fields. The full regular-cover barrier is retained. Every original child, including the sixteen H8 carriers, occurs once. ∎ + +No E2 input code at an incomplete frame has been assumed. In particular, this theorem does not infer an F1 operation by conjugating an available output word through F2. + +## 4. Exact caller algebra for that changed provider + +**Theorem C4.** Write T(B,C,K)(x,z,y)=(x,z+Bx,y+Cx+Kz). Two compatible chronological services satisfy + + T(B2,C2,K2)T(B1,C1,K1) + =T(B1+B2,C1+C2+K2B1,K1+K2). + +If actual supplied operators satisfy K2=-K1, their receiver-to-receiver blocks cancel, with remaining SOURCE coefficient C1+C2-K1B1. All original inputs remain independent. + +**Proof.** Substitute z1=z+B1x and y1=y+C1x+K1z into the second service. The resulting ordinary receiver is y+(C1+C2+K2B1)x+(K1+K2)z. No factors are commuted. ∎ + +C3 is a constructive changed service, not a cheaper restoration of the original joined service. The Kz term must be retained in any actual caller. C4 does not assert K cancellation for the two different routed D25 stages. Their actual K operators contain their own E_t routes. No profitable compatible Gaussian caller or literal prefix deletion was established here. In particular, sixteen modes do not by themselves replace ninety-six port-dependent line queries by sixteen common queries. + +## Attribution and evidence + +The BIT source is ai-nanachi PR5512's retained G20 word, with Ali Romman PR5421's ownership method, DreamingOfClouds PR589 following eumemic PR555, Cinna Davis's physical/ROW/controller/cover interfaces, rohanarun PR185/PR199/PR204, and the retained mixed-target, precision and compiler lineage. The nine actual cuts and their direct word transformation are in bit.md; this note gives their causal and matcher-explicit correctness support. + +The Gaussian prefix, all-input selected-carrier theorem, complete cover barrier, hole/full views and p8 invoice come from `research/centre-code-services/frozen/lanes/bridge-review-20261017/fixed-reader-service-review-20261020/REVIEW.md`. Its late query is from the fixed-reader-reuse review. Preserve its bridge-access, new-core-transfer, native-recipes, controller, phase and independent-review lane credit, including PR3133, PR3148, PR2588 and PR2226 and all retained source notices. The preceding borrowed-carrier completion is a direct predecessor; it restores the original provider and pays its hole correction, whereas C3 supplies an explicit changed operator to its caller. + +All sources were read at the retained revision `5e0052ca0aa3036a3afa8b0438927377c8d97d53`. Their historical checks are predecessor evidence, not new checks. New text is Apache-2.0 with substantial OpenAI Codex assistance. No formal verification, worldwide novelty priority or new multiplication κ is claimed. diff --git a/research/g20-helper-split/prior/strict_margins.py b/research/g20-helper-split/prior/strict_margins.py new file mode 100644 index 0000000000..d62d56f888 --- /dev/null +++ b/research/g20-helper-split/prior/strict_margins.py @@ -0,0 +1,51 @@ +"""Choose finite strict compiler margins for the retained G20 framework. + +The caller supplies a certified positive first-moment reserve. The tail bounds +are checked separately on the complete profile. Ali Romman with substantial +OpenAI Codex assistance. Apache-2.0. +""" +from fractions import Fraction as F + + +def need(ok,message): + if not ok:raise ValueError(message) + + +def tensor_degree(reserve): + need(F(0)=1024 and v%1024==0,'strict compiler inputs') + t,z=1-tested,1-uniform;z0=(t+z)/2;gap=z0-t;h=F(1,64) + rhs=gap*(5+8*h)*v+1+8*v*(1-z0) + h0=(rhs/(h*gap)).__floor__()+1 + h1=(h0*(1-z0)/(z-z0)).__floor__()+1 + need(h0>=8*v and h0*h*gap>rhs and h1*(z-z0)>h0*(1-z0),'strict finite cutoffs') + return h0,h1 + + +def below_grid(value,denominator): + need(isinstance(denominator,int) and denominator>0,'positive grid denominator') + out=F(-((-value.numerator*denominator)//value.denominator)-1,denominator) + need(0F(4,2**(v//32)),'positive exact contraction') + degrees[str(k)]=v + for value in (F(7,1000),F(701,100000),F(699,100000)): + need(below_grid(value,1000) 0 + counts['output_kernel'] += right > 0 + counts['both_kernels'] += left > 0 and right > 0 + counts['bank_fields_max'] = max(counts['bank_fields_max'], len(fields)) + counts['rank'+str(dim[entrance])+'_contexts'] += 1 + def header(dest, frame): + old = state[dest] + banks[old].remove(dest) + banks[frame].add(dest) + state[dest] = frame + return {old, frame} + for frame in list(banks): + check(frame) + before_erase, old_headers = {}, [] + for k, e in enumerate(program): + op, dest = e[:2] + old_headers.append(state[dest]) + affected = {state[dest]} + if op == 'ADD': + need(state[dest] == state[e[2]] == labels[e[-1]], 'Actual common frame') + a[dest] ^= a[e[2]] + b[e[2]] ^= b[dest] + elif op == 'ERASE': + before_erase[k] = a[dest] + a[dest] = 0 + b[dest] = after_erase[k] + if op in ('Q', 'ZERO_Q', 'ERASE', 'INIT'): + affected |= header(dest, labels[e[3] if op in ('Q', 'ZERO_Q') else e[2]]) + for frame in affected: + check(frame) + expected = [0 if i in owned else (1 << i) ^ ((1 << (i-111)) if 111 <= i < 222 else 0) for i in range(N)] + need(a == expected and b == [1 << i for i in range(N)], 'Complete RAW/DIRTY endpoint and suffix map') + forward, forward_counts = visited, dict(counts) + visited, counts = set(), Counter() + for frame in list(banks): + check(frame) + for k in range(len(program)-1, -1, -1): + e = program[k] + op, dest = e[:2] + affected = {state[dest]} + if op == 'ADD': + a[dest] ^= a[e[2]] + b[e[2]] ^= b[dest] + elif op == 'ERASE': + a[dest] = before_erase[k] + b[dest] = 0 + if op in ('Q', 'ZERO_Q', 'ERASE', 'INIT'): + affected |= header(dest, old_headers[k]) + for frame in affected: + check(frame) + need(a == [1 << i for i in range(N)] and b == first_b, 'Reverse traversal reaches the exact entry') + need(visited == forward and dict(counts) == forward_counts, 'Both traversals cover identical physical cut states') + need(paired_zero([0, 0], [0, 0])[0] is False, 'A true isolated helper channel must be detected') + need(paired_zero([1, 0], [0, 1])[0] is True, 'Orthogonal nonzero kernels are not a split') + need(paired_zero([1, 0], [1, 0])[0] is False, 'A nonzero pairing must be detected') + digests = sorted(hashlib.sha256(repr(k).encode()).hexdigest() for k in forward) + result = {'status': 'PASS_G20_ALL_HELPER_SPLIT_CUTS', 'events': len(program), 'cuts': len(program)+1, + 'original_frame_ids': len(frames), 'physical_frame_classes': len(shapes), + 'full_helpers': len(helpers), 'partial_helpers': 4, 'endpoint_groups': 4, **forward_counts, + 'cut_state_sha256': hashlib.sha256('\n'.join(digests).encode()).hexdigest()} + print(json.dumps(result, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/g20-helper-split/source/p104-split-proof.md b/research/g20-helper-split/source/p104-split-proof.md new file mode 100644 index 0000000000..e479b15351 --- /dev/null +++ b/research/g20-helper-split/source/p104-split-proof.md @@ -0,0 +1,204 @@ +# Independent helper splits and the complete cost + +This proof changes the helper input and output contract of the exact PR5580 +word. It retains every main endpoint, paid Gaussian call and owned lifetime. +All scalar identities below are over the rationals. The native check supplies +exact phases and the rule for every positive tensor width. + +## 1. A split criterion + +Let a group of helpers have the same initial chart U and final chart V. +The complete source word returns each of these helpers unchanged in normalized +coordinates and has no helper contribution to any other output. +Let F be a strict intermediate chart, with U contained in F and F contained +in V. At one chronological cut, let P be the scalar prefix matrix and S the +scalar suffix matrix. The matrices include every public input and output. +Owned fields follow the source initialization and erasure contract. + +Suppose a row a and a column b use only fields at chart F. Suppose c and d +use only the specified helper group, and + +```math +aP=c,\qquad Sb=d,\qquad ab=cd=1. +``` + +Choose a helper role p at F. There are invertible scalar matrices G and J +with + +```math +e_p^T G=c,\quad Gd=e_p,\qquad e_p^T J=a,\quad Jb=e_p. +``` + +Here G acts only on helpers with boundary charts U and V. J acts only on +fields at F. The construction emits these matrices as ADD and dyadic-unit +SCALE operations. Its row and column elimination uses the unit pairings. +The emitted program and its inverse are explicit; no dense matrix operation +is assigned zero implementation cost. + +Apply G inverse at the input. At the cut, apply J. Role p then contains the +independent coordinate t=c h. Retain p as an output at F. Introduce one new +independent input z at F. Use its new role in place of p in J inverse and in +the complete suffix. Finally apply G at V, with the same role substitution. +The suffix state changes by b(z-a P h), so its helper output is + +```math +h+d(z-ch). +``` + +The final change of basis gives + +```math +G[h+d(z-ch)]=Gh+e_p(z-t). +``` + +Thus the former p coordinate is replaced by the independent z coordinate; +all other helper coordinates and every main output retain their required +values. The old t coordinate has already been returned at F. This replaces +one U-to-V target by a U-to-F target and an F-to-V target. + +This uses a new input, not two outputs computed from one input. It does not +assume a helper is zero. The early output is a public field and stays live +until the caller returns. The successor input is public from the start and +is first used at the cut. No new COPY, CLEAR or owned lifetime is introduced. +The source's owned erasures remain charged under the inherited contract. + +All three basis changes use common physical charts. They therefore commute +with the relevant chart operator. Native normalization gives ranks +`dim(F)-dim(U)` and `dim(V)-dim(F)` with their exact phases. Scalar coefficients +stay outside the tensor substitution. The frame induction applies at every +positive width; it is not a test at width one alone. + +## 2. The first explicit split + +The source is PR5580 at `6efa248cf456d6101d757e9d09ba29711d18a13a`. +Use the cut after zero-based event 13778, chart 120 of dimension five, and +pivot 648. The boundary group has initial chart 3 (dimension zero) and final +chart 127 (dimension nine). With e_r the coordinate at role r, the exact +vectors are + +```math +a=e_{651}^T+(e_{648}^T+e_{649}^T)/2,\quad +b=e_{648}+e_{649}-e_{650}-e_{652}, +``` + +```math +c=(e_{648}^T+e_{649}^T)/2,\quad +d=e_{648}+e_{649}-e_{650}-e_{652}+2e_{205}. +``` + +The complete prefix gives aP=c; the complete suffix gives Sb=d. +Both pairings are one. The first basis change uses five ADDs, the local +basis uses five ADDs, and their two inverses use ten more ADDs. The first +split therefore adds 20 scalar events and replaces H9 by H5 and H4. +A later split divides this particular H5 target further. The full sequence, +including each updated event index, is in `SPLITS.json`. + +`check_cut` reconstructs each prefix functional and propagates each suffix +column. It checks that all other input and output coefficients are zero. +The verifier then checks every public and owned row after each complete +split. A separate dense-integer transpose replay checks all 574,564 entries +of the final 758 by 758 interface. + +## 3. The complete target change + +The fifteen splits are + +- six H9 to H4 + H5; +- five H9 to H2 + H7; +- three H9 to H1 + H8; +- one H5 to H1 + H4. + +They add 15 independent helper inputs. The source's 735 public fields become +750, of which 542 are helpers and 208 are main fields. Eight owned lifetime +roles remain; only one is live at a time. The 25,140 source events become +25,502. Every source paid occurrence remains, with the same ordered pair of +charts, rank and ownership. Some register names change to identify the +successor input. The new local helper profile is + +```text +{1:4, 2:5, 4:90, 5:10, 7:5, 8:18, 9:410}. +``` + +For every 0(a+b)^t`. Each split strictly increases the target moment and leaves +the paid moment fixed. The signed local target change is + +```math +4H_1+5H_2+7H_4+5H_5+5H_7+3H_8-14H_9. +``` + +Its rank mass is zero, as required. A source-bound complete caller, not a +standalone packing relaxation, supplies the resulting exponent claim. + +## 4. Native maps and the caller + +The exact signed-Pauli and phase verifiers check every paid chart change, +every helper target and every main adapter. The local replay checks a strict +nested chart relation on each public move and the source's descending owned +moves. Each helper target is strictly productive. + +Cinna Davis's p16/a7 controller and Ali Romman's all-forward implementation +from PR5544 remain literal inputs. All 18 full calls use the new local word +with fresh independent helpers. Sixteen backward main interfaces use the +retained signed exchanges and central-square translations. These wrappers +act only on the main pair. They do not alter a new helper output. + +The physical caller check retains all 104 central ports, 7,488 boundary +contacts, 53,248 central-square column checks, 3,328 main Gaussian targets, +15 thin query sites and 3,120 whole idle jobs. It checks native routes, +spectators, exact phases and every whole target. The complete counts are + +```text +paid calls: 66852 +productive fields: 13084 = 18*542 + 32*104 +rank mass surplus: 760 +maximum target: 145 +maximum paid rank: 72 +``` + +The invoice is counted twice, once from literal events and once from the +controller path lengths. Input and output normalizers, added scalar basis +operations, routes, owned allocation and erasure, queries and idles are all +included. The new independent field count enters the completion-tail bound. +It is not left at the old 12,814 value. + +## 5. Strictification, compiler and outer transfer + +Two independent rational interval engines evaluate the complete moments. +The exact raw crossing is in (0.00309839352211, 0.00309839352212). +`RESULT.json` gives its rational endpoints and the strict tested margin. The claimed kappa is 0.00309839 and the tested saving is +0.0030983905. Their gap funds the finite compiler and outer parameters. An exact negative +derivative bound on [0,0.0034] makes this crossing the raw ceiling for this +fixed invoice under the retained BIT cap. It is not a global optimum. + +Power 1024, cutoff 17, target floor 18 and tail offset 1/5 are retained. +The extra independent fields require a different tail bound: both charged +tail ratios are below 39/40, and `(39/40)^128 < 1/16`. Eight such blocks still +give the retained `2^-32` remainder. The fixed reserve is `10^-10`. +The complete normalized cost is strictly less than one. The old cutoff 20 +fails and is retained as a control. + +The compiler checks its finite integer threshold, initial range, shifted +exits, complement capacity, logarithm power 1024 and predecessor integer point. The old logarithm +power 1000 does not meet the new complement-capacity inequality. +The ordinary BIT saving remains 0.0034. All 54 strict outer conditions and +four functional conditions are checked with exact rational arithmetic. +The scalar growth bound uses fewer than 26,000 local operations and the +retained per-operation bound. The native growth bound uses the actual sum +of local paid ranks. The complete ordinary-work allowance remains below +`10^9`; the local scalar and route allowance remains below `10^7` per call. + +## 6. Scope of acceptance + +The five selected framework assumptions remain: native implementation at +all widths, owned erasure, uniform compiler closure, precision and tape +cost, and analytic integer recovery. The source helper-endpoint contract +also remains. This package proves the new finite interface, the chart +identities and every new numerical condition within that framework. + +The enormous uniform word and complete rounded multiplier are not +materialized. These are author-side checks by the same AI-assisted author. +They are not independent human acceptance or a proof-kernel theorem. +Two greedy cut orders on PR5569 reached the same fifteen-split histogram. +That observation does not prove a maximum over bases, cuts, scalar programs, +frames, controllers or multiplication algorithms. diff --git a/research/g20-helper-split/strict_margins.py b/research/g20-helper-split/strict_margins.py new file mode 100644 index 0000000000..d62d56f888 --- /dev/null +++ b/research/g20-helper-split/strict_margins.py @@ -0,0 +1,51 @@ +"""Choose finite strict compiler margins for the retained G20 framework. + +The caller supplies a certified positive first-moment reserve. The tail bounds +are checked separately on the complete profile. Ali Romman with substantial +OpenAI Codex assistance. Apache-2.0. +""" +from fractions import Fraction as F + + +def need(ok,message): + if not ok:raise ValueError(message) + + +def tensor_degree(reserve): + need(F(0)=1024 and v%1024==0,'strict compiler inputs') + t,z=1-tested,1-uniform;z0=(t+z)/2;gap=z0-t;h=F(1,64) + rhs=gap*(5+8*h)*v+1+8*v*(1-z0) + h0=(rhs/(h*gap)).__floor__()+1 + h1=(h0*(1-z0)/(z-z0)).__floor__()+1 + need(h0>=8*v and h0*h*gap>rhs and h1*(z-z0)>h0*(1-z0),'strict finite cutoffs') + return h0,h1 + + +def below_grid(value,denominator): + need(isinstance(denominator,int) and denominator>0,'positive grid denominator') + out=F(-((-value.numerator*denominator)//value.denominator)-1,denominator) + need(0F(4,2**(v//32)),'positive exact contraction') + degrees[str(k)]=v + for value in (F(7,1000),F(701,100000),F(699,100000)): + need(below_grid(value,1000)