From 55914a0de83df255bd7e7071d79ad04b81ca1070 Mon Sep 17 00:00:00 2001 From: Ali Romman <226877337+aliromman@users.noreply.github.com> Date: Sun, 25 Oct 2026 16:56:58 -0500 Subject: [PATCH 1/9] Retain the released PR5601 word for exact helper-split composition --- .../inputs/PR5601-WORD.json.gz | Bin 0 -> 105077 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 research/p104-helper-subspace-splits/inputs/PR5601-WORD.json.gz diff --git a/research/p104-helper-subspace-splits/inputs/PR5601-WORD.json.gz b/research/p104-helper-subspace-splits/inputs/PR5601-WORD.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..3c9a5ce8969f40f03724a73d34f984dd17efde96 GIT binary patch literal 105077 zcmZs>1z1#J(>G2owV)!kASvAq(jiE9!_wWcfPjRcpn%e>fWXqd2okcCNOyOMfGmx` z((zw?p7;HK-*tU^&GkDobI+Ok%$d8-(#PRr{QY6w@3r>Bc_mYF0{NU;!r4^;Sw|XQ zq)vu9BLUPZ%9uMk6jFbNB|$@HgXbKBwYZ&nYu4GVMmQk%6utt+%kUeN*WKOfeMR{7 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a/research/p104-helper-subspace-splits/inputs/PR5602-construct.py b/research/p104-helper-subspace-splits/inputs/PR5602-construct.py new file mode 100644 index 0000000000..ef5936ca89 --- /dev/null +++ b/research/p104-helper-subspace-splits/inputs/PR5602-construct.py @@ -0,0 +1,215 @@ +"""Construct the fixed helper basis changes and coupled handoffs. + +Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. +The source word and its contributors are recorded in SOURCES.json. +""" +from copy import deepcopy +from fractions import Fraction as Q +import local as L + + +def row(pairs): + out = {r: Q(q) for r, q in pairs} + L.need(len(out) == len(pairs) and all(out.values()), 'Unique nonzero witness row') + return out + + +def unit(q): + n, d = abs(q.numerator), q.denominator + return n > 0 and n & (n-1) == 0 and d & (d-1) == 0 + + +def main_fields(w): + return set(w['live']) | {r+112 for r in w['live']} + + +def prefix(w, cut): + n = w['public'] + rows = [{i: Q(1)} for i in range(n)] + [{} for _ in range(8)] + frames = w['initial'][:] + [None]*8 + L.need(0 <= cut < len(w['program']), 'Cut in the literal word') + for e in w['program'][:cut+1]: + op, r = e[:2] + if op == 'MOVE': + L.need(frames[r] == e[2], 'Prefix transport source') + frames[r] = e[3] + elif op in ('INIT', 'CLEAR'): + rows[r] = {} + frames[r] = e[2] if op == 'INIT' else None + else: + L.need(frames[r] == e[-1], 'Prefix scalar chart') + if op == 'SCALE': + rows[r] = {k: Q(e[-2])*v for k, v in rows[r].items()} + else: + L.need(frames[e[2]] == e[-1], 'Prefix source chart') + if op == 'COPY': + L.need(not rows[r], 'Source COPY into zero') + L.add(rows[r], rows[e[2]], Q(e[-2])) + return rows, frames + + +def suffix_columns(w, cut): + cols = [{i: Q(1)} for i in range(w['public'])] + [{} for _ in range(8)] + for e in reversed(w['program'][cut+1:]): + op, r = e[:2] + if op == 'MOVE': + continue + if op in ('INIT', 'CLEAR'): + cols[r] = {} + elif op == 'SCALE': + cols[r] = {k: Q(e[-2])*v for k, v in cols[r].items()} + else: + L.add(cols[e[2]], cols[r], Q(e[-2])) + if op == 'COPY': + cols[r] = {} + return cols + + +def transpose(w): + program = [] + for e in reversed(w['program']): + op, r = e[:2] + if op == 'MOVE': + z = ['MOVE', r, e[3], e[2], e[4]] + elif op in ('ADD', 'COPY'): + z = ['ADD', e[2], r, e[3], e[4]] + elif op == 'SCALE': + z = e[:] + else: + L.need(op in ('INIT', 'CLEAR'), 'Transpose opcode') + z = ['CLEAR' if op == 'INIT' else 'INIT', r, e[2]] + program.append(z) + return dict(w, initial=w['final'][:], final=w['initial'][:], program=program) + + +def boundary_basis(w, c): + w = transpose(w) if c['reverse'] else deepcopy(w) + h, cut, frame = c['helper'], c['cut'], c['frame'] + output, cancel = row(c['output']), row(c['cancel']) + helpers = set(range(w['public'])) - main_fields(w) + L.need(h in helpers and unit(output.get(h, Q(0))), 'Helper unit boundary pivot') + source = w['initial'][h] + L.need(set(output) <= {r for r in helpers if w['initial'][r] == source}, + 'Boundary basis uses one helper input chart') + rows, frames = prefix(w, cut) + L.need(frames[h] == frame and h not in cancel and + all(frames[r] == frame for r in cancel), 'Available boundary cancellation') + value = rows[h].copy() + for r, q in cancel.items(): + L.add(value, rows[r], -q) + L.need(value == output, 'Exact boundary helper relation') + tail = w['program'][cut+1:] + L.need(not any(e[0] in ('ADD', 'COPY') and e[2] == h for e in tail), + 'Retired helper has no later source read') + coefficient = output[h] + before = [['ADD', h, r, str(-q/coefficient), source] + for r, q in sorted(output.items()) if r != h] + middle = [['ADD', h, r, str(-q), frame] for r, q in sorted(cancel.items())] + if coefficient != 1: + middle.append(['SCALE', h, str(1/coefficient), frame]) + w['program'] = before + w['program'][:cut+1] + middle + [e for e in tail if e[1] != h] + w['final'][h] = frame + return transpose(w) if c['reverse'] else w + + +def inverse(ops): + out = [] + for e in reversed(ops): + z = e[:] + z[-2] = str(1/Q(e[-2]) if e[0] == 'SCALE' else -Q(e[-2])) + out.append(z) + return out + + +def basis(a, b, p, frame): + """Return a matrix R with a R = e_p^T and R e_p = b.""" + L.need(sum(a.get(h, 0)*q for h, q in b.items()) == 1, 'Dual basis pairing') + q = next((h for h in sorted(a) if unit(a[h])), None) + L.need(q is not None, 'Dyadic basis pivot') + ops = [] if p == q else [ + ['ADD', p, q, '1', frame], ['ADD', q, p, '-1', frame], + ['ADD', p, q, '1', frame], ['SCALE', q, '-1', frame]] + ops += [['ADD', j, q, str(c), frame] for j, c in sorted(b.items()) if j != q] + if a[q] != 1: + ops.append(['SCALE', q, str(1/a[q]), frame]) + ops += [['ADD', q, j, str(-c/a[q]), frame] for j, c in sorted(a.items()) if j != q] + return ops + + +def relabel(e, mapping): + z = e[:] + z[1] = mapping(z[1]) + if z[0] in ('ADD', 'COPY'): + z[2] = mapping(z[2]) + return z + + +def handoff(w, c): + n, cut, frame, p = w['public'], c['cut'], c['frame'], c['pivot'] + source, target = c['group'] + group = {h for h in range(n) if h not in main_fields(w) and + (w['initial'][h], w['final'][h]) == (source, target)} + v, u = row(c['v']), row(c['u']) + pairing = sum(v.get(h, 0)*q for h, q in u.items()) + L.need(unit(pairing), 'Nonzero dyadic handoff pairing') + v = {h: q/pairing for h, q in v.items()} + rows, frames = prefix(w, cut) + L.need(all(f is None for f in frames[n:]), 'No owned field at handoff cut') + L.need(p in group and frames[p] == frame and + all(0 <= h < n and frames[h] == frame for h in v.keys() | u.keys()), + 'Public handoff fields share the cut chart') + L.need(L.span(w['frames'][source]) < L.span(w['frames'][frame]) < + L.span(w['frames'][target]), 'Strict nested handoff boundaries') + cols, a, b = suffix_columns(w, cut), {}, {} + for r, q in v.items(): + L.add(a, rows[r], q) + for r, q in u.items(): + L.add(b, cols[r], q) + L.need(a == row(c['source_functional']) and b == row(c['output_direction']), + 'Exact prefix and suffix handoff witnesses') + L.need(set(a) <= group and set(b) <= group, 'Handoff has only helper boundary support') + input_ops, cut_basis = basis(a, b, p, source), basis(v, u, p, frame) + output_ops = inverse(input_ops) + for e in output_ops: + e[-1] = target + old = lambda r: r+1 if r >= n else r + tail = lambda r: n if r == p else old(r) + out = deepcopy(w) + out['public'] = n+1 + out['initial'].append(frame) + out['final'][p] = frame + out['final'].append(target) + out['program'] = input_ops + [relabel(e, old) for e in w['program'][:cut+1]] + out['program'] += inverse(cut_basis) + [relabel(e, tail) for e in cut_basis] + out['program'] += [relabel(e, tail) for e in w['program'][cut+1:]] + out['program'] += [relabel(e, tail) for e in output_ops] + return out + + +def restore_copy_opcodes(w): + fresh, copies = set(), 0 + for e in w['program']: + op, r = e[:2] + if op == 'INIT': + fresh.add(r) + elif r in fresh and op != 'MOVE': + L.need(op == 'ADD', 'First owned write is the retained copy') + e[0] = 'COPY' + fresh.remove(r) + copies += 1 + L.need(not fresh and copies == 8, 'All eight owned copy paths remain') + + +def construct(base, witness): + L.need(witness['schema'] == 'p104-coupled-helper-bases/1', 'Witness schema') + L.need([s['kind'] for s in witness['steps']] == + ['boundary_basis']*6 + ['coupled_handoff']*9, 'Fixed fifteen changes') + word, evidence = deepcopy(base), [] + for step in witness['steps']: + word = boundary_basis(word, step) if step['kind'] == 'boundary_basis' else handoff(word, step) + check = L.replay(word) + evidence.append(dict(kind=step['kind'], public=word['public'], + events=len(word['program']), paid=check['paid'], helpers=check['helpers'])) + restore_copy_opcodes(word) + L.replay(word) + return word, evidence From 3db0f4bb618f8607874f888b410715ea606ddb36 Mon Sep 17 00:00:00 2001 From: Ali Romman <226877337+aliromman@users.noreply.github.com> Date: Sun, 25 Oct 2026 17:10:02 -0500 Subject: [PATCH 3/9] Compose released boundary and frame gains for kappa 0.00310261 --- .../BOUNDARIES.json | 255 +++++++++++ research/p104-helper-subspace-splits/NOTICE | 4 +- research/p104-helper-subspace-splits/PROOF.md | 125 +++--- .../p104-helper-subspace-splits/README.md | 239 +++++----- .../p104-helper-subspace-splits/RESULT.json | 424 +++++++++++------- .../p104-helper-subspace-splits/SOURCES.json | 45 ++ .../p104-helper-subspace-splits/SPLITS.json | 133 +----- .../p104-helper-subspace-splits/TASK.json | 16 +- .../p104-helper-subspace-splits/VALIDATION.md | 62 +-- .../p104-helper-subspace-splits/VERIFY.json | 9 +- .../p104-helper-subspace-splits/WORD.json.gz | Bin 108031 -> 107694 bytes .../p104-helper-subspace-splits/construct.py | 35 ++ .../p104-helper-subspace-splits/pricing.py | 10 +- .../p104-helper-subspace-splits/verify.py | 49 +- 14 files changed, 869 insertions(+), 537 deletions(-) create mode 100644 research/p104-helper-subspace-splits/BOUNDARIES.json diff --git a/research/p104-helper-subspace-splits/BOUNDARIES.json b/research/p104-helper-subspace-splits/BOUNDARIES.json new file mode 100644 index 0000000000..45c824911d --- /dev/null +++ b/research/p104-helper-subspace-splits/BOUNDARIES.json @@ -0,0 +1,255 @@ +[ + { + "source_step": 0, + "anchor": [ + "ADD", + 653, + 652, + "-1", + 120 + ], + "witness": { + "kind": "boundary_basis", + "reverse": true, + "helper": 652, + "cut": 11355, + "frame": 120, + "output": [ + [ + 205, + "-2" + ], + [ + 648, + "-1" + ], + [ + 649, + "-1" + ], + [ + 650, + "1" + ], + [ + 652, + "1" + ] + ], + "cancel": [ + [ + 648, + "1" + ], + [ + 649, + "1" + ], + [ + 650, + "-1" + ] + ] + } + }, + { + "source_step": 1, + "anchor": [ + "ADD", + 346, + 341, + "1", + 240 + ], + "witness": { + "kind": "boundary_basis", + "reverse": false, + "helper": 341, + "cut": 11151, + "frame": 240, + "output": [ + [ + 93, + "-2" + ], + [ + 339, + "-2" + ], + [ + 341, + "1" + ], + [ + 351, + "2" + ] + ], + "cancel": [ + [ + 337, + "2" + ] + ] + } + }, + { + "source_step": 2, + "anchor": [ + "ADD", + 597, + 596, + "-1", + 1053 + ], + "witness": { + "kind": "boundary_basis", + "reverse": true, + "helper": 596, + "cut": 11373, + "frame": 1053, + "output": [ + [ + 188, + "-1" + ], + [ + 592, + "-1" + ], + [ + 593, + "1" + ], + [ + 594, + "1" + ], + [ + 596, + "1" + ] + ], + "cancel": [ + [ + 592, + "1" + ], + [ + 593, + "-1" + ], + [ + 594, + "-1" + ] + ] + } + }, + { + "source_step": 3, + "anchor": [ + "ADD", + 669, + 668, + "-1", + 1051 + ], + "witness": { + "kind": "boundary_basis", + "reverse": true, + "helper": 668, + "cut": 11444, + "frame": 1051, + "output": [ + [ + 115, + "2" + ], + [ + 664, + "1" + ], + [ + 665, + "1" + ], + [ + 666, + "-1" + ], + [ + 668, + "1" + ] + ], + "cancel": [ + [ + 664, + "-1" + ], + [ + 665, + "-1" + ], + [ + 666, + "1" + ] + ] + } + }, + { + "source_step": 4, + "anchor": [ + "ADD", + 685, + 684, + "-1", + 1049 + ], + "witness": { + "kind": "boundary_basis", + "reverse": true, + "helper": 684, + "cut": 11488, + "frame": 1049, + "output": [ + [ + 126, + "2" + ], + [ + 680, + "-1" + ], + [ + 681, + "1" + ], + [ + 682, + "1" + ], + [ + 684, + "1" + ] + ], + "cancel": [ + [ + 680, + "1" + ], + [ + 681, + "-1" + ], + [ + 682, + "-1" + ] + ] + } + } +] diff --git a/research/p104-helper-subspace-splits/NOTICE b/research/p104-helper-subspace-splits/NOTICE index f34687ff7e..b60fe03aef 100644 --- a/research/p104-helper-subspace-splits/NOTICE +++ b/research/p104-helper-subspace-splits/NOTICE @@ -4,7 +4,9 @@ The same assistant performed the construction and author-side checks. Retained contributions: Pierre-Loic Doulcet (hexapode): PR5565 commuting-contact construction, used as the exact source. -Ali Romman: PR5580 contact step and PR5544/5545 complete P104 caller. +Ali Romman: PR5602 fixed boundary relations, PR5601 three-contact frame +change, PR5580 contact step, +and PR5544/5545 complete P104 caller. Joel Pulikkan (GamingPuzzled): PR5569 priced helper handoff. DreamingOfClouds: PR5561 free helper endpoints and PR5568 search tools. thu-nmrc: PR5551 contact improvements. diff --git a/research/p104-helper-subspace-splits/PROOF.md b/research/p104-helper-subspace-splits/PROOF.md index ca97998444..c572f796aa 100644 --- a/research/p104-helper-subspace-splits/PROOF.md +++ b/research/p104-helper-subspace-splits/PROOF.md @@ -1,9 +1,10 @@ # Independent helper splits and the complete cost -This proof changes the helper input and output contract of the exact PR5565 -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. +This proof changes the helper input and output contract of the exact PR5601 +word. Five fixed PR5602 boundary relations remove five paid H5 calls. Nine +independent target splits then retain all remaining calls. Every main endpoint +and chronological owned path is preserved. Scalar identities are rational; +the native check supplies exact phases and the rule for every positive width. ## 1. A split criterion @@ -68,70 +69,88 @@ with the relevant chart operator. Native normalization gives ranks 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 +## 2. Five released boundary relations -The source is PR5565 at `9af814164b9dfc21f19ec737959d67cb71488c95`. -Use the cut after zero-based event 13775, 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 +The input is PR5601 at `8f7e870b22885a367b347dc12791da98fd53f83d`. +The retained PR5602 constructor and witness come from +`6c224aa720203c4f4615e6538d8038a275387db8`. No coefficient, helper, frame, +cancellation vector or output vector in those relations changes. Only the +chronological cut indices change, with explicit event anchors in `BOUNDARIES.json`. + +For a forward boundary relation, the complete prefix gives a helper input +combination after cancellation by coframed fields. A scalar input basis +makes this combination one independent input. The helper has no later source +read, so it can finish at that frame. The reverse relations supply the +corresponding early-input rule. The source constructor uses an algebraic +transpose to derive that rule; it does not execute the owned program backward. +The final program restores the eight COPY opcodes. Its complete subsequence +of operations involving owned fields equals the original chronological +subsequence, byte for byte, before the independent splits rename owned roles. + +The five fixed relations use helpers 652, 341, 596, 668 and 684. Each replaces +one H9 helper target by H4 and removes one paid H5. The complete arbitrary-input +interface is checked after every relation. The sixth PR5602 relation uses a +frame-597 contact absent from the PR5565 cascade; it is not used. + +## 3. Nine independent splits + +After those five changes, the first split uses the cut after zero-based +event 12504, chart 306 of dimension four, and pivot 259. Its helper 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_{261}^T+(e_{256}^T+e_9^T)/2+2e_{259}^T,\qquad b=e_{259}/2, +``` ```math -a=e_{652}^T,\quad b=e_{652}-e_{648}+e_{650}-e_{649}, +c=2(e_{259}^T+e_{61}^T+e_{265}^T), ``` ```math -c=e_{652}^T,\quad d=e_{652}-2e_{205}-e_{648}+e_{650}-e_{649}. +d=(e_{262}-e_{270}+e_{265}+e_{264}-e_{256}-e_{271}+e_{263})/2. ``` The complete prefix gives aP=c; the complete suffix gives Sb=d. -Both pairings are one. The boundary basis uses six scalar events and the -local basis uses five. With their inverses, the split adds eighteen ADDs -and four sign SCALEs. It replaces H9 by independent H5 and H4 targets. -The full sequence, including each updated event index, is in `SPLITS.json`. +Both pairings are one. The boundary basis has 14 scalar events and the +local basis has four. With their inverses, this adds 30 ADDs and six dyadic +SCALEs. It replaces one H9 target by independent H4 and H5 targets. +`SPLITS.json` gives every subsequent cut and all four exact vectors. `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 571,536 entries -of the final 756 by 756 interface. - -## 3. The complete target change - -The thirteen splits are - -- six H9 to H4 + H5; -- five H9 to H2 + H7; -- two H9 to H1 + H8. +column. It checks zero support on every other input and output. Full row +replay checks each intermediate construction. A separate dense-integer +transpose replay checks all 565,504 entries of the final 752 by 752 interface. -They add 13 independent helper inputs. The source's 735 public fields become -748, of which 540 are helpers and 208 are main fields. Eight owned lifetime -roles remain; only one is live at a time. The 25,133 source events become -25,475. 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 +The nine splits are two H9 to H4+H5, five H9 to H2+H7, and two H9 to H1+H8. +They add nine independent inputs. The source's 735 public fields become 744, +with 536 helpers and 208 main fields. Eight owned lifetimes remain, with +one live at a time. The source has 25,132 events; the boundary step has +25,137; the final word has 25,393. The split step adds 256 scalar events. +The new local helper profile is ```text -{1:2, 2:5, 4:89, 5:11, 7:5, 8:16, 9:412}. +{1:2, 2:5, 4:91, 5:6, 7:5, 8:16, 9:411}. ``` -The verifier also replays the retained PR5580 source. It checks that PR5565 -changes its local paid profile by `-8H1-H3-2H4+4H5` and its helper profile -by `-H8+H9`. These source changes are by Pierre-Loic Doulcet (hexapode). The new splits retain -that paid profile. The earlier fifteen-split component on PR5580 is frozen -at `31a4de233bbdd65c04c63dc3398ecf0eed8e1375`. Two of its cuts are absent -from the PR5565 composition, but the lower paid cost gives a larger kappa. +The verifier replays the retained PR5580 and PR5565 words. It checks the +PR5565 paid delta `-8H1-H3-2H4+4H5` and helper delta `-H8+H9`, then the +PR5601 paid delta `-2H2+2H3-2H4+H5` and helper delta `H4-H5`. These are +credited source changes, not new discoveries in this package. -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 +For 00. +Against the consumed PR5601 word, the complete target-minus-paid moment +increases by ```math -2H_1+5H_2+6H_4+6H_5+5H_7+2H_8-13H_9. +18[7g(4,5)+5g(2,7)+2g(1,8)]. ``` -Its rank mass is zero, as required. A source-bound complete caller, not a -standalone packing relaxation, supplies the resulting exponent claim. +Five g(4,5) terms come from the fixed boundary relations; two come from +independent splits. All new target credits and removed paid calls are +counted in the final invoice. The two complete rank masses both change; +their difference stays 760. The old components' reported kappa gains are +not added. ## 4. Native maps and the caller @@ -152,8 +171,8 @@ contacts, 53,248 central-square column checks, 3,328 main Gaussian targets, spectators, exact phases and every whole target. The complete counts are ```text -paid calls: 66726 -productive fields: 13048 = 18*540 + 32*104 +paid calls: 66618 +productive fields: 12976 = 18*536 + 32*104 rank mass surplus: 760 maximum target: 145 maximum paid rank: 72 @@ -168,9 +187,9 @@ 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 (0.00310045630724, 0.00310045630725). -`RESULT.json` gives its rational endpoints and the strict tested margin. The claimed kappa is 0.00310045 and the tested saving is -0.0031004505. Their gap funds the finite compiler and outer parameters. An exact negative +The exact raw crossing is in (0.00310261511129, 0.00310261511130). +`RESULT.json` gives its rational endpoints and the strict tested margin. The claimed kappa is 0.00310261 and the tested saving is +0.0031026105. 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. @@ -202,7 +221,7 @@ 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. -The final exact discovery screen tests 52 boundary groups and finds no +The final exact discovery screen tests 47 boundary groups and finds no further candidate in its finite basis-pair class. It does not prove a maximum over bases, cuts, scalar programs, frames, controllers or multiplication algorithms. diff --git a/research/p104-helper-subspace-splits/README.md b/research/p104-helper-subspace-splits/README.md index f6303a8813..d2d30b06c2 100644 --- a/research/p104-helper-subspace-splits/README.md +++ b/research/p104-helper-subspace-splits/README.md @@ -1,45 +1,53 @@ -# Conditional kappa 0.00310045 from independent helper splits - -This construction raises complete conditional **kappa to 0.00310045**. -The gain over [PR5565](https://github.com/CrocSwap/integer-mult-bounds/pull/5565) -(0.00308520) is **0.00001525**, about **0.4943%**. The gain over selected -0.003027288235 is **0.000073161765**. The selected record is unchanged. - -The mechanism changes the independent helper basis. At a common-frame cut, -one helper combination can finish early and a fresh independent input can -use the remaining program. Thirteen explicit splits replace 527 helper -jobs by 540 helper jobs. They add 342 scalar events and no recursive Gaussian -call. Both input and output support are checked over every field; a local -pure row alone does not earn a new target. - -Read the [proof](PROOF.md), [exact cuts](SPLITS.json), [complete word](WORD.json.gz), -[receipt](RESULT.json), [source pins](SOURCES.json), and [validation record](VALIDATION.md). -The first split is an explicit 22-event change from one H9 target to independent -H5 and H4 targets. The complete caller uses the new word at all 18 full sites. +# Conditional kappa 0.00310261 from composed helper splits + +This construction gives complete conditional **kappa 0.00310261**. +It improves the consumed [PR5601](https://github.com/CrocSwap/integer-mult-bounds/pull/5601) +claim by **0.00001666** and the released +[PR5602](https://github.com/CrocSwap/integer-mult-bounds/pull/5602) claim by +**0.00000281**. The gain over selected 0.003027288235 is **0.000075321765**. +The selected record is unchanged. + +At a common-frame cut, a pure helper input functional and a pure helper +output direction can have unit pairing. Explicit scalar bases then let one +independent target finish early and a fresh independent input use the rest +of the program. Both complete boundary supports must be proved. A pure +intermediate row alone does not earn a second target. + +The final construction first applies five fixed boundary relations released +in PR5602 to the PR5601 word. It then splits nine independent helper targets. +The five relations remove five paid H5 calls per local use. The nine splits +add nine independent helper inputs and no paid Gaussian call. Together they +give a larger complete gain than the earlier fifteen-split component. + +Read the [proof](PROOF.md), [five fixed relations](BOUNDARIES.json), +[nine exact cuts](SPLITS.json), [complete word](WORD.json.gz), +[receipt](RESULT.json), [source pins](SOURCES.json), and +[validation record](VALIDATION.md). | Quantity | Result | | --- | ---: | -| Local public inputs | 748 | -| Independent helpers per full call | 540 | +| Local public inputs / independent helpers | 744 / 536 | | Owned lifetimes / peak owned fields | 8 / 1 | -| Local events | 25,475 | -| Complete paid calls | 66,726, unchanged | -| Complete productive fields | 13,048 | -| Complete rank-mass surplus | 760, unchanged | -| Tested saving | 0.0031004505 | -| Complete conditional kappa | 0.00310045 | -| Raw crossing | (0.00310045630724, 0.00310045630725) | -| Exact native maps | 2,923 | - -The added helpers enter the complete completion-tail calculation. The tail -bound changes to 39/40, with `(39/40)^128 < 1/16`. The compiler logarithm -power changes from 1000 to 1024. Every native map, helper normalizer, main -adapter, scalar basis operation, route, COPY/CLEAR cost, thin query and -whole idle is included. The ordinary BIT saving remains 0.0034. Two exact -moment engines and all 54 strict plus four functional outer conditions are -checked. The receipt gives the raw crossing and the finite compiler threshold. -A negative derivative bound supplies the raw ceiling for this fixed invoice -on [0,0.0034]; it does not bound other constructions. +| Local events | 25,393 | +| Complete paid calls | 66,618 | +| Complete productive fields | 12,976 | +| Complete rank-mass surplus | 760 | +| Tested saving | 0.0031026105 | +| Complete conditional kappa | 0.00310261 | +| Raw crossing | (0.00310261511129, 0.00310261511130) | +| Exact native maps | 2,920 | + +Every helper normalizer, main adapter, scalar basis operation, route, +COPY/CLEAR path, thin query and whole idle is charged. The independent field +count enters the completion-tail bound. Tail decay is 39/40 and the compiler +logarithm power is 1024. The ordinary BIT saving stays at 0.0034. Two exact +moment engines, every compiler condition, 54 strict outer conditions and +four functional conditions are checked. The finite compiler threshold is +`N = 2^707182000000000`; that word is not materialized. + +A negative derivative bound gives the raw ceiling for this fixed invoice +on [0,0.0034]. The final discovery screen finds no further tested basis pair +in 47 boundary groups. Neither result proves a global optimum. ## Reproduce @@ -50,8 +58,8 @@ python3 -B scripts/research_package.py --package research/p104-helper-subspace-s python3 -B scripts/research_package.py --package research/p104-helper-subspace-splits ``` -The registered hook runs normally and with `-O`. Its success markers are -`PASS_P104_HELPER_SUBSPACE_KAPPA_00310045` and +The registered hook runs normally and with `-O`. Success markers are +`PASS_P104_HELPER_SUBSPACE_KAPPA_00310261` and `PASS_REGISTERED_RESEARCH_PACKAGE`. Direct replay needs no Git or network: ```sh @@ -59,109 +67,84 @@ python3 -I -B research/p104-helper-subspace-splits/verify.py python3 -I -O -B research/p104-helper-subspace-splits/verify.py ``` -Normal replay is read-only. `--write` explicitly regenerates the two result -artifacts. Inputs are authenticated before imported source code executes. -Each replay uses a fresh bytecode-cache path. The checks reject contaminated -prefix and suffix vectors, missing boundary basis operations, an unearned -whole target, extra helper credit, a missing paid call, a wrong native phase, -a missing central translation, an inadequate cutoff and insufficient BIT stock. +Normal replay is read-only. `--write` explicitly regenerates the word and +receipt. Sixteen live inputs are authenticated before any source import. +The checks reject a wrong boundary event, contaminated prefix or suffix, +missing basis work, unearned target credit, a missing paid call, a wrong +native phase, a missing central translation, an inadequate cutoff and +insufficient BIT stock. All eight chronological owned paths stay unchanged. -## Scope and coordination +## Sources and coordination -The scientific base is canonical main +The branch starts from canonical main `5e0052ca0aa3036a3afa8b0438927377c8d97d53`, priority revision 7. The [canonical claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19183208) -records the changed question and local screens. The final publication overlap -cache covered 334 open PRs and 4,863 Discussion records, with complete remote -pagination and incomplete sparse local coverage. Source and coverage details -are coordination evidence, not a novelty proof. - -The consumed PR5565 word is pinned to -`9af814164b9dfc21f19ec737959d67cb71488c95`. It includes Pierre-Loic Doulcet's published -commuting-contact cascade and the released PR5580/PR5569/PR5561 lineage. -The source copy is retained in this branch at commit -`bf64e66656843a64e798b8374cd9f53add3f6f46`. Its SHA256 and Git blob match -the recorded PR5565 source. The PR5580 copy remains an active comparison -input: replay checks the exact paid and helper changes supplied by PR5565. -Registered replay needs this branch history and its main base; it does not -need cached objects from unmerged PR branches. +records the changed question, released components and composition checks. +The latest full overlap snapshot covered 340 open PRs and 4,874 Discussion +records, with complete remote pagination and incomplete sparse local coverage. +These counts describe coverage; they are not a novelty proof. + +The main input is PR5601 at +`8f7e870b22885a367b347dc12791da98fd53f83d`. It contains Pierre-Loic Doulcet's +PR5565 cascade and the PR5580/PR5569/PR5561 lineage. The fixed boundary +constructor and witnesses are from PR5602 at +`6c224aa720203c4f4615e6538d8038a275387db8`. Their bytes are retained unchanged. +Only the five published relations with helpers 652, 341, 596, 668 and 684 +are used. The sixth relation uses a contact removed by PR5565 and is omitted. +No new paid-boundary, commuting-contact or frame search is introduced. + +The verifier also replays the retained PR5580 and PR5565 words and checks +both source deltas. Each retained input is pinned to an ancestor of this +branch. Registered replay needs no cached unmerged-branch objects. The earlier fifteen-split component on PR5580 remains frozen at -`31a4de233bbdd65c04c63dc3398ecf0eed8e1375`. Two cuts are absent from this -composition. PR5565's lower paid cost more than offsets that lost target -gain. The complete claim increases by 0.00000206 over that component. -This package introduces no new commuting-contact search. -No new Gaussian itinerary is introduced. Active frame-extension work in -[Discussion5575](https://github.com/CrocSwap/integer-mult-bounds/discussions/5575) -is a separate investigation. - -The final refresh also found [parallel coupled-basis and handoff work](https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19154639). -It uses the same rank-one mechanism and separately changes paid boundary -work. The [public composition handoff](https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19183908) -releases the earlier fifteen cuts and leaves the six paid-boundary changes -with the parallel claim. That claim is testing their composition. This -package composes only the released PR5565 source with helper splits. No -exclusive method novelty or gain from the parallel paid changes is claimed. -The new scalar contacts and input count change the hypotheses of -[PR5590](https://github.com/CrocSwap/integer-mult-bounds/pull/5590)’s fixed-contact floor. - -The scope changes the scalar word, the input count and the target contract. -It therefore differs from a scalar-only simplification or a fixed-input -helper stop. The unchanged paid histogram now supports a different, -fully independent target histogram. +`31a4de233bbdd65c04c63dc3398ecf0eed8e1375`. The +[parallel claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19154639) +released PR5602 before this final composition check. The shared rank-one +mechanism and every reused boundary relation are credited. No exclusive +method discovery is claimed. The old components' reported gains are not +added: this word, its full native interface and its complete bill are checked. + +## Credit and limits + +- **Ali Romman**, with OpenAI Codex assistance: independent helper splits; + the separate PR5602 boundary relations and PR5601 three-contact change; + PR5580 contact step and PR5544/5545 complete P104 caller and replay. +- **Pierre-Loic Doulcet / hexapode**: PR5565 commuting-contact cascade. +- **Joel Pulikkan / GamingPuzzled**: PR5569 priced handoff and PR5472 successor + construction. **DreamingOfClouds**: PR5561 free endpoints and PR5568 tools. + **thu-nmrc**: PR5551 contact improvements. +- **Gareth Davidson / bitplane**, **David Arias** and **Cinna Davis**: PR2305 + composition, PR2152 coalesced word, PR2219 private reuse and controller + lineage. **Jacob Alan Sussman**: productive mixed-target recursion. + **zxv** and **Cao Yifan**: retained interval, compiler and native/pricing + lineage. Earlier geometry, BIT and analytic credit remains in source notices. + +The elementary basis identity is not claimed as a new general theorem. +This package supplies an explicit independent-target construction and a +complete conditional price. The same AI-assisted author constructed and +checked it; no subagents or independent human review. Apache-2.0. See [NOTICE](NOTICE). The five selected framework assumptions remain: native implementation at all widths, owned erasure, uniform compiler closure, precision and tape cost, -and analytic recovery. The helper-endpoint contract also remains. -The complete rounded multiplier and enormous uniform compiler word are not -materialized. The same AI-assisted author constructed and checked this -package. Independent human review, proof-kernel acceptance and global -optimality are not claimed. - -## Sources and credit - -- **Pierre-Loic Doulcet / hexapode**: [PR5565](https://github.com/CrocSwap/integer-mult-bounds/pull/5565) - supplies the exact commuting-contact source word. -- **Ali Romman**: [PR5580](https://github.com/CrocSwap/integer-mult-bounds/pull/5580) - supplies its preceding contact step; [PR5544](https://github.com/CrocSwap/integer-mult-bounds/pull/5544) - and [PR5545](https://github.com/CrocSwap/integer-mult-bounds/pull/5545) supply - the complete P104 caller and source replay. -- **Joel Pulikkan / GamingPuzzled**: [PR5569](https://github.com/CrocSwap/integer-mult-bounds/pull/5569) - supplies the priced helper handoff; [PR5472](https://github.com/CrocSwap/integer-mult-bounds/pull/5472) - supplies an earlier successor-handoff construction. -- **DreamingOfClouds**: [PR5561](https://github.com/CrocSwap/integer-mult-bounds/pull/5561) - supplies free helper endpoints and PR5568 supplies search tools. - **thu-nmrc** supplies the PR5551 contact improvements. -- **Gareth Davidson / bitplane**, **David Arias** and **Cinna Davis** supply - the PR2305 composition, PR2152 coalesced word and PR2219 private reuse. - Cinna Davis also supplies the controller lineage. -- **Jacob Alan Sussman** supplies productive mixed-target recursion. - **zxv** and **Cao Yifan** supply the retained interval, compiler and - native/pricing lineage. Source notices preserve earlier geometry, BIT - and analytic credit. - -The elementary rank-one basis identity is not claimed as a new general -linear-algebra theorem. The contribution is this explicit independent-target -construction and its complete conditional price. New work is by Ali Romman -with substantial OpenAI Codex assistance; no subagents. Apache-2.0. -See [NOTICE](NOTICE). +and analytic recovery. The helper-endpoint contract also remains. The full +rounded multiplier and huge uniform word are not materialized. Independent +scientific acceptance and global optimality are not claimed. ## Open next questions -An independent reviewer can check the first split and then replay the complete -package. Further gains could use a different compatible cut order, basis or -frame itinerary. Both prefix and suffix support must be proved before a -new target receives credit. The finite discovery screen does not establish a global -maximum. [TASK.json](TASK.json) gives the first checks and remaining obligations. +An independent reviewer can check the fixed boundary relations and the first +split, then replay the complete package. More general bases, cut orders or +new frame paths remain open. Every additional target needs a clean independent +input/output contract and a complete caller bill. [TASK.json](TASK.json) +records the remaining obligations. -The optional continuation screen is reproducible with: +The finite continuation screen is available with: ```sh python3 -I -B research/p104-helper-subspace-splits/search.py ``` -It tests exact elimination-basis pairs at cuts immediately after MOVE events, -inside equal-boundary helper groups. On the final word it finds no further -candidate in 52 groups. This result covers those tested pairs. It does not -exclude different cut sequences, arbitrary basis combinations or new frames. -The complete-kappa verifier does not depend on a discovery search failure. +It tests exact elimination-basis pairs after MOVE events within equal-boundary +helper groups. Its failure to find another candidate is not an optimum proof. +The complete-kappa verifier does not depend on that search failure. diff --git a/research/p104-helper-subspace-splits/RESULT.json b/research/p104-helper-subspace-splits/RESULT.json index 35f75c8555..df8a2e3ea1 100644 --- a/research/p104-helper-subspace-splits/RESULT.json +++ b/research/p104-helper-subspace-splits/RESULT.json @@ -1,27 +1,134 @@ { - "authenticated_inputs": 13, + "authenticated_inputs": 16, + "boundaries": [ + { + "cut": 11355, + "events": 25134, + "helper": 652, + "helpers": { + "4": 85, + "5": 4, + "8": 14, + "9": 424 + }, + "paid": { + "1": 2203, + "2": 457, + "3": 495, + "4": 90, + "5": 168, + "6": 18, + "7": 14 + }, + "reverse": true + }, + { + "cut": 11151, + "events": 25131, + "helper": 341, + "helpers": { + "4": 86, + "5": 4, + "8": 14, + "9": 423 + }, + "paid": { + "1": 2203, + "2": 457, + "3": 495, + "4": 90, + "5": 167, + "6": 18, + "7": 14 + }, + "reverse": false + }, + { + "cut": 11373, + "events": 25133, + "helper": 596, + "helpers": { + "4": 87, + "5": 4, + "8": 14, + "9": 422 + }, + "paid": { + "1": 2203, + "2": 457, + "3": 495, + "4": 90, + "5": 166, + "6": 18, + "7": 14 + }, + "reverse": true + }, + { + "cut": 11444, + "events": 25135, + "helper": 668, + "helpers": { + "4": 88, + "5": 4, + "8": 14, + "9": 421 + }, + "paid": { + "1": 2203, + "2": 457, + "3": 495, + "4": 90, + "5": 165, + "6": 18, + "7": 14 + }, + "reverse": true + }, + { + "cut": 11488, + "events": 25137, + "helper": 684, + "helpers": { + "4": 89, + "5": 4, + "8": 14, + "9": 420 + }, + "paid": { + "1": 2203, + "2": 457, + "3": 495, + "4": 90, + "5": 164, + "6": 18, + "7": 14 + }, + "reverse": true + } + ], "complete_cost": { "compiler": { "H": 707182000000000, "N": "2^707182000000000", "eta": { - "lower": "0.000000136964415492079857925247", - "upper": "0.000000136964415492079857925248" + "lower": "0.000000135464721119037040631275", + "upper": "0.000000135464721119037040631276" }, "gap": "1/14000000000", "integer_test_exponent": 50513, "logarithm_power": 1024, "theta": "63/64", - "uniform_saving": "21703153/7000000000", + "uniform_saving": "21718273/7000000000", "word_materialized": false }, "full_forward_calls": 18, - "gain": "61/4000000", - "kappa": "62009/20000000", - "kappa_decimal": ".00310045", + "gain": "833/50000000", + "kappa": "310261/100000000", + "kappa_decimal": ".00310261", "margin_at_previous": { - "lower": "3.715057037515374246068780385152", - "upper": "3.715057037515374246068780385153" + "lower": "4.055279776144727228742393529621", + "upper": "4.055279776144727228742393529622" }, "negative_controls": { "old_BIT": "Rejected by outer inequalities", @@ -29,9 +136,9 @@ }, "nonrecursive": { "fixed_scalar_growth_bound": "At most 2^(16*26000) before native factors; a declared constant, not an attained norm.", - "local_paid_rank_mass": 6014, - "local_routes": 5183000, - "local_scalar": 220232, + "local_paid_rank_mass": 5988, + "local_routes": 5169000, + "local_scalar": 219666, "peak_owned_fields": 1, "raw_budget": 1000000000, "raw_scalar_upper": 184647552, @@ -53,82 +160,82 @@ "new_semantic_group_guard": "3/14000000000" }, "margins": { - "boundary_algebraic_matrix": "607688255956593697/196000000000000000000", - "fused_gaussian": "607688255869781091/196000000000000000000", - "global_coordinate_router": "1356447/437500000", - "group_bit_router": "18990258433430659/6125000000000000000", + "boundary_algebraic_matrix": "608111615956563457/196000000000000000000", + "fused_gaussian": "608111615869690371/196000000000000000000", + "global_coordinate_router": "84837/27343750", + "group_bit_router": "1187718027089239/382812500000000000", "group_scans": "6999999999/7000000000", - "main_transform": "607688241956593697/196000000000000000000", + "main_transform": "608111601956563457/196000000000000000000", "microbox_face_corrections": "269500000001/3500000000", "polynomial_products": "13999999999/14000000000", - "sparse_union_movement": "80232688255956593697/196000000000000000000" + "sparse_union_movement": "80233111615956563457/196000000000000000000" }, "parameters": { - "a": "1356447/437500000", - "b": "8681261/2800000000", + "a": "84837/27343750", + "b": "8687309/2800000000", "beta": "13999999997/14000000000", "bit_saving": "17/5000", - "cap_xi": "178232688241956593697/196000000000000000000", - "complex_uniform_saving": "21703153/7000000000", + "cap_xi": "178233111601956563457/196000000000000000000", + "complex_uniform_saving": "21718273/7000000000", "d": "1/14000000000", "epsilon": "13999999999/14000000000", - "kappa": "62009/20000000", - "lambda_": "3987598199/4000000000", - "lambda_prime": "13956593697/14000000000", + "kappa": "310261/100000000", + "lambda_": "3987589559/4000000000", + "lambda_prime": "13956563457/14000000000", "layout": "1/14000000000", - "q": "43406303/14000000000", + "q": "43436543/14000000000", "r0": "1/140000000000", "stop": "1/14000000000", - "tested_saving": "6200901/2000000000" + "tested_saving": "6205221/2000000000" }, "strict_checks": { - "actual_bit_above_effective": "131053/437500000", + "actual_bit_above_effective": "32527/109375000", "actual_logarithmic_gamma_guard": "1/14000000000", - "actual_logarithmic_group_guard": "17767311779043406303/98000000000000000000", + "actual_logarithmic_group_guard": "17766888419043436543/98000000000000000000", "alpha_logarithm_absorption": "1/140000000000", - "boundary_algebraic_matrix_above_kappa": "55956593697/196000000000000000000", - "cap_above_band": "80232688241956593697/196000000000000000000", - "cap_below_cell": "17767311744043406303/196000000000000000000", - "cap_below_phase_cell_power": "213767311758043406303/196000000000000000000", + "boundary_algebraic_matrix_above_kappa": "55956563457/196000000000000000000", + "cap_above_band": "80233111601956563457/196000000000000000000", + "cap_below_cell": "17766888384043436543/196000000000000000000", + "cap_below_phase_cell_power": "213766888398043436543/196000000000000000000", "complex_above_effective": "1/14000000000", - "complex_below_one_over_32": "78818739/2800000000", + "complex_below_one_over_32": "78812691/2800000000", "complex_endpoint": "1/7000000000", "epsilon_below_one": "1/14000000000", "epsilon_positive": "13999999999/14000000000", "fine_prime_halo_umbrella": "7/2", - "fused_gaussian_above_kappa": "55869781091/196000000000000000000", - "gaussian_above_main": "6956593697/98000000000000000000", + "fused_gaussian_above_kappa": "55869690371/196000000000000000000", + "gaussian_above_main": "6956563457/98000000000000000000", "global_coordinate_router_above_kappa": "1/3500000000", "global_gamma_power_slack": "9/140000000000", "group_below_dimension": "1/7000000000", - "group_bit_router_above_kappa": "2183430659/6125000000000000000", - "group_gauge_power_slack": "17767311778343406303/98000000000000000000", + "group_bit_router_above_kappa": "136464239/382812500000000000", + "group_gauge_power_slack": "17766888418343436543/98000000000000000000", "group_key_fits_record": "1/7000000000", "group_positive": "13999999997/14000000000", - "group_scans_above_kappa": "6978296849/7000000000", + "group_scans_above_kappa": "6978281729/7000000000", "halo_covers_generic_inverse_radius": "5", - "improvement_over_user_baseline": "684739790400418148631/500000000000000000000000", + "improvement_over_user_baseline": "685819790400418148631/500000000000000000000000", "lambda_above_internal": "1/28000000000", "lambda_above_sigma": "3/28000000000", "lambda_above_tau": "1/28000000000", "lambda_prime_above_lambda": "1/28000000000", - "lambda_prime_above_leaf": "5591318739/39200000000000000000", - "leaf_saving_above_effective": "2791318739/39200000000000000000", - "main_transform_above_kappa": "41956593697/196000000000000000000", + "lambda_prime_above_leaf": "5591312691/39200000000000000000", + "leaf_saving_above_effective": "2791312691/39200000000000000000", + "main_transform_above_kappa": "41956563457/196000000000000000000", "membership_arithmetic_fits_record": "1/14000000000", - "microbox_face_corrections_above_kappa": "134744574213/1750000000", + "microbox_face_corrections_above_kappa": "134744570433/1750000000", "microbox_halo_volume": "1106000000003/14000000000", "new_complex_uniform_saving_above_b": "1/14000000000", "new_semantic_guard_with_C1_one": "1/14000000000", - "polynomial_products_above_kappa": "13956593699/14000000000", + "polynomial_products_above_kappa": "13956563459/14000000000", "positive_layout_slack": "1/14000000000", "q_below_effective": "1/14000000000", "q_below_internal": "1/14000000000", - "q_below_leaf": "5591318739/39200000000000000000", - "q_positive": "43406303/14000000000", - "short_record_fallback": "2791318739/2800000000", + "q_below_leaf": "5591312691/39200000000000000000", + "q_positive": "43436543/14000000000", + "short_record_fallback": "2791312691/2800000000", "source_axis_superpolynomial": "1/14000000000", - "sparse_union_movement_above_kappa": "79625000055956593697/196000000000000000000", + "sparse_union_movement_above_kappa": "79625000055956563457/196000000000000000000", "stop_below_one": "13999999999/14000000000", "stop_positive": "1/14000000000", "strassen_integer_power_gap": "1951441519231", @@ -141,55 +248,55 @@ "paid": { "1": 41214, "16": 416, - "2": 8262, + "2": 8226, "24": 416, - "3": 8874, + "3": 8910, "32": 416, - "4": 1656, + "4": 1620, "40": 416, "48": 416, - "5": 3024, + "5": 2952, "56": 416, "6": 324, "64": 416, "7": 252, "72": 208 }, - "paid_calls": 66726, - "previous_open_pr5565": "7713/2500000", - "productive_fields": 13048, + "paid_calls": 66618, + "previous_open_pr5601": "61719/20000000", + "productive_fields": 12976, "query_shears": 15, "rank_mass_surplus": 760, "raw_ceiling": { - "derivative_upper": "-741665511346505619707405027113237790341393747177503845065075007/3138550867693340381917894711603833208051177722232017256448", + "derivative_upper": "-741137887493541669102966595261937530737206077417060081274735543/3138550867693340381917894711603833208051177722232017256448", "interval": [ "0", "17/5000" ] }, "raw_headroom": [ - "157681/25000000000000", - "25229/4000000000000" + "511129/100000000000000", + "51113/10000000000000" ], "raw_root_interval": [ - "77511407681/25000000000000", - "12401825229/4000000000000" + "310261511129/100000000000000", + "31026151113/10000000000000" ], - "relative_gain_percent": "7625/15426", + "relative_gain_percent": "4760/8817", "strictification": { "alpha": { - "lower": "0.999999994094860604597376680636", - "upper": "0.999999994094860604597376680637" + "lower": "0.999999995305110567061964349881", + "upper": "0.999999995305110567061964349882" }, "cutoff": 17, "delta": { - "lower": "0.972208404163139976829701213167", - "upper": "0.972208404163139976829701213168" + "lower": "0.968727156203994946664783179549", + "upper": "0.968727156203994946664783179550" }, "floor": 18, "gamma": { - "lower": "0.967537821927968182942254182934", - "upper": "0.967537821927968182942254182935" + "lower": "0.967922322455985687870219506154", + "upper": "0.967922322455985687870219506155" }, "normalized_paid_upper": "5242880004882813/5242880536870912", "power": 1024, @@ -197,7 +304,7 @@ "tail_block": 128, "tail_decay": "39/40", "tail_offset": "1/5", - "tested": "6200901/2000000000" + "tested": "6205221/2000000000" }, "targets": { "1": 36, @@ -206,16 +313,16 @@ "2": 90, "25": 416, "33": 416, - "4": 1602, + "4": 1638, "41": 416, "49": 416, - "5": 198, + "5": 108, "57": 416, "65": 416, "7": 90, "73": 208, "8": 288, - "9": 7416 + "9": 7398 }, "whole_idle_jobs": 3120 }, @@ -225,55 +332,55 @@ "No independent human or proof-kernel acceptance or global optimality is claimed." ], "local": { - "endpoint_coefficients": 571536, + "endpoint_coefficients": 565504, "helpers": { "1": 2, "2": 5, - "4": 89, - "5": 11, + "4": 91, + "5": 6, "7": 5, "8": 16, - "9": 412 + "9": 411 }, "owned_lifetimes": 8, "paid": { "1": 2203, - "2": 459, - "3": 493, - "4": 92, - "5": 168, + "2": 457, + "3": 495, + "4": 90, + "5": 164, "6": 18, "7": 14 }, - "paid_rank_mass": 6014, + "paid_rank_mass": 5988, "peak_owned_fields": 1, - "public_inputs": 748, - "real_scalar_allowance": 220232 + "public_inputs": 744, + "real_scalar_allowance": 219666 }, "local_helper_delta": { "1": 2, "2": 5, - "4": 6, - "5": 6, + "4": 2, + "5": 2, "7": 5, "8": 2, - "9": -13 + "9": -9 }, "native": { - "distinct_maps": 2923, - "helper_normalizers": 1080, + "distinct_maps": 2920, + "helper_normalizers": 1072, "helpers": { "1": 2, "2": 5, - "4": 89, - "5": 11, + "4": 91, + "5": 6, "7": 5, "8": 16, - "9": 412 + "9": 411 }, "main_adapters": 208, "proof": "Every signed Pauli image and exact global phase; frame induction at every positive tensor width", - "recipe_payload_sha256": "b2e6b538f6152ccf0024ca57381e46b2fe6b75b89504d935009dade234cc3f18", + "recipe_payload_sha256": "5bdbaf3edb3e9d13449afbb202fb284533928a276abeb40f6300ef7bf8194a06", "wrong_phase_rejected": true }, "negative_controls": { @@ -284,7 +391,8 @@ "missing_input_basis": "All public and owned rows", "missing_output_basis": "All public and owned rows", "unearned_whole_target": "All public and owned exits", - "unpaid_gaussian": "Complete field and call counts" + "unpaid_gaussian": "Complete field and call counts", + "wrong_boundary_event": "Exact boundary event anchor" }, "physical_caller": { "central_square_columns": 53248, @@ -335,153 +443,127 @@ ] }, "published_source_delta": { - "helpers": { - "8": -1, - "9": 1 + "PR5565": { + "helpers": { + "8": -1, + "9": 1 + }, + "paid": { + "1": -8, + "3": -1, + "4": -2, + "5": 4 + } }, - "paid": { - "1": -8, - "3": -1, - "4": -2, - "5": 4 + "PR5601": { + "helpers": { + "4": 1, + "5": -1 + }, + "paid": { + "2": -2, + "3": 2, + "4": -2, + "5": 1 + } } }, "separate_columns": { "arithmetic": "Dense integer rows with binary denominators; reverse chronology", - "coefficients": 571536, - "columns": 756 + "coefficients": 565504, + "columns": 752 }, "splits": [ { - "cut_after": 13775, - "events": 25155, - "pivot": 648, - "public": 736, - "ranks": [ - 5, - 4 - ] - }, - { - "cut_after": 13765, - "events": 25177, - "pivot": 592, - "public": 737, - "ranks": [ - 5, - 4 - ] - }, - { - "cut_after": 13706, - "events": 25195, - "pivot": 664, - "public": 738, - "ranks": [ - 5, - 4 - ] - }, - { - "cut_after": 13673, - "events": 25217, - "pivot": 680, - "public": 739, - "ranks": [ - 5, - 4 - ] - }, - { - "cut_after": 12526, - "events": 25253, + "cut_after": 12504, + "events": 25173, "pivot": 259, - "public": 740, + "public": 736, "ranks": [ 4, 5 ] }, { - "cut_after": 12448, - "events": 25285, + "cut_after": 12426, + "events": 25205, "pivot": 432, - "public": 741, + "public": 737, "ranks": [ 4, 5 ] }, { - "cut_after": 13961, - "events": 25299, + "cut_after": 13893, + "events": 25219, "pivot": 722, - "public": 742, + "public": 738, "ranks": [ 2, 7 ] }, { - "cut_after": 13647, - "events": 25317, + "cut_after": 13611, + "events": 25237, "pivot": 14, - "public": 743, + "public": 739, "ranks": [ 2, 7 ] }, { - "cut_after": 13648, - "events": 25335, + "cut_after": 13612, + "events": 25255, "pivot": 76, - "public": 744, + "public": 740, "ranks": [ 2, 7 ] }, { - "cut_after": 13648, - "events": 25369, + "cut_after": 13612, + "events": 25287, "pivot": 345, - "public": 745, + "public": 741, "ranks": [ 2, 7 ] }, { - "cut_after": 13637, - "events": 25419, + "cut_after": 13600, + "events": 25337, "pivot": 573, - "public": 746, + "public": 742, "ranks": [ 2, 7 ] }, { - "cut_after": 12078, - "events": 25445, + "cut_after": 12055, + "events": 25363, "pivot": 405, - "public": 747, + "public": 743, "ranks": [ 8, 1 ] }, { - "cut_after": 12610, - "events": 25475, + "cut_after": 12587, + "events": 25393, "pivot": 225, - "public": 748, + "public": 744, "ranks": [ 8, 1 ] } ], - "status": "PASS_P104_HELPER_SUBSPACE_KAPPA_00310045" + "status": "PASS_P104_HELPER_SUBSPACE_KAPPA_00310261" } diff --git a/research/p104-helper-subspace-splits/SOURCES.json b/research/p104-helper-subspace-splits/SOURCES.json index f83bf3c818..4395ffcd48 100644 --- a/research/p104-helper-subspace-splits/SOURCES.json +++ b/research/p104-helper-subspace-splits/SOURCES.json @@ -99,6 +99,27 @@ "git_blob": "4ebe6fcb7adf319bf6b247cf23d89eb1ca4cd914", "sha256": "3d62828f53e654e3db218bf4611a47aed4a677d48043713dc004db0f8a32990d", "pin": "head:bf64e66656843a64e798b8374cd9f53add3f6f46:research/p104-helper-subspace-splits/inputs/PR5565-WORD.json.gz" + }, + { + "path": "research/p104-helper-subspace-splits/inputs/PR5601-WORD.json.gz", + "usage": "input", + "git_blob": "3c9a5ce8969f40f03724a73d34f984dd17efde96", + "sha256": "ac81682679d1eb628a2a0a330b55a7a79722531ca163cd565a3eba5d87589979", + "pin": "head:55914a0de83df255bd7e7071d79ad04b81ca1070:research/p104-helper-subspace-splits/inputs/PR5601-WORD.json.gz" + }, + { + "path": "research/p104-helper-subspace-splits/inputs/PR5602-construct.py", + "usage": "input", + "git_blob": "ef5936ca89d6502d7f6af1ce6903d8500c117401", + "sha256": "2360066b0a1390c60a86d9788ada1504478e7e48bbfe3fcdf27a5563379fc001", + "pin": "head:0bccb2ff858db877119217f7d98409ee6a24ccce:research/p104-helper-subspace-splits/inputs/PR5602-construct.py" + }, + { + "path": "research/p104-helper-subspace-splits/inputs/PR5602-WITNESS.json", + "usage": "input", + "git_blob": "8073b3c9772a4a7c94e07d613c2f5c45b1c650fc", + "sha256": "e4dfc526453eb9d232772ffdb587fff1923e247341405aee031318b0fb9cb638", + "pin": "head:0bccb2ff858db877119217f7d98409ee6a24ccce:research/p104-helper-subspace-splits/inputs/PR5602-WITNESS.json" } ], "external_inputs": [ @@ -117,6 +138,30 @@ "source_path": "research/p104-commuting-contact/WORD.json.gz", "sha256": "3d62828f53e654e3db218bf4611a47aed4a677d48043713dc004db0f8a32990d", "git_blob": "4ebe6fcb7adf319bf6b247cf23d89eb1ca4cd914" + }, + { + "local_path": "inputs/PR5601-WORD.json.gz", + "source_repository": "aliromman/integer-mult-bounds", + "source_commit": "8f7e870b22885a367b347dc12791da98fd53f83d", + "source_path": "research/p104-coupled-frame-step/WORD.json.gz", + "sha256": "ac81682679d1eb628a2a0a330b55a7a79722531ca163cd565a3eba5d87589979", + "git_blob": "3c9a5ce8969f40f03724a73d34f984dd17efde96" + }, + { + "local_path": "inputs/PR5602-construct.py", + "source_repository": "aliromman/integer-mult-bounds", + "source_commit": "6c224aa720203c4f4615e6538d8038a275387db8", + "source_path": "research/p104-coupled-helper-bases/construct.py", + "sha256": "2360066b0a1390c60a86d9788ada1504478e7e48bbfe3fcdf27a5563379fc001", + "git_blob": "ef5936ca89d6502d7f6af1ce6903d8500c117401" + }, + { + "local_path": "inputs/PR5602-WITNESS.json", + "source_repository": "aliromman/integer-mult-bounds", + "source_commit": "6c224aa720203c4f4615e6538d8038a275387db8", + "source_path": "research/p104-coupled-helper-bases/WITNESS.json", + "sha256": "e4dfc526453eb9d232772ffdb587fff1923e247341405aee031318b0fb9cb638", + "git_blob": "8073b3c9772a4a7c94e07d613c2f5c45b1c650fc" } ], "code_derivation": [ diff --git a/research/p104-helper-subspace-splits/SPLITS.json b/research/p104-helper-subspace-splits/SPLITS.json index 5108daabf7..62bdf08179 100644 --- a/research/p104-helper-subspace-splits/SPLITS.json +++ b/research/p104-helper-subspace-splits/SPLITS.json @@ -1,118 +1,6 @@ [ { - "cut_after": 13775, - "frame": 120, - "pivot": 648, - "a": { - "652": "1" - }, - "b": { - "652": "1", - "648": "-1", - "650": "1", - "649": "-1" - }, - "c": { - "652": "1" - }, - "d": { - "652": "1", - "205": "-2", - "648": "-1", - "650": "1", - "649": "-1" - }, - "ranks": [ - 5, - 4 - ] - }, - { - "cut_after": 13765, - "frame": 1053, - "pivot": 592, - "a": { - "596": "1" - }, - "b": { - "596": "1", - "594": "1", - "592": "-1", - "593": "1" - }, - "c": { - "596": "1" - }, - "d": { - "596": "1", - "594": "1", - "188": "-1", - "592": "-1", - "593": "1" - }, - "ranks": [ - 5, - 4 - ] - }, - { - "cut_after": 13706, - "frame": 1051, - "pivot": 664, - "a": { - "668": "1" - }, - "b": { - "668": "1", - "665": "1", - "666": "-1", - "664": "1" - }, - "c": { - "668": "1" - }, - "d": { - "668": "1", - "115": "2", - "665": "1", - "666": "-1", - "664": "1" - }, - "ranks": [ - 5, - 4 - ] - }, - { - "cut_after": 13673, - "frame": 1049, - "pivot": 680, - "a": { - "684": "1" - }, - "b": { - "684": "1", - "681": "1", - "680": "-1", - "682": "1" - }, - "c": { - "684": "1" - }, - "d": { - "684": "1", - "681": "1", - "126": "2", - "680": "-1", - "682": "1" - }, - "ranks": [ - 5, - 4 - ] - }, - { - "cut_after": 12526, + "cut_after": 12504, "frame": 306, "pivot": 259, "a": { @@ -144,7 +32,7 @@ ] }, { - "cut_after": 12448, + "cut_after": 12426, "frame": 516, "pivot": 432, "a": { @@ -178,7 +66,7 @@ ] }, { - "cut_after": 13961, + "cut_after": 13893, "frame": 424, "pivot": 722, "a": { @@ -205,7 +93,7 @@ ] }, { - "cut_after": 13647, + "cut_after": 13611, "frame": 462, "pivot": 14, "a": { @@ -233,7 +121,7 @@ ] }, { - "cut_after": 13648, + "cut_after": 13612, "frame": 252, "pivot": 76, "a": { @@ -261,7 +149,7 @@ ] }, { - "cut_after": 13648, + "cut_after": 13612, "frame": 391, "pivot": 345, "a": { @@ -284,7 +172,6 @@ "350": "-1/2", "343": "1/2", "93": "-1", - "341": "-1", "347": "1/2", "349": "1/2", "348": "1/2", @@ -296,7 +183,7 @@ ] }, { - "cut_after": 13637, + "cut_after": 13600, "frame": 603, "pivot": 573, "a": { @@ -314,7 +201,6 @@ }, "d": { "710": "1/2", - "115": "1", "572": "1", "498": "2", "306": "-1", @@ -327,6 +213,7 @@ "456": "2", "252": "-1", "247": "-1", + "115": "1", "311": "-2", "205": "-1", "126": "-1", @@ -340,7 +227,7 @@ ] }, { - "cut_after": 12078, + "cut_after": 12055, "frame": 477, "pivot": 405, "a": { @@ -372,7 +259,7 @@ ] }, { - "cut_after": 12610, + "cut_after": 12587, "frame": 267, "pivot": 225, "a": { diff --git a/research/p104-helper-subspace-splits/TASK.json b/research/p104-helper-subspace-splits/TASK.json index a230fe5b90..b468ddbbcf 100644 --- a/research/p104-helper-subspace-splits/TASK.json +++ b/research/p104-helper-subspace-splits/TASK.json @@ -46,33 +46,27 @@ ] }, "scope_status": "changed", - "actual_scope": "Change the independent P104 helper basis and split 13 targets into two independent targets at common-frame cuts. Verify a complete conditional kappa gain on the published PR5565 word.", + "actual_scope": "Compose five fixed published PR5602 boundary relations with the released PR5601 word, then split nine independent helper targets. Verify the complete conditional kappa gain.", "scope_change_reason": "The donor explicitly requested a different mechanism and a kappa gain. This changes the scalar word, independent input count and helper target contract. It is outside fixed-endpoint retiming and the historical frozen provider catalogue. The card classifies this assigned work; no task was rerolled.", - "bottleneck_link": "At unchanged recursive paid cost relative to PR5565, 13 independent target splits strictly increase the concave target moment. Every new input has an explicit returned Gaussian target.", + "bottleneck_link": "Five fixed boundary relations remove paid H5 calls and nine independent target splits increase the concave target moment. The complete physical caller charges all changed helpers, fields, native maps and compiler costs.", "budget_minutes": null, "stop_rule": "Require full arbitrary-input and native identities and a complete improved kappa. Stop the finite discovery scan after no further tested split remains; do not claim global optimality.", "outcome": "completed", - "evidence": "SPLITS.json, PROOF.md and RESULT.json bind each cut, the complete word, native maps and full price. VALIDATION.md records executed checks.", + "evidence": "BOUNDARIES.json, SPLITS.json, PROOF.md and RESULT.json bind the fixed source relations, independent cuts, complete word, native maps and full price. VALIDATION.md records the executed checks.", "author": "Ali Romman with OpenAI Codex assistance", "ai_assistance": "Substantial OpenAI Codex assistance. The same assistant constructed and checked the result. No subagents or independent human review.", "open_questions": [ { "question": "Can an independent reviewer accept the new helper basis, every returned independent target and the complete conditional price?", "why_it_matters": "Author-side exact checks do not replace independent scientific review.", - "first_step": "Check the first rank-one split in PROOF.md, then replay all cuts, native maps and the complete price.", + "first_step": "Check the five fixed boundary relations and the first rank-one split in PROOF.md, then replay all cuts, native maps and the complete price.", "blocked_by": "No missing technical input; independent review is pending." }, { "question": "Can a different compatible cut order or changed common frame support more independent target splits?", "why_it_matters": "The finite exact screen does not prove a global maximum.", - "first_step": "Use the new word and test both prefix and suffix support before assigning credit. Coordinate with Discussion5575 for any changed frame itinerary.", + "first_step": "Use the final word and test both prefix and suffix support before assigning target credit. Check live Discussion scopes before changing bases or frame paths.", "blocked_by": "Every added target must have a clean independent input/output contract and a complete caller bill." - }, - { - "question": "Can the fifteen released target splits compose with the six paid-boundary changes in the parallel Discussion claim?", - "why_it_matters": "The target gain and paid gain could be compatible, but the input bases and cuts must be checked together.", - "first_step": "Use the public handoff at discussioncomment-19183908. The parallel claim has released its word at 8384fb9eda5a2fd47556364b26185f3ba3cbd050 and is testing the earlier fifteen-split component. Coordinate there before testing any further composition.", - "blocked_by": "The parallel claim owns the paid-boundary synthesis. This package does not assert a combined certificate with that work." } ] } diff --git a/research/p104-helper-subspace-splits/VALIDATION.md b/research/p104-helper-subspace-splits/VALIDATION.md index 7f73fd1454..2a210131ff 100644 --- a/research/p104-helper-subspace-splits/VALIDATION.md +++ b/research/p104-helper-subspace-splits/VALIDATION.md @@ -7,45 +7,55 @@ The scientific base is canonical main ## Current composition -The direct isolated normal replay passed with explicit artifact generation: +The direct isolated normal replay passed with artifact generation: ```sh python3 -I -B research/p104-helper-subspace-splits/verify.py --write ``` -It checked 13 prefix and suffix witnesses, each complete arbitrary-input -interface, 571,536 final transpose coefficients, 2,923 exact native maps, -1,080 helper normalizers, 208 main adapters and the complete physical caller. -Two exact moment engines, all compiler conditions, 54 strict outer conditions -and four functional conditions passed. All eight local/controller mutation -controls rejected. The retained wrong-phase, old-cutoff and old-BIT controls -also rejected. The raw crossing is in -(0.00310045630724, 0.00310045630725). - -The verifier authenticates 13 live inputs before importing any source code. -It replays both retained source words and checks the exact paid and helper -deltas supplied by PR5565. All new splits preserve the PR5565 paid profile. -The new local paid rank mass is 6014 and enters the native growth bound. -The exact discovery run tested 52 final boundary groups and found no further +It checked five fixed published boundary relations and nine independent +prefix/suffix cuts. Every intermediate arbitrary-input interface passed. +The final checks cover 565,504 transpose coefficients, 2,920 exact native +maps, 1,072 helper normalizers, 208 main adapters and the complete physical +caller. The complete subsequence of owned operations is unchanged by the +boundary changes; all eight COPY paths remain charged. + +Two exact moment engines, every compiler condition, 54 strict outer conditions +and four functional conditions passed. Nine local/controller mutation controls +rejected, as did the retained wrong-phase, old-cutoff and old-BIT controls. +The exact raw crossing is in (0.00310261511129, 0.00310261511130). +The native growth bound uses the new local paid rank mass 5988. + +The verifier authenticates 16 live inputs before source imports. It replays +PR5580, PR5565 and PR5601 and checks the exact source deltas. The retained +PR5602 constructor and witness are byte-exact copies. That constructor uses +this package's rational local checker. Only the first five published boundary +relations are applied, at newly checked event positions. + +The final discovery run tested 47 boundary groups and found no further candidate in its finite basis-pair class. This is not a global optimum. +The registered normal/optimized replay, committed-byte check and fresh +read-only Git-free replay are pending for this final composition. -Registered normal/optimized replay is in progress. The committed-byte check -and fresh read-only Git-free export will follow. These checks are not yet -claimed for this composition in this revision. - -## Retained evidence +## Retained evidence and limits The earlier fifteen-split component on PR5580 passed normal, optimized, registered and read-only Git-free replay at scientific commit `31a4de233bbdd65c04c63dc3398ecf0eed8e1375`. That evidence applies to its -0.00309839 claim. It is not substituted for the new composition checks. +0.00309839 claim. The PR5565 composition at +`09dd0965711ca7eeb169057a420abab1c9052137` passed direct and registered +normal/optimized replay for 0.00310045. The PR5601 composition passed a +complete direct check for 0.00310120 before the final boundary composition. +Those checks are not substituted for the final checks above. The source copies are pinned to their retained paths at ancestor commits -`29fe88ba218b5d2192d8e31f07a01d1141afdacd` (PR5580) and -`bf64e66656843a64e798b8374cd9f53add3f6f46` (PR5565). Each SHA256 and Git blob -equals the recorded published source. Registered replay needs no cached -unmerged-branch objects. Full-history preflight was not run because this -checkout is shallow. +`29fe88ba218b5d2192d8e31f07a01d1141afdacd` (PR5580), +`bf64e66656843a64e798b8374cd9f53add3f6f46` (PR5565), +`55914a0de83df255bd7e7071d79ad04b81ca1070` (PR5601), and +`0bccb2ff858db877119217f7d98409ee6a24ccce` (PR5602 constructor and witness). +Each SHA256 and Git blob equals its recorded published source. Registered +replay needs no cached unmerged-branch objects. Full-history preflight was +not run because this checkout is shallow. Independent human review and hosted CI are pending. No complete rounded multiplier or enormous uniform word was materialized. diff --git a/research/p104-helper-subspace-splits/VERIFY.json b/research/p104-helper-subspace-splits/VERIFY.json index f02fe9b970..43a3385a89 100644 --- a/research/p104-helper-subspace-splits/VERIFY.json +++ b/research/p104-helper-subspace-splits/VERIFY.json @@ -16,7 +16,10 @@ "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py", "research/query-thinned-controllers/RESULT.json", "research/p104-helper-subspace-splits/inputs/PR5580-WORD.json.gz", - "research/p104-helper-subspace-splits/inputs/PR5565-WORD.json.gz" + "research/p104-helper-subspace-splits/inputs/PR5565-WORD.json.gz", + "research/p104-helper-subspace-splits/inputs/PR5601-WORD.json.gz", + "research/p104-helper-subspace-splits/inputs/PR5602-construct.py", + "research/p104-helper-subspace-splits/inputs/PR5602-WITNESS.json" ], "commands": [ { @@ -26,7 +29,7 @@ "{package}/verify.py" ], "timeout_seconds": 600, - "checks": "Check all 13 independent cuts, every rational row and reverse column, native maps, complete caller and invoice, two moment engines, compiler and outer predicates; reject false inputs, outputs, target credit and cost." + "checks": "Check five published boundary changes and nine independent cuts, every rational row and reverse column, native maps, complete caller and invoice, two moment engines, compiler and outer predicates; reject false inputs, outputs, target credit and cost." }, { "argv": [ @@ -36,7 +39,7 @@ "{package}/verify.py" ], "timeout_seconds": 600, - "checks": "Check all 13 independent cuts, every rational row and reverse column, native maps, complete caller and invoice, two moment engines, compiler and outer predicates; reject false inputs, outputs, target credit and cost." + "checks": "Check five published boundary changes and nine independent cuts, every rational row and reverse column, native maps, complete caller and invoice, two moment engines, compiler and outer predicates; reject false inputs, outputs, target credit and cost." } ] } diff --git a/research/p104-helper-subspace-splits/WORD.json.gz b/research/p104-helper-subspace-splits/WORD.json.gz index e325091e3051afe37a2d9c82f85afe9028510edb..099522d7fcd741974db4be09b50a74848c3e99c3 100644 GIT binary patch delta 100622 zcmZU)1z20n^EQk_af&;|i@UoOclY8_q_`iXxO;JTcPmzkyEQm%aSiVBrO)&G+xz93 z+h7LvboGVELRt9-;N`;U^+ojQ2)Ipu zJ#czq*?DOLE=`^W^k3@wc3z!CU7pDs7KiQ!UhmZ6j+|(6M5o4p6qlF!%MZdp^X2f< zHZ>z%#=3<^(z2WtT}BRs=yi!^h$`y~+8)Uns5CCST~k-l=?RY>%4w@a39uksQ`^(& z36AD|UQu50m}^aL&1rUkp>q%%eUSU9(io6*om`lQ^IW`7CoTH^L2gzh>a%)GvRO7x zkzq+}@~3QzEoy-H(ur=FZ}f@!GI>IULv-}1_$>Lm3UaStp9;ro2ow46JynkA#eGq> z=<$=aPy7yk+g9=6SE5h~cF`IQK}%i>Nc06={@jmvaBx@^mfKbgMQf|yXBJbGhA zA9XLg+@)HtF57gRa$KztpU%e5vYrU;aR2c@4M-+`olo0;*&Kwcs(9wrH=ItTHh8qw z*y_bLA3g-;=T-n^@GI5GirUL~@dIJuwWz@w@NzyaN;WB=w7woO`Kq@y*7(c|B)g)IR*a`78jKI4>!o=lS~F z@GkQ;3i@$a#xaW6Vz$-$g>|X!yt$G*#C!1%hNMSr(jH4a+$4GL^LhIG58>N1kBRBM 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