diff --git a/research/partial-cache-minimax-floor/INPUTS.json b/research/partial-cache-minimax-floor/INPUTS.json new file mode 100644 index 0000000000..095c1bc3e4 --- /dev/null +++ b/research/partial-cache-minimax-floor/INPUTS.json @@ -0,0 +1,42 @@ +[ + { + "local": "source/provider.json", + "path": "research/native-rank8-helper-provider/PROVIDER.json", + "repository": "CrocSwap/integer-mult-bounds", + "commit": "32890bc5de034ab8fc93ac88ead7279a6a416d04", + "sha256": "676de7551d3364598f4a7e29ae97cae0e4364348786bbe70435b84294ba7dd65", + "git_blob": "0afd30ed01202eb6ce62462dcf8bc9164f3b0455" + }, + { + "local": "source/provider-proof.md", + "path": "research/native-rank8-helper-provider/PROOF.md", + "repository": "CrocSwap/integer-mult-bounds", + "commit": "32890bc5de034ab8fc93ac88ead7279a6a416d04", + "sha256": "2d59282f3b5e9fb848d0099ce91729fa433162e6975f877a441e2ab4f57a29c5", + "git_blob": "5cbfc4fd02dce926c3d235f1549bdb2035dea088" + }, + { + "local": "source/normalizers.json", + "path": "research/coded-native-caller/NORMALIZERS.json", + "repository": "CrocSwap/integer-mult-bounds", + "commit": "32890bc5de034ab8fc93ac88ead7279a6a416d04", + "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da", + "git_blob": "bca92c222c395d3d75c047fbb678f3cd0947c60f" + }, + { + "local": "source/observer-proof.md", + "path": "research/partial-cache-history-observer/PROOF.md", + "repository": "JoyboyBrian/integer-mult-bounds", + "commit": "da7f5a0c005130873f45c8e5073cd5c989cd5feb", + "sha256": "11a34c0fe4b5a75b855ea73a78627de0d50a49e6b4222416737571a0f4d9afdc", + "git_blob": "4cfe97e3a4fbd2a6a8c5f2260b68550e0d794e70" + }, + { + "local": "source/kernel.json", + "path": "research/partial-cache-history-observer/KERNEL.json", + "repository": "JoyboyBrian/integer-mult-bounds", + "commit": "da7f5a0c005130873f45c8e5073cd5c989cd5feb", + "sha256": "def77e3bcd50a4c992d9fecc660bbbc9dcdad37da22151351e346f62c9c4593f", + "git_blob": "92ca0f83330a8e6ef265ca05df2b5f6b472af9a0" + } +] diff --git a/research/partial-cache-minimax-floor/README.md b/research/partial-cache-minimax-floor/README.md new file mode 100644 index 0000000000..ad504234f8 --- /dev/null +++ b/research/partial-cache-minimax-floor/README.md @@ -0,0 +1,148 @@ +# A physical error floor for the partial-cache observer + +For every positive tensor width, the exact observation channel in PR #5498 +cannot approximate its coupled-query target uniformly on the physical input +unit ball to error less than `1/sqrt(19)`. The decoder can be nonlinear and +can use the complete supplied history. A randomized decoder has worst-case +expected squared error at least `1/19`. + +This is a new quantitative application of an existing exact kernel. It uses +the actual PR #5402 entrance basis. It is sharp on the specified kernel +subspace, not a claim about the optimum on the full input ball. No new kappa, +paid-call bound or complete multiplication theorem follows. + +## Source and observation contract + +Use canonical main `32890bc5de034ab8fc93ac88ead7279a6a416d04`, priority revision 7. +JoyboyBrian's [PR #5498](https://github.com/CrocSwap/integer-mult-bounds/pull/5498), +head `da7f5a0c005130873f45c8e5073cd5c989cd5feb`, supplies the +[exact kernel and proof](https://github.com/JoyboyBrian/integer-mult-bounds/blob/da7f5a0c005130873f45c8e5073cd5c989cd5feb/research/partial-cache-history-observer/PROOF.md). +Dillon Amburgey's [PR #5402](https://github.com/CrocSwap/integer-mult-bounds/pull/5402) +supplies the [physical provider](https://github.com/CrocSwap/integer-mult-bounds/blob/32890bc5de034ab8fc93ac88ead7279a6a416d04/research/native-rank8-helper-provider/PROOF.md). +The five exact source copies and their Git/SHA256 pins are in `source/` and +`INPUTS.json`. Source copies retain their original bytes and attribution. + +The observer sees every full-nine-axis-frame value during the raw backward +word and all eight partial-frame endpoint caches. It sees 5,897 full-frame +events and the caches at roles 633 through 640. It does not see other main +values, other partial histories, original helper retractions or additional +paid responses. All 632 original inputs are independent. The nine owned +inputs can be zero for the lower-bound instances. + +The predecessor proves that its scalar vector k annihilates this entire +channel in the free-word algebra. Thus k times any field v has zero +observation at every positive width. It also proves that the actual physical +target b changes only in mode one, by + + delta b_1 = -2 Km_1^-1 R v. (1) + +This complete history identity is a credited proof premise. We do not rerun +its 21,473-record history interpreter. The native map R is the full Gaussian +on nine axes. It and the monomial Km are unitary in the Euclidean field norm. +Their all-width physical realization remains a source assumption. + +## Pull the witness back through the physical entrance + +Let V be the complex field space at one fixed positive width, with its usual +Euclidean norm. Give the physical input bank the direct-sum Euclidean norm. +Let L be the provider's scalar helper entrance basis. The checker obtains + + sum_X k_j^2 = 60, sum_Y k_j^2 = 12, + sum_H k_j^2 = 68, L^-1 k_H = -4 e_225. (2) + +It checks (2) both by the supplied exit basis and by reversing and inverting +every entrance operation. A forward application of L to -4 e_225 gives +exactly the 44 nonzero helper entries in the source kernel. Both full inverse +products are also checked on all 122 basis owners. + +Physical main inputs use unitary monomial entrance wrappers B_X,j and B_Y,j. +The raw X role has a unitary native birth frame F_X,j; its raw logical value +is F_X,j^-1 B_X,j x_phys,j. The raw Y roles have ground birth frames. Set +the physical X displacement to k_j B_X,j^-1 F_X,j v, and the physical Y +displacement to k_j B_Y,j^-1 v. The backward conjugation convention is kept +in F_X,j. Each native frame is a product of unitary Gaussian factors, so +this extra X frame preserves the norm. It is not omitted from J. +The physical helper entrance applies 2 Km_1 on role 225 before L. Therefore +set the sole nonzero physical helper displacement to -2 Km_1^-1 v. All other +physical helpers and all owned inputs have zero displacement. Call this +physical input map J:V -> input bank. Its raw image is precisely k v, and + + O J = 0, ||J v||^2 = (60+12+4)||v||^2 = 76||v||^2, + T J v = (0,-2 Km_1^-1 R v,0,...,0), + ||T J v||^2 = 4||v||^2. (3) + +Here O is the stated observation channel and T is the eight-mode physical +target. The 61 nonzero physical roles comprise 57 X, three Y and one helper. +Using the raw norm 140 would give the weaker squared ratio 1/35. Treating the +helper basis as an isometry would be incorrect. Formula (3) accounts for its +actual nonunitary scalar basis and its factor two. + +The scalar coefficients in (2) act once. They are not raised to the tensor +width. The unitary one-column address maps remain unitary under tensor powers. +Thus 76 and 4 in (3) hold at every positive width. + +## Minimax proof + +Choose any unit v in V and put u=Jv/sqrt(76), t=TJv/sqrt(76). Both u and -u +are in the physical input unit ball. Their complete observations are zero, +and their targets are t and -t, with ||t||=1/sqrt(19). + +A deterministic decoder must give the same output z on both inputs. The +triangle inequality gives + + max(||z-t||, ||z+t||) >= ||t|| = 1/sqrt(19). (4) + +For a randomized decoder the output distribution is also identical for the +two inputs. The parallelogram identity gives, pointwise in its randomness, + + (||z-t||^2 + ||z+t||^2)/2 = ||z||^2 + ||t||^2. + +Taking expectations proves that at least one input has expected squared +error at least 1/19. Infinite second moment already satisfies the bound. +No assumption of linear postprocessing or a bounded instruction count enters +this argument. + +On the restricted domain `{Jv: ||Jv||<=1}`, the constant-zero decoder has +maximum error exactly 1/sqrt(19), by (3). It also attains squared risk 1/19. +This proves sharpness on that subspace. It supplies only a lower bound on +the full physical unit ball. It does not show a sharp global optimum. + +## Verification and limitations + +Run `python3.12 -B scripts/research_package.py --package research/partial-cache-minimax-floor`. +Python 3.12 and its standard library suffice. Both registered commands use +isolated, warning-strict Python, normally and under `-O`. Each checks five +source copies, 244 basis inverse products, 115,200 literal monomial address +actions, the exact native one-axis unitarity identity, 117 rational complex +square-loss identities and 14 rejection controls. The output is +`PASS_PARTIAL_CACHE_MINIMAX_FLOOR`. + +The all-width statement is the written proof, not an extrapolation from +finite address tests. The finite tests bind the consumed basis, unitary +wrappers and target coefficients. The complete predecessor history proof and +native semantics are explicit premises; their full suites, a cold selected +replay, human review and a proof-kernel check were not run. This bound uses +continuous complex inputs and Euclidean error. It does not establish a bound +for a restricted integer lattice, a particular rounding algorithm, paid work, +whole-machine observations or the changed selected completion. + +## Open next questions + +- Can one additional retained observation separate the subspace J(V)? This + would change the observer contract. Start with a versioned partial-history + row and compute its action on J; physical availability and retention are + still required. +- What is the full norm of T restricted to ker O? This determines the sharp + linear-information error on the full ball. Start with a fixed-width exact + observation matrix. Its size and an all-width spectral argument remain open. +- Can admissible discrete inputs realize a comparable pair? Start with the + actual input lattice and all entrance denominators. The continuous bound + alone does not answer that precision question. + +Credit JoyboyBrian (@JoyboyBrian) for the exact partial-cache kernel and target +binding; Dillon Amburgey (@dillona) for the native coupled provider and basis; +and the retained Mark/Matarener, THU New Media Research Center, zxv, Cao Yifan, +Cinna Davis, Dugongue, Chris R, native and compiler lineage in those sources. +Ali Romman (@aliromman) supplies this norm calculation and minimax application, +with substantial OpenAI Codex assistance. Apache-2.0. No independent human or +formal-kernel acceptance is claimed. diff --git a/research/partial-cache-minimax-floor/SOURCES.json b/research/partial-cache-minimax-floor/SOURCES.json new file mode 100644 index 0000000000..e6d294e5bf --- /dev/null +++ b/research/partial-cache-minimax-floor/SOURCES.json @@ -0,0 +1,60 @@ +{ + "schema_version": 1, + "base_commit": "32890bc5de034ab8fc93ac88ead7279a6a416d04", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "fc3d4ba105e1f097d0d7d051a308281e86ab1446", + "sha256": "66974efdced4083c00025f97d95d83909a226cdf801edb9301c195c6641f6903" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602", + "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72" + }, + { + "path": "research/native-rank8-helper-provider/PROVIDER.json", + "usage": "provenance", + "git_blob": "0afd30ed01202eb6ce62462dcf8bc9164f3b0455", + "sha256": "676de7551d3364598f4a7e29ae97cae0e4364348786bbe70435b84294ba7dd65" + }, + { + "path": "research/native-rank8-helper-provider/PROOF.md", + "usage": "provenance", + "git_blob": "5cbfc4fd02dce926c3d235f1549bdb2035dea088", + "sha256": "2d59282f3b5e9fb848d0099ce91729fa433162e6975f877a441e2ab4f57a29c5" + }, + { + "path": "research/coded-native-caller/NORMALIZERS.json", + "usage": "provenance", + "git_blob": "bca92c222c395d3d75c047fbb678f3cd0947c60f", + "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da" + }, + { + "path": "research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz", + "usage": "provenance", + "git_blob": "46d929df83817b85a5387bcdb9745e0627d6366e", + "sha256": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05" + } + ], + "external_provenance": [ + { + "local": "source/observer-proof.md", + "path": "research/partial-cache-history-observer/PROOF.md", + "repository": "JoyboyBrian/integer-mult-bounds", + "commit": "da7f5a0c005130873f45c8e5073cd5c989cd5feb", + "sha256": "11a34c0fe4b5a75b855ea73a78627de0d50a49e6b4222416737571a0f4d9afdc", + "git_blob": "4cfe97e3a4fbd2a6a8c5f2260b68550e0d794e70" + }, + { + "local": "source/kernel.json", + "path": "research/partial-cache-history-observer/KERNEL.json", + "repository": "JoyboyBrian/integer-mult-bounds", + "commit": "da7f5a0c005130873f45c8e5073cd5c989cd5feb", + "sha256": "def77e3bcd50a4c992d9fecc660bbbc9dcdad37da22151351e346f62c9c4593f", + "git_blob": "92ca0f83330a8e6ef265ca05df2b5f6b472af9a0" + } + ] +} diff --git a/research/partial-cache-minimax-floor/TASK.json b/research/partial-cache-minimax-floor/TASK.json new file mode 100644 index 0000000000..80cc79abc9 --- /dev/null +++ b/research/partial-cache-minimax-floor/TASK.json @@ -0,0 +1,74 @@ +{ + "schema_version": 1, + "task_id": "uniform-transfer-audit", + "priority_revision": 7, + "base_commit": "32890bc5de034ab8fc93ac88ead7279a6a416d04", + "original_card": { + "id": "uniform-transfer-audit", + "question": "Does one quantified step of the proposed #4100 all-size construction hold at its actual caller?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/unconditional-batched-crt/README.md" + ], + "methods": [ + "Prove one missing implication with explicit quantified hypotheses.", + "Find an exact counterexample at the claimed interface boundary." + ], + "acceptance_gate": "Identify the proposition and what would change downstream; do not equate a finite replay with a universal proof.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read PROOF.md and AUDIT.md in #4100. Select one distinct obligation: CRT total repair, native/free-algebra lifting, precision/conditioning, or complete fixed-tape cost. This is an author-submitted proof, not an accepted unconditional theorem.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "Check live handoffs; name one proposition, its caller, quantified domain and dependency closure. Independently prove the implication or exhibit a precise gap/counterexample. Prioritize CRT.md total repair or COMPLEX.md free-algebra lift only if unclaimed. Stop at the chosen obligation; do not substitute finite samples or root arithmetic for an all-size proof, or launch the complete package by default.", + "bottleneck_link": "Finite supplier improvements are useful only under the retained transfer obligations.", + "allowed_variations": [ + "One CRT repair, native lift, precision/conditioning or tape-cost proposition, with its exact caller." + ], + "scope_change_triggers": [ + "Replacing a quantified obligation with another finite smoke test.", + "Treating archive intake, an author PASS receipt or a finite composed fixture as discharge of the universal hypotheses." + ], + "overlap_terms": [ + "uniform transfer", + "all-size", + "precision", + "4100", + "unconditional-batched-crt" + ], + "existing_checks": [ + { + "scope": "PR #4100: proposed unconditional construction and finite checks, without independent acceptance.", + "evidence": "research/unconditional-batched-crt/README.md", + "remaining": "Independent proof audit of one caller-bound all-size implication; all other premises remain explicit.", + "status": "author-checked", + "source_commit": "337d04939571a637aeab54a0f58f54fde811663a", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + "scope_status": "changed", + "actual_scope": "Quantify the physical unit-ball approximation error for the exact partial-cache observer of PR #5498.", + "scope_change_reason": "A completed live observer result leaves its approximation boundary open. Bind that boundary to the actual native provider entrance, as required by priority revision 7.", + "bottleneck_link": "This excludes an approximate passive decoder under a concrete physical observation contract.", + "budget_minutes": 60, + "stop_rule": "Stop after the physical norm, minimax proof and exact controls; do not extend the observer or infer a paid-call bound.", + "outcome": "completed", + "evidence": "README.md and registered normal/optimized verify.py checks.", + "author": "Ali Romman", + "ai_assistance": "Substantial OpenAI Codex assistance.", + "open_questions": [ + { + "question": "Which additional retained observation separates J(V)?", + "why_it_matters": "A changed observer can evade this bound.", + "first_step": "Evaluate a versioned partial-history row on J.", + "blocked_by": "Physical availability and retention costs remain open." + } + ] +} diff --git a/research/partial-cache-minimax-floor/VERIFY.json b/research/partial-cache-minimax-floor/VERIFY.json new file mode 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+ ], + "recoding_bill": {"forward_prefix_component_l1_upper":57,"forward_update_coefficient":"-1/4","inverse_output_prefix_component_l1_upper":"69/13","inverse_prefix_component_l1_upper":56,"inverse_update_coefficient":"-1/52","monomial_field_maps":224,"output_scaled_adds":448,"owned_fields":8,"owned_initial_clears":8,"owned_terminal_clears":8,"signed_mode_adds":448}, + "schema": "coded-native-real-normalizers/1", + "scope": "Exact physical central ABI and local gauges; not full-controller or multiplication admission.", + "source_payload_sha256": "cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd", + "status": "PASS_CODED_NATIVE_REAL_NORMALIZERS" +} diff --git a/research/partial-cache-minimax-floor/source/observer-proof.md b/research/partial-cache-minimax-floor/source/observer-proof.md new file mode 100644 index 0000000000..4cfe97e3a4 --- /dev/null +++ b/research/partial-cache-minimax-floor/source/observer-proof.md @@ -0,0 +1,182 @@ +# Eight retained partial caches still do not identify the required observer + +The observation channel is the raw PR5402 backward WORD, with **every** +full-nine-dimensional-frame value retained throughout its execution, enlarged +by all eight nonzero endpoint partial-frame cache values. This is the concrete +channel excluded from PR5447's full-frame-only theorem. We prove that even +arbitrary nonlinear postprocessing of this enlarged channel cannot determine +the actual consumer target `b=ZQY_return=ZRy` on arbitrary independent inputs. + +This is not a statement about the whole machine state. In particular the +lower-frame current main inputs/outputs, original helper observations, +additional paid responses and PR5413's changed completion are not supplied +by this observation interface. No source instruction, cache lifetime or +selected provider is changed. + +## 1. Source object and original-input convention + +The canonical base is `32890bc5de034ab8fc93ac88ead7279a6a416d04`. +SOURCES.json pins the exact raw source, modified WORD, provider contracts and +physical normalizers by Git object and SHA256. The backward WORD contains +21,473 records. Native chart semantics are those of the pinned provider: +ordinary ADD/SCALE/COPY act on normalized rows at compatible charts; paid +climbs change the chart; warp records act by their signed invertible native +letter; only owned fields may be cleared. `phase` records are stage labels, +and `adapter` records retain physical entrance/exit bindings, not row updates. +These inherited native semantics and their all-width physical realization +are explicit premises, not a new supplier admission. + +Let the 632 independent original logical fields be x_0,...,x_111, +y_0,...,y_111 and h_0,...,h_407. The nine initially arbitrary owned fields +are independent too; their displacement in the two inputs below is zero. +The full-row checker initializes all 641 independent columns, verifies their +owned clearing and retains all observation events, including after intended +exits. There are 5,897 full-frame touches, with 4,891 distinct nonzero rows. +The eight endpoint caches have roles C1,...,C8 (indices 633,...,640), at +frames 254,274,619,279,621,280,624,281, respectively; every frame has rank eight. +No current main X or Y value is silently appended to the channel. + +## 2. Exact finite certificate + +KERNEL.json supplies a scalar vector k on the 632 original roles, with 104 +nonzero integer entries. Its Y block has just + + delta y_1=-2v, delta y_2=2v, delta y_12=-2v, + +where v is one arbitrary whole-field value. The file gives every compensating +X and dirty-helper coefficient; no coefficient is inferred from an endpoint +label or a clean-helper assumption. All initial owned displacements are zero. +No support-minimality claim is made. + +Write an actual normalized observation row as + + O_j = sum_(s,w) a_(j,s,w) w z_s, + +where w is a reduced free word in the source warp letters and their inverses, +and a is an exterior rational scalar. The complete full-row replay checks + + sum_s a_(j,s,w) k_s = 0 + +for every word w of every retained full-frame row. It also checks that each +of the eight complete endpoint cache rows annihilates k. The free-word +histories contain 119,521 terms. This is not PR5447's 119,515-term actual +monomial canonicalization: six terms have not been identified by additional +one-column operator relations here. The new certificate is checked in the +stronger free-word grammar, using only adjacent inverse cancellation. + +A separate direct-displacement interpreter starts with k_s v and executes +the same pinned instruction stream. It stores chronological words in the +opposite order and imports no primary parser/row code. Every one of the +5,897 full-frame events has zero displacement, including repeated/zero rows, +and all nine endpoint owned displacements are zero. This is a distinct +execution check; both implementations inherit the same source semantics. + +Let M^T be the source's eight-by-112 `mode_columns` matrix. Exact arithmetic +on the supplied vector gives + + M^T delta y = (0,-4,0,0,0,0,0,0)^T v. (1) + +Thus the target ambiguity is not inferred from dimension counting or a +numerical nonmembership result: it has a complete input witness and nonzero +specified target image. Sparse rational elimination was used only to discover +the vector. Neither its rank nor its search procedure is a proof dependency. + +## 3. Every positive width, and the actual physical target + +At width f assign each free letter its actual conjugated backward native +operator lifted columnwise to f factors, with spectators unchanged. Assign +inverse letters inverse operators. A reduced-word cancellation remains an +operator identity. Exterior rational coefficients k_s and a_(j,s,w) are +applied once; they are not tensor-powered. Therefore the coefficientwise zero +above evaluates to zero at every positive width for every v. No independence +of actual monomial matrices, width-one sum relation, Gram lift or numerical +cutoff is required. + +Physical values at a fixed chart differ from normalized rows by the chart's +invertible frame map. Zero differences remain zero at every observed full +or partial frame. Physical provider entry includes invertible birth frames, +input wrappers and its invertible helper basis/scalings. Hence the raw +logical displacement k v corresponds to two valid physical input states; +we do not claim that preparing that displacement is free. + +To bind (1) to the actual consumer, distinguish raw logical y here from the +standardized physical input y_phys of the provider contract. The checker +evaluates all 112 literal input wrappers on all 512 one-column addresses, +including absolute phase, and establishes `B_Y,j=K_p,j`. Since raw Y enters +ground chart, `y_j=K_p,j y_phys,j`. The pinned provider establishes + + Z = diag(K_m^-1) M^T diag(K_p)/2, + K_p,j R = R K_p,j, Y_return=D y_phys, R=DQ. + +These monomial/full-Gaussian identities lift multiplicatively to every width; +the scalar owner coefficients stay exterior. Consequently the actual target +in raw input coordinates is + + b_k = (1/2) K_m,k^-1 R sum_j M_kj y_j. (2) + +No separate commutation of K_p with Q or D is asserted. Inserting (1) gives +zero change in seven target modes and + + delta b_1 = -2 K_m,1^-1 R v. (3) + +R and K_m,1 are invertible, so (3) is nonzero for every nonzero v and ranges +over the whole target field. Two valid inputs have identical entire supplied +channels and identical other seven b modes, but arbitrary differing b_1. +No deterministic exact decoder of this channel can recover b, or any +nonconstant function of b_1 alone. Randomness cannot give a universally exact +decoder of indistinguishable inputs either. No approximation/error lower bound +or physical price lower bound is inferred. + +## 4. Why helper versions matter + +The checker reconstructs every coefficient of all eight cache rows and binds +their slot, chart, permutation and signed scale to PROVIDER.json: + + c_i = f_i (E_k h_original - M_k^T y), + f_i = 1/(2 cache_scalar_i), k=mode(i). (4) + +For the new witness, `E delta h_original` equals the right side of (1). +The helper changes exactly hide the Y change in every cache. The old +fixed-helper ambiguity `(delta x,delta y,delta h)=(v,v,0)` is insufficient +here: the eight new caches genuinely add information. Eight separate controls +take y=M_k and x=y; full-frame values still agree, while exactly cache mode k +changes, using `M^T M=56 I`. We do not just reuse the earlier kernel. + +If the **original** eight retractions `e=E h_original` were separately supplied, +(4) would give `M_k^T y=e_k-c_i/f_i`, and then (2) is an unrestricted linear +decoder for b. This is a changed observation interface; it does not establish +that e was retained, that an inverse cache-frame map is ordinary, or that the +required R action is free. Every such observation/transform and its retention +would need a physical bill before supplier use. + +The tempting substitute `E h_current` is invalid. Fresh complete-row replay +proves `E h_current=0` at the raw WORD endpoint, for every original input. +For this witness `E delta h_original` has mode one equal to -4v, while the +same endpoint expression remains zero. Using it in the conditional decoder +would return zero change although the true target changes by (3). Freezing +the witness's helper displacements also exposes 821 full-frame observations; +the first is at zero-based event 16,366. Removing its X compensation exposes +924 observations, first at event 15,523. The roles and versions are substantive +parts of the impossibility statement. + +## 5. Scope, consequences and credit + +This closes the passive endpoint-cache candidate for this exact observer: +retaining all full-frame values and all eight already-created endpoint caches +still does not supply `ZQY_return` on unrestricted original inputs. It does not +exclude a different partial-frame history, an original-helper observation, +retained current Y, changed producer, new paid call or a relation restricting +the independent inputs. Ordinary output-basis operations cannot rescue this +channel: they combine already retained full-frame endpoints, and normalizing +or relabelling the eight caches preserves their zero differences. The whole +machine state is not claimed to be Y-blind. No recursive profile, selected +frontier, complete multiplication theorem or new kappa is asserted. + +Credit Dillon Amburgey / dillona's PR5402 source and cache equations; Ali +Romman's cache/retraction and basis lineage; Mark/Matarener's PR5427 event and +versioned-history question; THU New Media Research Center's PR5447 full-frame +kernel and explicitly excluded partial-cache boundary; zxv's PR5415/5419 +actual consumer and observer contract; Cao Yifan's native word and the +retained Cinna Davis, Dugongue, Chris R and native/phase/compiler/analytic +contributors. JoyboyBrian with substantial OpenAI Codex assistance. +Apache-2.0. No independent human or proof-kernel acceptance is claimed. diff --git a/research/partial-cache-minimax-floor/source/provider-proof.md b/research/partial-cache-minimax-floor/source/provider-proof.md new file mode 100644 index 0000000000..5cbfc4fd02 --- /dev/null +++ b/research/partial-cache-minimax-floor/source/provider-proof.md @@ -0,0 +1,236 @@ +# A source-bound backward provider with eight coupled rank-eight outputs + +The construction has 632 arbitrary original inputs and nine arbitrary owned +inputs. Its paid native profile is +`{1:2193,2:412,3:510,4:127,5:40}`. It returns 400 unchanged native helper jobs +and a coupled block on the 224 main and eight remaining helper owners: + +\[ + X=Dx-Ry+RW h,\qquad Y=Dy,\qquad H=D(h-Zy). \tag{1} +\] + +Here `R=DQ` is the full native rank-nine Gaussian, `D` acts on the eight +noncentral axes, and `Q` acts on the central axis. The eight `H` outputs remain +coupled; they are **not eight autonomous H8 targets**. No complete caller or +new multiplication exponent follows. All nine owned outputs are zero. + +## 1. Exact source and the changed word + +`SOURCES.json` pins the main-branch source, code, normalizers and Clifford +compiler. The native source's decompressed SHA256 is +`cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd`. +`WITNESS.json` retains Ali Romman's PR5383 candidate verbatim, with SHA256 +`24599011da06325e1012619b2b84a4dd3aceb90ab42d3caaf6414879e7d16591`. +It supplies candidate sites and rational rows; it is not a proof oracle or a +pending Git-object dependency. Every used identity is checked again against +the pinned main source. + +For witness row `i`, after the indicated original `cached_event`, CLEAR owned +`C[i+1]` and COPY the indicated persistent row into it at its actual chart. +Every cache precedes every removed center. At the original center event, +replace the H8 call by CLEAR `C0`, then COPY `C[i+1]` into `C0` at that same +rank-eight chart. At the indicated later H1 call, replace the call by a +`zero_retag`: this is physical identity on the **exactly zero** field, with +its bookkeeping chart changed to the old call's output chart. All other +instructions, including inherited physical metadata, remain unchanged. +`WORD.json.gz` emits the complete resulting backward native word; the verifier +regenerates it from the canonical source and compares its parsed content. + +The replay begins with one independent formal column per field, including +all nine owned fields. It tracks exact rational coefficients in the free +group on the source's native warp symbols, their inverses, and actual chart +tags. Every ordinary operation is checked at its true chart. COPY fills only +owned zero; CLEAR acts only on owned fields. Before each of the eight retags, +every one of the 641 input coefficients is zero. All initial owned dirt is +cleared before use and is absent from every endpoint. + +The source's ten `phase` records are named stage annotations, not scalar +Clifford phase gates; its 448 `adapter` records retain the predecessor's +physical entrance/exit bindings (there are no `residual_adapter` records in +this backward word). As in the pinned predecessor normalized-row semantics, +these do not update formal rows. They are preserved in the emitted word, +not deleted or priced away. Their physical interpretation and native cost +are inherited; this package separately verifies every new physical boundary +identity including absolute phase. + +The same interpreter replays the original source, obtaining its full +632-row normalized backward endpoint `(x-y,y,h)` and clean original temporary. +It separately replays center deletion to derive the native coupling below. +The changed word has eight fewer H8 and eight fewer H1 calls than the original +source, with no additional Gaussian call. It has 16 extra COPYs and 16 extra +CLEARs. This is a changed source construction, not a constraint such as +`Delta h=0` on otherwise independent inputs. + +## 2. Source-derived coupling and an ordinary helper basis + +Use the inherited 112-by-8 matrix `M`, stored transposed as `mode_columns`. +The verifier checks all entries of + +\[ + M^T M=56I_8,\qquad A=I-MM^T/4. +\] + +Fresh replay of the center-deleted source gives + +\[ + X=x-A^Ty,\qquad Y=y,\qquad H=h-B^TM^Ty. +\] + +The verifier derives every entry of `B` by projecting the actual 408-by-112 +helper-to-Y coefficient matrix onto `M/56`; it then checks the entire +factorization and all 632 endpoints. The eight candidate rows `Delta` satisfy +`Delta B^T = S`, an exactly checked signed permutation. Put `E=S^-1 Delta`. +Thus `E B^T=I8`. Fresh original-prefix replay also binds the candidate cache +rows, their chronology and their actual rank-eight charts. + +In these coordinates the changed word has normalized endpoint + +\[ + X=x-y+(M/4)Eh,\quad Y=y,\quad H=(I-B^TE)h, \tag{2} +\] + +and its canonical mode-`k` cache is + +\[ + f_i(E_kh-M_k^Ty),\qquad f_i=\texttt{zero_factor}_i\,S_{ik}. \tag{3} +\] + +The registered check composes all changed endpoint rows with the following +basis, rather than accepting (2) or (3) from a saved endpoint registry. + +The union of supports of `B` and `E` comprises 122 actual cold H9 owners: each +has ground entrance chart and full-R exit chart. Choose the eight original +mode owners `[224,225,227,229,240,241,256,257]`. Define `L` on these 122 owners: +its mode columns are `B^T`; its other columns are `(I-B^TE)e_j`. Exact +Gauss-Jordan reduction constructs `L^-1` and verifies both inverse products, +`EL` selecting precisely the eight mode coordinates, and `L^-1B^T` embedding +precisely those coordinates. Every coefficient is dyadic. The emitted +`input_basis_program` and `output_basis_program` execute these two maps in +place, without extra owned basis storage. + +Both bases mix only fields sharing the appropriate physical chart, so scalar +owner operations implement them ordinarily. After entrance `L` and exit +`L^-1`, every one of the 632 persistent rows is checked: the eight selected +helper rows are zero, the other 400 helper rows are unchanged, `Y=y`, and +`X=x-y+(M/4)h_mode`. Each cache is exactly +`f_i(h_mode,k-M_k^T y)`. Thus the cache fills a vacated original direction; +it supplies no additional productive input or job credit. + +## 3. Literal physical boundary maps and ownership + +Backward frames use complex conjugation of the native frames, as in the +pinned source convention; they are not silently replaced by adjoints. Let +`Kp` be the 112 inherited main normalizers. For each actual cache frame `F8`, +the verifier constructs an orthogonal, phase-correct monomial `Km` from its +unique missing odd noncharacteristic line, and compiles a monomial `N` with + +\[ + N\overline{F8}K_m=D,\qquad K_mR=RK_m. +\] + +`PROVIDER.json` contains all eight literal `Km` and `N` words, signed tableaux +and nonzero zero-column phase anchors. The compiler's output is checked +explicitly even under Python `-O`. All `Kp` commute with `R`, including +absolute phase. Every boundary word contains only monomial gates. + +Apply `2Km` to the eight original mode inputs before `L`. At the exit, apply +`N/(2f_i)` to each cache. Use the inherited **fused compiled** backward main +input/output wrappers. The verifier checks 336 main diagonal/shear blocks, +896 nonzero main/helper coupling blocks and eight helper diagonal blocks, +for 1,240 exact physical equations. Comparison includes the signed tableau +and exact zero-state vector, so an undetected global phase is impossible +within this Clifford model. These equations yield (1), with + +\[ + W=\operatorname{diag}(K_p^{-1})M\operatorname{diag}(K_m)/2, + \quad + Z=\operatorname{diag}(K_m^{-1})M^T\operatorname{diag}(K_p)/2. +\] + +The main code is the predecessor's `C=diag(Kp^-1) A diag(Kp)`. Exact word +cancellation and the scalar factorization give +`ZW=14I8`, `WZ=I-C`; `W` and `Z` intertwine `R` on their respective banks. +No commutation with `D` or `Q` is assumed. These are finite ordinary code +maps with exterior scalar coefficients, not additional Gaussian calls. + +After normalization, SWAP each cache's **whole physical field and chart tag** +with its identically zero original mode output. The original owner now holds +the normalized coupled output; the owned slot holds zero and can be CLEARed. +There is no persistent erasure and no attempted free chart conversion of a +nonzero field. `C0` is already zero, so all nine owned outputs are zero. +Ordering the coupled input/output banks as `(y,h,x)` makes (1) triangular +with invertible diagonal `D`. Together with the 400 unchanged native jobs, +this proves preservation of all 632 original input directions. It does not +emit an inverse schedule or establish a same-cost inverse/transpose. + +## 4. Exact local bill + +Relative to the original raw backward source, the selected schedule adds: + +| Ordinary operation | Added field operations | +| --- | ---: | +| ADD | 1,644 | +| SCALE | 40 | +| COPY | 16 | +| CLEAR | 24 | +| Whole-field SWAP, with chart tag | 8 | +| Monomial field map | 464 | + +Each basis direction uses 822 ADD and 12 SCALE: its three elimination swaps +are expanded into three ADDs and one SCALE each. Eight input scalings and +eight cache scalings give the remaining 16 SCALEs. The source rewrite adds +16 COPY and 16 CLEAR; final cache consumption adds eight CLEAR. The 464 +monomial maps are 448 fused inherited main standardizers, eight `Km` and +eight `N`. This counts the newly installed boundary schedule; all unchanged +source warp/phase/adapter traffic and native child implementations remain in +the emitted word and retain their inherited costs. In particular, this table +does not assert that a field monomial map is zero machine work. + +The original source has 16,273 ADD, 1,164 SCALE and 16 CLEAR. Including the +new boundary scalars, the schedule therefore has 17,917 ADD, 1,204 SCALE, +16 COPY, 40 CLEAR and eight whole-field SWAP, plus the explicitly described +monomial boundary maps and inherited native operations. Nine owned fields +suffice: the original center temporary and eight retained caches. Their +initial values are arbitrary; their final values are zero. The autonomous +helper profile is `{4:28,7:7,8:47,9:318}`. The physical implementations of +those unchanged native helper jobs are inherited from the pinned source; +scalar identity rows alone are not a new proof of those implementations. + +For an explicit local stability bound, use the maximum of field Euclidean +norms. ADD by `a` has norm at most `1+|a|`, SCALE has norm at most +`max(1,|a|)`, and unitary Gaussian/monomial maps, COPY, CLEAR and SWAP have +norm at most one. The verifier sums upward-rounded base-two logarithms for +every scalar operation in this finite schedule, obtaining **18,996**. Hence +every suffix amplifies an injected field error by at most `2^18996`; at most +`m` injections of norm `epsilon` give the conservative bound +`m*2^18996*epsilon`. All dyadic constants and word lengths are fixed. This +establishes local bounded amplification, not a complete coordinate rounding, +tape movement, recursive precision or outer multiplier budget. + +## 5. Every positive fiber width and verification boundary + +A free-group identity evaluates in any assignment of invertible native warp +operators. Therefore the exact rational row equalities and zero-retag +premises hold uniformly when native operations act on any positive fiber +width `f`. The scalar owner coefficients and scalar `L/L^-1` programs stay +outside the tensor product; in particular `ZW=14I`, not `14^f I`. Each +compiled monomial word uses the inherited prescription: `P` and `X` act +columnwise, `D` sums its Z4 polynomial over the columns, and a `phase` gate +contributes its phase once per column. Each address-operator identity is lifted +columnwise; an absolute phase `i^gamma` lifts to `i^(f gamma)`, rather than +being confused with an exterior scalar sign. Exact one-column operator +identities, word cancellation and rational matrix identities then prove the +same physical boundary composition for every `f`. The inherited native +uniform implementation hypotheses remain inherited. + +The registered verifier performs complete 641-column native row replay, +exact scalar endpoint composition, and the 1,240 physical boundary checks. +It does not claim a separately flattened 641-column physical-matrix replay, +a formal-kernel proof, independent human approval, hosted CI, or a complete +caller. It rejects a nonzero zero-retag, a single changed basis ADD +coefficient, a changed saved-cache coefficient and a phase-only error with +the correct tableau. Normal and optimized runs use explicit checks for the +new claims. 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], + [ + 0, + 160, + 2 + ], + [ + 0, + 192, + 2 + ], + [ + 0, + 254, + 2 + ], + [ + 0, + 256, + 2 + ] + ], + "zero_column_anchor": { + "index": 384, + "gaussian_numerator": [ + -1, + 0 + ], + "denominator_power2": 0 + } + } + } + ], + "ordered_schedule": [ + "Main input wrappers: NORMALIZERS.ports[j].compiled_wrappers.backward_input_X/Y.", + "On each mode owner apply input_K and scalar 2; run input_basis_program.", + "Run every instruction of WORD.json.gz; C0..C8 initially arbitrary.", + "Run output_basis_program on the 122 persistent common-chart helpers.", + "For each mode apply cache_scalar and output_N to its owned cache; SWAP the whole field and chart with its zero original owner; CLEAR the owned zero.", + "Main output wrappers: NORMALIZERS.ports[j].compiled_wrappers.backward_output_X/Y." + ], + "paid": { + "1": 2193, + "2": 412, + "3": 510, + "4": 127, + "5": 40 + }, + "autonomous_native_helpers": { + "4": 28, + "7": 7, + "8": 47, + "9": 318 + }, + "owned_fields": { + "count": 9, + "initial_values": "arbitrary", + "final_values": "zero", + "productive_credit": 0 + }, + "added_ordinary_work_vs_original_raw_source": { + "ADD": 1644, + "SCALE": 40, + "COPY": 16, + "CLEAR": 24, + "whole_field_SWAP": 8, + "monomial_field_maps": 464, + "monomial_breakdown": { + "fused_inherited_main_standardizers": 448, + "mode_inputs": 8, + "cache_outputs": 8 + } + }, + "local_error_amplification_power2_bound": 18996, + "source_original_scalar_counts": { + "add": 16273, + "clear": 16, + "scale": 1164 + }, + "source_changed_scalar_counts": { + "add": 16273, + "clear": 32, + "copy": 16, + "scale": 1164 + }, + "physical_phase_bindings": { + "main_diagonal_and_shear": 336, + "two_coupling_directions": 896, + "helper_diagonal": 8 + }, + "exact_zero_retags": [ + [ + 15608, + 92, + 254, + 1 + ], + [ + 15894, + 9, + 624, + 1 + ], + [ + 15900, + 11, + 621, + 1 + ], + [ + 17269, + 240, + 280, + 1 + ], + [ + 17280, + 81, + 619, + 1 + ], + [ + 17288, + 57, + 274, + 1 + ], + [ + 17604, + 288, + 281, + 1 + ], + [ + 17746, + 224, + 279, + 1 + ] + ], + "formula": { + "X": "D x - R y + R W h", + "Y": "D y", + "H": "D (h - Z y)", + "W": "diag(K_port^-1) M diag(K_mode)/2", + "Z": "diag(K_mode^-1) M^T diag(K_port)/2" + }, + "failure_controls": [ + "nonzero zero-retag rejected", + "one altered basis ADD coefficient rejected", + "same-tableau phase-only cache error rejected", + "one altered saved-cache coefficient rejected" + ], + "scope": "Changed coupled backward provider. No autonomous credit for eight coupled outputs; no completed caller, inverse/transpose implementation, new kappa or selected-result change." +} diff --git a/research/partial-cache-minimax-floor/verify.py b/research/partial-cache-minimax-floor/verify.py new file mode 100644 index 0000000000..2c67b76609 --- /dev/null +++ b/research/partial-cache-minimax-floor/verify.py @@ -0,0 +1,203 @@ +"""Check the physical kernel norm and the minimax constant with exact arithmetic.""" +from copy import deepcopy +from fractions import Fraction as F +import hashlib +import json +from pathlib import Path + +HERE = Path(__file__).resolve().parent + + +def require(test, message): + if not test: + raise ValueError(message) + + +def authenticate(data, row): + require(hashlib.sha256(data).hexdigest() == row['sha256'], 'source SHA256') + blob = b'blob ' + str(len(data)).encode() + b'\0' + data + require(hashlib.sha1(blob).hexdigest() == row['git_blob'], 'source Git object') + + +def program(ops, vector): + out = list(vector) + for op in ops: + if op[0] == 'add': + out[op[1]] += F(op[3]) * out[op[2]] + elif op[0] == 'scale': + require(F(op[2]) != 0, 'zero basis scale') + out[op[1]] *= F(op[2]) + else: + raise ValueError('unknown basis operation') + return out + + +def inverse(ops): + out = [] + for op in reversed(ops): + if op[0] == 'add': + out.append(['add', op[1], op[2], str(-F(op[3]))]) + elif op[0] == 'scale': + out.append(['scale', op[1], str(1 / F(op[2]))]) + else: + raise ValueError('unknown inverse operation') + return out + + +def norm2(vector): + return sum(x * x for x in vector) + + +def monomial_unitary(word): + """Check the permutation and fourth-root phases on all 512 addresses.""" + images = [] + for start in range(512): + x, phase = start, 0 + for op in word: + if op[0] == 'P': + require(len(op[1]) == 9, 'matrix size') + require(all(type(r) is int and 0 <= r < 512 for r in op[1]), 'matrix row') + x = sum(((x & row).bit_count() % 2) << j for j, row in enumerate(op[1])) + elif op[0] == 'X': + require(type(op[1]) is int and 0 <= op[1] < 512, 'translation') + x ^= op[1] + elif op[0] == 'D': + require(len(op[1]) == len(op[2]) == 9, 'phase size') + require(all(type(r) is int and 0 <= r < 512 for r in op[1]), 'phase row') + require(all(type(r) is int for r in op[2]), 'phase coefficient') + phase += sum(op[2][j] for j in range(9) if x >> j & 1) + phase += 2 * sum((op[1][j] & x & ((1 << j) - 1)).bit_count() + for j in range(9) if x >> j & 1) + elif op[0] == 'phase': + require(type(op[1]) is int, 'global phase') + phase += op[1] + else: + raise ValueError('nonmonomial gate') + require(0 <= phase % 4 < 4, 'unit phase') + images.append(x) + require(len(set(images)) == 512, 'nonunitary address map') + + +def target_image(normalizers, raw): + y = raw[112:224] + return [sum(F(a) * b for a, b in zip(row, y)) / 2 + for row in normalizers['mode_columns']] + + +def audit(provider, normalizers, raw): + require(sum(bool(x) for x in raw) == 104, 'raw support') + require([norm2(raw[a:b]) for a, b in [(0,112),(112,224),(224,632)]] + == [60,12,68], 'raw norm blocks') + decoded = program(provider['output_basis_program'], raw) + recovered = program(inverse(provider['input_basis_program']), raw) + require(decoded == recovered, 'independent inverse program') + require([(i, x) for i, x in enumerate(decoded[224:], 224) if x] == [(225,F(-4))], + 'helper basis image') + forward = raw[:224] + [F(0)] * 417 + forward[225] = -4 + require(program(provider['input_basis_program'], forward) == raw, 'forward source binding') + physical = list(decoded) + for role in provider['mode_owners']: + physical[role] /= 2 + require([norm2(physical[a:b]) for a,b in [(0,112),(112,224),(224,632)]] + == [60,12,4], 'physical norm blocks') + require(norm2(physical) == 76, 'physical input norm') + require(sum(bool(x) for x in physical) == 61, 'physical support') + t = target_image(normalizers, raw) + require(t == [0,-2,0,0,0,0,0,0], 'actual target coefficient') + independent = [F(row[2] - row[1] - row[12]) for row in normalizers['mode_columns']] + require(t == independent, 'three-entry target calculation') + require(norm2(t) / norm2(physical) == F(1,19), 'minimax squared floor') + return physical, t + + +def main(): + controls = 0 + + def rejected(call): + nonlocal controls + try: + call() + except ValueError: + controls += 1 + else: + raise ValueError('negative control accepted') + + pins = json.loads((HERE / 'INPUTS.json').read_text()) + for row in pins: + data = (HERE / row['local']).read_bytes() + authenticate(data, row) + rejected(lambda: authenticate(data + b' ', row)) + provider = json.loads((HERE / 'source/provider.json').read_text()) + normalizers = json.loads((HERE / 'source/normalizers.json').read_text()) + kernel = json.loads((HERE / 'source/kernel.json').read_text()) + raw = [F(0)] * 641 + pairs = kernel['original_input_displacement'] + require(len({i for i, _ in pairs}) == len(pairs), 'duplicate role') + for i, value in pairs: + require(0 <= i < 632, 'role range') + raw[i] = F(value) + physical, target = audit(provider, normalizers, raw) + + # Check both full basis products, not only the selected displacement. + for role in provider['basis_roles']: + v = [F(0)] * 641 + v[role] = F(1) + for first, second in [('input_basis_program','output_basis_program'), + ('output_basis_program','input_basis_program')]: + require(program(provider[second], program(provider[first], v)) == v, + 'full basis inverse product') + + words = [port['compiled_wrappers'][name]['word'] for port in normalizers['ports'] + for name in ['backward_input_X','backward_input_Y']] + mode_one = next(x for x in provider['mode_boundaries'] if x['mode'] == 1) + words.append(mode_one['input_K']['literal_word']) + for word in words: + monomial_unitary(word) + + # For G=aI+bX, these are the diagonal and off-diagonal entries of G*G. + a, b = (F(1,2),F(1,2)), (F(1,2),F(-1,2)) + require(norm2(a)+norm2(b) == 1 and sum(x*y for x,y in zip(a,b)) == 0, + 'native one-axis unitarity') + + for role in [0,113,224]: + changed = list(raw) + changed[role] += 1 + rejected(lambda: audit(provider, normalizers, changed)) + changed = deepcopy(provider) + changed['mode_owners'].remove(225) + rejected(lambda: audit(changed, normalizers, raw)) + changed = deepcopy(provider) + changed['input_basis_program'][0][3] = str(F(changed['input_basis_program'][0][3]) + 1) + v = [F(0)] * 641 + v[changed['input_basis_program'][0][2]] = 1 + rejected(lambda: require(program(changed['output_basis_program'], + program(changed['input_basis_program'],v)) == v, + 'changed basis coefficient')) + changed = deepcopy(normalizers) + changed['mode_columns'][1][1] += 1 + rejected(lambda: audit(provider, changed, raw)) + bad = deepcopy(words[0]) + next(op for op in bad if op[0] == 'P')[1][0] = 0 + rejected(lambda: monomial_unitary(bad)) + rejected(lambda: require(norm2(target)/norm2(raw) == F(1,19), 'raw is not physical norm')) + rejected(lambda: require(norm2(target)*19 > norm2(physical), 'larger claimed constant')) + + # Check the antipodal square-loss identity with rational complex outputs. + loss_checks = 0 + for real in range(-6,7): + for imag in range(-4,5): + z = (F(real,3),F(imag,5)) + average = ((z[0]-2)**2+z[1]**2+(z[0]+2)**2+z[1]**2)/2 + require(average == norm2(z)+4 and average/76 >= F(1,19), 'antipodal loss') + loss_checks += 1 + print(json.dumps(dict(status='PASS_PARTIAL_CACHE_MINIMAX_FLOOR', + source_copies=len(pins), basis_products=2*len(provider['basis_roles']), + monomial_address_checks=512*len(words), loss_checks=loss_checks, + raw_norm_squared=str(norm2(raw)), physical_norm_squared='76', + target_norm_squared='4', squared_floor='1/19', controls=controls), + sort_keys=True)) + + +if __name__ == '__main__': + main()