diff --git a/research/qq16-paired-precision/COST.json b/research/qq16-paired-precision/COST.json new file mode 100644 index 0000000000..465710456b --- /dev/null +++ b/research/qq16-paired-precision/COST.json @@ -0,0 +1,70 @@ +{ + "N": "2^(73 lambda) complex payload coordinates per owner, lambda positive integer", + "baseline": { + "CLEAR": 416, + "H1": 224, + "cover_maps": 352, + "cover_numeric_ops_per_N": 1408, + "monomial_wrappers": 448, + "native_numeric_ops_per_lambda_N": 2240, + "numeric_constant_per_N": 12352, + "private_peak": 16, + "quarter_ADD": 896, + "scalar_allowance": 26944, + "scalar_numeric_ops_per_N": 8256, + "unit_ADD": 1920, + "wrapper_numeric_ops_per_N": 2688 + }, + "candidate": { + "CLEAR": 416, + "H1": 224, + "cover_maps": 352, + "cover_numeric_ops_per_N": 1408, + "monomial_wrappers": 448, + "native_numeric_ops_per_lambda_N": 2240, + "numeric_constant_per_N": 12152, + "private_peak": 16, + "quarter_ADD": 896, + "scalar_allowance": 26144, + "scalar_numeric_ops_per_N": 8056, + "unit_ADD": 1820, + "wrapper_numeric_ops_per_N": 2688 + }, + "common_width_tariff": "For each reference primitive priced at any common positive tau(W), candidate prescribed bill is200N tau(W) smaller; logical allowance model separately gives800 tau_L(W). These are comparisons of prescribed bounds, not lower bounds on optimal implementations.", + "logical_allowance_difference": "800 allowance units; distinct from200N numeric operations", + "numeric_bound_per_owner": { + "baseline": "(12352+2240 lambda)N", + "candidate": "(12152+2240 lambda)N", + "difference": "200N numeric word operations" + }, + "numeric_storage_bound": "(930N+12) signed W-bit component slots, including448 persistent complexfields,16 privatefields,one complex permutation buffer,and12 scalar native temporaries", + "premises": [ + "Common sufficient range/grid certificate for every numerical reference interior.", + "Exact dyadic divisions and no overflow/underflow at the stated common W.", + "Pair-first coordinate Gaussian reference is permitted for this numerical bill; it is not inferred to implement a paid recursive child tariff." + ], + "reference_lowering": { + "CLEAR": "2N zero stores", + "buffer_protocol": "Two-leg out-of-place permutation returns to its fixed external bank; address/control work is outside numeric count.", + "cover": "2N outward copies plus2N copies back to the fixed destination bank", + "quarter_ADD": "2N exact binary shifts by two (one W-bit shift primitive per component) plus 2N additions/subtractions", + "signed_H1": "lambda coordinate Gaussian lines; each at most4N additions,2N exact halves,4N copies", + "unit_ADD": "2N real-component additions or subtractions", + "wrapper": "2N component sign operations plus2N outward copies and2N copies back to the fixed destination bank" + }, + "status": "PASS_CONDITIONAL_COMMON_WIDTH_NUMERIC_REFERENCE_COMPARISON", + "unpriced": [ + "Owner/payload address generation and control", + "physical movement and placement tariffs", + "actual recursive native child error/width/cost contract", + "native workspace exclusivity in a recursive implementation", + "caller entry-format conversion", + "recursive usage and supplier caps" + ], + "width_mismatch_break_even": { + "equal_width": "Delta=0 satisfies bothstrictinequalities for everylambda>=1 andW>0", + "general": "tau(W_candidate)/tau(W_baseline) < (12352+2240 lambda)/(12152+2240 lambda)", + "linear_tau_W": "Delta < 200 W_baseline/(12152+2240 lambda), forW_candidate=W_baseline+Delta", + "logical_allowance_only": "tau_L(W_candidate)/tau_L(W_baseline) < 26944/26144" + } +} diff --git a/research/qq16-paired-precision/POLYNOMIAL.json b/research/qq16-paired-precision/POLYNOMIAL.json new file mode 100644 index 0000000000..91d8828324 --- /dev/null +++ b/research/qq16-paired-precision/POLYNOMIAL.json @@ -0,0 +1,95 @@ +{ + "baseline": { + "envelope_coefficients": [ + "445", + "28230", + "96", + "142272" + ], + "observation_sha256": "d08d4039097f4e20f423bbcd432272759853e4cd86116b76dda02258f14ab6f0", + "observations": 4032, + "peaks": [ + [ + 3797, + "post W0" + ], + [ + 3798, + "post W7" + ], + [ + 3799, + "post W20" + ], + [ + 3800, + "post W27" + ], + [ + 3801, + "post W36" + ], + [ + 3802, + "post W46" + ], + [ + 3803, + "post W57" + ], + [ + 3804, + "post W111" + ] + ], + "proof": "Every F-observation has nonnegative coefficients after x=1+y; F(1)=171043 and degree3 give F(x)<=171043*x^3.", + "variable": "x=2^(lambda-1)>=1" + }, + "candidate": { + "envelope_coefficients": [ + "445", + "28230", + "96", + "142272" + ], + "observation_sha256": "d9b4d9bf395ced9ed19a4ed56086d85ce4115c0c7366ab8efd4fe0a47d190751", + "observations": 3932, + "peaks": [ + [ + 3697, + "post W0" + ], + [ + 3698, + "post W7" + ], + [ + 3699, + "post W20" + ], + [ + 3700, + "post W27" + ], + [ + 3701, + "post W36" + ], + [ + 3702, + "post W46" + ], + [ + 3703, + "post W57" + ], + [ + 3704, + "post W111" + ] + ], + "proof": "Every F-observation has nonnegative coefficients after x=1+y; F(1)=171043 and degree3 give F(x)<=171043*x^3.", + "variable": "x=2^(lambda-1)>=1" + }, + "negative_control": "Understate cubic coefficient142272 by1: both inductive certificates reject. Not a minimum-physical-width lower bound." +} diff --git a/research/qq16-paired-precision/PREDECESSORS.json b/research/qq16-paired-precision/PREDECESSORS.json new file mode 100644 index 0000000000..c8bb9374b3 --- /dev/null +++ b/research/qq16-paired-precision/PREDECESSORS.json @@ -0,0 +1,46 @@ +{ + "schema_version": 1, + "files": [ + { + "pr": 4106, + "head": "48529915d50bb59b53db53686c4add1cf53429dd", + "path": "research/qq16-sequential-recovery/WORD.json", + "local": "vendor/PR4106-WORD.json", + "sha256": "b4f2b5662734178d02a5d620ebd071bc284abd4d9b6dbe11b5d9646455a0f021", + "git_blob": "6c6f726cd14010f9763155518f833862eb167263" + }, + { + "pr": 4106, + "head": "48529915d50bb59b53db53686c4add1cf53429dd", + "path": "research/qq16-sequential-recovery/CONSTRUCTION.json", + "local": "vendor/PR4106-CONSTRUCTION.json", + "sha256": "dbf7b1d077b1b58262afe22aceeac02262c50c6597392676ea7a98e7d9cdd075", + "git_blob": "f4376037d5a574e56d46f95997b64a50eb86dcf2" + }, + { + "pr": 4106, + "head": "48529915d50bb59b53db53686c4add1cf53429dd", + "path": "research/qq16-sequential-recovery/PROOF.md", + "local": "vendor/PR4106-PROOF.md", + "sha256": "5d79ac0fafa95c81f000f1da9802abfaac5adedd9017d0d5e651220bb682e2a7", + "git_blob": "4518e496f89f59b20562ebfef360a7b404b66d98" + }, + { + "pr": 4015, + "head": "0fff81d8997cef646538bcd4f60d7d455cf93b8e", + "path": "research/qq16-streaming-recovery/WORD.json", + "local": "vendor/PR4015-WORD.json", + "sha256": "272d8c1bd172c29044eb227ec6d67a882501250978234685e035158f4479aa58", + "git_blob": "9a57a6f9c2fd8cdc4e5934408d78ef54e5f266b6" + }, + { + "pr": 4015, + "head": "0fff81d8997cef646538bcd4f60d7d455cf93b8e", + "path": "research/qq16-streaming-recovery/PROOF.md", + "local": "vendor/PR4015-PROOF.md", + "sha256": "81f0fa19b19fa7302ba9c61f4f1b2e11758f973b964240ba48c16ae9b6997396", + "git_blob": "8fd64e85e3e595403fe3ae4ed60b9ff368c9a3f5" + } + ], + "credit": "PR3985 owns336-to224native reduction; PR4015 streaming/outputhosting; PR4106 scalarpairing; PR4003 residual. Native/decoder math ywz65/2707, Arham Tahir/2681, Ali Romman and retainedlineage. Producer-grid3303 NickPetalas, independent3652 ToikY. Tekalign/tekuuu4030 shared-framegate isdistinct. Newaudit ChrisR/Clear1nsight with substantialOpenAIassistance. No predecessor executable imported; endpoint identities inherited ratherthanrerun." +} diff --git a/research/qq16-paired-precision/PROOF.md b/research/qq16-paired-precision/PROOF.md new file mode 100644 index 0000000000..06286a2fca --- /dev/null +++ b/research/qq16-paired-precision/PROOF.md @@ -0,0 +1,222 @@ +# PR4106: range, rounding and the 800-unit saving + +This is a scoped numerical audit of the unchanged PR4106 word against PR4015. +Endpoint/frame identity and the logical inverse are inherited from their pinned +proofs, not reproved by importing their executables. The new interpreters execute +neither predecessor code nor the canonical decoder verifier. Exact retained bytes, +source heads and canonical semantic inputs are authenticated before analysis. + +## 1. Common sufficient format for every tensor depth + +Let lambda>=1, t=lambda-1, h=2^z with integer z, and integer P>=0. Every real and +imaginary component of the 224 borrowed entry fields must belong to hZ and have +absolute value strictly below B=2^P h, uniformly over owners and payloads. Owned +and private storage may be dirty until its first charged CLEAR. Native/cover +semantics are the pinned full tensor semantics, not a finite sample of payloads. + +Both complete words admit + +``` +q = h 2^(-9-3t), W = P+28+6t signed component bits. +``` + +The component induction in [range-proof.md](range-proof.md) tracks magnitude, +lattice and both tensor-depth exponents. It includes scalar partials, the two +halvings implementing a quarter coefficient, all coordinate Gaussian interiors, +private state and the deferred tenth output definition. A coordinate Gaussian +has output component bound2L and cross-numerator bound4L, even though it is unitary +in a different norm. Repeated across lambda coordinate layers, these bounds +produce the grouped all-depth rules. This is a specified pair-first numerical +reference, not an unpriced replacement for a recursive child. + +Both words yield M<=171043, g<=9 and depth exponents a,b<=3. Therefore every +observed component is on the q lattice and has magnitude + +``` +<171043 B 2^(3t) < 2^(P+18+3t) h = 2^(W-1) q. +``` + +All specified shifts are divisible on this lattice. Thus signed W bits suffice +without overflow or arithmetic rounding. The new D+=E temporary doubles a local +bound230 to460, but lies below the agreeing completed-query bound11864. Every +one of the224 endpoint envelopes agrees; the whole prefix and suffix were +included. An uninitialized deferred host is never treated as a bounded number. + +A second certificate uses a different representation and dispatcher. Put u=2^t. +`independent.py` propagates exact positive polynomials and observes every logical +write and largest native cross numerator. For + +``` +F(u)=445+28230u+96u^2+142272u^3, +``` + +each difference F-observation has nonnegative coefficients after substituting +u=1+y. Hence it is nonnegative for all u>=1. There are3932 candidate and4032 +baseline observations; the observation streams are hashed. Since F(1)=171043 +and degreeF=3 with nonnegative coefficients, F(u)<=171043u^3. Decreasing its +cubic coefficient by1 makes both certificates reject. This is a certificate +control, not a lower bound on an optimal physical width. A separate explicit +coordinate recurrence at depths1,2,3,8 checks the grouped rule; these finite +checks do not supply the all-depth quantifier. Independent agent calculations +also checked depth17 during development. + +The result concerns a **common sufficient uniform format**. It does not prove +minimum widths, equal attainable maxima, or domination over a baseline whose +operations use separately optimized widths. + +## 2. Rounding: three distinct implications + +First, the specified exact reference above has zero arithmetic residual. There +is no precision surcharge relative to PR4015 in this domain. + +Second, approximate native callbacks can still give relative bit identity under +explicit fixed-grid premises. Both words must use common q and format; changed +unit additions must be exact and non-overflowing. Every normalizer/map callback +must be deterministic, bank-independent and isolated, with the same specified +scratch entry/return contract. `binding.py` verifies from the literal words: + +- the prefix differs only by deferring the tenth host's original X-copy; +- each of104 captured sources has exactly the same port/map/inverse-line recipe; +- queries never alter their captured borrowed or corrected sources; +- response arithmetic is identical; +- nine versus ten output definitions are charged, and the subsequent suffix is + identical; the old tenth host had no earlier consumer. + +The actual query subsequences agree on all104 source coefficient vectors and two +mixed integer regressions. For arbitrary q-integers, distributivity and integer +associativity prove that equal-sign pair sharing and independent source +reordering preserve all eight completed queries. Identical deterministic response +and suffix callbacks then preserve final bits. This permits common approximate +normalizer outputs, but does not certify their absolute accuracy, native interior +range or exact private cleanup. The exact-reference range proof alone cannot be +used to assert nonoverflow of an approximate implementation. + +Third, floating significand rounding is not associative. The exact rational +precision2, ties-to-even rounder in `rounding.py` executes the actual query scalar +subsequences with supplied normalized components v76=4,v87=v92=1, others0. +Baseline Q0=RN(RN(4+1)+1)=4; candidate Q0=RN(4+RN(1+1))=6. The other query +components agree. This is a query-cut countermodel to automatic rounded bit +transfer, not a reachability claim for a complete rounded caller. + +For a conservative absolute error comparison, let epsilon bound entry component +errors, eta the residual of each complete scalar ADD against ideal dst+c*src, +and nu the output residual of each complete signed native call. Eta includes +scaling, addition and storage error; neither eta nor nu is assumed to equal one +unit roundoff. CLEAR, covers and monomial signed permutations are exact. With +x=2^lambda, the new interpreter propagates + +``` +ADD: E_dst <- E_dst+|c|E_src+eta; native: E <- xE+nu. +``` + +Both words have identical224 endpoint polynomials, in six distinct classes. Both +also have the same coefficientwise whole-word logical-cut enclosure: + +``` +E_entry =445+14115x+2964x^2+17784x^3, +E_scalar =16380+14451x+19104x^2+17784x^3, +E_native =14121+2964x+17784x^2. +``` + +Triangle inequalities prove this for arbitrarily correlated errors; shared sum +errors are counted in every affected channel. Coefficient maxima need not occur +at the same cut and do not enclose native interiors. See +[rounding-proof.md](rounding-proof.md) for the complete recurrence and witness. + +The common signed format has logical-cut margin + +``` +(2^18-171043) B 2^(3t) = 91101 B 2^(3t). +``` + +Thus E_entry epsilon+E_scalar eta+E_native nu strictly below that margin is a +sufficient logical-cut nonoverflow condition. At lambda1 this reads +`182803epsilon+263970eta+91185nu < 91101B`. Native interiors, actual error-width +relations and private restoration remain separate premises; this inequality is +not an implementation admission. + +## 3. Cost comparison with declared units + +The frozen words contain1920 versus1820 unit ADDs. Both have896 quarter ADDs, +416 CLEARs,224 signed H1 calls,448 monomial wrappers and352 covers. Private peak16 +and persistent banks are unchanged. Hence their inherited logical scalar +allowances26944 and26144 differ by800. A common positive tariff at the common +width preserves that logical saving. + +For an explicit distinct numerical reference set N=2^(73lambda) complex coordinates +per owner. Count2N component adds for each unit ADD;2N shifts by two plus2N adds +for a quarter ADD;2N zero stores per CLEAR. Each coordinate Gaussian costs10N +numeric primitives:4N adds,2N halves,4N copies. A signed monomial costs6N +(2N signs plus out-and-back copies); a cover costs4N copies. Both permutations +use one reusable complex buffer and return to the original fixed bank, so no +free handle rebinding is assumed. The prescribed bills are + +``` +baseline: (12352+2240lambda)N, +candidate:(12152+2240lambda)N. +``` + +The difference is exactly200N real-component additions. Under a common uniform +positive primitive tariff tau(W), the reference bound falls by200N tau(W). +Under distinct primitive tariffs, unchanged counts cancel and the differing +real additions still cost200N times their common-width price. Storage is at most +(930N+12) W-bit component slots in this numerical model, including224 borrowed, +224 owned,16 private complex fields, one complex permutation buffer and12 scalar +temporaries. Physical addressing, placement and native recursive workspace are +outside this count. See [cost-proof.md](cost-proof.md). + +If an actual implementation forces different widths, its uniform-tariff +break-even condition is + +``` +tau(W_c)/tau(W_b) < (12352+2240lambda)/(12152+2240lambda). +``` + +For tau(W)=W and extra candidate bits Delta, the condition is +`Delta < 200 W_b/(12152+2240lambda)`. Equal sufficient widths satisfy it. This +makes the precision boundary measurable without claiming minimality or assigning +a fictitious recursive tariff. + +## 4. Producer connection and precise remaining obstruction + +The canonical #3303 producer theorem is inherited, not rerun. It provides quantum +`q_prod=h2^(-71-19t)` and signed width `W_prod=P+215+38t` for its different producer +entry contract. Its outputs consequently have absolute value strictly below +`2^(P+214+38t)q_prod`. Substituting `h_D=q_prod` and `P_D=P+214+38t` into this audit +gives the conditional numerical composition + +``` +q_joint=h2^(-80-22t), W_joint=P+242+44t. +``` + +This substitution does not establish that the selected F0 caller supplies that +producer, its decoder entry or native workspace. It does not pay conversion or +physical movement. Neither selected kappa nor any supplier record changes. + +The next justified experiment is to pin **one actual recursive H1 implementation** +and its caller's entry grid and range. Obtain its component width, complete +output residual nu(W,lambda), interior range and scratch restoration contract, +plus tariff and layout costs. Use that one contract to test the logical margin, +private cleanup, full native interiors and the break-even inequality above. A +missing bound or forced width surcharge is a precise stopping obstruction. More +floating samples or another isolated decoder constant do not supply this missing +contract. + +## Evidence and credit + +RANGE.json, ROUNDING.json, COST.json, POLYNOMIAL.json and RESULT.json are entirely +recomputed and compared with type-sensitive equality. Gaussian elementary cases, +actual query regressions, dirty reads, altered captures, missing restoration, +changed coefficients and missing natives are exercised. Tests reject source, +manifest and retained-data corruption before analysis, duplicate keys, false +receipts and attempts to overwrite receipts. Registered normal/optimized and +Git-free read-only replay preserve every exported byte. + +PR3985 owns the336-to224 native reduction; PR4015 owns streaming and output hosting; +PR4106 owns the scalar pair construction. PR4003 supplies the residual lineage. +Retain ywz65/#2707, Arham Tahir/#2681, Ali Romman and the native/decoder/compiler +lineage recorded in retained proofs. NickPetalas/#3303 owns the producer grid +and ToikY/#3652 its independent review; Tekalign/tekuuu/#4030 is a distinct shared +frame gate. This new audit is by Chris R / Clear1nsight with substantial OpenAI +Codex assistance, including independent range, rounding/cost and adversarial +agents. This is AI-assisted mathematical evidence, not human or formal approval. diff --git a/research/qq16-paired-precision/RANGE.json b/research/qq16-paired-precision/RANGE.json new file mode 100644 index 0000000000..0799acf2e0 --- /dev/null +++ b/research/qq16-paired-precision/RANGE.json @@ -0,0 +1,3016 @@ +{ + "candidate": { + "model": "strict input component bound 2^P h; lattice hZ; t=lambda-1>=0", + "events": 3713, + "counts": { + "clear": 416, + "add": 2716, + "line": 224, + "map": 352, + "begin": 2, + "end": 2, + "checkpoint": 1 + }, + "private_peak": 16, + "max_M": "171043", + "ceil_log2_max_M": 18, + "max_g": 9, + "max_a": 3, + "max_b": 3, + "quantum": { + "h_power_two_constant": -9, + "h_power_two_t": -3 + }, + "signed_width": { + "P_coefficient": 1, + "constant": 28, + "t_coefficient": 6 + }, + "witnesses": { + "m": [ + 3697, + "event output W0", + [ + "171043", + 9, + 3, + 3 + ] + ], + "a": [ + 2439, + "Gaussian pair sums", + [ + "23728", + 6, + 3, + 3 + ] + ], + "b": [ + 2439, + 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"587", + 5, + 1, + 1 + ], + "Z98": [ + "587", + 5, + 1, + 1 + ], + "Z99": [ + "587", + 5, + 1, + 1 + ] + } + }, + "same_sufficient_quantum": true, + "same_sufficient_width": true, + "same_final_component_envelopes": true, + "completed_query_cuts": { + "candidate": { + "before_event": 2434, + "query_bounds": { + "Z1": [ + "11864", + 4, + 2, + 2 + ], + "Z2": [ + "11864", + 4, + 2, + 2 + ], + "Z3": [ + "11864", + 4, + 2, + 2 + ], + "Z4": [ + "11864", + 4, + 2, + 2 + ], + "Z5": [ + "11864", + 4, + 2, + 2 + ], + "Z6": [ + "11864", + 4, + 2, + 2 + ], + "Z8": [ + "11864", + 4, + 2, + 2 + ], + "Z9": [ + "11864", + 4, + 2, + 2 + ] + }, + "scratch_D": [ + "460", + 4, + 2, + 2 + ], + "tenth_host": [ + "230", + 4, + 2, + 2 + ] + }, + "baseline": { + "before_event": 2536, + "query_bounds": { + "Z1": [ + "11864", + 4, + 2, + 2 + ], + "Z2": [ + "11864", + 4, + 2, + 2 + ], + "Z3": [ + "11864", + 4, + 2, + 2 + ], + "Z4": [ + "11864", + 4, + 2, + 2 + ], + "Z5": [ + "11864", + 4, + 2, + 2 + ], + "Z6": [ + "11864", + 4, + 2, + 2 + ], + "Z8": [ + "11864", + 4, + 2, + 2 + ], + "Z9": [ + "11864", + 4, + 2, + 2 + ] + }, + "scratch_D": [ + "230", + 4, + 2, + 2 + ], + "tenth_host": [ + "1", + 0, + 0, + 0 + ] + } + }, + "first_new_pair_sum": { + "event": 1714, + "opcode": [ + "add", + "Z10", + "Z11", + "1" + ], + "bound": [ + "460", + 4, + 2, + 2 + ] + }, + "independent_depth_checks": [ + { + "lambda": 1, + "max_magnitude": "171043", + "max_grid": 9, + "coordinate_Gaussian_lines": 224 + }, + { + "lambda": 2, + "max_magnitude": "1195465", + "max_grid": 12, + "coordinate_Gaussian_lines": 448 + }, + { + "lambda": 3, + "max_magnitude": "9220309", + "max_grid": 15, + "coordinate_Gaussian_lines": 672 + }, + { + "lambda": 8, + "max_magnitude": "298371196093", + "max_grid": 30, + "coordinate_Gaussian_lines": 1792 + } + ] +} diff --git a/research/qq16-paired-precision/README.md b/research/qq16-paired-precision/README.md new file mode 100644 index 0000000000..06f43afdbf --- /dev/null +++ b/research/qq16-paired-precision/README.md @@ -0,0 +1,71 @@ +# QQ16 paired recovery: range and rounding audit of PR4106 + +**The800-unit scalar allowance saving survives in a common sufficient finite +format.** For every lambda>=1, t=lambda-1, both frozen words admit component +quantum `q=h2^(-9-3t)` and signed width `W=P+28+6t`, provided borrowed entry +components lie in hZ with magnitude<2^P h. No extra candidate width is required +for the specified exact pair-first numerical reference. This is a uniform +sufficient-format comparison, not an optimal-width or recursive supplier claim. + +| Quantity | PR4015 baseline | PR4106 candidate | +|---|---:|---:| +| Logical scalar allowance |26944|26144| +| Unit ADD sites |1920|1820| +| Explicit numeric primitive bill per owner |(12352+2240lambda)N|(12152+2240lambda)N| +| Sufficient signed component bits |P+28+6t|P+28+6t| +| Sufficient component quantum |h2^(-9-3t)|h2^(-9-3t)| + +Here N=2^(73lambda) complex coordinates per owner. The numeric reference includes +Gaussian interiors, shifts, zero stores, monomial signs, out-and-back permutation +copies and a buffer. It saves200N real additions, a different unit from800 logical +allowance. Physical addressing, movement/placement, actual recursive workspace, +usage and supplier caps remain unpriced. + +Two independent all-depth magnitude representations certify the result. Their +largest envelope is171043<2^18, including new shared-sum intermediates. A separate +error interpreter gives identical224 endpoint error polynomials for both words, +without assuming independent rounding errors. Under exact non-overflowing common +grid additions and deterministic isolated callbacks, the fixed-point queries and +outputs are relatively bit-identical. Floating significand rounding can differ: +a literal query-cut example yields Q0=4 versus6 at precision2. That example does +not claim full rounded-caller reachability. + +Read [PROOF.md](PROOF.md) for the main argument and scope, with separate +[range](range-proof.md), [rounding](rounding-proof.md) and [cost](cost-proof.md) +notes. [RESULT.json](RESULT.json) contains the conclusion, fixed-word structural +binding and remaining premises. [SOURCES.json](SOURCES.json) pins five canonical +semantic/proof inputs plus historical provenance; [PREDECESSORS.json](PREDECESSORS.json) +pins the retained PR4106/4015 words, construction and proofs. No predecessor +executable is imported. Endpoint/frame correctness is inherited from those proofs; +this package replays numerical obligations on the whole frozen schedules. + +From the repository root: + +```sh +python3 -B scripts/research_package.py --package research/qq16-paired-precision --check-only +python3.12 -B scripts/research_package.py --package research/qq16-paired-precision +``` + +The registered commands include type-sensitive whole-receipt comparison, +source-first authentication, meaningful corruption controls and normal/optimized +Git-free read-only replay. Success is `PASS_QQ16_PAIRED_PRECISION_CONDITIONAL`. +Tests and AI adversarial review support the stated proof; they are not formal or +human certification. Earlier source package proofs and selected kappa are not +cold-replayed here. + +## Open next questions + +The next viable step is a single actual recursive native/caller contract: pin its +entry lattice/range, output error versus width, native interiors, private return +and tariff/layout. The proof supplies a91101 B2^(3t) logical-cut error margin and +an explicit width-tariff break-even threshold. Neither a real selected supplier +connection nor its physical bill has been supplied, so no new kappa is claimed. +The source-selected value remains836330098538459/500000000000000000. + +Credit: PR3985 native reduction; PR4015 streaming/hosting; PR4106 scalar pairing; +PR4003 residual; ywz65/#2707, Arham Tahir/#2681, Ali Romman and retained native +lineage; NickPetalas/#3303 producer grid; ToikY/#3652 independent review; +Tekalign/tekuuu/#4030 distinct frame gate. New audit by Chris R / Clear1nsight +with substantial OpenAI Codex assistance. New work Apache-2.0; retained notices +and attribution remain in vendor proofs. See TASK.json for the assigned scope, +family gate, overlap limits and agent responsibilities. diff --git a/research/qq16-paired-precision/RESULT.json b/research/qq16-paired-precision/RESULT.json new file mode 100644 index 0000000000..ab94eda144 --- /dev/null +++ b/research/qq16-paired-precision/RESULT.json @@ -0,0 +1,477 @@ +{ + "answer": "No extra width in the declared common sufficient exact-reference format. Actual recursive-child/caller/physical implementation remains conditional, not admitted.", + "checks": { + "Gaussian_reference": { + "controls": [ + "x=1+i,y=1-i gives a component2: norm-one assumption fails", + "x=1,y=0 gives half-integers: unrefined unit grid is not closed" + ], + "cross_numerator_factor": 4, + "native_component_output_factor": 2, + "scope": "Elementary signed Gaussian reference. Tensor/cover/native recipe semantics inherited; this is not an implementation of a recursive child tariff.", + "signed_two_site_cases": 1250 + }, + "all224_endpoint_error_polynomials_equal": true, + "explicit_coordinate_depths": [ + 1, + 2, + 3, + 8 + ], + "independent_polynomial_observations": 3932, + "integer_query_regressions": 106, + "negative_controls": [ + "dirty E read", + "unsupported scalar", + "native inside private scope", + "changed shared sum", + "missing native error/cost contribution", + "changed captured-source recipe", + "missing paid tenth restoration" + ], + "range_observations": 8664 + }, + "conditional_producer_composition": { + "decoder_entry_P": "P+214+38t", + "inherited_producer_q": "h*2^(-71-19t)", + "inherited_producer_width": "P+215+38t", + "joint_q": "h*2^(-80-22t)", + "joint_width": "P+242+44t", + "scope": "Algebraic substitution of source producer sufficient format into new decoder entry theorem. Producer theorem/source semantics inherited, not rerun; actual selected provider/caller linkage and conversion costs unestablished." + }, + "exact_format": { + "arithmetic_residual": "zero for permitted pair-first exact numerical reference", + "input": "h=2^z,z integer;P>=0 integer;each borrowed real/imaginary component in hZ,abs<2^P*h;owned/private dirt unread untilCLEAR;lambda>=1 integer", + "new_minus_baseline_bits": 0, + "optimality": "Sufficient uniform format; no minimality or optimized variable-precision dominance claim", + "q": "h*2^(-9-3t)", + "signed_component_bits": "P+28+6t", + "t": "lambda-1" + }, + "fixed_point_relative_identity": "Exact changed unitADDs,nooverflow,common q,deterministic isolated bank-independent native/map/quarter callbacks imply identical captured sources,queries and downstream outputs. Existing common defects do not become accuracy guarantees.", + "fixed_point_word_binding": { + "baseline_cuts": [ + 1696, + 2536, + 2600 + ], + "candidate_cuts": [ + 1694, + 2434, + 2498 + ], + "captured_ports": [ + 1, + 2, + 3, + 4, + 5, + 6, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 21, + 22, + 23, + 24, + 25, + 26, + 28, + 29, + 30, + 31, + 32, + 33, + 34, + 35, + 37, + 38, + 39, + 40, + 41, + 42, + 43, + 44, + 45, + 47, + 48, + 49, + 50, + 51, + 52, + 53, + 54, + 55, + 56, + 58, + 59, + 60, + 61, + 62, + 63, + 64, + 65, + 66, + 67, + 68, + 69, + 70, + 71, + 72, + 73, + 74, + 75, + 76, + 77, + 78, + 79, + 80, + 81, + 82, + 83, + 84, + 85, + 86, + 87, + 88, + 89, + 90, + 91, + 92, + 93, + 94, + 95, + 96, + 97, + 98, + 99, + 100, + 101, + 102, + 103, + 104, + 105, + 106, + 107, + 108, + 109, + 110 + ], + "captured_recipe_sha256": "95d5fef8a3848b299965098eda83c4c429af6ffb36016034b3016c0d960904c4", + "conclusion": "Captured normalized values, completed queries, response and final suffix outputs have identical bits under the stated fixed-grid premises; no accuracy or actual native-supplier contract inferred.", + "paid_output_definitions": [ + 9, + 10 + ], + "premises": "All callbacks same common q/format, bank-independent and deterministic with isolated scratch; exact changed unitADDs and nooverflow. Query integer coefficient identity separately checked on all104 source basis vectors.", + "response_sha256": "8df8c0af14f361a3ca79ba462124566d23ac48be5a82646c12066f6f7a00698c", + "suffix_sha256": "e1ea4996c41f21b1bdb5bbe0272d53b5f266e0ac07b72823e09b86349debd03f" + }, + "floating_countermodel": { + "all_other_normalized_components_at_observed_coordinate": "0", + "baseline": { + "normalized_ports": [ + 1, + 2, + 3, + 4, + 5, + 6, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 22, + 23, + 24, + 25, + 26, + 28, + 29, + 30, + 31, + 32, + 33, + 34, + 35, + 38, + 39, + 40, + 41, + 42, + 43, + 44, + 45, + 48, + 49, + 50, + 51, + 52, + 53, + 54, + 55, + 56, + 58, + 59, + 60, + 61, + 62, + 63, + 64, + 65, + 66, + 67, + 68, + 69, + 70, + 71, + 72, + 73, + 74, + 75, + 77, + 78, + 79, + 80, + 82, + 83, + 84, + 85, + 86, + 88, + 89, + 90, + 91, + 93, + 94, + 95, + 96, + 97, + 98, + 99, + 100, + 101, + 102, + 103, + 104, + 105, + 106, + 107, + 108, + 109, + 21, + 37, + 47, + 76, + 81, + 87, + 92, + 110 + ], + "queries": [ + "4", + "3", + "4", + "-2", + "0", + "0", + "0", + "0" + ], + "response_start": 2536, + "start": 1696 + }, + "bits": 2, + "candidate": { + "normalized_ports": [ + 76, + 81, + 87, + 92, + 10, + 11, + 62, + 63, + 70, + 71, + 90, + 91, + 2, + 72, + 9, + 79, + 25, + 89, + 61, + 94, + 12, + 56, + 17, + 77, + 31, + 100, + 38, + 103, + 18, + 19, + 39, + 40, + 54, + 55, + 101, + 102, + 24, + 32, + 35, + 85, + 45, + 98, + 48, + 107, + 22, + 23, + 33, + 34, + 49, + 50, + 108, + 109, + 1, + 75, + 6, + 82, + 28, + 86, + 58, + 93, + 29, + 30, + 59, + 60, + 73, + 74, + 83, + 84, + 3, + 66, + 8, + 80, + 26, + 88, + 67, + 95, + 4, + 5, + 64, + 65, + 68, + 69, + 96, + 97, + 14, + 15, + 41, + 42, + 52, + 53, + 105, + 106, + 13, + 43, + 16, + 78, + 44, + 99, + 51, + 104, + 21, + 37, + 47, + 110 + ], + "queries": [ + "6", + "3", + "4", + "-2", + "0", + "0", + "0", + "0" + ], + "response_start": 2434, + "start": 1694 + }, + "normalized_component_values": { + "76": "4", + "87": "1", + "92": "1" + }, + "rounding": "nearest, ties to even, unbounded exponent", + "scope": "Actual query scalar subsequences with exact supplied normalization outputs; not a full rounded-caller counterexample." + }, + "question": "Does the frozen paired word require extra precision that repays800 scalar allowance?", + "retained": { + "vendor/PR4015-PROOF.md": { + "head": "0fff81d8997cef646538bcd4f60d7d455cf93b8e", + "sha256": "81f0fa19b19fa7302ba9c61f4f1b2e11758f973b964240ba48c16ae9b6997396" + }, + "vendor/PR4015-WORD.json": { + "head": "0fff81d8997cef646538bcd4f60d7d455cf93b8e", + "sha256": "272d8c1bd172c29044eb227ec6d67a882501250978234685e035158f4479aa58" + }, + "vendor/PR4106-CONSTRUCTION.json": { + "head": "48529915d50bb59b53db53686c4add1cf53429dd", + "sha256": "dbf7b1d077b1b58262afe22aceeac02262c50c6597392676ea7a98e7d9cdd075" + }, + "vendor/PR4106-PROOF.md": { + "head": "48529915d50bb59b53db53686c4add1cf53429dd", + "sha256": "5d79ac0fafa95c81f000f1da9802abfaac5adedd9017d0d5e651220bb682e2a7" + }, + "vendor/PR4106-WORD.json": { + "head": "48529915d50bb59b53db53686c4add1cf53429dd", + "sha256": "b4f2b5662734178d02a5d620ebd071bc284abd4d9b6dbe11b5d9646455a0f021" + } + }, + "rounded_logical_cut_headroom": { + "general": "E_entry(lambda)*epsilon+E_scalar(lambda)*eta+E_native(lambda)*nu < 91101*(2^P*h)*2^(3*(lambda-1))", + "lambda1": "182803epsilon+263970eta+91185nu < 91101*(2^P*h)", + "scope": "Sufficient common-width logical-cut nonoverflow margin only. Actual eta/nu and native interiors/private cleanup remain separate premises." + }, + "same_width_costs": { + "N": "2^(73lambda) complex coordinates per owner", + "actual_recursive_child_tariff": "unknown; pair-first numerical reference is not free substitution", + "logical_allowance_after": 26144, + "logical_allowance_before": 26944, + "logical_difference": 800, + "numeric_after": "(12152+2240lambda)N", + "numeric_before": "(12352+2240lambda)N", + "numeric_difference": "200N real-component additions/subtractions at common W" + }, + "scope": "Exact/common-grid reference plus conditional error/bit-cost comparisons; endpoint/frame identity inherited from frozen4106/4015. No predecessor executable imported. No actual recursive supplier admission, physical gain, human/formal proof or newkappa.", + "source_inputs": { + "research/joint-query/evidence/JOINT-QUERY-TRANSFER.md": "9e13e73ebf3192a6548798c2f1d13bd4d83957e8db0dc34de12b1a5311a52a75", + "research/qq16-all-depth-producer-grid/PROOF.md": "6dd878aa01807eecf4a37f7ce3fbc1105d79f6b1b06791b23d4deeef90b7d994", + "research/qq16-line-normalized-decoder/PROOF.md": "0a0995e70f2a64c15cdd1aee66634d1ba221cbcb2a7cfa3a4d4950a37d0e143a", + "research/qq16-line-normalized-decoder/verify.py": "0f6fb86aafb74b9722f20cc97af70a3a3c78bd012c142b2eaa19cb00e02d1fe9", + "research/qq16-producer-defect-transfer/README.md": "30cf4389425f7704b1ed45af6cf4b5165e7b5c04af5077640ac96399c61cd703" + }, + "status": "PASS_QQ16_PAIRED_PRECISION_CONDITIONAL" +} diff --git a/research/qq16-paired-precision/REVIEWS.json b/research/qq16-paired-precision/REVIEWS.json new file mode 100644 index 0000000000..01bbf1f7e9 --- /dev/null +++ b/research/qq16-paired-precision/REVIEWS.json @@ -0,0 +1,33 @@ +{ + "scope": "Assisted mathematical review, not human or formal approval. No blocking correction remains in the stated conditional domain.", + "reviewer": "precision_adversary", + "checks": [ + "Independent direct-depth recurrence lambda1,2,3,8,17", + "All-depth shifted positive-polynomial envelope", + "Shared q/W and signed width calculation", + "Fixed-bank numerical invoice including return copies", + "Producer-grid substitution and logical-cut headroom", + "Literal captured-source/response/suffix binding; altered port, missing tenth restoration, changed response rejected" + ], + "correction_applied": "Cost proof explicitly identifies direct C_q formula; no extra phase operation. Range proof distinguishes producer output phase from direct C_q.", + "reviewed_sha256": { + "verify.py": "483356a1326de5f11a33bcc44ce6487bc96ad7a5c399e5ca450c79b297c185ea", + "binding.py": "82276de49c4fd64719ac2edcc110bebcf6236de30251be0f9771b7ce10a5446f", + "independent.py": "9f44ad5c70af9082330f0125d20cd49504c45eba69e98295a9c26f142d8e3732", + "range.py": "5a3082ae94c3bd6bdb1f4e73750d768c83c971e995803e6ed13a974add114eca", + "range-proof.md": "669bb117fe6c2162e85b3838cd6e9f4f1c776a08b43221627abec9b644173923", + "rounding.py": "0f86a534f8ab1a32a5db04443028560764439b29d1265b671b07109432120813", + "rounding-proof.md": "787e0dffff0e6f1b4475e4cca5cc3f5d13a734e7e9dd13b072b8aa8d34090ca3", + "numeric-cost.py": "79056708c1655d5897ef88c6fa803b8c2557fb487d9a574f5a0df42e8a7d0e64", + "cost-proof.md": "b6c27163ed4c1e20d8f999c8ed1d481ad266cea4834090167c77232a8f7ce998", + "RANGE.json": "dc25c3fb8f22b067cd66be38f34825a98433eb6c83544e7d868c96d3fe89f5bb", + "ROUNDING.json": "fe30882cfa9a3839e760398063c8dd13d44676f2fa6423f63e25d9823a30191d" + }, + "central_prose_review": { + "conclusion": "Accepted within conditional scope; no overclaim or missing implication found in final central proof and README.", + "sha256": { + "PROOF.md": "d9c13e5128800015b04f3a3060d1e7dfc0bdbb6285d4ee799019da4c033813bc", + "README.md": "7c6700b0e22b192c06d5c67ce7f0843f26dcab7e4ee54b614f305bf4dc03c246" + } + } +} diff --git a/research/qq16-paired-precision/ROUNDING.json b/research/qq16-paired-precision/ROUNDING.json new file mode 100644 index 0000000000..649cb169e0 --- /dev/null +++ b/research/qq16-paired-precision/ROUNDING.json @@ -0,0 +1,873 @@ +{ + "all_224_endpoint_envelopes_equal": true, + "correlation": "Each shared pair residual is reused in all equal-sign channels; no independence or root-sum-square assumption.", + "endpoint_envelope_classes": [ + { + "fields": [ + "W0", + "W111", + "W20", + "W27", + "W36", + "W46", + "W57", + "W7" + ], + "polynomial": [ + [ + "entry", + 0, 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"Z27", + "Z36", + "Z46", + "Z57", + "Z7" + ], + "polynomial": [ + [ + "entry", + 0, + "444" + ], + [ + "entry", + 1, + "14112" + ], + [ + "entry", + 2, + "16" + ], + [ + "entry", + 3, + "11856" + ], + [ + "native", + 0, + "14116" + ], + [ + "native", + 1, + "208" + ], + [ + "native", + 2, + "11856" + ], + [ + "scalar", + 0, + "16373" + ], + [ + "scalar", + 1, + "14336" + ], + [ + "scalar", + 2, + "12736" + ], + [ + "scalar", + 3, + "11856" + ] + ] + }, + { + "fields": [ + "Z1", + "Z10", + "Z100", + "Z101", + "Z102", + "Z103", + "Z104", + "Z105", + "Z106", + "Z107", + "Z108", + "Z109", + "Z11", + "Z12", + "Z13", + "Z14", + "Z15", + "Z16", + "Z17", + "Z18", + "Z19", + "Z2", + "Z22", + "Z23", + "Z24", + "Z25", + "Z26", + "Z28", + "Z29", + "Z3", + "Z30", + "Z31", + "Z32", + "Z33", + "Z34", + "Z35", + "Z38", + "Z39", + "Z4", + "Z40", + "Z41", + "Z42", + "Z43", + "Z44", + "Z45", + "Z48", + "Z49", + "Z5", + "Z50", + "Z51", + "Z52", + "Z53", + "Z54", + "Z55", + "Z56", + "Z58", + "Z59", + "Z6", + "Z60", + "Z61", + "Z62", + "Z63", + "Z64", + "Z65", + "Z66", + "Z67", + "Z68", + "Z69", + "Z70", + "Z71", + "Z72", + "Z73", + "Z74", + "Z75", + "Z77", + "Z78", + "Z79", + "Z8", + "Z80", + "Z82", + "Z83", + "Z84", + "Z85", + "Z86", + "Z88", + "Z89", + "Z9", + "Z90", + "Z91", + "Z93", + "Z94", + "Z95", + "Z96", + "Z97", + "Z98", + "Z99" + ], + "polynomial": [ + [ + "entry", + 0, + "9" + ], + [ + "entry", + 1, + "289" + ], + [ + "native", + 0, + "289" + ], + [ + "scalar", + 0, + "334" + ], + [ + "scalar", + 1, + "289" + ] + ] + }, + { + "fields": [ + "Z110", + "Z21", + "Z37", + "Z47", + "Z76", + "Z81", + "Z87", + "Z92" + ], + "polynomial": [ + [ + "entry", + 0, + "4" + ], + [ + "entry", + 1, + "8" + ], + [ + "entry", + 2, + "16" + ], + [ + "entry", + 3, + "11856" + ], + [ + "native", + 0, + "12" + ], + [ + "native", + 1, + "208" + ], + [ + "native", + 2, + "11856" + ], + [ + "scalar", + 0, + "24" + ], + [ + "scalar", + 1, + "232" + ], + [ + "scalar", + 2, + "12736" + ], + [ + "scalar", + 3, + "11856" + ] + ] + } + ], + "fixed_point_condition": "Exact nonoverflowing integer unitADDs imply same queries for arbitrary supplied normalization outputs on a common lattice; deterministic isolated normalizers and unchanged response/suffix then imply relative bitidentity, including any common preexisting defects.", + "fixed_point_query_regression_cases": 106, + "floating_no_automatic_bitwise_transfer": true, + "model": { + "entry": "epsilon per borrowed input real/imaginary component", + "exact": [ + "CLEAR", + "cover permutations", + "signed monomial permutations" + ], + "native": "nu per complete signed tensor-native output component", + "restriction": "No relation between eta/nu and a machine significand, nor an overflow guarantee, is inferred.", + "scalar": "eta absolute residual of complete scalar ADD versus ideal dst+c*src, including product/division, addition and storage errors; ideal coefficient exact", + "x": "2^lambda" + }, + "peak_scope": "Logical cuts only; internal approximate native arithmetic is supplied by the native contract, not inferred.", + "query_accumulation_scalar_error_multiplicities": [ + 52, + 52, + 52, + 52, + 52, + 52, + 52, + 52 + ], + "restoration_boundary": "Rounded envelope alone does not certify zero private-scratch restoration; exact-grid theorem or a native/private cleanup contract is needed.", + "rounded_query_witness": { + "all_other_normalized_components_at_observed_coordinate": "0", + "baseline": { + "normalized_ports": [ + 1, + 2, + 3, + 4, + 5, + 6, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 22, + 23, + 24, + 25, + 26, + 28, + 29, + 30, + 31, + 32, + 33, + 34, + 35, + 38, + 39, + 40, + 41, + 42, + 43, + 44, + 45, + 48, + 49, + 50, + 51, + 52, + 53, + 54, + 55, + 56, + 58, + 59, + 60, + 61, + 62, + 63, + 64, + 65, + 66, + 67, + 68, + 69, + 70, + 71, + 72, + 73, + 74, + 75, + 77, + 78, + 79, + 80, + 82, + 83, + 84, + 85, + 86, + 88, + 89, + 90, + 91, + 93, + 94, + 95, + 96, + 97, + 98, + 99, + 100, + 101, + 102, + 103, + 104, + 105, + 106, + 107, + 108, + 109, + 21, + 37, + 47, + 76, + 81, + 87, + 92, + 110 + ], + "queries": [ + "4", + "3", + "4", + "-2", + "0", + "0", + "0", + "0" + ], + "response_start": 2536, + "start": 1696 + }, + "bits": 2, + "candidate": { + "normalized_ports": [ + 76, + 81, + 87, + 92, + 10, + 11, + 62, + 63, + 70, + 71, + 90, + 91, + 2, + 72, + 9, + 79, + 25, + 89, + 61, + 94, + 12, + 56, + 17, + 77, + 31, + 100, + 38, + 103, + 18, + 19, + 39, + 40, + 54, + 55, + 101, + 102, + 24, + 32, + 35, + 85, + 45, + 98, + 48, + 107, + 22, + 23, + 33, + 34, + 49, + 50, + 108, + 109, + 1, + 75, + 6, + 82, + 28, + 86, + 58, + 93, + 29, + 30, + 59, + 60, + 73, + 74, + 83, + 84, + 3, + 66, + 8, + 80, + 26, + 88, + 67, + 95, + 4, + 5, + 64, + 65, + 68, + 69, + 96, + 97, + 14, + 15, + 41, + 42, + 52, + 53, + 105, + 106, + 13, + 43, + 16, + 78, + 44, + 99, + 51, + 104, + 21, + 37, + 47, + 110 + ], + "queries": [ + "6", + "3", + "4", + "-2", + "0", + "0", + "0", + "0" + ], + "response_start": 2434, + "start": 1694 + }, + "normalized_component_values": { + "76": "4", + "87": "1", + "92": "1" + }, + "rounding": "nearest, ties to even, unbounded exponent", + "scope": "Actual query scalar subsequences with exact supplied normalization outputs; not a full rounded-caller counterexample." + }, + "status": "PASS_CONDITIONAL_ROUNDING_ENVELOPE_AND_CHANGED_DAG_WITNESS", + "whole_word_logical_cut_coefficient_envelope": [ + [ + "entry", + 0, + "445" + ], + [ + "entry", + 1, + "14115" + ], + [ + "entry", + 2, + "2964" + ], + [ + "entry", + 3, + "17784" + ], + [ + "native", + 0, + "14121" + ], + [ + "native", + 1, + "2964" + ], + [ + "native", + 2, + "17784" + ], + [ + "scalar", + 0, + "16380" + ], + [ + "scalar", + 1, + "14451" + ], + [ + "scalar", + 2, + "19104" + ], + [ + "scalar", + 3, + "17784" + ] + ], + "whole_word_logical_cut_coefficient_envelope_equal": true +} diff --git a/research/qq16-paired-precision/SOURCES.json b/research/qq16-paired-precision/SOURCES.json new file mode 100644 index 0000000000..b679389760 --- /dev/null +++ b/research/qq16-paired-precision/SOURCES.json @@ -0,0 +1,48 @@ +{ + "schema_version": 1, + "base_commit": "bb4bccbf42844d2801487450727c2f63e10d1d0f", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81", + "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "67f085acd86acd7d4e03922d9cf4b26bca66fed5", + "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0" + }, + { + "path": "research/joint-query/evidence/JOINT-QUERY-TRANSFER.md", + "usage": "input", + "git_blob": "a6805c58f23132f9420efebf90f5b7e863c2e179", + "sha256": "9e13e73ebf3192a6548798c2f1d13bd4d83957e8db0dc34de12b1a5311a52a75" + }, + { + "path": "research/qq16-line-normalized-decoder/PROOF.md", + "usage": "input", + "git_blob": "f7c694ff54e590416e4a52fa762f9d3b9474bccb", + "sha256": "0a0995e70f2a64c15cdd1aee66634d1ba221cbcb2a7cfa3a4d4950a37d0e143a" + }, + { + "path": "research/qq16-line-normalized-decoder/verify.py", + "usage": "input", + "git_blob": "a8f3c811108414eda0b507d295cfc9301c04d585", + "sha256": "0f6fb86aafb74b9722f20cc97af70a3a3c78bd012c142b2eaa19cb00e02d1fe9" + }, + { + "path": "research/qq16-all-depth-producer-grid/PROOF.md", + "usage": "input", + "git_blob": "9cf1ec57646fb760fd26f206d754e52c99c347e3", + "sha256": "6dd878aa01807eecf4a37f7ce3fbc1105d79f6b1b06791b23d4deeef90b7d994" + }, + { + "path": "research/qq16-producer-defect-transfer/README.md", + "usage": "input", + "git_blob": "16903a0090c020d033d24712cce11c633031e688", + "sha256": "30cf4389425f7704b1ed45af6cf4b5165e7b5c04af5077640ac96399c61cd703" + } + ] +} diff --git a/research/qq16-paired-precision/TASK.json b/research/qq16-paired-precision/TASK.json new file mode 100644 index 0000000000..feb246d9a3 --- /dev/null +++ b/research/qq16-paired-precision/TASK.json @@ -0,0 +1,152 @@ +{ + "schema_version": 1, + "task_id": "joint-query-controller", + "priority_revision": 6, + "base_commit": "bb4bccbf42844d2801487450727c2f63e10d1d0f", + "original_card": { + "id": "joint-query-controller", + "question": "Can a literal QQ16 producer meet the proposed completed-output error budgets with dirty helpers and an affordable physical consumer?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/joint-query/README.md", + "research/joint-query/evidence/QQ16-SELECTED-WITNESS.md", + "research/joint-query/evidence/JOINT-QUERY-TRANSFER.md", + "docs/research/community-efficient1000-review.md", + "research/qq16-producer-defect-transfer/README.md" + ], + "methods": [ + "Derive one literal producer's completed-output defects and intermediate dirty-helper bounds, with its physical bill.", + "Design or audit one consumer, retention or hosting boundary and its complete cost for the pinned producer/decoder." + ], + "acceptance_gate": "Name the changed premise of the fixed F0/B1 observation obstruction. Show exactly which query is recovered, legal native reads and restoration, and a full favorable budget including cover maps, helpers and endpoints. Local inverse identities alone do not close the global controller. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read the revision-6 family record and #2965 producer-defect transfer after the local QQ16 decoder contract. Its author-checked output-error estimate does not implement producer interiors, bound dirty helpers, or pay for the consumer; independently check the implication used.", + "scope": "Source-bound orientation only. Read the named package and review before relying on its local evidence; this command is not its replay or supplier admission." + }, + "first_experiment": "Pin one literal F0/B1 producer and its native-child contracts; derive the actual intermediate magnitude ledger and completed-output defects, including dirty helpers and correlations. Compare with #2965 budgets and price storage, movement, cleanup and F17 consumption. Stop with a precise missing bound if no producer contract supplies it; do not optimize another decoder precision constant in isolation.", + "bottleneck_link": "The native local words exist; retained query information and its physical access are the missing link to a composed recursive interface.", + "allowed_variations": [ + "One paid query, one changed first pair, or one precisely specified affine helper state.", + "A counterexample or lower bound for that exact proposed repair.", + "One unresolved obligation of a newer local decoder, with exact source heads and a distinct claim/domain." + ], + "scope_change_triggers": [ + "Retaining the fixed first pair and ordinary schedule while allowing only homogeneous selected-only control, already excluded by the witness.", + "Treating cover-map counts as zero-cost physical address operations.", + "Recreating the pending complete local decoder or early-record/output-bank coalescing already under investigation without a distinct audit or changed premise.", + "Treating a completed-output defect inequality as a producer-interior, dirty-range or physical-cost certificate." + ], + "overlap_terms": [ + "QQ16", + "joint-query", + "changing-chart controller", + "selected observation", + "1969", + "2540", + "early record", + "output-bank retention", + "complete native decoder", + "2965", + "producer defect", + "dirty-helper range", + "F17 consumer" + ] + }, + "scope_status": "changed", + "actual_scope": "Range, rounding and finite-width cost audit of the unchanged224-output paired-source recovery WORD at PR4106.", + "scope_change_reason": "Explicit assigned audit of the new arithmetic DAG; closes a remaining precision obligation rather than another inverse or isolated producer constant.", + "bottleneck_link": "The new shared-source arithmetic changes intermediate range and rounded correlation. A common all-depth format and cost comparison closes that relative obligation, while the missing actual recursive native/caller error-width, workspace and tariff contract still blocks physical composition.", + "budget_minutes": 60, + "stop_rule": "One frozen-word audit, at most one justified precision-contract pivot; science freeze01:50UTC, verification reserve01:55\u201302:10UTC. Stop at a certified same-width result or precise model/format obstruction.", + "outcome": "completed", + "evidence": "Common all-depth sufficient q=h2^(-9-3t), W=P+28+6t for both complete frozen words; second independent positive-polynomial certificate; identical224 endpoint error polynomials; literal fixed-point binding; actual floating query-cut witness; numeric bills12352+2240lambda vs12152+2240lambda timesN. Scoped audit complete; actual supplier and kappa remain unestablished.", + "author": "Chris R / Clear1nsight with OpenAI Codex assistance", + "ai_assistance": "Substantial OpenAI Codex assistance in research, code, proofs, documentation and review. Root integrated; separate range and rounding/cost workers; independent adversarial reviewer. Python exact rational arithmetic and symbolic recurrences; authenticated Git and GitHub browser used for source pins and publication. No human or formal proof approval.", + "open_questions": [ + { + "question": "Does one actual recursive H1 child used by the F0 caller satisfy the common-grid finite-width and error/interior contract at a favorable full tariff?", + "why_it_matters": "The logical saving and exact numerical reference do not establish native interior overflow, scratch restoration, error versus width or a selected caller connection. These can change the full cost and any kappa implication.", + "first_step": "Pin one actual child and caller source head. Extract entry grid/range, output nu(W,lambda), native-interior range and scratch return contract, and tariff/layout. Test the91101 B2^(3t) logical margin, all native interiors and tau(Wc)/tau(Wb)<(12352+2240lambda)/(12152+2240lambda), with entry conversion and physical costs charged.", + "blocked_by": "No actual recursive implementation/caller contract supplying these quantities is established by4106,4015 or this audit; do not replace its tariff by the coordinate reference for free." + } + ], + "boundary": { + "sources": "Mainbb4bccbf42844d2801487450727c2f63e10d1d0f;4106head48529915d50bb59b53db53686c4add1cf53429dd,4015head0fff81d8997cef646538bcd4f60d7d455cf93b8e. Literalwords frozen.", + "interface": "All224 original outputs F17,224 borrowed currentXY values/frames unchanged;224 ownedoutputs,privatepeak16; ten vsnine deferredoutputhosts; native/private exclusion inherited.", + "precision": "Exact common q=h2^(-9-3t), W=P+28+6t under stated lattice/range and pair-first native reference. Fixed-grid relative bit identity conditional on exact nonoverflowing unit adds and isolated deterministic callbacks; floating bit transfer fails at actual query cut. Approximate native interiors/cleanup remain separate.", + "objective": "Prove whether finite-width numerical costs preserve800scalarallowance under statedmodel; unknown physical/native-workspace/caller costs remain unknown.", + "alphabet": "Existing literalADD\u00b11,\u00b11/4,CLEAR,maps,signednative lines,begin/end/checkpoint; no word changes." + }, + "expansion_decision": { + "source_status": "4106 exact localword+hostedreplay reproduced priorround;4043 supplies conditionalsame-DAGtransfer only; producer3303 excludesdecoder.", + "costs": "Common sufficient width confirmed.26144 vs26944 logical allowance;224H1,448wrappers,352maps unchanged. Explicit fixed-bank numerical reference12152+2240lambda vs12352+2240lambda timesN saves200Nrealadds. Physical addresses/movement, actual recursive workspace, usage/caps and caller entry conversion remain unpriced.", + "decision_change": "Arithmetic sharing saves100ADDsites butnewD+=E intermediates andcorrelatedrounding mayrepay it. AuditactualwholeDAG ratherthan transferoldcertificate.", + "decision": "Complete this one finite-format audit and stop. Next experiment requires one actual recursive child/caller contract; no new decoder construction or selected frontier change.", + "stop": "No newnative/physicalsupplierorKclaim withoutthosecontracts; retain preciseobstruction if sourcefinitepremise unavailable." + }, + "round": { + "start_utc": "2026-10-20T01:10:28Z", + "target_end_utc": "2026-10-20T02:10:28Z", + "upstream_main": "bb4bccbf42844d2801487450727c2f63e10d1d0f", + "priority_revision": 6, + "overlap": "helper39localrecords/21matches, missingghremotePR/Discussiondata; boundedall-stateQQ16roundingsearch andnewestDiscussion1166 inspected, broadercoveragepartial.", + "checkpoint_utc": "2026-10-20T01:31:00Z", + "checkpoint_result": "Canonical main and4106/4015 heads unchanged. Re-read current priorities/family status and contribution scope. All-state QQ16 precision/range/rounding search includes concurrent4108headedd6426abf8341daee53d898d81d709d8c7680bd: distinct current-output factor/native acquisition obstruction; inspected body as advisory, not executable dependency or verified theorem. No overlapping4106 precision audit found in bounded search; broader remote coverage partial." + }, + "candidate": { + "q": "h2^(-9-3t),t=lambda-1>=0", + "W": "P+28+6t", + "status": "Confirmed by integrated exact replay and independent assisted adversarial review; a sufficient uniform-format implication, not optimized-width dominance.", + "rounding_models": "Exactdyadicreference zeroerror; fixedq exactunitADD relativebittransferconditionalonnooverflow; floating significandroundingcan differ.", + "cost_boundary": "Uniformsufficientformat comparison vs4015, notoptimizedvariableprecision dominance oractualrecursivesupplier." + }, + "scope_key": "5423eef254a4943f6bf1", + "workers": [ + { + "agent": "range_audit", + "ownership": [ + "range.py", + "RANGE.json", + "range-proof.md" + ], + "method": "All-depth lattice/component induction plus independent explicit depth recurrence. Primary numerical analysis paired with ordered dyadic lattice bounds." + }, + { + "agent": "rounding_cost_audit", + "ownership": [ + "rounding.py", + "ROUNDING.json", + "rounding-proof.md", + "numeric-cost.py", + "cost-proof.md" + ], + "method": "Correlated forward-error polynomials, exact rational floating rounder and integer circuit associativity; explicit primitive/copy invoice." + }, + { + "agent": "precision_adversary", + "ownership": "Read-only independent audit", + "method": "Independent direct-depth recurrence, shifted positive-polynomial certificate, binding mutations and proof/cost review; assisted review only." + }, + { + "agent": "root", + "ownership": [ + "verify.py", + "independent.py", + "binding.py", + "test_verify.py", + "PROOF.md", + "README.md", + "metadata", + "integration", + "publication" + ], + "method": "Source authentication, literal boundary binding, independent certificate implementation, producer substitution and residual-headroom gates; registered and exported replay." + } + ] +} diff --git a/research/qq16-paired-precision/VERIFICATION.json b/research/qq16-paired-precision/VERIFICATION.json new file mode 100644 index 0000000000..a57c6109f1 --- /dev/null +++ b/research/qq16-paired-precision/VERIFICATION.json @@ -0,0 +1,17 @@ +{ + "status": "PASS_REGISTERED_RESEARCH_PACKAGE", + "python": "3.12.3", + "commands": [ + "python3.12 -B scripts/research_package.py --package research/qq16-paired-precision", + "python3.12 -I -O -Werror -B research/qq16-paired-precision/test_verify.py" + ], + "tests": "Four boundary groups passed; registered primary and full boundary suite passed. Test suite28.669seconds under registered interpreter; normal and optimized Git-free read-only content equality included.", + "scope": "Source integrity and numerical conditional contract only. No full predecessor/selected cold replay, no native supplier/caller admission or human/formal proof approval.", + "receipts_sha256": { + "RANGE.json": "dc25c3fb8f22b067cd66be38f34825a98433eb6c83544e7d868c96d3fe89f5bb", + "ROUNDING.json": "fe30882cfa9a3839e760398063c8dd13d44676f2fa6423f63e25d9823a30191d", + "COST.json": "48ef92c528fde3ccbcb820f32d7673327dd1c35b2da87363f14bdb0b5df956f7", + "POLYNOMIAL.json": "62ee2d1cdf1a949c2032c59c2c8b7c96acdcadf2b2a93aa572b9b3c7aa0d63aa", + "RESULT.json": "f5dcaa599862d60493a1a9a9fcdd5bbfaf814d2cb426d2aa1bcff8183fb6d7bf" + } +} diff --git a/research/qq16-paired-precision/VERIFY.json b/research/qq16-paired-precision/VERIFY.json new file mode 100644 index 0000000000..4cd6f1e25c --- /dev/null +++ b/research/qq16-paired-precision/VERIFY.json @@ -0,0 +1,39 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/joint-query/evidence/JOINT-QUERY-TRANSFER.md", + "research/qq16-all-depth-producer-grid/PROOF.md", + "research/qq16-line-normalized-decoder/PROOF.md", + "research/qq16-line-normalized-decoder/verify.py", + "research/qq16-producer-defect-transfer/README.md" + ], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-O", + "-Werror", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 120, + "checks": "Authenticate all five canonical and five retained inputs before new analyzers; recompute whole range, rounding, fixed-point literal binding, cost, independent all-depth polynomial and typed receipts; actual Gaussian and semantic controls." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-Werror", + "-B", + "{package}/test_verify.py" + ], + "timeout_seconds": 500, + "checks": "Git-free read-only normal/optimized replay; unchanged content snapshot; source-before-analysis authentication; manifest/vendor corruption; typed whole receipts, duplicate keys and exclusive creation." + } + ] +} diff --git a/research/qq16-paired-precision/binding.py b/research/qq16-paired-precision/binding.py new file mode 100644 index 0000000000..dc35f75e38 --- /dev/null +++ b/research/qq16-paired-precision/binding.py @@ -0,0 +1,53 @@ +"""Literal binding for the conditional fixed-grid reassociation theorem. +Chris R / Clear1nsight with OpenAI assistance. Apache-2.0. +No native implementation or predecessor executable is invoked. +""" +import hashlib,json +QUERY=['Z1','Z2','Z3','Z4','Z5','Z6','Z8','Z9'] +def need(ok,why): + if not ok:raise ValueError(why) +def digest(obj):return hashlib.sha256(json.dumps(obj,separators=(',',':')).encode()).hexdigest() +def cut(word): + start=word.index(['clear','Z1','query2']) + response=word.index(['clear','Z10','query2'],start+8) + restore=word.index(['clear','Z1','current'],response) + return start,response,restore + +def sources(word,start,response): + captured={} + for i in range(start,response): + e=word[i] + if e[0]=='line': + _,name,p,sign=e + expected=[['clear',name,'current'],['add',name,'W'+str(p),'1'],['map',name,2,p,False],['line',name,p,-1]] + need(sign==-1 and word[i-3:i+1]==expected,'source normalization recipe') + need(p not in captured,'source acquired twice') + captured[p]=[v[0:1]+['TEMP']+v[2:] for v in expected] + need(not(e[0] in ('clear','add','line','map') and e[1].startswith(('X','Y','W'))),'query changes captured source/borrowed value') + need(len(captured)==104,'all104 actual normalized sources') + return captured + +def audit(baseline,candidate): + bs,br,bt=cut(baseline);cs,cr,ct=cut(candidate) + definition=[['clear','Z11','current'],['add','Z11','X11','1']] + idx=baseline.index(definition[0]);need(baseline[idx:idx+2]==definition and idx+2<=bs,'tenth definition prefix') + oldprefix=baseline[:idx]+baseline[idx+2:bs] + need(oldprefix==candidate[:cs],'prefix differs beyond tenth deferral') + oldsources=sources(baseline,bs,br);newsources=sources(candidate,cs,cr) + need(oldsources==newsources,'normalized source tags differ') + need(baseline[br:bt]==candidate[cr:ct],'response arithmetic differs') + olddefinitions=sum(([['clear',n,'current'],['add',n,'X'+n[1:],'1']] for n in QUERY+['Z10']),[]) + newdefinitions=olddefinitions+definition + need(baseline[bt:bt+18]==olddefinitions,'nine baseline output definitions') + need(candidate[ct:ct+20]==newdefinitions,'ten paid candidate output definitions') + need(baseline[bt+18:]==candidate[ct+20:],'preserved suffix differs') + # The old tenth host has no numerical consumer before its preserved suffix; + # otherwise delaying the original copy would need another proof. + refs=[i for i,e in enumerate(baseline[:bt+18]) if 'Z11' in e[1:3]] + need(refs==[idx,idx+1],'tenth host live before suffix') + return {'baseline_cuts':[bs,br,bt],'candidate_cuts':[cs,cr,ct], + 'captured_ports':sorted(oldsources),'captured_recipe_sha256':digest(oldsources), + 'response_sha256':digest(baseline[br:bt]),'suffix_sha256':digest(baseline[bt+18:]), + 'paid_output_definitions':[9,10], + 'premises':'All callbacks same common q/format, bank-independent and deterministic with isolated scratch; exact changed unitADDs and nooverflow. Query integer coefficient identity separately checked on all104 source basis vectors.', + 'conclusion':'Captured normalized values, completed queries, response and final suffix outputs have identical bits under the stated fixed-grid premises; no accuracy or actual native-supplier contract inferred.'} diff --git a/research/qq16-paired-precision/cost-proof.md b/research/qq16-paired-precision/cost-proof.md new file mode 100644 index 0000000000..8ac76aee17 --- /dev/null +++ b/research/qq16-paired-precision/cost-proof.md @@ -0,0 +1,75 @@ +# A finite-width comparison with declared units + +The literal words have the following complete local counts, independently +recounted by numeric-cost.py. All prices below are prescribed reference bills, +not lower bounds on optimal machines. + +| Quantity | PR4015 | PR4106 | +|---|---:|---:| +| Unit ADD |1920|1820| +| Quarter ADD |896|896| +| CLEAR |416|416| +| Signed H1 calls |224|224| +| Monomial wrappers |448|448| +| Covers |352|352| +| Private peak |16|16| +| Logical scalar allowance |26944|26144| + +Under the common sufficient width W=P+28+6(lambda-1) and quantum supplied by the +range audit, neither reference needs extra relative precision. If one allowance +unit is assigned a common positive tariff tau_L(W), the prescribed scalar +allowance decreases by exactly800 tau_L(W). This restates a logical allowance +comparison; it does not measure actual processor instructions or recursive cost. + +For a distinct, explicit numeric reference, let N=2^(73lambda) complex payload +coordinates per owner. A complex unit ADD costs2N real adds/subtractions. A quarter +ADD costs2N exact shifts by two (one W-bit shift primitive per component) and2N adds/subtractions. The grid proof covers the two intermediate halvings without pricing two shift instructions. CLEAR costs2N zero stores. +A coordinate Gaussian line uses the direct C_q pair-first formula in range-proof.md: at most4N +real additions,2N exact halvings and4N component copies. There are lambda such +lines per rank-one H1 call. A signed monomial uses2N sign operations and4N copies; a cover uses4N copies. Each permutation writes2N components into one reusable complex buffer and copies2N components back to the original fixed external bank. This pays the return leg without relying on handle rebinding. Address construction, control work and physical movement tariffs are outside this numeric count. + +Thus the prescribed numeric bounds per owner are + +``` +PR4015: (12352 + 2240 lambda) N +PR4106: (12152 + 2240 lambda) N. +``` + +The difference is **200N numeric word operations**, distinct from800 logical +allowance units. Their scalar-only numeric bills are8256N and8056N; unchanged +wrappers/covers contribute4096N and Gaussian interiors2240lambda N. The reference +can use at most930N+12 signed W-bit component slots:448 persistent complex fields, +16 private complex fields, one complex permutation buffer and12 scalar temporaries. +This counts logical numeric storage, not a verified placement or recursive native +workspace. The literal words never overlap private scopes with native calls. + +For any common strictly positive primitive tariff tau(W), the reference bound +falls by200N tau(W). For example tau(W)=W gives the symbolic bit-operation reference +bill200NW less. This deliberately declares one uniform price for every counted +primitive; an actual machine can instead attach distinct positive prices, in +which case the only differing counts are200N real additions/subtractions, so the +saving is200N times their common-width price. Unchanged primitive counts cancel +only when both runs use the same tariff and implementation contract. + +If candidate and baseline widths differ, the uniform-tariff break-even condition is + +``` +tau(W_candidate)/tau(W_baseline) + < (12352+2240lambda)/(12152+2240lambda). +``` + +For tau(W)=W and W_candidate=W_baseline+Delta, this is +`Delta < 200 W_baseline/(12152+2240lambda)`. The logical allowance comparison alone +instead has ratio threshold26944/26144. Equal width satisfies both strict +conditions for every lambda>=1 and W>0. These are useful failure boundaries if a +later native/caller contract forces extra candidate precision; there is no claim +that the current sufficient W is minimal for either word. + +The pair-first coordinate reference is an explicitly permitted implementation +premise for this numerical count. It is **not** a replacement at no cost for a +charged recursive H1 child. The actual child can have a different error/width +contract and tariff. Neither this count nor exact-grid execution prices physical +addresses, movement/placement, native recursive workspace, entry conversion, +recursive usage or supplier caps. Those obligations prevent admission of a new +supplier or a change in kappa. The result closes the relative scalar-width issue +in the declared finite arithmetic domain and gives exact conditions for extending it. diff --git a/research/qq16-paired-precision/independent.py b/research/qq16-paired-precision/independent.py new file mode 100644 index 0000000000..f63eb7c963 --- /dev/null +++ b/research/qq16-paired-precision/independent.py @@ -0,0 +1,69 @@ +"""Second all-depth range certificate, using exact positive polynomials. + +Chris R / Clear1nsight with OpenAI assistance; Apache-2.0. +Derived independently during adversarial review; imports no range.py or predecessor. +""" +from fractions import Fraction as Q +from math import comb +import hashlib,json +F = (Q(445),Q(28230),Q(96),Q(142272)) +def need(ok,why): + if not ok:raise ValueError(why) +def plus(a,b,c=Q(1)): + out=[Q(0)]*max(len(a),len(b)) + for i,v in enumerate(a):out[i]+=v + for i,v in enumerate(b):out[i]+=c*v + while len(out)>1 and not out[-1]:out.pop() + return tuple(out) +def mulx(a,c):return (Q(0),)+tuple(c*v for v in a) +def shifted(a): + return tuple(sum(a[i]*comb(i,j) for i in range(j,len(a))) for j in range(len(a))) +def dominates(bound,value):return all(c>=0 for c in shifted(plus(bound,value,-1))) +def audit(word,bound=F): + state={s+str(p):(Q(1),) for s in ('X','Y') for p in range(112)} + owned={s+str(p) for s in ('Z','W') for p in range(112)} + active=set();observations=[];peaks=[] + def obs(i,name,value): + need(dominates(bound,value),'polynomial envelope understated at '+str(i)+' '+name) + observations.append([i,name,list(map(str,value))]) + if value==bound:peaks.append([i,name]) + for i,e in enumerate(word): + op=e[0] + if op=='begin': + need(not active and e[2] in (8,16),'private overlap') + active={s+str(k) for s in (('F','G') if e[2]==16 else ('F',)) for k in range(8)} + for n in active:state.pop(n,None) + elif op=='end': + need(len(active)==e[2] and all(state.get(n)==(Q(0),) for n in active),'private return') + for n in active:state.pop(n) + active=set() + elif op=='checkpoint':need(not active,'active checkpoint') + else: + name=e[1];need(name in owned|active,'write borrowed') + if op=='clear':state[name]=(Q(0),) + elif op=='add': + c=abs(Q(e[3]));need(c in (1,Q(1,4)) and name!=e[2],'coefficient/alias') + need(name in state and e[2] in state,'dirty read') + state[name]=plus(state[name],state[e[2]],c) + elif op=='line': + need(not active and name in state,'native boundary') + obs(i,'native cross '+name,mulx(state[name],4)) + state[name]=mulx(state[name],2) + elif op=='map':need(not active and name in state,'map boundary') + else:raise ValueError('opcode') + obs(i,'post '+name,state[name]) + need(not active and all(n in state for n in owned),'outputs incomplete') + return {'variable':'x=2^(lambda-1)>=1','envelope_coefficients':list(map(str,bound)), + 'proof':'Every F-observation has nonnegative coefficients after x=1+y; F(1)=171043 and degree3 give F(x)<=171043*x^3.', + 'observations':len(observations),'peaks':peaks, + 'observation_sha256':hashlib.sha256(json.dumps(observations,separators=(',',':')).encode()).hexdigest()} +def compare(candidate,baseline): + a,b=audit(candidate),audit(baseline) + need(a['observations']==3932 and b['observations']==4032,'observation census') + need(sum(F)==171043 and len(F)==4,'fixed polynomial') + bad=list(F);bad[3]-=1 + for w in (candidate,baseline): + try:audit(w,tuple(bad)) + except ValueError:pass + else:raise ValueError('accepted understated cubic envelope') + return {'candidate':a,'baseline':b,'negative_control':'Understate cubic coefficient142272 by1: both inductive certificates reject. Not a minimum-physical-width lower bound.'} diff --git a/research/qq16-paired-precision/numeric-cost.py b/research/qq16-paired-precision/numeric-cost.py new file mode 100644 index 0000000000..85e792c20d --- /dev/null +++ b/research/qq16-paired-precision/numeric-cost.py @@ -0,0 +1,94 @@ +"""Independent operation counts for an explicit common-width numeric reference. + +This is not the recursive child tariff and does not price owner addressing. +No runtime inputs beyond caller-authenticated literal words are consumed. +""" +from collections import Counter +from fractions import Fraction as Q + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def count(word): + c = Counter() + active = 0 + peak = 0 + for e in word: + op = e[0] + if op == 'add': + alpha = abs(Q(e[3])) + need(alpha in (Q(1), Q(1, 4)), 'unpriced scalar coefficient') + c['unit_ADD' if alpha == 1 else 'quarter_ADD'] += 1 + elif op == 'clear': + c['CLEAR'] += 1 + elif op == 'line': + need(active == 0 and e[3] in (-1, 1), 'native scope/sign') + c['H1'] += 1 + c['monomial_wrappers'] += 2 + elif op == 'map': + need(active == 0, 'cover inside private scope') + c['cover_maps'] += 1 + elif op == 'begin': + need(active == 0 and e[2] in (8, 16), 'private begin') + active = e[2] + peak = max(peak, active) + elif op == 'end': + need(active == e[2], 'private end') + active = 0 + elif op == 'checkpoint': + pass + else: + raise ValueError('unknown opcode') + need(active == 0, 'live private scope') + c['private_peak'] = peak + c['scalar_allowance'] = 8*c['unit_ADD'] + 12*c['quarter_ADD'] + 2*c['CLEAR'] + # Per complex payload coordinate; subtract and add have the same tariff. + c['scalar_numeric_ops_per_N'] = 2*c['unit_ADD'] + 4*c['quarter_ADD'] + 2*c['CLEAR'] + c['wrapper_numeric_ops_per_N'] = 6*c['monomial_wrappers'] + c['cover_numeric_ops_per_N'] = 4*c['cover_maps'] + c['native_numeric_ops_per_lambda_N'] = 10*c['H1'] + c['numeric_constant_per_N'] = c['scalar_numeric_ops_per_N'] + c['wrapper_numeric_ops_per_N'] + c['cover_numeric_ops_per_N'] + return dict(sorted(c.items())) + + +def audit(baseline, candidate): + b, c = count(baseline), count(candidate) + for key in ('H1', 'monomial_wrappers', 'cover_maps', 'private_peak', 'quarter_ADD', 'CLEAR'): + need(b[key] == c[key], 'changed common bill '+key) + need((b['unit_ADD'], c['unit_ADD']) == (1920,1820), 'unit ADD invoice') + need((b['scalar_allowance'],c['scalar_allowance']) == (26944,26144), 'logical invoice') + need((b['numeric_constant_per_N'],c['numeric_constant_per_N']) == (12352,12152), 'numeric reference invoice') + need(c['native_numeric_ops_per_lambda_N'] == 2240, 'native numeric reference invoice') + return { + 'status': 'PASS_CONDITIONAL_COMMON_WIDTH_NUMERIC_REFERENCE_COMPARISON', + 'baseline': b, 'candidate': c, + 'N': '2^(73 lambda) complex payload coordinates per owner, lambda positive integer', + 'reference_lowering': { + 'unit_ADD': '2N real-component additions or subtractions', + 'quarter_ADD': '2N exact binary shifts by two (one W-bit shift primitive per component) plus 2N additions/subtractions', + 'CLEAR': '2N zero stores', + 'signed_H1': 'lambda coordinate Gaussian lines; each at most4N additions,2N exact halves,4N copies', + 'wrapper': '2N component sign operations plus2N outward copies and2N copies back to the fixed destination bank', + 'cover': '2N outward copies plus2N copies back to the fixed destination bank', + 'buffer_protocol': 'Two-leg out-of-place permutation returns to its fixed external bank; address/control work is outside numeric count.', + }, + 'numeric_bound_per_owner': {'baseline': '(12352+2240 lambda)N', 'candidate': '(12152+2240 lambda)N', 'difference': '200N numeric word operations'}, + 'numeric_storage_bound': '(930N+12) signed W-bit component slots, including448 persistent complexfields,16 privatefields,one complex permutation buffer,and12 scalar native temporaries', + 'logical_allowance_difference': '800 allowance units; distinct from200N numeric operations', + 'common_width_tariff': 'For each reference primitive priced at any common positive tau(W), candidate prescribed bill is200N tau(W) smaller; logical allowance model separately gives800 tau_L(W). These are comparisons of prescribed bounds, not lower bounds on optimal implementations.', + 'width_mismatch_break_even': { + 'general': 'tau(W_candidate)/tau(W_baseline) < (12352+2240 lambda)/(12152+2240 lambda)', + 'linear_tau_W': 'Delta < 200 W_baseline/(12152+2240 lambda), forW_candidate=W_baseline+Delta', + 'logical_allowance_only': 'tau_L(W_candidate)/tau_L(W_baseline) < 26944/26144', + 'equal_width': 'Delta=0 satisfies bothstrictinequalities for everylambda>=1 andW>0', + }, + 'premises': ['Common sufficient range/grid certificate for every numerical reference interior.', + 'Exact dyadic divisions and no overflow/underflow at the stated common W.', + 'Pair-first coordinate Gaussian reference is permitted for this numerical bill; it is not inferred to implement a paid recursive child tariff.'], + 'unpriced': ['Owner/payload address generation and control', 'physical movement and placement tariffs', + 'actual recursive native child error/width/cost contract', 'native workspace exclusivity in a recursive implementation', + 'caller entry-format conversion', 'recursive usage and supplier caps'], + } diff --git a/research/qq16-paired-precision/range-proof.md b/research/qq16-paired-precision/range-proof.md new file mode 100644 index 0000000000..862594c515 --- /dev/null +++ b/research/qq16-paired-precision/range-proof.md @@ -0,0 +1,142 @@ +# Range and exact lattice certificate for the two frozen recovery words + +Fix the literal PR4106 and PR4015 WORDs and their full tensor-native semantics. +Let lambda be any positive integer and put t=lambda−1. Let h=2^z for an +integer z and let P be a nonnegative integer. At the decoder entry, suppose +all real and imaginary components of the 224 borrowed X/Y fields, uniformly +over every owner and payload coordinate, lie in h Z and have magnitude +strictly below 2^P h. Owned output and private fields can contain arbitrary +dirt: each must be cleared before its first numerical use, as checked by the +standalone interpreter. No magnitude premise is imposed on unread dirt. + +Both frozen words have the following **common sufficient exact format**: + +``` +q = h · 2^(−9−3t), +W = P + 28 + 6t signed bits per real or imaginary component. +``` + +Every visited component, scalar partial and Gaussian interior fits this +format. Hence the specified arithmetic incurs zero rounding or overflow. +This is an entry-domain implication and sufficient format, not a claim that +this format is minimal or that an actual recursive caller supplies that entry +domain. Logical frame/output correctness remains the independently replayed +PR4106 premise; this certificate analyzes both complete arithmetic schedules. + +## Component induction + +A field carries a quadruple (M,g,a,b), meaning + +``` +|component| < 2^P h M · 2^(a t), +component ∈ h · 2^(−g−b t) Z, +``` + +for nonzero M; the canonical M=0 bound means exact zero. Entry borrowed +fields have (1,0,0,0). A CLEAR produces zero. A signed addition combines +nonzero fields using M=M1+M2 and the componentwise maxima of g,a,b. If one +operand is proved zero, retain the other bound exactly. Signs can only reduce +the actual magnitude, so this induction does not assume independent values +or discard a harmful correlation. + +An exact ±1/4 coefficient changes M to M/4 and g to g+2. The implementation +observes the unscaled source, the first halving (M/2,g+1,a,b), and the final +halving before accumulation. Thus division is not silently treated as a +rounding primitive, and its intermediate lattice requirements are included. +All observed exponents are bounded by the common q exponent below. + +Tensor monomial wrappers and full cover maps are signed component +permutations, hence preserve magnitude and lattice. This relies on the +source native/cover semantics uniformly over owners; a cover is not presumed +to be an owner-local payload permutation. + +For one coordinate Gaussian line C_q, use the direct pair-first lowering + +``` +s=x+y, d=x−y; +outputs=((s+i d)/2,(s−i d)/2). +``` + +The source producer proof writes the second output as (d+i s)/2, which is +i times the direct C_q second output; this is a phase difference, not a +componentwise identity. Either expression has the same range and lattice +bounds. This proof uses direct C_q and the frozen word's already charged +native monomial wrappers; no extra uncharged phase operation is inserted. +Signs in the inverse line leave these component bounds unchanged. If input +components are bounded by L, pair sums are bounded by 2L, cross numerators by +4L, and output components by 2L. The halving refines the lattice by at most +one bit. A rank-one native line at tensor depth lambda performs this rule +once in each of its lambda coordinate layers, retaining the original order +inside each layer. Scalar port coefficients still act once, not lambda +times. Before layer j, magnitude is at most 2^(j−1)L and the lattice has +refined by j−1. Since 1≤j≤lambda=t+1, all its interiors are dominated by + +``` +pair sums: (2M, g, a+1, b+1), +cross numerators:(4M, g, a+1, b+1), +completed output:(2M, g+1, a+1, b+1). +``` + +These are grouped upper bounds, not identities for every interior grid. +They bound all earlier-layer outputs too. Native calls have no active private +scope in either word. Private fields are created dirty, cleared before use, +and required to be zero at scope exit; the maximum active private count is16. + +The tensor/native arithmetic and proof pattern are credited to the canonical +`research/qq16-all-depth-producer-grid/PROOF.md` and its native predecessor +lineage. Its producer numerical constants are not reused for the decoder. +`range.py` is a new standalone interpreter that imports no inherited +executable. Its caller must authenticate the literal input words first. + +## Whole-word constants and the changed cut + +Induction over all 3,713 candidate and 3,813 baseline events, including the +unchanged prefix, query acquisition, response and suffix, gives in both cases + +``` +maximum M = 171043 < 2^18, +maximum g = 9, +maximum a = maximum b = 3. +``` + +The maximum M first occurs after W0 at zero-based candidate event3697, +baseline event3797. All224 final component-envelope quadruples agree. +Every component therefore has magnitude strictly below +`2^P h · 2^(18+3t)` and belongs to `h·2^(−9−3t) Z`. +In units of q the magnitude is strictly below +`2^(P+27+6t)=2^(W−1)`, proving the signed-width statement. Because each +intermediate is on the q lattice, the explicit halvings are exact in this +format, including their divisibility requirements. + +The new arithmetic does increase one temporary's local envelope. Candidate +event1714 is the first D+=E operation (physical host Z10 receiving Z11), with +bound (460,4,2,2). The baseline's single-source D has bound at most +(230,4,2,2). This local doubling is included, rather than transferred through +an unchanged-DAG claim. Each of the eight completed query fields has the +same bound (11864,4,2,2) in both words: immediately before candidate event2434 +and baseline event2536. Thus the new pair sum is already dominated by the +completed query envelope. More generally, a same-support pair contributes +its two positive source envelopes to an agreeing query row, so sharing that +sum cannot exceed the full row's nonnegative sum. The entire following +response and suffix consequently reproduce the same envelope bounds. + +The first literal word difference is earlier, at index37, due to deferring +the tenth host's X-copy. A deferred uninitialized slot is not a numerical +intermediate. The interpreter rejects any attempt to read it before CLEAR. +The host's charged restoration remains part of the whole-word calculation. + +## Separate finite checks and limits + +A second numeric recurrence in `audit_depth` does not use Bound, the grouped +rule or the symbolic dispatcher. It explicitly expands every coordinate +Gaussian line. At depths1,2,3,8 both complete words have identical magnitude +bounds 171043,1195465,9220309,298371196093 and grid exponents9,12,15,30. +These check the finite arithmetic behind the induction; the preceding +symbolic proof, not a sampled-depth test, supplies the universal quantifier. + +The result shows that this particular sufficient format needs no widening +for the paired word. It does not say that the two schedules attain equal +true maximum magnitudes, that their errors coincide under an arbitrary +rounded format, or that their separately optimal widths coincide. An +existing caller's input conversion, physical layout/movement, native +workspace, recursive tariff and supplier caps require their own contracts. diff --git a/research/qq16-paired-precision/range.py b/research/qq16-paired-precision/range.py new file mode 100644 index 0000000000..1924ae4499 --- /dev/null +++ b/research/qq16-paired-precision/range.py @@ -0,0 +1,244 @@ +"""Independent whole-word all-depth component magnitude / dyadic-grid induction. + +No predecessor code is executed. Input words must be authenticated by the caller. +The rules are the elementary pair-first Gaussian calculation stated in range-proof.md. +""" +from fractions import Fraction +import hashlib +import json + + +class Bound: + __slots__ = ('m', 'g', 'a', 'b') + def __init__(self, m=0, g=0, a=0, b=0): + self.m = Fraction(m) + self.g, self.a, self.b = (g, a, b) if self.m else (0, 0, 0) + def as_json(self): + return [str(self.m), self.g, self.a, self.b] + def scale(self, coefficient): + c = Fraction(coefficient) + if not c or not self.m: + return Bound() + if c not in (1, -1, Fraction(1, 4), Fraction(-1, 4)): + raise ValueError('unsupported scalar') + return Bound(abs(c) * self.m, self.g + (2 if abs(c) == Fraction(1, 4) else 0), self.a, self.b) + def plus(self, other): + if not self.m: + return Bound(other.m, other.g, other.a, other.b) + if not other.m: + return Bound(self.m, self.g, self.a, self.b) + return Bound(self.m + other.m, max(self.g, other.g), max(self.a, other.a), max(self.b, other.b)) + + +def ceiling_log2(value): + value = Fraction(value) + if value <= 0: + raise ValueError('positive bound required') + k = value.numerator.bit_length() - value.denominator.bit_length() + if Fraction(2) ** k < value: + k += 1 + return k + + +def audit(word, include_trace=False): + if not isinstance(word, list): + raise ValueError('word list required') + states = {f'{side}{p}': Bound(1) for side in ('X', 'Y') for p in range(112)} + owned = {f'{side}{p}' for side in ('Z', 'W') for p in range(112)} + active = set() + scope = None + maxima = {'m': Fraction(0), 'g': 0, 'a': 0, 'b': 0} + witnesses = {} + counts = {} + observations = [] + state_trace = [] + private_peak = 0 + def observe(index, label, value): + observations.append([index, label, value.as_json()]) + for key in maxima: + x = getattr(value, key) + if x > maxima[key]: + maxima[key] = x + witnesses[key] = [index, label, value.as_json()] + def read(name): + if name not in states: + raise ValueError('dirty or unavailable read: ' + str(name)) + return states[name] + def write(name, value): + if name not in owned | active: + raise ValueError('unowned destination: ' + str(name)) + states[name] = value + for i, e in enumerate(word): + if not isinstance(e, list) or not e: + raise ValueError('invalid event') + op = e[0] + counts[op] = counts.get(op, 0) + 1 + if op == 'clear': + if len(e) != 3: + raise ValueError('clear shape') + write(e[1], Bound()) + elif op == 'add': + if len(e) != 4 or e[1] == e[2]: + raise ValueError('add shape or alias') + c = Fraction(e[3]) + source, dest = read(e[2]), read(e[1]) + if abs(c) == Fraction(1, 4): + observe(i, 'quarter predivision copy', source) + observe(i, 'quarter first exact halving', Bound(source.m/2, source.g+1, source.a, source.b)) + scaled = source.scale(c) + observe(i, 'scaled source', scaled) + write(e[1], dest.plus(scaled)) + elif op == 'line': + if len(e) != 4 or e[3] not in (-1, 1) or active: + raise ValueError('line shape or private overlap') + v = read(e[1]) + if v.m: + observe(i, 'Gaussian pair sums', Bound(2*v.m, v.g, v.a+1, v.b+1)) + observe(i, 'Gaussian cross numerators', Bound(4*v.m, v.g, v.a+1, v.b+1)) + write(e[1], Bound(2*v.m, v.g+1, v.a+1, v.b+1)) + else: + write(e[1], Bound()) + elif op == 'map': + if len(e) != 5 or active: + raise ValueError('map shape or private overlap') + read(e[1]) + elif op == 'begin': + if len(e) != 3 or active or e[2] not in (8, 16): + raise ValueError('begin shape or overlap') + active = {f'F{j}' for j in range(8)} + if e[2] == 16: + active |= {f'G{j}' for j in range(8)} + scope = e[1] + private_peak = max(private_peak, len(active)) + elif op == 'end': + if len(e) != 3 or not active or scope != e[1] or len(active) != e[2]: + raise ValueError('end mismatch') + if any(read(name).m for name in active): + raise ValueError('private field not cleared') + for name in active: + del states[name] + active, scope = set(), None + elif op == 'checkpoint': + if len(e) != 2: + raise ValueError('checkpoint shape') + else: + raise ValueError('unknown opcode: ' + str(op)) + if op in ('clear', 'add', 'line', 'map'): + observe(i, 'event output ' + e[1], read(e[1])) + state_trace.append([i, op, e[1] if len(e)>1 else None, + read(e[1]).as_json() if op in ('clear','add','line','map') else None]) + if active or any(name not in states for name in owned): + raise ValueError('incomplete word') + exponent = ceiling_log2(maxima['m']) + receipt = { + 'model': 'strict input component bound 2^P h; lattice hZ; t=lambda-1>=0', + 'events': len(word), 'counts': counts, 'private_peak': private_peak, + 'max_M': str(maxima['m']), 'ceil_log2_max_M': exponent, + 'max_g': maxima['g'], 'max_a': maxima['a'], 'max_b': maxima['b'], + 'quantum': {'h_power_two_constant': -maxima['g'], 'h_power_two_t': -maxima['b']}, + 'signed_width': {'P_coefficient': 1, 'constant': exponent+maxima['g']+1, 't_coefficient': maxima['a']+maxima['b']}, + 'witnesses': witnesses, 'observation_count': len(observations), + 'observation_sha256': hashlib.sha256(json.dumps(observations,separators=(',',':')).encode()).hexdigest(), + 'state_trace_sha256': hashlib.sha256(json.dumps(state_trace,separators=(',',':')).encode()).hexdigest(), + 'final_bounds': {name: states[name].as_json() for name in sorted(owned)}, + } + + if include_trace: + receipt['trace'] = state_trace + return receipt + + +def compare(candidate, baseline): + a, b = audit(candidate), audit(baseline) + return {'candidate': a, 'baseline': b, + 'same_sufficient_quantum': a['quantum'] == b['quantum'], + 'same_sufficient_width': a['signed_width'] == b['signed_width'], + 'same_final_component_envelopes': a['final_bounds'] == b['final_bounds'], + 'completed_query_cuts': {'candidate': query_cut(candidate), 'baseline': query_cut(baseline)}, + 'first_new_pair_sum': pair_cut(candidate), + 'independent_depth_checks': depth_checks(candidate, baseline)} + + +def audit_depth(word, depth): + """Separate numeric recurrence; explicitly expands each Gaussian coordinate. + + This check does not call Bound, audit, or the grouped tensor rule. It + checks the finite constants at selected depths; the proof supplies all depths. + """ + if type(depth) is not int or depth < 1: + raise ValueError('positive integer depth') + fields = {f'{side}{p}': (Fraction(1), 0) for side in ('X','Y') for p in range(112)} + max_m, max_g = Fraction(1), 0 + native_coordinate_lines = 0 + def visit(m,g): + nonlocal max_m,max_g + max_m, max_g = max(max_m,m), max(max_g,g if m else 0) + for event in word: + op = event[0] + if op == 'clear': + fields[event[1]] = (Fraction(0),0) + elif op == 'add': + dm,dg=fields[event[1]]; sm,sg=fields[event[2]] + c=abs(Fraction(event[3])) + if c == Fraction(1,4): + visit(sm,sg);visit(sm/2,sg+1) + sm,sg=sm/4,sg+2 + elif c != 1: + raise ValueError('unexpected scalar') + visit(sm,sg) + m=dm+sm + g=max(dg if dm else 0,sg if sm else 0) if m else 0 + fields[event[1]]=(m,g) + visit(m,g) + elif op == 'line': + m,g=fields[event[1]] + for _ in range(depth): + native_coordinate_lines += 1 + visit(2*m,g);visit(4*m,g) + if m: + m,g=2*m,g+1 + visit(m,g) + fields[event[1]]=(m,g) + elif op in ('map','begin','checkpoint'): + pass + elif op == 'end': + for j in range(8): + fields.pop(f'F{j}',None) + if event[2] == 16: + fields.pop(f'G{j}',None) + else: + raise ValueError('unexpected opcode') + return {'lambda':depth,'max_magnitude':str(max_m),'max_grid':max_g, + 'coordinate_Gaussian_lines':native_coordinate_lines, + 'final_bounds':{n:[str(m),g] for n,(m,g) in sorted(fields.items()) if n[0] in 'ZW'}} + + +def depth_checks(candidate,baseline,depths=(1,2,3,8)): + ca,ba=audit(candidate),audit(baseline) + result=[] + for depth in depths: + c,b=audit_depth(candidate,depth),audit_depth(baseline,depth) + for exact,grouped in ((c,ca),(b,ba)): + if Fraction(exact['max_magnitude']) > Fraction(grouped['max_M'])*2**(grouped['max_a']*(depth-1)): + raise ValueError('grouped magnitude failed') + if exact['max_grid'] > grouped['max_g']+grouped['max_b']*(depth-1): + raise ValueError('grouped grid failed') + if c != b: + raise ValueError('numeric whole-word envelope differs') + result.append({k:v for k,v in c.items() if k!='final_bounds'}) + return result + + +def query_cut(word): + index=next(i for i,e in enumerate(word) if e == ['clear','Z10','query2']) + trace=audit(word,include_trace=True)['trace'] + latest={row[2]:row[3] for row in trace[:index] if row[3] is not None} + names=['Z1','Z2','Z3','Z4','Z5','Z6','Z8','Z9'] + return {'before_event':index,'query_bounds':{name:latest[name] for name in names}, + 'scratch_D':latest['Z10'],'tenth_host':latest['Z11']} + + +def pair_cut(word): + index=next(i for i,e in enumerate(word) if e == ['add','Z10','Z11','1']) + trace=audit(word,include_trace=True)['trace'] + return {'event':index,'opcode':word[index],'bound':trace[index][3]} diff --git a/research/qq16-paired-precision/rounding-proof.md b/research/qq16-paired-precision/rounding-proof.md new file mode 100644 index 0000000000..4799d38e3c --- /dev/null +++ b/research/qq16-paired-precision/rounding-proof.md @@ -0,0 +1,126 @@ +# Rounding on the changed query DAG + +This audit consumes the frozen literal PR4015 and PR4106 words and the latter's +construction data. It executes no predecessor code. The endpoint semantics and +source authenticity are established by the central package and prior paid-word +replays. This note supplies numerical implications, not a caller admission. + +## Exact common grid + +The independent range induction gives both words the sufficient format + +``` +t=lambda-1, q=h 2^(-9-3t), W=P+28+6t. +``` + +Its premise is entry real and imaginary components in h Z, of magnitude strictly +below 2^P h, uniformly over all owners and payload coordinates. This includes +all quarter divisions and the pair-first Gaussian reference interiors. Every +stored intermediate is a q-integer, each division has the required divisibility, +and all numerators fit signed W bits. Consequently **both numerical references +have zero arithmetic rounding error**. No extra relative width is required by +the paired query. This conclusion does not choose the implementation or tariff +of a recursive H1 child. + +## Relative fixed-point identity with approximate normalizers + +There is also a narrower implication that does not require exact normalization. +Suppose both words use the same common component lattice q Z; all unit additions +are exact and do not overflow; covers/sign changes are exact; and each captured +normalizer is an isolated deterministic function of its input, returning q-grid +components. Its internal state must be restored or otherwise have the same +specified entry state at every call. The same corrected W input reaches each +port's same normalizer, so both words receive identical normalized arrays v_p. +Changing the order of independent normalizations has no effect under this premise. + +For an equal-sign row of a pair, integer associativity gives + +``` +(Q + s v_p) + s v_q = Q + s(v_p+v_q), s in {-1,1}. +``` + +For differing-sign rows the two deposits are unchanged. Reordering independent +source deposits likewise preserves their integer sum. Thus all eight query arrays +are bit-identical for arbitrary normalized q-integers, including approximate +ones. The response, quarter operations and suffix are unchanged, receive identical +inputs and therefore have identical results if their primitives are deterministic. +This is a relative statement: common existing rounding defects or failures of +private cleanup remain common; it does not prove they meet a caller tolerance. +It also does not allow the new pair sum to overflow. The exact-grid range theorem +supplies nonoverflow only in its stated exact-reference domain; an approximate +native contract must supply adequate range margins separately. + +The checker runs the actual query scalar subsequences on 104 one-source integer +basis inputs, an 80-bit alternating cancellation input, and another mixed integer +input. These 106 regressions support the word binding; associativity proves the +statement for all lattice inputs. No floating-point associativity is assumed. + +## Rounded primitive envelope + +For a separate abstract rounded model, let epsilon bound each borrowed entry +component error, eta the absolute residual of each complete scalar ADD implementation relative to ideal `dst+c*src`, and nu the absolute output residual of each complete signed rank-one tensor-native call. The ideal coefficient c is exact. Eta includes all product/division, addition and storage errors together; scaling within the implementation need not be exact. Identifying eta with one rounding step requires a separate implementation proof. CLEAR, signed monomials and covers are exact. Neither +eta nor nu is silently identified with a chosen mantissa width. Native interiors, +overflow and private cleanup remain separate contracts. + +Put x=2^lambda. A rank-one tensor Gaussian line has component-infinity operator +norm at most x: each coordinate layer has bound2, and there are lambda layers. +The proof uses this factor, never the invalid componentwise factor1 inferred from +unitarity. At each logical cut propagate a polynomial with nonnegative rational +coefficients in x, linear in epsilon, eta and nu: + +``` +CLEAR: E <- 0 +ADD c: E_dst <- E_dst + |c| E_src + eta +signed native: E_dst <- x E_dst + nu +cover / signed monomial: unchanged +``` + +Triangle inequalities prove this enclosure for all lambda>=1, including fully +correlated rounding errors. The independent interpreter runs both complete words. +Their 224 endpoint polynomials are equal coefficient by coefficient (six distinct +classes, all fields explicitly listed in ROUNDING.json). Their whole-word logical +cut coefficient envelopes are also equal: + +``` +entry: (445 + 14115 x + 2964 x^2 + 17784 x^3) epsilon +scalar: (16380 + 14451 x + 19104 x^2 + 17784 x^3) eta +native: (14121 + 2964 x + 17784 x^2) nu. +``` + +This envelope takes the maximum of each coefficient across all visited logical +writes; it need not be simultaneously attained and is not an optimal norm. It +excludes approximate native interiors, whose contract is supplied separately. +Each query row has52 source coefficients. An equal-sign pair injects one shared +sum residual and one deposit residual, giving2eta, exactly the conservative bound +for its two original deposits. Differing rows still have two deposits. Therefore +each channel's query-accumulation bound remains52eta. A shared residual is present +in several channels; no independence or square-root aggregation is used. + +The endpoint envelope does not establish exact private-helper restoration in a +rounded execution. The exact-grid path has no such scalar arithmetic defect; +otherwise restoration and actual native guarantees must be checked separately. + +## Actual changed-site floating counterexample + +A distinct model rounds every scalar query addition to a binary significand of +precision2, nearest with ties to even, with unbounded exponent. Supply exact +normalizer outputs at one observed real component as + +``` +v_76=4, v_87=1, v_92=1; all other v_p=0. +``` + +The checker executes the literal query scalar events, replacing each paid +normalization output by that supplied value. In PR4015's source order Q0 receives +4,1,1 separately. RN(4+1)=4 at a tie, twice, so Q0=4. PR4106's pair(87,92) forms +RN(1+1)=2 at event1729 and adds it to Q0 at event1730, giving RN(4+2)=6. The full +query vectors are respectively `(4,3,4,-2,0,0,0,0)` and `(6,3,4,-2,0,0,0,0)`. +The precision2 rounder is exact rational code, including ties-to-even. + +This is a counterexample to automatic bitwise transfer of the query arithmetic +under floating rounding. It is intentionally a query-cut example with supplied +normalization outputs, not a full rounded recursive-caller counterexample. The +invertibility of exact normalizers explains the algebraic availability of these +arrays, but does not establish their reachability under a particular rounded +prefix or recursive native implementation. It is compatible with the equal +conservative error envelopes and with the exact fixed-point result above. diff --git a/research/qq16-paired-precision/rounding.py b/research/qq16-paired-precision/rounding.py new file mode 100644 index 0000000000..70f8ff08ff --- /dev/null +++ b/research/qq16-paired-precision/rounding.py @@ -0,0 +1,199 @@ +"""Independent rounded-operation envelopes and a concrete reassociation witness. + +Input words and construction metadata must be authenticated by the caller. +This module imports no predecessor executable. Fractions are exact. +""" +from fractions import Fraction as Q + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def plus(a, b): + c = dict(a) + for k, v in b.items(): + c[k] = c.get(k, Q(0)) + v + return {k: v for k, v in c.items() if v} + + +def scale(a, c): + return {k: v * c for k, v in a.items() if v * c} + + +def native(a): + # x=2**lambda bounds a rank-one tensor Gaussian line in component infinity norm. + return {(kind, degree + 1): v for (kind, degree), v in a.items()} + + +def encode(a): + return [[kind, degree, str(v)] for (kind, degree), v in sorted(a.items())] + + +def envelope(word, with_peak=False): + """Error <= E(x)*epsilon+A(x)*eta+H(x)*nu, x=2**lambda. + + epsilon bounds each borrowed input component error, eta each COMPLETE scalar + ADD implementation residual relative to ideal dst+c*src, including product, + division, addition and storage errors together, and nu each COMPLETE signed- + native operation output residual. CLEAR, cover and signed monomials are exact. + The reference coefficient is exact; no implementation scaling exactness is + assumed. A one-rounding eta requires a separate implementation proof. + The model is explicitly not a certificate for a concrete floating format. + """ + values = {f'{s}{p}': {('entry', 0): Q(1)} for s in 'XY' for p in range(112)} + values.update({f'{s}{p}': {} for s in 'ZW' for p in range(112)}) + active = set() + peak = {} + for i, e in enumerate(word): + op = e[0] + if op == 'clear': + values[e[1]] = {} + elif op == 'add': + need(e[1] in values and e[2] in values, f'unknown ADD field at {i}') + c = abs(Q(e[3])) + need(c in (Q(1), Q(1, 4)), 'scalar alphabet') + values[e[1]] = plus(plus(values[e[1]], scale(values[e[2]], c)), {('scalar', 0): Q(1)}) + elif op == 'line': + need(e[1] in values and e[3] in (-1, 1), 'signed native alphabet') + values[e[1]] = plus(native(values[e[1]]), {('native', 0): Q(1)}) + elif op == 'map': + need(e[1] in values, 'map field') + elif op == 'begin': + need(not active, 'nested private scope') + need(e[2] in (8, 16), 'private size') + active = {f'F{k}' for k in range(8)} + if e[2] == 16: + active |= {f'G{k}' for k in range(8)} + for key in active: + values[key] = {('entry', 0): Q(1)} + elif op == 'end': + need(active, 'unopened private scope') + for key in active: + del values[key] + active = set() + elif op == 'checkpoint': + pass + else: + raise ValueError(f'unknown opcode {op}') + if op in ('clear', 'add', 'line'): + for key, value in values[e[1]].items(): + peak[key] = max(peak.get(key, Q(0)), value) + need(not active, 'private scope left live') + outputs = {key: values[key] for key in values if key[0] in 'ZW'} + return (outputs, peak) if with_peak else outputs + + +def round_binary(value, bits=2): + """Unbounded-exponent binary rounding to nearest, ties to even.""" + value = Q(value) + need(bits >= 2, 'significand width') + if not value: + return value + sign = 1 if value > 0 else -1 + a = abs(value) + exponent = a.numerator.bit_length() - a.denominator.bit_length() + if a < Q(2) ** exponent: + exponent -= 1 + quantum = Q(2) ** (exponent - bits + 1) + scaled = a / quantum + lo, rem = divmod(scaled.numerator, scaled.denominator) + if 2 * rem > scaled.denominator or (2 * rem == scaled.denominator and lo % 2): + lo += 1 + return sign * lo * quantum + + +def query_at_cut(word, construction, normalized, bits=2): + """Execute actual frozen query scalar events, supplying exact normalized W. + + This deliberately isolates query arithmetic; it is not a full floating + decoder execution. Native/map normalization is an exact supplied premise. + """ + aliases = construction['hosting']['aliases'] + query = {aliases[f'Q{k}']: Q(0) for k in range(8)} + state = dict(query) + query_names = set(query) + start = next(i for i,e in enumerate(word) if e == ['clear', aliases['Q0'], 'query2']) + response = next(i for i in range(start + 8, len(word)) + if word[i] == ['clear', aliases['D'], 'query2']) + observed_ports = [] + for i, e in enumerate(word[start:response], start): + if e[0] == 'clear': + state[e[1]] = Q(0) + elif e[0] == 'line': + need(e[3] == -1, 'normalizing negative line') + state[e[1]] = Q(normalized.get(e[2], 0)) + observed_ports.append(e[2]) + elif e[0] == 'map': + pass + elif e[0] == 'add': + if e[2].startswith('W'): + state[e[1]] = Q(0) # Replaced at the paid normalizer output. + else: + need(e[1] in state and e[2] in state, 'query scalar field') + exact = state[e[1]] + Q(e[3]) * state[e[2]] + state[e[1]] = exact if bits is None else round_binary(exact, bits) + else: + raise ValueError('unexpected query opcode') + need(len(observed_ports) == len(set(observed_ports)) == 104, 'complete query normalization') + return {'queries': [str(state[aliases[f'Q{k}']]) for k in range(8)], + 'start': start, 'response_start': response, 'normalized_ports': observed_ports} + + +def audit(baseline, candidate, construction): + (eb, pb), (ec, pc) = envelope(baseline, True), envelope(candidate, True) + need(eb == ec, 'endpoint envelope changed') + need(pb == pc, 'whole-word logical-cut error envelope changed') + pairs = construction['factoring']['pairs'] + multiplicity = [0] * 8 + for row in pairs: + for k in row['same']: + multiplicity[k] += 2 # shared sum residual plus channel deposit + for k in row['different']: + multiplicity[k] += 2 + need(multiplicity == [52] * 8, 'uniform query rounding envelope') + supplied = {76: Q(4), 87: Q(1), 92: Q(1)} + wb = query_at_cut(baseline, construction, supplied) + wc = query_at_cut(candidate, construction, supplied) + need(wb['queries'][0] == '4' and wc['queries'][0] == '6', 'rounded query reassociation witness') + # Integer additions model a common fixed-point lattice without overflow. + integer_checks = 0 + ports = sorted(wb['normalized_ports']) + patterns = [{p: Q(1)} for p in ports] + patterns += [{p: Q(((-1)**j) * (2**80 + j)) for j,p in enumerate(ports)}, + {p: Q((j*j*17)%131 - 65) for j,p in enumerate(ports)}] + for values in patterns: + ib = query_at_cut(baseline, construction, values, None)['queries'] + ic = query_at_cut(candidate, construction, values, None)['queries'] + need(ib == ic, 'exact integer query identity') + integer_checks += 1 + classes = {} + for key, value in sorted(ec.items()): + token = tuple(sorted(value.items())) + classes.setdefault(token, []).append(key) + return { + 'status': 'PASS_CONDITIONAL_ROUNDING_ENVELOPE_AND_CHANGED_DAG_WITNESS', + 'model': {'x': '2^lambda', 'entry': 'epsilon per borrowed input real/imaginary component', + 'scalar': 'eta absolute residual of complete scalar ADD versus ideal dst+c*src, including product/division, addition and storage errors; ideal coefficient exact', + 'native': 'nu per complete signed tensor-native output component', + 'exact': ['CLEAR', 'cover permutations', 'signed monomial permutations'], + 'restriction': 'No relation between eta/nu and a machine significand, nor an overflow guarantee, is inferred.'}, + 'all_224_endpoint_envelopes_equal': True, + 'endpoint_envelope_classes': [{'fields': fields, 'polynomial': encode(dict(token))} + for token, fields in classes.items()], + 'whole_word_logical_cut_coefficient_envelope_equal': True, + 'whole_word_logical_cut_coefficient_envelope': encode(pc), + 'peak_scope': 'Logical cuts only; internal approximate native arithmetic is supplied by the native contract, not inferred.', + 'query_accumulation_scalar_error_multiplicities': multiplicity, + 'correlation': 'Each shared pair residual is reused in all equal-sign channels; no independence or root-sum-square assumption.', + 'rounded_query_witness': {'bits': 2, 'rounding': 'nearest, ties to even, unbounded exponent', + 'normalized_component_values': {str(k): str(v) for k,v in supplied.items()}, + 'all_other_normalized_components_at_observed_coordinate': '0', + 'baseline': wb, 'candidate': wc, + 'scope': 'Actual query scalar subsequences with exact supplied normalization outputs; not a full rounded-caller counterexample.'}, + 'floating_no_automatic_bitwise_transfer': True, + 'fixed_point_query_regression_cases': integer_checks, + 'fixed_point_condition': 'Exact nonoverflowing integer unitADDs imply same queries for arbitrary supplied normalization outputs on a common lattice; deterministic isolated normalizers and unchanged response/suffix then imply relative bitidentity, including any common preexisting defects.', + 'restoration_boundary': 'Rounded envelope alone does not certify zero private-scratch restoration; exact-grid theorem or a native/private cleanup contract is needed.', + } diff --git a/research/qq16-paired-precision/test_verify.py b/research/qq16-paired-precision/test_verify.py new file mode 100644 index 0000000000..44d3ad0600 --- /dev/null +++ b/research/qq16-paired-precision/test_verify.py @@ -0,0 +1,42 @@ +"""Authentication, typed receipts and Git-free normal/optimized replay controls. +Chris R / Clear1nsight with OpenAI Codex assistance. Apache-2.0. +""" +import hashlib,json,shutil,subprocess,sys,tempfile,unittest +from pathlib import Path +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +def snapshot(root):return {str(p.relative_to(root)):hashlib.sha256(p.read_bytes()).hexdigest() for p in root.rglob('*') if p.is_file()} +class Boundary(unittest.TestCase): + def setUp(self): + self.temp=tempfile.TemporaryDirectory(prefix='qq16-precision-export-');self.addCleanup(self.temp.cleanup) + self.root=Path(self.temp.name)/'checkout';self.package=self.root/'research'/HERE.name + shutil.copytree(HERE,self.package,ignore=shutil.ignore_patterns('__pycache__')) + for row in json.loads((HERE/'SOURCES.json').read_text())['files']: + if row['usage']=='input': + dest=self.root/row['path'];dest.parent.mkdir(parents=True,exist_ok=True);shutil.copyfile(ROOT/row['path'],dest) + def replay(self,*args,optimized=True,ok=True,needle='PASS_QQ16_PAIRED_PRECISION_CONDITIONAL'): + result=subprocess.run([sys.executable,'-I','-Werror','-B',*(['-O'] if optimized else []),str(self.package/'verify.py'),*args],cwd=self.root,capture_output=True,text=True,timeout=120) + output=result.stdout+result.stderr;self.assertEqual(result.returncode==0,ok,output) + if needle:self.assertIn(needle,output) + return output + def test_normal_and_optimized_readonly_export(self): + for p in self.root.rglob('*'): + if p.is_file():p.chmod(0o444) + before=snapshot(self.root);self.replay(optimized=False);self.replay() + self.assertFalse((self.root/'.git').exists());self.assertEqual(before,snapshot(self.root)) + def test_source_authentication_before_analyzers(self): + source=self.root/'research/qq16-line-normalized-decoder/verify.py';raw=source.read_bytes() + source.write_bytes(b"raise RuntimeError('SOURCE_EXECUTION_SENTINEL')\n"+raw) + analyzer=self.package/'range.py';analyzer.write_text("raise RuntimeError('ANALYZER_EXECUTION_SENTINEL')\n") + output=self.replay(ok=False,needle='source integrity:') + self.assertNotIn('SOURCE_EXECUTION_SENTINEL',output);self.assertNotIn('ANALYZER_EXECUTION_SENTINEL',output) + def test_manifest_vendor_and_exclusive_write(self): + for name,needle in [('SOURCES.json','source manifest integrity'),('PREDECESSORS.json','predecessor manifest integrity'),('vendor/PR4106-WORD.json','retained source integrity:'),('vendor/PR4015-PROOF.md','retained source integrity:')]: + p=self.package/name;raw=p.read_bytes();p.write_bytes(raw+b' ');self.replay(ok=False,needle=needle);p.write_bytes(raw) + before=snapshot(self.root);self.replay('--write',ok=False,needle='refuse overwrite');self.assertEqual(before,snapshot(self.root)) + def test_whole_typed_receipts_and_duplicate_keys(self): + mutations=[('RESULT.json',lambda r:r['exact_format'].__setitem__('new_minus_baseline_bits',False),'whole typed receipt mismatch:RESULT.json'),('RANGE.json',lambda r:r.__setitem__('same_sufficient_width',False),'range receipt mismatch'),('ROUNDING.json',lambda r:r.__setitem__('all_224_endpoint_envelopes_equal',False),'rounding receipt mismatch'),('COST.json',lambda r:r.__setitem__('forged_saving',800),'whole typed receipt mismatch:COST.json'),('POLYNOMIAL.json',lambda r:r.__setitem__('forged_degree',2),'whole typed receipt mismatch:POLYNOMIAL.json')] + for name,mutate,needle in mutations: + p=self.package/name;raw=p.read_bytes();obj=json.loads(raw);mutate(obj);p.write_text(json.dumps(obj));self.replay(ok=False,needle=needle);p.write_bytes(raw) + p=self.package/'RESULT.json';raw=p.read_bytes();p.write_bytes(b'{"status":false,'+raw.lstrip()[1:]);self.replay(ok=False,needle='duplicate JSON key:status') +if __name__=='__main__':unittest.main() diff --git a/research/qq16-paired-precision/vendor/PR4015-PROOF.md b/research/qq16-paired-precision/vendor/PR4015-PROOF.md new file mode 100644 index 0000000000..8fd64e85e3 --- /dev/null +++ b/research/qq16-paired-precision/vendor/PR4015-PROOF.md @@ -0,0 +1,256 @@ +# Streaming complete QQ16 recovery inside nine existing output banks + +## Statement and boundary + +The primary construction hosts its eight persistent full-cover query sums and +one reusable work bank in **nine deferred Z_U output banks**, requiring **zero +additional owned banks**. Its complete local bill is **224 H1 children, 448 +wrappers, 352 maps and 26,944 scalar allowance**, with 416 CLEARs and 3,813 word +events. Only nine output definitions move. The changed future block has no +owner-private body; the whole-word private peak stays 16. + +We first prove the standalone nine-owned-bank streaming schedule, then prove +its explicit output-bank hosting transformation. Both words are regenerated; +the standalone variant is also replayed independently as a comparison. The +hosted variant is the published `WORD.json` and primary `RESULT.json` invoice. + + +## Standalone nine-bank reference + +For the pinned full decoder, the future-query correction can be evaluated with +**eight owned full-cover query banks and one reusable owned full-cover work +bank**, replacing PR3985's 112 simultaneous owned temporary arrays. The whole +word still returns all 224 original x0/y0 arrays in F17. It leaves all 224 +current X/Y inputs borrowed and unchanged, with X entering in F17 and each Y_p +in the source's F17 C_qp^(-1) frame. The initial Y normalization and complete +inverse suffix remain present and paid. + +The complete local bill is 224 H1 children, 448 native wrappers, 352 cover maps, +1,920 unit ADDs, 896 quarter ADDs and 425 CLEARs: scalar allowance 26,962. +Compared with PR3985 this removes 103 owned temporary banks, 111 CLEARs and +222 scalar allowance. It does not establish a physical tape count or a new κ. + +All nine new banks can enter with arbitrary content. Their first use is CLEAR, +and each returns zero in identity frame before the inverse-B1 checkpoint. +They require exclusive ownership only during the changed block. The eight +query banks are **full-cover owned storage**, not owner-private scratch carried +across a native call. Peak private scratch for the complete word remains 16 in +the unchanged F0 inverse; the changed future block has no private body. + +## Ordered operator identity + +Retain the canonical PR2707/PR2681 source conventions. For each port p, let +M_p be the actual stage-2 affine cover map, including its source-derived +translation, and C_qp its rank-one native line. Let T_p be the ordered owner +routing operator. The inherited full phase identity is + + C_qp^(-1) M_p F17 = F16 T_p, + +where F16 is the common frame on axes 9 through 24. Its inverse is the actual +source-ordered inverse map after C_qp; the affine inverse translation is not +silently dropped. The checker compares all 73 phase coordinates at every ADD. + +At the changed-block entrance W_p = F17 u_p. The needed future query is + + q_k = sum_(p in U+T) R[k,p] T_p u_p, k = 0,...,7. + +There are 104 query ports and eight response ports A, with disjoint supports. +The required update is + + W_p <- F17 (u_p - T_p^(-1) sum_k R[k,p] q_k / 4), p in A. + +Every U+T output remains unchanged. There is no commutation of different owner +operators in this identity. + +Initialize Q_0,...,Q_7 to zero in F16. For each p in the source order U+T: + +1. Clear reusable D in F17 and copy W_p to D. +2. Apply M_p and then C_qp^(-1) to D. +3. For every nonzero R[k,p], add R[k,p] D to Q_k. + +After processing the first j source ports, induction gives + + Q_k = F16 sum_(p among first j) R[k,p] T_p u_p. + +The statement holds for arbitrary routed arrays: the maps are the original +ordered maps, each sum is in the same exact frame, and every use of D occurs +before its next CLEAR. At j=104 the eight banks contain the full required +query. The source and query loops have exchanged order; exact addition permits +this exchange. A former floating-point evaluation order is not preserved. + +For each of the eight response ports p, clear D in F16 and form +`-sum_k R[k,p] Q_k/4`. Apply C_qp and the actual inverse M_p, then add D to W_p. +The query banks remain unchanged during all eight responses. Finally clear D +and all Q banks in identity frame. The result at the block exit equals the +materialized correction exactly, so the unchanged full suffix has the same +224 outputs. + +The checker also computes exact rational row ranks: the query matrix on U+T +has rank eight, as does the response matrix on A. Thus the materialized query +has eight independent components. In a fixed-dimension linear query-only +summary interface, its rank precludes fewer than eight independent full-cover +summary fields. This is not a universal workspace lower bound: rereading +sources, recomputation, changed encodings and output-bank hosting are outside +that restricted observation. In particular no nine-bank optimality is claimed. + +## Pebbling and lifetime ledger + +The 104 aligned query copies are intermediate values, not output obligations. +Once one copy has contributed to the eight running sums it is dead and D may +be overwritten. Responses need only the eight completed sums and one staging +bank. This is a constructive pebbling schedule for the existing linear map; +it changes the intermediate storage contract without extra native recomputation. + +Zero-based event positions in the complete 3,822-event word are: + +| Bank | First CLEAR | Final CLEAR | Frame while retained | Native calls during allocation | +|---|---:|---:|---|---:| +| Q0 through Q7 | 1714 through 1721 | 2619 through 2626 | F16 | 112 each | +| D | 1722 | 2618 | F17/F16 through the stated maps | 112 | + +The next event, 2627, begins the preserved 112-instruction Z update; the +inverse-B1 checkpoint follows at 2739. `RESULT.json` records each +bank separately. All first uses initialize arbitrary dirt; all final uses +clear the owned field to zero/identity. No borrowed X/Y, output Z/W or private +F/G array is silently aliased. The prefix and suffix have no Q/D references, +so their ownership interval can be restricted to this block. Physical +allocation, placement and release costs remain unknown. + +## Hosting the nine roles in deferred output banks + +Choose the first nine U ports in the pinned source order and injectively assign +Q0,...,Q7,D to their Z output banks. The generator independently checks every +reference before the first post-query Z update. For each chosen Z_p, +there are exactly two references before this cut: its initial `CLEAR Z_p current` and `ADD Z_p X_p 1`. +It is neither read nor updated anywhere else before that cut. These +are exact source def-use facts, not an assumption that all output banks are +free. Selected T outputs have live prefix uses and are rejected by this census. + +Delete the nine original two-instruction output definitions from the prefix. +Execute the streamed block with the injective aliases. Every role's first use +is still its paid CLEAR, so arbitrary output-bank dirt is initialized. After +the final response, restore the nine original definitions, in order, before +the first preserved Z update. All X fields are still borrowed, unchanged and in F17, so +these deferred definitions produce exactly the original Z values and frames. +The unchanged suffix therefore sees its original full boundary. + +The standalone roles' nine terminal zero/identity CLEARs are unnecessary in +this hosted contract: each same owned bank is immediately reinitialized by +the charged output CLEAR/X-copy. Remove those terminal clears, not the output +initialization. The temporary roles no longer have a separate zero-return ABI; +their obligation is the correct owned output state, which is checked at the +checkpoint and full-word exit. No borrowed storage is erased. + +The source census, exact alias map, role first/last uses and output-redefinition +events are all recorded in `RESULT.json`. All old owned-output and borrowed +input dirt/restoration checks remain enabled. This construction uses only nine +deferred U outputs, unlike the parallel materialized-copy hosting approach's +104 deferred output definitions. The parallel agent supplied the output-lifetime +insight; this package derives its own nine-bank def-use proof and executes no +sibling code. + +## Complete primitive bill and access obligations + +| Charge | PR2707 | PR3985 | Nine external banks | Hosted stream | +|---|---:|---:|---:|---:| +| H1 children | 336 | 224 | 224 | 224 | +| Native wrappers | 672 | 448 | 448 | 448 | +| Cover maps | 464 | 352 | 352 | 352 | +| Unit ADDs | 1808 | 1920 | 1920 | 1920 | +| Quarter ADDs | 896 | 896 | 896 | 896 | +| CLEARs | 312 | 536 | 425 | 416 | +| Scalar allowance | 25840 | 27184 | 26962 | 26944 | +| Owned output banks | 224 | 224 | 224 | 224 | +| Additional owned full-cover banks | 0 | 112 | 9 | 0 | +| Whole-word private peak | 16 | 16 | 16 | 16 | + + +Scalar allowance is 8 times unit ADDs plus 12 times quarter ADDs plus 2 times +CLEARs. The streamed block has 560 ADDs and 129 CLEARs: eight initial Q clears, +104 query D clears, eight response D clears and nine terminal clears. The +materialized block had 240 CLEARs. No native call, wrapper or map is erased by +calling it a relocation. The nine-bank word also removes the old future-private +begin/end markers, giving 3,822 events rather than 3,935. Output-bank hosting +then removes nine terminal clears, giving 3,813 events and scalar allowance +26,944. Relative to PR3985 the total reduction is 120 CLEARs / 240 scalar +allowance and all 112 additional owned banks. + +For an explicit abstract scalar-access protocol, execute one complete cover +pass per ADD or CLEAR. If a bank has N scalar entries, read both operands and +write the destination on each ADD; write the destination on each CLEAR. The +standalone nine-bank block has **689 scalar passes, 1120N scalar reads and 689N scalar +writes**, in addition to 112 native calls and 112 cover maps. These counts +assume no fusion or cache credit. They count scalar-array accesses, not bit +operations or tape-head steps, and do not price native/wrapper/map traffic. In the hosted block, including +the nine moved output definitions, the counts are 698 scalar passes, 1138N +reads and 698N writes. The prefix loses 18 passes, 18N reads and 18N writes; +thus the whole-word delta versus nine external banks is nine fewer passes and +9N fewer writes, with the same read count. These are exact for the declared +scalar-access protocol, not head-motion bounds. + +| Obligation | Status | +|---|---| +| Exact full-output map and native frames | Proved under the retained source contracts; checked on the whole word | +| Named primitive invoice and nine output-bank role lifetimes | Constructive, exact | +| Declared scalar-pass read/write count | Exact for the stated access protocol | +| Physical placement, seeks, traversal, instruction control and return | Unknown | +| Bit encoding, precision, intermediate range and rounding error | Unknown | +| Outer invocation incidence, productive-family stock and idle coverage | Unknown for this changed module | +| Both all-depth supplier caps and improved κ | Not established | + +The change exchanges 104 simultaneous materialized copies and an owner-private +query sweep for persistent query banks and serial full-cover access. Fewer +banks do not imply cheaper head movement. PR2722 and PR2794 price different +fixed scalar words and access layouts; their tariffs are not imported here. +Likewise no numerical budget or κ gain is inferred merely from fewer banks. + +## Evidence and limits + +The verifier authenticates all 22 canonical runtime files before executing the +credited PR2707 loader or PR2681 algebra. It regenerates the canonical full word +and the PR3985 comparison word, checking every event against the narrowly +retained pending-head WORD data. No unmerged executable is imported. + +It replays the complete new word on independent current X/Y symbols and on +independent original x0/y0 symbols forwarded through F0/B1. It checks the +intermediate inverse-B1 checkpoint, all final arrays/frames, arbitrary owned +and private dirt, borrowed restoration and all nine hosted output reconstructions. The standalone nine-bank word is +also replayed with its separate zero/identity-return requirement. The adapted +signed native checker covers both signs on all 112 ports and 512 columns +(114,688 columns), binds all 224 occurrences and rejects an incorrect negative +wrapper translation. The source algebra is reused, not claimed code-disjoint. + +Controls reject missing dirty clears, reuse without initialization, premature +query clearing, native/map errors, missing output reinitialization/restoration, borrowed-output alias, +and private scratch held across a native call. Whole-word, typed-receipt, +retained-comparator and canonical-source integrity are checked separately. +Finite symbolic replay supports the ordered linear proof; it is not a complete +physical supplier, rounded implementation or formal-kernel verification. + +## Open next questions + +1. Bind the unchanged 224-output ownership contract to an actual outer caller. + This package eliminates extra query-bank allocation but does not establish + the caller's 224 output banks, their geometry or terminal consumption. +2. Choose one concrete bank layout and access protocol, then price all 689 + scalar passes (698 in the hosted block including moved definitions), plus native/map/wrapper transitions and head returns. Compare + the total to the materialized implementation before expanding construction. +3. If a complete caller budget permits it, bound the changed accumulation + order's intermediate magnitudes and rounding defects. Exact algebra alone + does not transfer a previous rounded-error estimate. + +## Attribution + +Credit ywz65 / PR2707 for full F17 normalization and its native word; Arham +Tahir / PR2681 for the ordered inverse and retained algebra; the QQ16/native, +geometry and supplier lineage credited in those sources; and Chris R / +Clear1nsight with OpenAI assistance / PR3985 for the rectangular correction. +The current change is the explicit persistent-query/reusable-work schedule, +its nine-output deferral and hosting proof, exact storage/scalar delta, and +verification. Credit the parallel output-lifetime agent for the deferred-output +observation and the coordinating agent for this bounded composition proposal; +all work is within the disclosed Codex-assisted session. Streaming linear +sums and pebbling are standard methods, not newly claimed mathematical tools. +PR2722 (Nick Petalas) and PR2794 (Arham Tahir) are distinct access predecessors. +Substantial OpenAI Codex assistance is disclosed. Apache-2.0; no independent +human or proof-assistant review is claimed. diff --git a/research/qq16-paired-precision/vendor/PR4015-WORD.json b/research/qq16-paired-precision/vendor/PR4015-WORD.json new file mode 100644 index 0000000000..9a57a6f9c2 --- /dev/null +++ b/research/qq16-paired-precision/vendor/PR4015-WORD.json @@ -0,0 +1 @@ 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recovery boundary + +## Statement and domain + +For the canonical QQ16 packet and ordered routes pinned in SOURCES.json, replace +only the future-query recovery interval of the complete PR2707 decoder by the +literal WORD.json schedule. Subject to the same native common-label, owner-map, +phase-frame and recursive child contracts as that decoder, the new schedule +returns all224 original outputs in F17 and preserves all224 current borrowed +X/Y values and frames. Every owned bank may initially contain arbitrary dirt. +Its complete scalar allowance is26144 under the inherited unit/quarter/CLEAR +upper tariffs8/12/2, versus26944 in PR4015 and27184 in PR3985. Native count224, +rank-one children,448 wrappers and352 maps are unchanged. This theorem about +the logical word does not supply a physical or finite-precision implementation. + +## The exact residual is retained + +At the canonical first future-map cut, the actual corrected W values differ +from borrowed Y by Δ. With the original order g1 then g2, their query difference +is + +`Q2(Δ) = Q2(X_T) − M21 Q1(Y)`, + +`M21 = (1/4) Σ_(p∈U∪T) r_p r_pᵀ [g2,p g1,p]`. + +The narrow PR4003 witness logic is retained in residual.py, with all inherited +inputs authenticated by the enclosing verifier before execution. It reconstructs +the literal prefix and checks this identity over independent current arrays. +The character1 images of the104 ordered owner products are all distinct. +The00 diagonal has52 distinct images, each with coefficient1/4, and no original +character1 term. On constants the operator is13I, but that specialization does +not give the general operator. The admissible current state +`Y_A=K1,A a`, `Y_(U∪T)=0`, `X=0` realizes arbitrary query a. The A-response is +injective after undoing its maps and applying R_A; thus the missing residual +cannot disappear at the outputs. Reversed products, missingT and zero/13I +correction all fail. These are reproduced predecessor results, not new claims. + +The candidate copies every actual W_U and W_T once after the same paid prefix. +No Q1 retention is assumed. Q1's private registers are cleared at1585–1592, +before end1593 and future map1714. The independent acquisition audit accounts +for104 CLEARs/copies/maps/negative lines, eight query initializations and all +response deposits. Keeping these corrected sources retains both residual terms. + +## New scalar identity and lifetime + +For each same-support pair p,q, separately normalize into F16 sources D=v_p, +E=v_q with the original charged map and signed line. If m supported coefficients +agree, deposit both originals into the4−m differing query channels before +changing D. Execute one charged `D+=E`, then use D in each of the m agreeing +channels with their common sign. The resulting coefficient of v_p and v_q in +every channel is exactly the original R entry. Cost is `2(4−m)+1+m=9−m` +unit ADDs, replacing8. Actual52pairs consist of48 withm3 and4 withm2, giving +`48×2+4×1=100` removed ADDs. This is a deterministic bounded matching within +same-support groups of size4 or8, not global arithmetic-circuit optimization. + +Q0..Q7,D,E use ten existing unused Z_U output slots. Their early CLEAR/X-copy +definitions are delayed after verifying no intervening source-word use. Every +query/source first use initializes arbitrary dirt with a paid CLEAR. All ten +output definitions are restored by their paid CLEAR/X-copy at2498:2518 before +the literal1195-event suffix. Prefix1694events are exact after those deferrals; +no native call overlaps private scratch. Eight response corrections and the +entire canonical F0 inverse/checkpoint/output suffix remain exact. The full +replay proves final output values/frames and borrowed return, rather than +inferring them from local matrix identities. See the two detailed proofs. + +The extraE cleanup is discharged by its tenth output restoration; it does not +create a second independent two-unit saving. Whole-word CLEAR count stays416. +The full bill is `8×1820+12×896+2×416=26144`. The1040 difference from3985 +includes4015's240 lifetime saving, which is credited separately. + +## Evidence and limits + +The whole word and construction receipt regenerate byte/value exactly. Both +original routed recovery (including intermediate checkpoint) and arbitrary +current recovery against the canonical inverse formula pass on exact rational +group-ring expressions and full73-coordinate phase polynomials. Signed native +recipes are checked on114688 local basis columns and every224 occurrence is +bound to its recipe. This is a recipe-basis test, not224 new native proofs. + +A separately implemented two-symbol pair identity and event/acquisition recount +check the new work. Separate agent executions and a read-only adversarial review +share canonical routed code and PR4015's replay engine; they do not constitute +independent human or formal proof. Moving D+=E ahead of differing reads leaves +the bill unchanged but fails recovery; missingT normalization, E initialization, +tenth-output return, response inverse and private exclusion are also rejected. +Hashes and final review coverage are recorded in REVIEWS.json. + +Reassociation changes ranges and rounding. PR4043's same-DAG transfer is +inapplicable. Physical head movement/control, tag ABI, actual native exclusivity, +allocation, precision/bit costs, outer invocation and productive coverage, idle +credits and both all-depth caps remain unknown. The native moment remains the +same224 rank-one contributions at the inherited child sizes; no unit-mixing or +κ reduction follows. PR4105's actual selected-only bridge repair obstruction +continues to apply in its own domain; a valid outer connection remains absent. + +Credit3985's336→224 native reduction,4015's streaming/hosting,4003's residual, +ywz65/2707, Arham Tahir/2681 and all retained source notices. Tekalign/tekuuu's +4030 normalization gate is a distinct result; this construction keeps every +source normalizer. New paired arithmetic and integration by Chris R/Clear1nsight +with substantial OpenAI Codex assistance; Apache-2.0. diff --git a/research/qq16-paired-precision/vendor/PR4106-WORD.json b/research/qq16-paired-precision/vendor/PR4106-WORD.json new file mode 100644 index 0000000000..6c6f726cd1 --- /dev/null +++ b/research/qq16-paired-precision/vendor/PR4106-WORD.json @@ -0,0 +1 @@ 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diff --git a/research/qq16-paired-precision/verify.py b/research/qq16-paired-precision/verify.py new file mode 100644 index 0000000000..eeeef7fb3c --- /dev/null +++ b/research/qq16-paired-precision/verify.py @@ -0,0 +1,158 @@ +#!/usr/bin/env python3 +"""Complete common-format audit of frozen QQ16 recovery words. Apache-2.0. +Chris R / Clear1nsight with substantial OpenAI Codex assistance. +No predecessor executable is imported. Source semantics are inherited with pins. +""" +import argparse,hashlib,json,types +from copy import deepcopy +from fractions import Fraction as Q +from itertools import product +from pathlib import Path +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +STATUS='PASS_QQ16_PAIRED_PRECISION_CONDITIONAL' +def need(ok,why): + if not ok:raise ValueError(why) +def unique(pairs): + out={} + for k,v in pairs: + need(k not in out,'duplicate JSON key:'+k);out[k]=v + return out +def parse(raw):return json.loads(raw,object_pairs_hook=unique) +def typed(v): + if isinstance(v,dict):return ('dict',tuple((k,typed(x)) for k,x in sorted(v.items()))) + if isinstance(v,list):return ('list',tuple(map(typed,v))) + return (type(v).__name__,v) +def sha(raw):return hashlib.sha256(raw).hexdigest() +def blob(raw):return hashlib.sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest() +def module(name): + path=HERE/name;m=types.ModuleType(name.replace('.','_'));m.__file__=str(path) + exec(compile(path.read_bytes(),str(path),'exec'),m.__dict__);return m +def authenticate(): + raw=(HERE/'SOURCES.json').read_bytes() + need(sha(raw)=='ebb8c000a803b2a39f7bea7b206bad36bdbfd265081934affbba04fbb6b2a703','source manifest integrity') + inputs={} + for r in parse(raw)['files']: + if r['usage']!='input':continue + data=(ROOT/r['path']).read_bytes() + need(sha(data)==r['sha256'] and blob(data)==r['git_blob'],'source integrity:'+r['path']) + inputs[r['path']]=r['sha256'] + need(len(inputs)==5,'complete declared canonical input set') + raw=(HERE/'PREDECESSORS.json').read_bytes() + need(sha(raw)=='72fe4f1f3c56e07407e1bd37a3a075baf95f9c046f5251dceb2dbf75ee684b88','predecessor manifest integrity') + retained={} + for r in parse(raw)['files']: + data=(HERE/r['local']).read_bytes() + need(sha(data)==r['sha256'] and blob(data)==r['git_blob'],'retained source integrity:'+r['local']) + retained[r['local']]={'head':r['head'],'sha256':r['sha256']} + need(len(retained)==5,'complete retained set') + return inputs,retained + +def gaussian_checks(): + """Independent two-site rational Cq oracle against integer exact halves.""" + count=0;norm_witness=None;grid_witness=None + for a,b,c,d in product(range(-2,3),repeat=4): + for sign in (1,-1): + # Physical real/imaginary component formulas; stored quantum is h/2. + s=(2*(a+c),2*(b+d));delta=(2*(a-c),2*(b-d)) + numerators=(s[0]-sign*delta[1],s[1]+sign*delta[0],s[0]+sign*delta[1],s[1]-sign*delta[0]) + need(all(n%2==0 for n in numerators),'exact native divisibility') + got=tuple(Q(n//2,2) for n in numerators) + expected=(Q(a+c-sign*(b-d),2),Q(b+d+sign*(a-c),2),Q(a+c+sign*(b-d),2),Q(b+d-sign*(a-c),2)) + need(got==expected,'signed native numeric kernel') + L=max(abs(v) for v in (a,b,c,d)) + need(all(abs(v)<=4*L for v in (Q(n,2) for n in numerators)),'cross numerator bound') + need(all(abs(v)<=2*L for v in got),'native output bound') + if (a,b,c,d,sign)==(1,1,1,-1,1):norm_witness=got + if (a,b,c,d,sign)==(1,0,0,0,1):grid_witness=got + count+=1 + need(any(v.denominator==2 for v in grid_witness),'halving seed') + # Attained local values refute tempting but invalid componentwise norm-one + # and an unchanged coarse h grid, without claiming global format minimality. + need(norm_witness==(Q(0),Q(0),Q(2),Q(0)) and max(map(abs,norm_witness))>1,'norm-one control') + return {'signed_two_site_cases':count,'native_component_output_factor':2,'cross_numerator_factor':4, + 'controls':['x=1+i,y=1-i gives a component2: norm-one assumption fails','x=1,y=0 gives half-integers: unrefined unit grid is not closed'], + 'scope':'Elementary signed Gaussian reference. Tensor/cover/native recipe semantics inherited; this is not an implementation of a recursive child tariff.'} + +def reject_controls(R,E,C,B,candidate,baseline,construction): + controls=[] + def reject(label,call): + try:call() + except (ValueError,KeyError):controls.append(label);return + raise ValueError('accepted control:'+label) + w=deepcopy(candidate);w.pop(w.index(['clear','Z11','current'])) + reject('dirty E read',lambda:R.audit(w)) + w=deepcopy(candidate);w[w.index(['add','Z10','Z11','1'])][3]='2' + reject('unsupported scalar',lambda:R.audit(w)) + w=deepcopy(candidate);w.insert(next(i for i,e in enumerate(w) if e[0]=='line'),['begin','illegal',8]) + reject('native inside private scope',lambda:R.audit(w)) + w=deepcopy(candidate);w[w.index(['add','Z10','Z11','1'])][3]='-1' + reject('changed shared sum',lambda:E.audit(baseline,w,construction)) + w=deepcopy(candidate);w.pop(next(i for i,e in enumerate(w) if e[0]=='line')) + reject('missing native error/cost contribution',lambda:C.audit(baseline,w)) + w=deepcopy(candidate);i=w.index(['map','Z11',2,87,False]) if ['map','Z11',2,87,False] in w else next(i for i,e in enumerate(w) if e[0]=='map' and i>1700);w[i][3]+=1 + reject('changed captured-source recipe',lambda:B.audit(baseline,w)) + w=deepcopy(candidate);_,_,i=B.cut(w);w.pop(i+18) + reject('missing paid tenth restoration',lambda:B.audit(baseline,w)) + return controls + +def compute(): + inputs,retained=authenticate() # Before any numerical analyzer executes. + candidate=parse((HERE/'vendor/PR4106-WORD.json').read_text()) + baseline=parse((HERE/'vendor/PR4015-WORD.json').read_text()) + construction=parse((HERE/'vendor/PR4106-CONSTRUCTION.json').read_text()) + R=module('range.py');E=module('rounding.py');C=module('numeric-cost.py');I=module('independent.py');B=module('binding.py') + ranges=R.compare(candidate,baseline) + need(typed(parse((HERE/'RANGE.json').read_text()))==typed(ranges),'range receipt mismatch') + rounding=E.audit(baseline,candidate,construction) + need(typed(parse((HERE/'ROUNDING.json').read_text()))==typed(rounding),'rounding receipt mismatch') + costs=C.audit(baseline,candidate);poly=I.compare(candidate,baseline);binding=B.audit(baseline,candidate) + need(ranges['same_sufficient_quantum'] and ranges['same_sufficient_width'] and ranges['same_final_component_envelopes'],'common format') + for r in (ranges['candidate'],ranges['baseline']): + need((r['max_M'],r['max_g'],r['max_a'],r['max_b'])==('171043',9,3,3),'all-depth constants') + need(r['signed_width']=={'P_coefficient':1,'constant':28,'t_coefficient':6},'signed width') + need(rounding['all_224_endpoint_envelopes_equal'],'rounded envelope') + # Inspect the exact coefficient enclosure, keeping x=2^lambda distinct from + # the independent range certificate's x=2^(lambda-1). + at_one={'entry':Q(0),'scalar':Q(0),'native':Q(0)} + for kind,degree,c in rounding['whole_word_logical_cut_coefficient_envelope']: + at_one[kind]+=Q(c)*2**degree + need(at_one=={'entry':182803,'scalar':263970,'native':91185},'lambda1 error headroom gate') + headroom=2**18-171043;need(headroom==91101,'range headroom') + primitives=gaussian_checks() + controls=reject_controls(R,E,C,B,candidate,baseline,construction) + result={'status':STATUS,'source_inputs':inputs,'retained':retained, + 'question':'Does the frozen paired word require extra precision that repays800 scalar allowance?', + 'answer':'No extra width in the declared common sufficient exact-reference format. Actual recursive-child/caller/physical implementation remains conditional, not admitted.', + 'exact_format':{'input':'h=2^z,z integer;P>=0 integer;each borrowed real/imaginary component in hZ,abs<2^P*h;owned/private dirt unread untilCLEAR;lambda>=1 integer', + 't':'lambda-1','q':'h*2^(-9-3t)','signed_component_bits':'P+28+6t','new_minus_baseline_bits':0,'arithmetic_residual':'zero for permitted pair-first exact numerical reference', + 'optimality':'Sufficient uniform format; no minimality or optimized variable-precision dominance claim'}, + 'same_width_costs':{'logical_allowance_before':26944,'logical_allowance_after':26144,'logical_difference':800, + 'numeric_before':'(12352+2240lambda)N','numeric_after':'(12152+2240lambda)N','numeric_difference':'200N real-component additions/subtractions at common W', + 'N':'2^(73lambda) complex coordinates per owner','actual_recursive_child_tariff':'unknown; pair-first numerical reference is not free substitution'}, + 'conditional_producer_composition':{'inherited_producer_q':'h*2^(-71-19t)','inherited_producer_width':'P+215+38t','decoder_entry_P':'P+214+38t', + 'joint_q':'h*2^(-80-22t)','joint_width':'P+242+44t', + 'scope':'Algebraic substitution of source producer sufficient format into new decoder entry theorem. Producer theorem/source semantics inherited, not rerun; actual selected provider/caller linkage and conversion costs unestablished.'}, + 'rounded_logical_cut_headroom':{'general':'E_entry(lambda)*epsilon+E_scalar(lambda)*eta+E_native(lambda)*nu < 91101*(2^P*h)*2^(3*(lambda-1))', + 'lambda1':'182803epsilon+263970eta+91185nu < 91101*(2^P*h)', + 'scope':'Sufficient common-width logical-cut nonoverflow margin only. Actual eta/nu and native interiors/private cleanup remain separate premises.'}, + 'fixed_point_word_binding':binding, + 'fixed_point_relative_identity':'Exact changed unitADDs,nooverflow,common q,deterministic isolated bank-independent native/map/quarter callbacks imply identical captured sources,queries and downstream outputs. Existing common defects do not become accuracy guarantees.', + 'floating_countermodel':rounding['rounded_query_witness'], + 'checks':{'range_observations':ranges['candidate']['observation_count'],'independent_polynomial_observations':poly['candidate']['observations'], + 'explicit_coordinate_depths':[1,2,3,8],'all224_endpoint_error_polynomials_equal':True,'integer_query_regressions':rounding['fixed_point_query_regression_cases'], + 'Gaussian_reference':primitives,'negative_controls':controls}, + 'scope':'Exact/common-grid reference plus conditional error/bit-cost comparisons; endpoint/frame identity inherited from frozen4106/4015. No predecessor executable imported. No actual recursive supplier admission, physical gain, human/formal proof or newkappa.'} + return result,costs,poly + +def main(): + ap=argparse.ArgumentParser();ap.add_argument('--write',action='store_true');a=ap.parse_args() + names=('RESULT.json','COST.json','POLYNOMIAL.json') + if a.write:need(not any((HERE/n).exists() for n in names),'refuse overwrite') + objects=compute() + for n,obj in zip(names,objects): + if a.write: + with (HERE/n).open('x') as f:f.write(json.dumps(obj,indent=2,sort_keys=True)+'\n') + else:need(typed(parse((HERE/n).read_text()))==typed(obj),'whole typed receipt mismatch:'+n) + print(STATUS);print('same_q=h2^(-9-3t) same_W=P+28+6t logical_saving800 numeric_saving200N conditional_no_new_kappa') +if __name__=='__main__':main()