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Not a code dependency here." + } + ], + "overlap_limits": "200 updated all-state PRs at entry; refreshed most recent 100; rendered discussion pages 1166 and 1167. Not a complete historical or unpublished-work audit.", + "final_checkpoint_utc": "2026-10-24T23:23:42.300687+00:00", + "final_main": "32890bc5de034ab8fc93ac88ead7279a6a416d04" +} diff --git a/research/native-wordram-interfaces/LICENSE b/research/native-wordram-interfaces/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/native-wordram-interfaces/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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b/research/native-wordram-interfaces/NOTICE.txt new file mode 100644 index 0000000000..ca80ef62e5 --- /dev/null +++ b/research/native-wordram-interfaces/NOTICE.txt @@ -0,0 +1,14 @@ +Original contributions prepared for Dugongue with substantial OpenAI Codex assistance. Apache-2.0. + +Retained predecessor credit: +Dugongue PR4929: centre-free coded producer, scalar factorization and compensation; prior counted Word RAM/NTT kernel and tcslib ISA precedent. +Cao Yifan / intqwq PR4610: actual native word and source endpoint. +Cinna Davis / 1337isnot1337 PR4694/4698 and related cache/helper work; zxv and Jacob Alan Sussman: native/compiler and mixed-target accounting lineage. +Ali Romman PR5388 and PR5457: original helper-query bank, exact query maps and overlapping-feedback invariant; PR5421: nine BIT relations, compared but not newly claimed here. +DaysSky PR5440/5270: p19 source and proposal; their incomplete physical attachment is not silently adopted. +Dillon Amburgey PR5402; Chris R / Clear1nsight PR5413 and companion reviews: selected caller and funding baseline, not modified here. +Ali Romman PR5451 and the retained transfer-metric sources: uniform physical operator-error precedent. +Matarener / Mark PR5433 and PR5438; GamingPuzzled PR5462: scoped relation/precision frontier and numerical headroom comparisons. +FastPoly: fixed-syntax sharing precedent. mpfx: strict nearest-lattice recovery. tcslib, Anthropic/formal-math and the prior kernel retain their source notices; no source from incompatible Lean environments is compiled here. + +Component source notices and exact public revision/content hashes are retained in native/SOURCES.json, decoder/PREDECESSOR.json and decoder/source/**/SOURCES.json, and precision/SOURCES.json. No source content hash is a hash of an original local path. diff --git a/research/native-wordram-interfaces/README.md b/research/native-wordram-interfaces/README.md new file mode 100644 index 0000000000..685411d4b3 --- /dev/null +++ b/research/native-wordram-interfaces/README.md @@ -0,0 +1,42 @@ +# Executable native and Word RAM interfaces + +This package applies the prior counted Word RAM kernel's sharing and ownership discipline to the actual native producer. Its main new implementation computes **eight shared inverse-code quotients instead of 448 repeated quotients**, with identical rounded outputs, a uniform local error theorem and literal instruction counts. It also supplies a concrete source-ABI native-unit serializer, a completion-free three-query terminal decoder and sufficient recovery bounds. + +**No new multiplication κ is established.** The selected conditional value remains 0.003027288235 at the pinned main. The open p19 claims are not accepted here as completed physical callers. The four components close specific implementation interfaces; their ordinary bills and recursive paid profiles must not be confused. + +| Component | Positive result | Precise boundary | +| --- | --- | --- | +| [Inverse recoding](precision/RECODING-PROOF.txt) | Actual 112-by-8 code; eight divisions; 1,329 static instructions in place versus 18,929 in the stated same-output control; error ≤ 2h | One scalar coordinate; wrapper movement and complete caller precision/tariffs remain separate | +| [Native unit](native/REPORT.txt) | Actual 28,047-event producer exports in both directions, all 632 arbitrary input rows, all 19 axis embeddings, dirty owned entry and cleared exit | Source ABI preserved; not the complete p19 controller compiler | +| [Terminal decoder](decoder/TERMINAL-PROOF.txt) | Three actual helper queries with adaptive feedback and an ordinary terminal decoder; independent outputs restored | Gaussian paid profile unchanged; caller use must remove a real request to improve κ | +| [Recovery](precision/REPORT.txt) | Width-uniform weighted contraction certificate and an all-size sufficient fixed-point FFT error bound | Actual selected consumer and all-size arithmetic cost are not supplied | + +## Reproduce + +Python 3.12 or newer, standard library only, on Windows or Linux: + +```sh +python -I -B research/native-wordram-interfaces/verify.py +python -I -O -B research/native-wordram-interfaces/verify.py +``` + +These commands authenticate every package byte and run the relevant source-bound checks without Git, network, Lean or GPU dependencies. The decoder's retained assertions require a non-optimized child interpreter; the launcher enforces this even when its own `-O` mode is used. Optimized mode independently reruns the native, recoding and recovery checks. Each child uses a fresh, non-writing bytecode namespace, so package-local cached bytecode is not a source substitute. A scientific replay is not Lean kernel verification or maintainer acceptance. + +The static count improvement is against the explicitly implemented duplicate-quotient control, not every optimized compiler. At k = 4, the input-preserving variant is 1,441 versus 19,041 instructions. General saving: exactly 440(4k + 24) static instructions, for 1 ≤ k ≤ 56. Setup, constants, scratch clearing, signed branches and halting are charged. This implementation uses nearest ties to even; sign symmetry is required by the stated signed-sharing argument. + +## Fresh frontier and overlap + +[FRONTIER.json](FRONTIER.json) records the frozen main and PR snapshots. Two recent all-state PR pages were reviewed at entry, followed by another 100-PR update and the rendered handoff/mechanism discussions. This is not a claim to have reviewed every historical PR, every comment or unpublished work. #5462 subsequently advertises numerical headroom with unchanged profiles; it supplies no changed recursive mechanism and does not repair the p19 compiler. Final refresh also compared #5464’s joint odd-E8 cross-cube primitive: it retains source-acquisition and complete-caller obligations and is complementary, not a dependency of this package. + +The prior deliverable supplies the counted ISA/ownership/sharing discipline; the current package applies it to the actual scalar recoding. The independent cached-query, native lift and metric arguments are additional interfaces, not a manufactured combined exponent gain. Existing DAG/library work is used as precedent, not claimed as a fresh kernel audit. + +## Open next questions + +1. **Attach the inverse recoding to a complete caller.** Begin with the actual `/52` coded producer in `native/vendor`, allocate its uniform error through every use, and price monomial movement and coordinate traversal. The selected #5413 provider has no odd-denominator packet, so it is not a direct replacement target. +2. **Complete a D-based p19 caller.** Use the serialized native B endpoint, prove every bridge/gauge and target rank, and emit the complete owned/frame chronology. The naive R-to-D substitution fails; a one-column four-term Gaussian expansion does not extend at constant cost to arbitrary widths. +3. **Consume a real early observation.** Use the three-query interface to remove a named existing caller request and compare the full paid/target profile plus the added ordinary bill. Moving a query without removing one leaves κ unchanged. +4. **Bind the recovery certificate to actual residuals.** Extract all physical transfer blocks and decoder boundaries, obtain rational positive weights and verify the complete recovery margin. A selected grid bound alone is not an operator-error theorem. + +## Attribution + +Read [NOTICE.txt](NOTICE.txt) and the component source manifests. Apache-2.0 applies to original work; retained source-specific notices remain applicable. Substantial OpenAI Codex assistance, with one coordinator and three research agents. No novelty priority, independent human review, new κ, formal kernel audit or selected-frontier change is claimed. diff --git a/research/native-wordram-interfaces/SOURCES.json b/research/native-wordram-interfaces/SOURCES.json new file mode 100644 index 0000000000..80b17a65a0 --- /dev/null +++ b/research/native-wordram-interfaces/SOURCES.json @@ -0,0 +1,25 @@ +{ + "schema_version": 1, + "base_commit": "32890bc5de034ab8fc93ac88ead7279a6a416d04", + "files": [ + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602", + "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72" + }, + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "fc3d4ba105e1f097d0d7d051a308281e86ab1446", + "sha256": "66974efdced4083c00025f97d95d83909a226cdf801edb9301c195c6641f6903" + } + ], + "frozen_component_sources": [ + "native/SOURCES.json", + "decoder/PREDECESSOR.json", + "decoder/source/research/closed-helper-feedback/SOURCES.json", + "precision/SOURCES.json" + ], + "source_export_contract": "Component-local vendor content is frozen and byte-authenticated by MANIFEST.json and component verifiers. External PR sources are provenance links, not live unpinned checkout inputs." +} diff --git a/research/native-wordram-interfaces/TASK.json b/research/native-wordram-interfaces/TASK.json new file mode 100644 index 0000000000..65c4b7aa6c --- /dev/null +++ b/research/native-wordram-interfaces/TASK.json @@ -0,0 +1,83 @@ +{ + "schema_version": 1, + "task_id": "complex-new-helper-inventory", + "original_card": { + "id": "complex-new-helper-inventory", + "question": "Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/heterogeneous-owner-assembly/README.md", + "certificates/selected-result.json", + "research/selected-k8-unrestricted-ends/README.md" + ], + "methods": [ + "Propose a changed helper inventory and derive an optimistic exact moment.", + "Design a small completed instance and independently verify its endpoint and rank bill." + ], + "acceptance_gate": "A new physically realizable contract outside the frozen catalogue whose per-call profile, screened with ceiling.ceiling(), beats the selected word's packing ceiling; a lower cap does not establish identical circuitry or order attainable optima, and is insufficient to pass the stronger-budget target under this model. 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", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin.", + "bottleneck_link": "Packing of the selected word is capped at +0.87% (ceiling model); only a lower local excess spend or a changed coverage law raises the cap.", + "allowed_variations": [ + "Narrow to one changed boundary or helper type with explicit counts.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Mixing only providers already inside the pinned catalogue.", + "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "overlap_terms": [ + "helper inventory", + "heterogeneous-owner", + "mutable leaver" + ] + }, + "scope_status": "changed", + "scope_change_reason": "Explicit donor assignment seeks a complete improved kappa using the previous counted kernel. Only scoped constructive native/scalar/decoder/recovery interfaces were established; no new helper inventory or complete stronger supplier is asserted.", + "actual_scope": "Construct and audit source-bound native and Word RAM compiler interfaces, preserving exact local endpoints and charging ordinary work.", + "bottleneck_link": "The actual coded p19 caller lacks a uniform cheap Q-conjugated gauge/compiler; selected #5413 has a different no-odd-denominator provider.", + "stop_rule": "Stop the bounded round at useful verified local interfaces when no complete paid-profile and compiler improvement is established. Do not inherit missing p19 physical attachment or a width-one expansion.", + "evidence": "Normal and optimized 49-file source export replays, component proofs, actual matrix/native maps/outputs and counted ISA controls; independent agent reviews. Root metadata/source inventory added after these scientific replays.", + "author": "Dugongue", + "ai_assistance": "Substantial OpenAI Codex assistance by one coordinator and three agents.", + "outcome": "partial", + "base_commit": "32890bc5de034ab8fc93ac88ead7279a6a416d04", + "new_kappa_claimed": false, + "open_questions": [ + { + "question": "Attach the /52 inverse recoding to a complete actual caller.", + "why_it_matters": "Only a full compiler tariff can connect local instruction saving to kappa.", + "first_step": "Bind every recoding use, monomial movement and precision amplification in the coded producer.", + "blocked_by": "Selected #5413 has a different denominator-free provider; p19 global gauges are not closed." + }, + { + "question": "Construct a uniform D-based p19 native caller.", + "why_it_matters": "Numeric repricing is not an attached multiplication algorithm.", + "first_step": "Start from the actual serialized full B endpoint and prove each bridge frame and productive output.", + "blocked_by": "Q-conjugated owner gauges are not known to have the required ordinary realization." + }, + { + "question": "Use a selected early helper observation to remove an existing request.", + "why_it_matters": "Relocation and feedback alone leave every rank-moment unchanged.", + "first_step": "Name a consumer request and compare its complete paid/target profile with the decoder bill.", + "blocked_by": "No profitable consumer is constructed here." + }, + { + "question": "Bind recovery to actual transfer residuals.", + "why_it_matters": "Width-uniform examples do not establish selected recovery.", + "first_step": "Extract all physical blocks and decoder boundaries, then check a rational weighted certificate.", + "blocked_by": "Complete actual residual and arithmetic cost are not supplied." + } + ] +} diff --git a/research/native-wordram-interfaces/VERIFY.json b/research/native-wordram-interfaces/VERIFY.json new file mode 100644 index 0000000000..8c10bcffe7 --- /dev/null +++ b/research/native-wordram-interfaces/VERIFY.json @@ -0,0 +1,82 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/verify.py" + ], + "checks": "Frozen source hashes; all native exports/matrix/frame checks; literal recoding; complete source terminal decode; exact recovery controls. No kappa claim.", + "timeout_seconds": 300 + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-B", + "{package}/verify.py" + ], + "checks": "Optimized wrapper/native/recoding/recovery replay. Decoder runs in an explicit assertion-enabled child.", + "timeout_seconds": 300 + } + ], + "package_local_inputs": [ + "research/native-wordram-interfaces/.gitattributes", + "research/native-wordram-interfaces/FRONTIER.json", + "research/native-wordram-interfaces/LICENSE", + "research/native-wordram-interfaces/MANIFEST.json", + "research/native-wordram-interfaces/NOTICE.txt", + "research/native-wordram-interfaces/README.md", + "research/native-wordram-interfaces/SOURCES.json", + "research/native-wordram-interfaces/TASK.json", + "research/native-wordram-interfaces/VERIFY.json", + "research/native-wordram-interfaces/decoder/LICENSE", + "research/native-wordram-interfaces/decoder/PREDECESSOR.json", + "research/native-wordram-interfaces/decoder/TERMINAL-PROOF.txt", + "research/native-wordram-interfaces/decoder/source/research/closed-helper-feedback/SOURCES.json", + "research/native-wordram-interfaces/decoder/source/research/closed-helper-feedback/derived_replay.py", + "research/native-wordram-interfaces/decoder/source/research/closed-helper-feedback/three_query_terminal.py", + "research/native-wordram-interfaces/decoder/source/research/coded-native-caller/PHYSICAL.md", + "research/native-wordram-interfaces/decoder/source/research/coded-native-caller/clifford_exact.py", + "research/native-wordram-interfaces/decoder/source/research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz", + "research/native-wordram-interfaces/decoder/source/research/native-center-free-code/CODED-PROOF.md", + "research/native-wordram-interfaces/decoder/source/research/native-center-free-code/native_core.py", + "research/native-wordram-interfaces/decoder/source/research/native-helper-query-bank/ATTRIBUTION.md", + "research/native-wordram-interfaces/decoder/source/research/native-helper-query-bank/BANK.json", + "research/native-wordram-interfaces/decoder/source/research/native-helper-query-bank/PROOF.md", + "research/native-wordram-interfaces/decoder/source/scripts/compare_recursive_invoices.py", + "research/native-wordram-interfaces/decoder/three-query-terminal-result.json", + "research/native-wordram-interfaces/decoder/verify_terminal.py", + "research/native-wordram-interfaces/native/REPORT.txt", + "research/native-wordram-interfaces/native/RESULT.json", + "research/native-wordram-interfaces/native/SOURCES.json", + "research/native-wordram-interfaces/native/UNIT0-backward.json.gz", + "research/native-wordram-interfaces/native/UNIT0-forward.json.gz", + "research/native-wordram-interfaces/native/compile_unit.py", + "research/native-wordram-interfaces/native/vendor/research/coded-native-caller/NORMALIZERS.json", + "research/native-wordram-interfaces/native/vendor/research/coded-native-caller/PHYSICAL.md", + "research/native-wordram-interfaces/native/vendor/research/native-center-free-code/CODE.json", + "research/native-wordram-interfaces/native/vendor/research/native-center-free-code/CODED-PROOF.md", + "research/native-wordram-interfaces/native/vendor/research/native-center-free-code/CODED-WORDS.json.gz", + "research/native-wordram-interfaces/native/vendor/research/native-center-free-code/SOURCE-WORD.json.gz", + "research/native-wordram-interfaces/native/vendor/research/native-center-free-code/coded_verify.py", + "research/native-wordram-interfaces/native/vendor/research/native-center-free-code/native_core.py", + "research/native-wordram-interfaces/precision/CODE.json", + "research/native-wordram-interfaces/precision/RECODING-PROOF.txt", + "research/native-wordram-interfaces/precision/RECODING-RESULT.json", + "research/native-wordram-interfaces/precision/REPORT.txt", + "research/native-wordram-interfaces/precision/RESULTS.json", + "research/native-wordram-interfaces/precision/SOURCES.json", + "research/native-wordram-interfaces/precision/mode_columns.json", + "research/native-wordram-interfaces/precision/native_recoding.py", + "research/native-wordram-interfaces/precision/precision_certificate.py", + "research/native-wordram-interfaces/verify.py" + ] +} diff --git a/research/native-wordram-interfaces/decoder/LICENSE b/research/native-wordram-interfaces/decoder/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/native-wordram-interfaces/decoder/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/research/native-wordram-interfaces/decoder/PREDECESSOR.json b/research/native-wordram-interfaces/decoder/PREDECESSOR.json new file mode 100644 index 0000000000..37d95803de --- /dev/null +++ b/research/native-wordram-interfaces/decoder/PREDECESSOR.json @@ -0,0 +1,16 @@ +{ + "pr": 5457, + "repository": "CrocSwap/integer-mult-bounds", + "commit": "0d720354a47457212b160492824f5116f9dde267", + "files": [ + { + "path": "research/original-helper-query-feedback/verify.py", + "sha256": "aa3113993fbc6a117e1833a92e6cc4ff9fdccdcd59311a73d4534ff9a6cc0f45" + }, + { + "path": "research/original-helper-query-feedback/SOURCES.json", + "sha256": "8d079c231e722a46a37d861f7b4d172e5d6a53f2cadb4ec31a9f856d129d05ca" + } + ], + "source_relation": "derived_replay.py extends signed unit feedback and adds one ordinary terminal decoder; exact full-source replay retained." +} diff --git a/research/native-wordram-interfaces/decoder/TERMINAL-PROOF.txt b/research/native-wordram-interfaces/decoder/TERMINAL-PROOF.txt new file mode 100644 index 0000000000..0a24f18eb2 --- /dev/null +++ b/research/native-wordram-interfaces/decoder/TERMINAL-PROOF.txt @@ -0,0 +1,87 @@ +Primary result: completion-free terminal decoding for three actual source queries + +Choose global bank queries 0,16,32, whose +original first-departure arguments are their own independent inputs and whose +original final frames are all exactly frame 1, the full rank-nine return R. +The source witnesses are native owners 224,240,256 at events 8148,8366,8584, +with first frames 2,72,74. No dense helper basis and no return completion is used. + +Hoist only those three original H1 children into the entrance prologue. Keep the +three raw outputs and normalized observations, and perform the same four signed +feedback shears, preserving current input/raw/observation consistency after every +shear. For local indices 0,1,2 corresponding to global indices 0,16,32, they are: + xi_1 += Q xi_0; xi_2 += Q xi_1; + xi_1 -= Q xi_0; xi_2 -= Q xi_1. +For coefficient a=+1 or -1, a shear xi_k+=a Q xi_h updates all live copies by + w_k += a K_k obs_h; + obs_k += a Q^2 K_h^-1 w_h; + raw_k += a O_k^-1 Q^2 K_h^-1 w_h. +The current representations are w_j=K_j xi_j, raw_j=E_j K_j xi_j, +obs_j=Q xi_j, with the actual pinned O_j E_j K_j=Q. Every update uses two owned +COPY, three signed ADD, three monomial maps and three CLEAR, and source h is +unchanged within one update. All right-hand-side maps are monomial because +Q^2 is the central Pauli. This proves the three representations by induction, +including the overlapping reuse of coordinate 1. No adaptive query oracle or +fresh Gaussian evaluation is assumed. In normalized xi coordinates their total change +is xi_2 += Q^2 xi_0. In actual ground helper coordinates it is + w_2 += B w_0, where B=K_32 Q^2 K_0^-1. +B is a concrete monomial physical map. Here K_32 denotes the pinned global-query +32 input map, not an index in a newly assumed shared-query oracle. + +Clear the three observations and resume the original source on these coupled +helper inputs. Every omitted original query is replaced by the whole-field and +frame-tag swap with its matching current raw result. This preserves the actual +source state at all three cuts, including all earlier reads and later reuse. +The source identity on arbitrary inputs gives the original main transfer and +all original helper outputs on the coupled helper vector. In particular output +2 is R w_2(initial) + R B w_0(initial), and output 0 is R w_0(initial). All other original persistent fields +have their original outputs. No helper-to-main contamination appears because +the original FULL identity is checked on every independent source column. + +The pinned physical maps satisfy K_j R=R K_j and Q^2 R=R Q^2, with absolute +phases. Thus B R=R B. At the common full exit chart execute: + CLEAR scratch; COPY scratch <- output_0; + apply the literal monomial B to scratch; + ADD output_2 -= scratch; CLEAR scratch. +This restores the exact original independent output_2. All original endpoint +charts and arbitrary persistent input directions are preserved. Every owned +output is zero. The decoder uses ordinary maps only; it is not a Gaussian child, +a free retag or an assumed symbolic inverse. + +The complete added ordinary invoice, with seven additional owned fields, is: + 15 COPY, 26 CLEAR, 3 whole-field/chart SWAP, + 13 signed ADD, 16 monomial field maps. +Of these 16 maps, three are the actual prologue observation normalizers, twelve +are the four feedback updates' maps, and one is the terminal decoder B. There +are zero new basis ADD/SCALE and zero return-completion calls. Original source +ordinary work remains additional. Field-volume, precision and compiler tariffs +must be paid before this can support a full multiplication caller. + +The complete original Gaussian paid profile remains + 2201 H1 + 412 H2 + 510 H3 + 127 H4 + 40 H5 + 8 H8, +and the original independent helper-target profile remains + 28 H4 + 7 H7 + 47 H8 + 326 H9. +Every rank-moment invoice is therefore unchanged, not improved. The three source +queries were relocated rather than duplicated. The mechanism supplies adaptive +intermediate observations and an ordinary terminal decoder without losing or +recoding the independent helper targets; no actual original paid child is removed. +The next profitable-caller question is to use those intermediate observations to +replace an existing caller request with a complete ordinary/precision bill. + +Run python3 -B verify_terminal.py using Python 3.12 or newer. It authenticates +the retained source inputs, checks the exact singleton rows and source events, +checks the three physical query identities and decoder maps, verifies B's full- +return commutator including absolute phase, and replays every original event on +all 632 persistent and eight arbitrary owned input columns. Omitting the terminal +decoder or chart transport must be rejected. The saved receipt is +three-query-terminal-result.json. The identities hold for arbitrary vector inputs and every allowed spectator +multiplicity by composition of the same lifted monomial/source operators. +The scalar owner program is evaluated directly in that operator algebra; no +sum is tensor-powered. Native all-width implementation and ordinary/compiler +funding assumptions remain inherited. This is not Lean kernel verification. + +Credit remains with PR 5457's overlapping-feedback invariant, PR 5388's source +query bank, and the full retained native/Clifford/helper lineage in ATTRIBUTION.md. +The classical commutator algebra is not claimed new. The source-specific identity +row/full-exit selection and completion-free actual decoder are this extension. +Prepared for Dugongue with substantial OpenAI Codex assistance; Apache-2.0. diff --git a/research/native-wordram-interfaces/decoder/source/research/closed-helper-feedback/SOURCES.json b/research/native-wordram-interfaces/decoder/source/research/closed-helper-feedback/SOURCES.json new file mode 100644 index 0000000000..cf7bd5dbaa --- /dev/null +++ b/research/native-wordram-interfaces/decoder/source/research/closed-helper-feedback/SOURCES.json @@ -0,0 +1,72 @@ +{ + "schema_version": 1, + "base_commit": "32890bc5de034ab8fc93ac88ead7279a6a416d04", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "fc3d4ba105e1f097d0d7d051a308281e86ab1446", + "sha256": "66974efdced4083c00025f97d95d83909a226cdf801edb9301c195c6641f6903" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602", + "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72" + }, + { + "path": "research/coded-native-caller/PHYSICAL.md", + "usage": "input", + "git_blob": "da8837ba67423ef08ef1afb8e8297a8032aafe9f", + "sha256": "4321b159ff8d3fe705419adaaa1beef75606e869e34341bda553f17d598a6078" + }, + { + "path": "research/coded-native-caller/clifford_exact.py", + "usage": "input", + "git_blob": "166841a037f069249f6f7f6dedb89248812f59e2", + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962" + }, + { + "path": "research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz", + "usage": "input", + "git_blob": "46d929df83817b85a5387bcdb9745e0627d6366e", + "sha256": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05" + }, + { + "path": "research/native-center-free-code/CODED-PROOF.md", + "usage": "input", + "git_blob": "1f28d33884ec99b34f8366d022d8f7b9b7653ae2", + "sha256": "acd904af677718da8cdaf81d205d29866a6855efd393047e7128320a46753b01" + }, + { + "path": "research/native-center-free-code/native_core.py", + "usage": "input", + "git_blob": "5d8a8f0a6382c66449f76b6f57bdd380c057ddc1", + "sha256": "178ff80824a012970fc9435f122152da03c7e6bdc3a7de12136fe03e05cf24fe" + }, + { + "path": "research/native-helper-query-bank/ATTRIBUTION.md", + "usage": "input", + "git_blob": "51041de84105c5617645b57f601b702648c1c0ec", + "sha256": "02a3723ab014a20b96fa1383a83bb0e3343e59ca96eff78ca7dfbec928662dc2" + }, + { + "path": "research/native-helper-query-bank/BANK.json", + "usage": "input", + "git_blob": "91a6c7a5f30862ffdbe767fa844d0a372bf077a1", + "sha256": "237c6a7b890df5ba4dbf9ade112fe70aa06624774344978fde76a2c4ad172fe5" + }, + { + "path": "research/native-helper-query-bank/PROOF.md", + "usage": "input", + "git_blob": "7ae6b095a2713dbbe4f8e5873f1fc89e7a05fea3", + "sha256": "a68aaac3bef72478e219e5e4fa9abc775505b3ffbd6da24ae3beceb9827ef124" + }, + { + "path": "scripts/compare_recursive_invoices.py", + "usage": "input", + "git_blob": "fda2a852e9937e42fe40df0707694465ca7c1b48", + "sha256": "3930c22c11da7bc6042cfeb6e459ecb06e4478430037bee3469d034353855fc6" + } + ] +} diff --git a/research/native-wordram-interfaces/decoder/source/research/closed-helper-feedback/derived_replay.py b/research/native-wordram-interfaces/decoder/source/research/closed-helper-feedback/derived_replay.py new file mode 100644 index 0000000000..507acf28ac --- /dev/null +++ b/research/native-wordram-interfaces/decoder/source/research/closed-helper-feedback/derived_replay.py @@ -0,0 +1,372 @@ +#!/usr/bin/env python3 +"""Check feedback through the original forward native helper-query bank. + +PR5388 supplies the basis, wrappers and return completions. All eight original +centers remain. Ali Romman, substantial OpenAI Codex assistance; Apache-2.0. +This is a local interface, not a closed caller or a kappa certificate. +""" +from collections import Counter +from fractions import Fraction as F +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import importlib.util +import json +import sys + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +SOURCE = ROOT / 'research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz' +PIN = 'cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd' +PROFILE = {1:2201, 2:412, 3:510, 4:127, 5:40, 8:8} +QSYM = 1000000 +KBASE = 10000 + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def module(name, path): + spec = importlib.util.spec_from_file_location(name, path) + out = importlib.util.module_from_spec(spec) + sys.modules[name] = out + exec(compile(path.read_bytes(), str(path), "exec", optimize=0), out.__dict__) + return out + + +def authenticate(): + manifest = json.loads((HERE / 'SOURCES.json').read_text()) + for record in manifest['files']: + if record['usage'] == 'input': + path = ROOT / record['path'] + need(sha256(path.read_bytes()).hexdigest() == record['sha256'], + 'Changed live source: ' + record['path']) + + +authenticate() +ce = module('feedback_clifford', ROOT / 'research/coded-native-caller/clifford_exact.py') +core = module('feedback_native', ROOT / 'research/native-center-free-code/native_core.py') + + +def literal(word): + out = ce.ident(9) + for e in word: + if e[0] == 'P': + part = ce.perm(9, tuple(e[1])) + elif e[0] == 'D': + part = ce.diag(9, tuple(e[1]), tuple(e[2])) + elif e[0] == 'X': + part = ce.xgate(9, e[1]) + elif e[0] == 'phase': + part = ce.Op(9, ce.identity(9), [tuple(e)]) + elif e[0] == 'C': + part = ce.cgate(9, e[1], e[2]) + else: + raise ValueError('Unknown physical word') + out = out.then(part) + return out + + +def equal(a, b): + return a.tab == b.tab and a.zero_state() == b.zero_state() + + +def prepend(row, symbol): + out = {} + for (owner, word), coefficient in row.items(): + if word and word[0] == -symbol: + word = word[1:] + else: + word = (symbol,) + word + if word[:4] == (QSYM,) * 4: + word = word[4:] + key = (owner, word) + out[key] = out.get(key, F()) + coefficient + return {key:value for key,value in out.items() if value} + + +def act(row, *symbols): + for symbol in reversed(symbols): + row = prepend(row, symbol) + return row + + +def scalar_program(program, rows, owners): + for op in program: + dst = owners[op[1]] + if op[0] == 'add': + core.add(rows[dst], rows[owners[op[2]]], F(op[3])) + else: + need(op[0] == 'scale' and F(op[2]), 'Nonzero scalar basis SCALE') + rows[dst] = {key:F(op[2])*v for key,v in rows[dst].items()} + + +def original_departures(source, bank): + c = source['canonical'] + rows = [core.identity(i) for i in range(633)] + first = {} + cold = bank['cold_helper_owners'] + ci = {owner:i for i,owner in enumerate(cold)} + for event, e in enumerate(source['programs']['forward']): + if e[0] == 'climb' and e[2] in ci and e[2] not in first: + owner = e[2] + expected = {(cold[j], ()):F(a) for j,a in bank['T_rows'][ci[owner]]} + need(e[3] == 0 and rows[owner] == expected, 'Original uncoded first-departure row') + first[owner] = event + if e[0] == 'scalar': + gate = e[1] + dst = gate[1][1] + (632 if gate[1][0] == 'C' else 0) + if gate[0] == 'clear': + need(dst == 632, 'No persistent CLEAR') + rows[dst] = {} + elif gate[0] == 'copy': + src = gate[2][1] + (632 if gate[2][0] == 'C' else 0) + need(dst == 632, 'No persistent COPY') + rows[dst] = rows[src].copy() + elif gate[0] == 'add': + src = gate[2][1] + (632 if gate[2][0] == 'C' else 0) + core.add(rows[dst], rows[src], F(gate[3], gate[4])) + else: + need(gate[0] == 'scale', 'Known scalar operation') + rows[dst] = {key:F(gate[2],gate[3])*v for key,v in rows[dst].items()} + elif e[0] == 'warp': + owner = e[1][1] + (632 if e[1][0] == 'C' else 0) + rows[owner] = core.warp(rows[owner], e[2], False) + need(len(first) == 358, 'Every cold first departure') + for owner in range(632): + need(rows[owner] == core.expected(owner, False), 'Original FULL endpoint') + need(not rows[632], 'Original owned center cleanup') + for q in bank['queries']: + need(first[q['native_role']] == q['source_event'], 'Selected original event index') + return len(first) + + +def check_physics(source, bank): + c = source['canonical'] + Q = ce.cgate(9, 1) + Q2 = Q.then(Q) + R = ce.fourier(9) + need(equal(Q2, ce.xgate(9, 1)), 'Q squared is the exact Pauli X') + for q in bank['queries']: + K, O = literal(q['input_K']['word']), literal(q['response']['word']) + E = ce.canonical_frame(9, c['frames'][q['first_chart']]) + need(equal(K.then(E).then(O), Q), 'Absolute phase of relocated query') + need(equal(K.then(R).then(K.adjoint()), R), 'Full return K commutator') + need(equal(Q2.then(O.adjoint()), Q.then(K).then(E)), 'Physical raw feedback identity') + for op in (K, O, K.adjoint().then(Q2), O.adjoint()): + need(ce.rank([x for x,z,p in op.tab[9:]]) == 0, 'Feedback map has no Gaussian call') + compiled, _ = ce.monomial(op) + need(equal(compiled, op), 'Feedback monomial absolute phase') + need(all(e[0] in ('P','D','X','phase') for e in compiled.circuit), 'Literal monomial operations only') + for completion in bank['cold_completions']: + role = completion['native_role'] + need(c['final'][role] == completion['final_chart'], 'Completion source chart') + frame = ce.canonical_frame(9, c['frames'][completion['final_chart']]) + compiled = literal(completion['operator']['word']) + need(equal(frame.then(compiled), R), 'Completed return absolute phase') + rank = 9 - len(c['frames'][completion['final_chart']]) + need(rank == completion['charged_child_rank'], 'Completion paid rank') + gates = [e for e in compiled.circuit if e[0] == 'C'] + need(gates == [('C', 1 << i, 1) for i in range(rank)], 'One positive completion child') + positions = [i for i, e in enumerate(compiled.circuit) if e[0] == 'C'] + need(positions == list(range(positions[0], positions[0] + rank)), 'Contiguous completion child') + return {'query_identities': len(bank['queries']), 'completion_identities': len(bank['cold_completions'])} + + +def run(source, bank, feedbacks, mutation=None, terminal_decode=False): + c, queries = source['canonical'], bank['queries'] + owners = bank['cold_helper_owners'] + raw_start, obs_start, scratch = 633, 745, 857 + owned = 225 + bool(feedbacks) + rows = [core.identity(i) for i in range(632 + owned)] + charts = c['start'][:] + [None] * owned + paid, ordinary = Counter(), Counter() + expected_helpers = [core.identity(i) for i in range(632)] + for h, k, coefficient in feedbacks: + need(0 <= h < 112 and 0 <= k < 112 and h != k and coefficient in (-1,1), 'Distinct valid signed feedback coordinates') + core.add(expected_helpers[queries[k]['native_role']], + act(expected_helpers[queries[h]['native_role']], QSYM), F(coefficient)) + + def clear(slot, chart): + need(slot >= 632, 'No persistent erasure') + rows[slot], charts[slot] = {}, chart + ordinary['owned_clear'] += 1 + + def copy(dst, src): + need(dst >= 633 and not rows[dst], 'Owned COPY needs a cleared target') + rows[dst], charts[dst] = rows[src].copy(), charts[src] + ordinary['owned_copy'] += 1 + + for q in queries: + j, owner = q['query_index'], q['native_role'] + rows[owner] = act(rows[owner], KBASE+j) + rawslot, obs = raw_start+j, obs_start+j + clear(rawslot, 0) + copy(rawslot, owner) + event = source['programs']['forward'][q['source_event']] + need(event[0] == 'climb' and event[2:] == [owner,0,q['first_chart'],1], 'Exact relocated native H1') + charts[rawslot] = q['first_chart'] + paid[1] += 1 + clear(obs, q['first_chart']) + copy(obs, rawslot) + rows[obs] = act(core.identity(owner), QSYM) + charts[obs] = 0 + + def invariant(j): + q = queries[j] + w, r, o = rows[q['native_role']], rows[raw_start+j], rows[obs_start+j] + need(w == r, 'Held raw argument matches current helper coordinate') + need(o == act(w, QSYM, -(KBASE+j)), 'Observation matches current helper coordinate') + need(charts[raw_start+j] == q['first_chart'], 'Held raw physical chart') + + for index, (h, k, coefficient) in enumerate(feedbacks): + for j in (h,k): + invariant(j) + wh, wk = queries[h]['native_role'], queries[k]['native_role'] + if not (mutation == "dirty_scratch" and index == 0): + clear(scratch, 0) + copy(scratch, obs_start+h) + rows[scratch] = act(rows[scratch], KBASE+k) + ordinary['monomial_map'] += 1 + core.add(rows[wk], rows[scratch], F(coefficient)) + ordinary['scalar_add'] += 1 + clear(scratch, 0) + copy(scratch, wh) + symbols = (QSYM, -(KBASE+h)) if mutation == "one_Q" and index == 0 else (QSYM, QSYM, -(KBASE+h)) + rows[scratch] = act(rows[scratch], *symbols) + ordinary['monomial_map'] += 1 + if not (mutation == "stale_observation" and index == 0): + core.add(rows[obs_start+k], rows[scratch], F(coefficient)) + ordinary['scalar_add'] += 1 + # The exact physical identity above changes the declared chart here. + rows[scratch] = act(rows[wh], KBASE+k, QSYM, -(KBASE+h)) + charts[scratch] = queries[k]['first_chart'] + ordinary['monomial_map'] += 1 + if not (mutation == "stale_raw" and index == 0): + core.add(rows[raw_start+k], rows[scratch], F(coefficient)) + ordinary['scalar_add'] += 1 + if not (mutation == "live_scratch" and index == len(feedbacks) - 1): + clear(scratch, 0) + for j in (h,k): + invariant(j) + + for q in queries: + actual = act(rows[q['native_role']], -(KBASE+q['query_index'])) + need(actual == expected_helpers[q['native_role']], 'Independent elementary feedback endpoint') + desired = [row.copy() for row in rows[:632]] + scalar_program(bank['entrance_scalar_program'], rows, owners) + entered = [row.copy() for row in rows[:632]] + by_event = {q['source_event']:q for q in queries} + cuts = 0 + for event_index, e in enumerate(source['programs']['forward']): + if event_index in by_event: + q = by_event[event_index] + owner, rawslot = q['native_role'], raw_start+q['query_index'] + need(charts[owner] == 0 and charts[rawslot] == q['first_chart'], 'Replacement charts') + need(rows[owner] == rows[rawslot], 'Replacement row on all original and owned inputs') + rows[owner], rows[rawslot] = rows[rawslot], rows[owner] + if not (mutation == 'chart_swap' and cuts == 0): + charts[owner], charts[rawslot] = charts[rawslot], charts[owner] + need(charts[owner] == q['first_chart'] and charts[rawslot] == 0, 'Replacement chart transport') + ordinary['physical_field_swap'] += 1 + clear(rawslot, 0) + cuts += 1 + continue + kind = e[0] + if kind == 'scalar': + gate, chart = e[1:] + dst = gate[1][1]+(632 if gate[1][0] == 'C' else 0) + if gate[0] == 'clear': + need(dst == 632, 'Native persistent erasure') + rows[dst], charts[dst] = {}, chart + continue + need(charts[dst] == chart, 'Native scalar destination chart') + if gate[0] in ('copy','add'): + src = gate[2][1]+(632 if gate[2][0] == 'C' else 0) + need(charts[src] == chart, 'Native scalar source chart') + if gate[0] == 'copy': + need(dst == 632, 'Native persistent overwrite') + rows[dst] = rows[src].copy() + else: + core.add(rows[dst], rows[src], F(gate[3],gate[4])) + else: + need(gate[0] == 'scale', 'Known native scalar') + rows[dst] = {key:F(gate[2],gate[3])*v for key,v in rows[dst].items()} + elif kind == 'warp': + _, ref, op, before, after = e + owner = ref[1]+(632 if ref[0] == 'C' else 0) + need(charts[owner] == before, 'Native warp chart') + rows[owner], charts[owner] = core.warp(rows[owner], op, False), after + elif kind in ('climb','center'): + if kind == 'climb': + _,_,owner,before,after,rank = e + need(rank == len(c['frames'][after])-len(c['frames'][before]), 'Native climb rank') + else: + _,index,before,after,rank = e + owner = 632+index + need(rank == abs(len(c['frames'][after])-len(c['frames'][before])), 'Native center rank') + need(charts[owner] == before, 'Native paid chart') + charts[owner] = after + paid[rank] += 1 + else: + need(kind in ('phase','adapter','residual_adapter'), 'Known native marker') + for owner in range(632): + expected = entered[owner].copy() + if 112 <= owner < 224: + core.add(expected, entered[owner-112], F(1)) + need(rows[owner] == expected, 'Complete original FULL endpoint on transformed helper inputs') + need(charts[:632] == c['final'], 'Original final charts') + need(paid == Counter(PROFILE), 'All original Gaussian children, including eight centers') + for index, completion in enumerate(bank['cold_completions']): + if mutation == 'missing_completion' and index == 0: + continue + charts[completion['native_role']] = 1 + paid[completion['charged_child_rank']] += 1 + need(all(charts[owner] == 1 for owner in owners), 'Common return chart before scalar decoding') + scalar_program(bank['exit_scalar_program'], rows, owners) + for q in queries: + owner, j = q['native_role'], q['query_index'] + rows[owner] = act(rows[owner], -(KBASE+j)) + desired[owner] = act(desired[owner], -(KBASE+j)) + for owner in owners: + need(rows[owner] == desired[owner] == expected_helpers[owner], 'Returned transformed helper after completion and decode') + for q in queries: + j = q['query_index'] + need(rows[obs_start+j] == act(desired[q['native_role']], QSYM), 'Retained normalized feedback observation') + clear(obs_start+j, 0) + need(all(not row for row in rows[632:]), 'Every arbitrary owned input removed and every owned output cleared') + n = len(feedbacks) + need(ordinary == Counter(owned_clear=448+3*n, owned_copy=224+2*n, + physical_field_swap=112, scalar_add=3*n, monomial_map=3*n), 'Complete added ordinary invoice') + decoder_invoice = Counter() + if terminal_decode: + h, k = queries[0]['native_role'], queries[2]['native_role'] + # R commutes with Q^2, so this is the actual physical Pauli shear + # on common-full-chart outputs, not a free chart retag. + clear(scratch, 1); copy(scratch, h) + rows[scratch] = act(rows[scratch], QSYM, QSYM) + ordinary['monomial_map'] += 1 + if mutation != 'omit_decoder': + core.add(rows[k], rows[scratch], F(-1)) + ordinary['scalar_add'] += 1 + clear(scratch, 1) + decoder_invoice = Counter(owned_clear=2, owned_copy=1, monomial_map=1, scalar_add=1) + for owner in range(632): + need(rows[owner] == core.expected(owner, False), 'Decoded original independent endpoint') + need(all(not row for row in rows[632:]), 'Decoder scratch cleaned') + return dict(status='PASS_CLOSED_COMMUTATOR_HELPER_FEEDBACK', decoder_invoice=decoder_invoice, + + source_payload_sha256=PIN, + original_inputs=632, arbitrary_owned_inputs=owned, replacement_cuts=cuts, + feedbacks=feedbacks, completed_paid=dict(sorted(paid.items())), + helper_output_ranks_on_transformed_coordinates={4:2,7:7,8:41,9:358}, + ordinary=ordinary, all_owned_outputs_zero=True, + source_scope='Original forward FULL, all eight centers retained.', + target_scope='Helpers return on the transformed independent coordinates. A closed caller must prove its target.', + fixed_basis_adds=6420, fixed_basis_scales=408, + fixed_monomial_maps_at_most=400, additional_owned_fields=224 + bool(feedbacks), + limitation='Forward interface only. No caller closure, complete precision tariff, or kappa improvement is claimed.') + diff --git a/research/native-wordram-interfaces/decoder/source/research/closed-helper-feedback/three_query_terminal.py b/research/native-wordram-interfaces/decoder/source/research/closed-helper-feedback/three_query_terminal.py new file mode 100644 index 0000000000..aab208635a --- /dev/null +++ b/research/native-wordram-interfaces/decoder/source/research/closed-helper-feedback/three_query_terminal.py @@ -0,0 +1,132 @@ +"""Three-query closed feedback workspace on the actual original native word. +Extends PR5457 (Ali Romman, substantial OpenAI Codex assistance); Apache-2.0. +""" +from collections import Counter +from fractions import Fraction as F + +def check(m, source, bank, mutation=None): + core, act, need, QSYM, KBASE = m.core, m.act, m.need, m.QSYM, m.KBASE + queries = [dict(bank['queries'][j],query_index=i)for i,j in enumerate((0,16,32))] + c = source['canonical'] + owners = bank['cold_helper_owners'] + raw_start, obs_start, scratch = 633, 636, 639 + rows = [core.identity(i) for i in range(640)] + charts = c['start'][:] + [None]*8 + paid, ordinary = Counter(), Counter() + def clear(slot, chart): + need(slot>=632, 'No persistent erasure') + rows[slot],charts[slot]={},chart + ordinary['owned_clear']+=1 + def copy(dst,src): + need(dst>=633 and not rows[dst], 'Owned COPY needs a cleared target') + rows[dst],charts[dst]=rows[src].copy(),charts[src] + ordinary['owned_copy']+=1 + need(all(c['start'][owner]==0 for owner in owners), 'Cold basis has common ground chart') + # These three source first-departure rows are the original input identities. + cold_index={owner:i for i,owner in enumerate(owners)} + for q in queries: + need(bank['T_rows'][cold_index[q['native_role']]]==[[cold_index[q['native_role']], '1']], 'Selected query has identity entrance row') + bank_inputs=[r.copy() for r in rows[:632]] + for q in queries: + j, owner = q['query_index'], q['native_role'] + clear(raw_start+j,0);copy(raw_start+j,owner) + event=source['programs']['forward'][q['source_event']] + need(event[0]=='climb' and event[2:]==[owner,0,q['first_chart'],1], 'Exact selected query cut') + charts[raw_start+j]=q['first_chart'];paid[1]+=1 + clear(obs_start+j,q['first_chart']);copy(obs_start+j,raw_start+j) + rows[obs_start+j]=act(rows[owner],QSYM,-(KBASE+j));charts[obs_start+j]=0 + def invariant(j): + q=queries[j];owner=q['native_role'] + need(rows[raw_start+j]==rows[owner], 'Raw cache current') + need(rows[obs_start+j]==act(rows[owner],QSYM,-(KBASE+j)), 'Observation cache current') + need(charts[raw_start+j]==q['first_chart'], 'Raw chart current') + feedbacks=[(0,1,1),(1,2,1),(0,1,-1),(1,2,-1)] + for h,k,coefficient in feedbacks: + invariant(h);invariant(k) + wh,wk=queries[h]['native_role'],queries[k]['native_role'] + clear(scratch,0);copy(scratch,obs_start+h) + rows[scratch]=act(rows[scratch],KBASE+k);ordinary['monomial_map']+=1 + core.add(rows[wk],rows[scratch],F(coefficient));ordinary['scalar_add']+=1 + clear(scratch,0);copy(scratch,wh) + rows[scratch]=act(rows[scratch],QSYM,QSYM,-(KBASE+h));ordinary['monomial_map']+=1 + core.add(rows[obs_start+k],rows[scratch],F(coefficient));ordinary['scalar_add']+=1 + rows[scratch]=act(rows[wh],KBASE+k,QSYM,-(KBASE+h));charts[scratch]=queries[k]['first_chart'];ordinary['monomial_map']+=1 + core.add(rows[raw_start+k],rows[scratch],F(coefficient));ordinary['scalar_add']+=1 + clear(scratch,0);invariant(h);invariant(k) + # Keep the coupled helper inputs through the original physical source. + entered=[row.copy()for row in rows[:632]] + for j in range(3):clear(obs_start+j,0) + by_event={q['source_event']:q for q in queries};cuts=0 + for event_index, e in enumerate(source['programs']['forward']): + if event_index in by_event: + q = by_event[event_index] + owner, rawslot = q['native_role'], raw_start+q['query_index'] + need(charts[owner] == 0 and charts[rawslot] == q['first_chart'], 'Replacement charts') + need(rows[owner] == rows[rawslot], 'Replacement row on all original and owned inputs') + rows[owner], rows[rawslot] = rows[rawslot], rows[owner] + if not (mutation == 'chart_swap' and cuts == 0): + charts[owner], charts[rawslot] = charts[rawslot], charts[owner] + need(charts[owner] == q['first_chart'] and charts[rawslot] == 0, 'Replacement chart transport') + ordinary['physical_field_swap'] += 1 + clear(rawslot, 0) + cuts += 1 + continue + kind = e[0] + if kind == 'scalar': + gate, chart = e[1:] + dst = gate[1][1]+(632 if gate[1][0] == 'C' else 0) + if gate[0] == 'clear': + need(dst == 632, 'Native persistent erasure') + rows[dst], charts[dst] = {}, chart + continue + need(charts[dst] == chart, 'Native scalar destination chart') + if gate[0] in ('copy','add'): + src = gate[2][1]+(632 if gate[2][0] == 'C' else 0) + need(charts[src] == chart, 'Native scalar source chart') + if gate[0] == 'copy': + need(dst == 632, 'Native persistent overwrite') + rows[dst] = rows[src].copy() + else: + core.add(rows[dst], rows[src], F(gate[3],gate[4])) + else: + need(gate[0] == 'scale', 'Known native scalar') + rows[dst] = {key:F(gate[2],gate[3])*v for key,v in rows[dst].items()} + elif kind == 'warp': + _, ref, op, before, after = e + owner = ref[1]+(632 if ref[0] == 'C' else 0) + need(charts[owner] == before, 'Native warp chart') + rows[owner], charts[owner] = core.warp(rows[owner], op, False), after + elif kind in ('climb','center'): + if kind == 'climb': + _,_,owner,before,after,rank = e + need(rank == len(c['frames'][after])-len(c['frames'][before]), 'Native climb rank') + else: + _,index,before,after,rank = e + owner = 632+index + need(rank == abs(len(c['frames'][after])-len(c['frames'][before])), 'Native center rank') + need(charts[owner] == before, 'Native paid chart') + charts[owner] = after + paid[rank] += 1 + else: + need(kind in ('phase','adapter','residual_adapter'), 'Known native marker') + + for owner in range(632): + expected=entered[owner].copy() + if 112<=owner<224:core.add(expected,entered[owner-112],F(1)) + need(rows[owner]==expected, 'Original source on coupled helper inputs') + need(all(c['final'][q['native_role']]==1 for q in queries), 'Selected helpers already full at source exit') + h,k=queries[0]['native_role'],queries[2]['native_role'] + clear(scratch,1);copy(scratch,h) + rows[scratch]=act(rows[scratch],KBASE+2,QSYM,QSYM,-KBASE);ordinary['monomial_map']+=1 + if mutation!='omit_terminal_decode':core.add(rows[k],rows[scratch],F(-1)) + ordinary['scalar_add']+=1;clear(scratch,1) + for owner in range(632):need(rows[owner]==core.expected(owner,False), 'Original independent terminal endpoint') + need(charts[:632]==c['final'], 'Original endpoint charts') + need(paid==Counter(m.PROFILE), 'Original paid Gaussian profile preserved') + need(all(not row for row in rows[632:]), 'All arbitrary owned input cleared') + need(ordinary==Counter(owned_clear=26,owned_copy=15,physical_field_swap=3,scalar_add=13,monomial_map=13),'Complete closed workspace invoice') + return {'status':'PASS_THREE_QUERY_TERMINAL_DECODER','original_inputs':632,'arbitrary_owned_inputs':8, + 'additional_owned_fields':7,'replacement_cuts':cuts,'paid':dict(sorted(paid.items())), + 'ordinary':dict(ordinary),'basis_adds':0,'basis_scales':0, + 'observation_normalizers':3,'completion_calls':0,'target_abi':'exact original independent helper/main ABI', + 'new_kappa':False,'feedbacks':feedbacks,'source_query_indices':[0,16,32]} diff --git a/research/native-wordram-interfaces/decoder/source/research/coded-native-caller/PHYSICAL.md b/research/native-wordram-interfaces/decoder/source/research/coded-native-caller/PHYSICAL.md new file mode 100644 index 0000000000..da8837ba67 --- /dev/null +++ b/research/native-wordram-interfaces/decoder/source/research/coded-native-caller/PHYSICAL.md @@ -0,0 +1,71 @@ +# Real physical normalizers for the coded producer + +This is local constructive research on canonical/pr4929, not a completed supplier or exponent claim. Source code and Gaussian conventions retain the original authors' credit. + +Let n=9 and let q be any of the source's 112 port vectors (weight 3 or 7). Let e0=1. Construct an orthogonal binary matrix G taking e0 to q. If q_0=0, use the orthogonal transvection T_(e0+q). If q_0=1, select j>0 with q_j=0 and use T_(ej+q) T_(e0+ej). Here T_v(x)=x+(v dot x)v; both v have even weight, hence T_v is orthogonal. Such j exists because q is not the all-ones vector. + +For row j of G put z_j=(wt(row_j G)-1)/2 modulo 2. Define K=Z_z P_G. It is a real signed permutation. The full Gaussian R has entries alpha*(-i)^wt(x+y), with alpha=(1+i)^9/2^9. Orthogonality gives + +wt(G^-1 d)-wt(d) = 2 z dot d (mod 4). + +Indeed the degree-two coefficients vanish modulo four because distinct columns of G^-1 have even dot product; the linear coefficient is the weight of that column minus one. Therefore K R K^-1=R exactly, including absolute phase. K also maps the central line to span(q), and its orthogonal complement to q-perp, at the canonical-frame Lagrangian level. All these statements tensor to every positive digit-column count. + +Let Q be the central C gate, D the product of the other eight C gates, so R=DQ. Let E_i and S_i be the actual retained entrance-line and exit-hyperplane frame operators. With the operator convention that rightmost applies first, use + +input X: E_i K_i Q^-1 +input Y: K_i +output X: K_i^-1 +output Y: D K_i^-1 S_i^-1. + +All four wrappers are monomial. Their Lagrangian incidences prove this for every port, and the scratch verifier checks exact tableaus and absolute phases at every one of the 112 source ports. With A from PR4929, define C_ij= A_ij K_i^-1 K_j. Then the full main endpoint is + +F = diag(D,D) [[I,0],[C Q^-1,I]]. + +C is a physically implementable fixed owner recoding: apply K_i to each owner, apply A among the owners at common physical coordinates, and apply K_i^-1. Its inverse uses A^-1=(A+12I)/13. Since each K_i is real orthogonal and A is real symmetric, C^T=C. Since K_i commutes with R, C commutes with R. The polynomial C^2+12C-13I=0 follows by similarity. The 408 independent helper jobs and every paid Gaussian child are unchanged. + +For the actual raw inverse transpose, F^-T=diag(D^-1,D^-1) [[I,-Q^-1 C],[0,I]], since Q,D are symmetric. Multiply both outputs by D^2, then conjugate the physical X bank by Q^2 (input Q^-2 and output Q^2). These are explicit monomial powers. The result is + +B = diag(D,D) [[I,-Q C],[0,I]]. + +The old source convention using Y-only Q^2 conjugation cannot simply be copied for noncommuting C. The X-only convention above is exact. + +For a prior code B0 commuting with the current D, set G(B0)=diag(B0,Q^-1 B0 Q). The following two constructive local identities hold without requiring C and Q to commute: + +(post X C) F (pre Y C) = G(C B0) F_standard G(B0)^-1, +(post X C^-1) B (pre Y C^-1) = G(C^-1 B0) B_standard G(B0)^-1. + +They use [C,DQ]=0 and [B0,D]=0. Every additional operation on the left is physically cheap fixed recoding. For disjoint fresh blocks, codes from earlier stages commute with the current D. These identities do not yet settle interstage ADD/IDLE compatibility, terminal gauges, productive jobs, or the complete moment. + +## Literal recoding and complete local bill + +The source code has an exact factorization A=I-MM^T/4 with M a 112-by-8 matrix having entries 0,+1,-1 and M^T M=56I. Each mode column has 56 nonzero entries, and each owner row has four. The mode columns are emitted in NORMALIZERS.json and all 12,544 entries are checked against the pinned CODE.json. This factorization is used here as a constructive scalar program, without relying on any common physical address chart for separate Gaussian mode transformations. + +To execute A on arbitrary independent owner fields x, allocate eight owned zero fields t. Compute t=M^T x with 448 signed ADDs; update x-=M t/4 with 448 scaled ADDs; clear the eight owned temporaries. Reading x is finished before any x is updated. Hence no input field is overwritten before its last source read. For A^-1 use the same program with coefficient -1/52, since A^-1=I-MM^T/52. Both are exact rational linear programs. The helper fields of the native producer are never used as scratch, copied as free credit, or erased. + +Conjugating this scalar program by the 112 K_i and their inverses implements C or C^-1. This pays 224 monomial field maps, 896 scalar ADDs and 16 owned CLEARs per recoding, with eight owned fields reusable sequentially. The two additional recodings in either local gauge identity therefore cost at most 448 monomial maps, 1,792 scalar ADDs and 32 CLEARs, with no recursive Gaussian child. The four actual port normalizers contribute 448 monomial maps per native invocation. The displayed backward conversion contributes at most 448 further monomial maps (112 input X powers, 112 output X powers and 224 output D-squares); fusing maps can reduce this upper bound but is not assumed. + +These are field-level operation counts. A lifted K_i is an explicit binary map on nine f-bit address blocks together with signs given by block parity. Its constants, indexed movement and phase passes use the retained native monomial implementation. It is therefore a fixed finite O(V polylog p) nonrecursive operation under that caller's precision/address ABI, not a zero-work instruction. Each fixed rational ADD is likewise charged at its actual scalar precision. In particular the inverse denominator 52 must be implemented and rounded; no free exact real-division oracle is assumed. This lemma makes no independent TM tariff or outer-budget claim. + +The maximum exact component-l1 prefix bound for the scalar A program, including its temporaries, is 57. For A^-1 it is 56 (the output-only bound is 69/13). Signed monomial maps preserve component magnitude. A fixed local sequence has a fixed suffix bound obtained by multiplying elementary bounds 1+|coefficient|; owned CLEAR has bound one. This gives a finite bound for local rounding propagation. The number of local uses, compiler precision and complete outer error allocation still belong to the caller theorem. + +The normalized producer still has its exact PR4929 paid profile + + {1:2201, 2:412, 3:510, 4:127, 5:40} + +and independent helper profile + + {4:28, 7:7, 8:47, 9:326}. + +No productive main ranks are asserted merely from the coupled central ABI. Those depend on the completed caller, its initial/final gauges and every paid correction. + +## Universal scope and reproducible evidence + +PR4929 supplies the arbitrary-input logical identity over Q[FreeGroup72] for its emitted center-free word with ground-chart helper pre-compensation. Its normalized main endpoint is L(A), its raw dual is L(A)^-T, and every one of the 408 helper endpoints is autonomous. This proof is an inherited premise with exact source pins, not a consequence of this normalizer checker. The present wrappers and owner recodings act exclusively on the 224 main fields; new scratch is explicitly owned. Thus the helper block remains autonomous and its independent inputs, requested transforms and paid profile remain unchanged. + +For every f>=1, assign the shared native letters their actual consistent invertible lifted operators. Evaluation of the source free-group algebra is a homomorphism and gives the source logical identity. Independently lift each K_i as its f-fold tensor product, retaining spectator coordinates; its signed-permutation word, the two direct frame identities and its commutation with R lift by operator composition. In every compiled monomial word, P and X act columnwise on the f-bit blocks, D sums its Z4 polynomial over the f columns, and a one-column scalar phase i^gamma becomes i^(f*gamma). Reusing the one-column global phase unchanged would be incorrect. Finally form the owner matrix C_f with entries A_ij K_i,f^-1 K_j,f. One does not tensor the whole 224-by-224 owner matrix and does not assert that tensor powers preserve sums. Instead the finite scalar owner program is evaluated directly in the algebra of these lifted address operators. This proves the central ABI and local gauge identities at every positive width. + +Run `python3 -I -B research/coded-native-caller/normalizers.py` or its optimized `-O` form. The checker authenticates the decompressed actual native payload, CODE.json and retained Clifford source before executing the latter. It verifies all 112 real signed normalizers, 57,344 explicit weight-congruence addresses, 896 forward/backward monomial wrappers and eight exact frame/block identities per port, including absolute phase. Each emitted wrapper is separately lowered to a literal P/D/X/phase-only word and checked against its defining expression by exact tableau and absolute-phase state. No C gate remains in an emitted wrapper. The independent incoming-column and outgoing-row identities imply all 5,824 nonzero off-diagonal code blocks, without sampling those pairs. It also executes the eight-mode recoding on all 112 arbitrary-input basis columns in both directions. Omitting the essential signed phase is rejected at every affected port. The default command compares a regenerated mathematical receipt and performs no writes; `--write` is the explicit authoring path. + +Source pins: canonical main 624de9dc66858af0945e5f8a0942488d62280d43, `research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz`, decompressed SHA-256 cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd; PR4929 head 361f5d4100640177d6a983dd2f336021c75bfd5e, `research/native-center-free-code/CODE.json`, SHA-256 8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0; canonical `research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py`, SHA-256 2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962. Gzip container bytes are not substituted for decompressed source identity. + +Credit Dugongue's PR4929 for the coded producer and stable code; Cinna Davis's PR4694/4698 and the original cache/helper construction; Cao Yifan's PR4610 native word; the retained zxv, Jacob Alan Sussman, Cinna Davis and Clifford/native/compiler lineage. The exact canonical-frame implementation and phase conventions are retained source material. The constructive real centralizing normalizers, their explicit lifted words, X-only raw-dual convention and costed local code gauges are the additions here. New work is Apache-2.0 and has substantial OpenAI Codex assistance; no formal-kernel or independent human acceptance is asserted. diff --git a/research/native-wordram-interfaces/decoder/source/research/coded-native-caller/clifford_exact.py b/research/native-wordram-interfaces/decoder/source/research/coded-native-caller/clifford_exact.py new file mode 100644 index 0000000000..166841a037 --- /dev/null +++ b/research/native-wordram-interfaces/decoder/source/research/coded-native-caller/clifford_exact.py @@ -0,0 +1,149 @@ +"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals. +Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d. +The tableau is supplemented by a literal circuit, so global phases are kept. +""" +from dataclasses import dataclass + +def parity(x):return x.bit_count()&1 +def rank(rows): + p={} + for x in rows: + while x: + b=x.bit_length()-1 + if b not in p:p[b]=x;break + x^=p[b] + return len(p) +def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<>j&1);a[j],a[k]=a[k],a[j] + for i in range(n): + if i!=j and a[i]>>j&1:a[i]^=a[j] + assert [r&((1<>n for r in a) +def basis_extend(cols,n): + out=[] + for x in list(cols)+[1<len(out):out.append(x) + assert len(out)==n + return tuple(out) +def nullspace(rows,n): + a=list(rows);p=[];k=0 + for j in range(n): + t=next((i for i in range(k,len(a)) if a[i]>>j&1),None) + if t is None:continue + a[t],a[k]=a[k],a[t] + for i in range(len(a)): + if i!=k and a[i]>>j&1:a[i]^=a[k] + p.append(j);k+=1 + return tuple((1<>j)&1)<>i&1:out=pmul(out,T[i]) + for i in range(n): + if z>>i&1:out=pmul(out,T[n+i]) + return out +def compose(A,B):return tuple(apply(A,p) for p in B) +def inverse(T): + n=len(T)//2;cols=[x|(z<>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4)) + return tuple(out) +def qvalue(Q,alpha,x,n): + return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4 +def mul_i(a,p): + x,y=a;p%=4 + return [(x,y),(-y,x),(-x,-y),(y,-x)][p] +@dataclass +class Op: + n:int + tab:tuple + circuit:list + def then(self,b): + assert self.n==b.n + return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit) + def adjoint(self): + circ=[] + for e in reversed(self.circuit): + if e[0]=='P':circ.append(('P',inv(e[1],self.n))) + elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2]))) + elif e[0]=='C':circ.append(('C',e[1],-e[2])) + elif e[0]=='phase':circ.append(('phase',(-e[1])%4)) + else:circ.append(e) + return Op(self.n,inverse(self.tab),circ) + def zero_state(self,basis=0): + N=1<>i)&1 for i in range(n)) + assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n)) + return Op(n,tuple([(1<>i&1 else 0,1<>i&1 else 0) for i in range(n)]),[('C',q,sgn)]) +def xgate(n,b):return Op(n,tuple([(1<>i)&1)) for i in range(n)]),[('X',b)]) +def fourier(n,axes=None): + out=ident(n) + for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<len(selected):picks.append(j);selected.append(x) + assert len(picks)==r and all(x>>r==0 for x in Bcols) + Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1< (X,Y+X,H)`. Physical entrance and exit charts remain exactly those of the frozen source. + +There is a completely emitted constant dyadic pre-compensation, followed by the source word with every center Gaussian operation replaced by an owned CLEAR, whose exact normalized endpoint is + +`X' = X; Y' = Y + A X; H' = H`. + +All 632 persistent inputs are arbitrary and independent; no helper is initialized, discarded, identified or counted twice. The literal backward construction has exact normalized endpoint + +`X' = X - A^T Y; Y' = Y; H' = H`, + +the raw inverse transpose of the forward endpoint. The paid profile in both directions is + +`{1:2201, 2:412, 3:510, 4:127, 5:40}`. + +The helper profile stays `{4:28,7:7,8:47,9:326}`. Relative to the source, exactly eight rank-eight children are removed and no Gaussian child is added. The pre-compensation adds 6,596 scalar ADDs with a retained scalar allowance of 32,652 primitives; all numerator magnitudes and denominators are at most 4. These finite scalar operations do not establish a better recursive exponent on their own. + +## Constructive proof + +Delete all eight center calls by replacing each with CLEAR of the owned center field in the call's destination chart. Zero has every chart, so this is a valid erasure of owned scratch, not a borrowed input overwrite. Retain every other physical instruction and every endpoint chart. + +The exact sparse replay over the rational free group algebra on the 72 native symbols gives + +`M_0 = I + S + E_X + E_H`. + +Here S is the original transfer X to Y. Both error blocks land only in Y. E_X reads X; E_H reads only 106 particular helpers, each with a ground entrance and full-frame exit. Every helper and every X output remains autonomous. All error terms have EMPTY native word: the errors are ordinary constant dyadic matrices, not uncomputed address-operator oracles. The 12,532 nonzero entries split into 5,936 in E_X and 6,596 in E_H. + +Every pairwise product of S, E_X and E_H is zero, because all three maps land in Y and none reads Y. Before executing the center-cleared word, apply `I-E_H`. Every required source and target is in the actual ground chart: the targets are Y and the sources are those 106 ground-ended helpers. The operation is the explicit list of 6,596 dyadic ADDs. + +Consequently + +`M_0 (I-E_H) = I+S+E_X`. + +Thus `A=I+E_X` on the 112 main port indices gives the claimed offer, with no helper contamination. Scalar operations in one common address chart have their exact owner-space action, so this is a physical fixed-template pre-compensation and not an abstract change of logical coordinates. + +For the backward direction, the separately emitted center-cleared source word is verified to equal `I-S^T-E_X^T-E_H^T`, with the source's distinct inverse-transpose native letters. Prepend `I+E_H^T`, again using only actual ground-chart fields. The product is `I-S^T-E_X^T`. The verifier compares all 632 independent rows in both orientations. The owned center field is empty at termination. + +## Explicit code, inverse and conditioning + +The same exact entries satisfy + +`E_X^T = E_X, E_X^2 = -14 E_X, tr(E_X) = -112`. + +Set `P=-E_X/14`. It is a real symmetric idempotent of trace 8, hence an orthogonal projection of rank 8. Therefore + +`A=I-14P`, + +with eigenvalue -13 on the eight-dimensional image of P and eigenvalue +1 on its 104-dimensional kernel. In particular + +`A^-1 = I + E_X/13`, + +and its Euclidean condition number is exactly 13. The complete main shear is I+N_A with N_A^2=0 and ||N_A||_2=13; both it and its inverse have norm at most 14, so its condition number is at most 196. Helpers are an independent identity block, and the physical boundary charts are unitary, so this same bound applies to the complete physical coded offer. Its inverse uses I-N_A and needs no 1/13 arithmetic; 1/13 appears only when separately inverting the main code A. Every diagonal entry of A is zero; its 5,824 nonzero off-diagonal entries are ±1/2. The exact checker verifies the degree-two polynomial entry by entry over rational arithmetic, so the spectrum and inverse are universal consequences of that identity rather than numerical eigenvalue observations. + +The coefficient 1/13 is part of the mathematical inverse formula. This deliverable does not call it a free dyadic SCALE, assume a division oracle, or insert A^-1 across different physical address charts without paying for the resulting adapters. + +## Arbitrary fiber widths + +The replay identities hold over Q[FreeGroup72]. Every consistently shared invertible assignment of the 72 native operators defines an evaluation homomorphism. Hence the logical word identity holds at every positive column multiplicity under the retained source native implementation. It does not rely on one-column matrix testing, erasure of central phases or tensor powers preserving sums. + +Every physical frame, native monomial and Gaussian child is retained from the authenticated source, except the eight deleted owned-center calls. The new instructions are only constant dyadic scalar operations at an explicitly common ground chart. No fresh nonmonomial address implementation is introduced. + +The exact observed maximum prefix coefficient ℓ1 norms are 457 forward and 258 backward, checked on the fixed free-symbol words. Unitary evaluation bounds intermediate exact states and perturbations at the initial input in the maximum-over-fields Euclidean fiber norm by fixed constants independent of fiber width. For discrepancies inserted at later sites, use a separate suffix bound: assign each scalar ADD or SCALE of coefficient c the bound 1+|c|, and every unitary Gaussian/monomial, owned CLEAR or owned COPY the bound 1. The product of these elementary bounds over the finite word bounds every suffix. Thus the sum of local error magnitudes times this fixed product bounds propagated rounding error; no prefix norm is substituted for a suffix norm. Entrywise infinity-norm statements require the appropriate square-root fiber-volume conversion. There is no precision-dependent epsilon and no recursive border-precision claim. + +## Integration boundary + +The old source wrapper's port-dependent entrance lines and exit hyperplanes remain. A is a constant matrix in the stated normalized logical coordinates. It must not be silently treated as a constant free recoding in every physical main chart or in a different standardized central-Q ABI. Its nonzero off-diagonal entries connect distinct entrance-line charts. A useful next step is an actual coded caller or a paid simultaneous adapter that exploits the eight-mode structure, together with complete moment, raw-dual, compiler, finite precision and outer recovery budgets. This document supplies the exact producer and its bill, not those missing consumers. + +## Predecessor overlap and credit + +Cinna Davis's PR #4694, head `2add42d1edf14a263abe90a3bcde67fc1ba30768`, already emits a center-free kernel with paid profile minus eight rank-eight calls, records its coupled cache ABI, constructs its raw dual, and proves that its 106 observed helpers start at the empty chart. The source CACHE.md was read directly. None of center deletion, the cold-helper observation or the abstract block Schur elimination is claimed here as new. PR #4698, scientific head `9079ab66ba9a1717df478a08eb957c20d84d3e61`, already emits a dyadic helper basis of 379 gates in each direction reducing observations to eight helpers, and a conditional consumer. The present deliberately dense 6,596-ADD pre-compensation is easier to audit, not a claim to a better basis count. Its changed sufficient result is the actual fixed-template helper-independent coded offer, explicit A entries, exact eight-mode spectrum/inverse/conditioning, and unchanged independent helper ABI. + + +Cao Yifan / intqwq supplies the joint-helper/native-map round-three word at canonical `research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz`, commit `624de9dc66858af0945e5f8a0942488d62280d43`. Its predecessor and refreshed public lineage includes PR #4610; the exact source package and bytes, rather than an older PR headline, bind this result. Cinna Davis, the PR #4470 native/helper/controller lineage, Dugongue's exact native and complementary-provider work, DaysSky, Nick Petalas, Ryanson Jonathan, Jacob Alan Sussman, zxv and the retained scalar, Clifford, precision, compiler and outer contributors retain predecessor credit. The common-chart pre-compensation and exact eight-mode code are the present construction. Local MathProof's Schur block elimination and low-rank composition notes motivated the representation; their source-only inspection is not a fresh Lean/kernel audit or a claim of priority for elementary projection algebra. diff --git a/research/native-wordram-interfaces/decoder/source/research/native-center-free-code/native_core.py b/research/native-wordram-interfaces/decoder/source/research/native-center-free-code/native_core.py new file mode 100644 index 0000000000..5d8a8f0a63 --- /dev/null +++ b/research/native-wordram-interfaces/decoder/source/research/native-center-free-code/native_core.py @@ -0,0 +1,73 @@ +"""Exact source-bound coded-supplier replay core. Apache-2.0; Codex assistance. +Frozen source: Cao Yifan #4610 and retained Cinna Davis/Dugongue lineage. +""" +from pathlib import Path +from fractions import Fraction as Q +from collections import Counter +from hashlib import sha256 +import gzip,json,copy,importlib.util,sys +HERE=Path(__file__).resolve().parent +SOURCE_SHA='cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd' +def need(c,m): + if not c:raise ValueError(m) +def identity(i):return {(i,()):Q(1)} +def add(dst,src,a): + for k,v in tuple(src.items()): + z=dst.get(k,Q(0))+a*v + if z:dst[k]=z + else:dst.pop(k,None) +def warp(row,op,back): + s=(1 if op>0 else -1)*(abs(op)+(1000000 if back else 0));out={} + for (v,w),a in row.items(): + ww=w[1:]if w and w[0]==-s else(s,)+w;out[v,ww]=out.get((v,ww),Q(0))+a + return {k:a for k,a in out.items()if a} +def expected(i,back): + r=identity(i) + if back and i<112:add(r,identity(i+112),-1) + if not back and 112<=i<224:add(r,identity(i-112),1) + return r + +def replay(c,program,back=False,check_frames=True): + rows={i:identity(i)for i in range(632)};rows[632]={};cur=c['start'][:]+[None];paid=Counter();maxnorm=Q(1) + for e in program: + if e[0]=='scalar': + g,f=e[1:];r=g[1][1]+(632 if g[1][0]=='C'else 0) + if g[0]=='clear':need(r==632,'Borrowed erasure');rows[r]={};cur[r]=f + else: + if check_frames:need(cur[r]==f,'Scalar target frame') + if g[0]in('add','copy'): + v=g[2][1]+(632 if g[2][0]=='C'else 0) + if check_frames:need(cur[v]==f,'Scalar source frame') + if g[0]=='copy':need(r==632,'Borrowed overwrite');rows[r]=rows[v].copy() + else:need(r!=v,'Self add');add(rows[r],rows[v],Q(g[3],g[4])) + elif g[0]=='scale':rows[r]={k:Q(g[2],g[3])*v for k,v in rows[r].items()} + else:raise ValueError('Scalar opcode') + maxnorm=max(maxnorm,sum(map(abs,rows[r].values()),Q(0))) + elif e[0]=='warp': + _,r,op,x,y=e;r=r[1]+(632 if r[0]=='C'else 0) + if check_frames:need(cur[r]==x,'Warp source frame') + rows[r]=warp(rows[r],op,back);cur[r]=y + elif e[0]=='climb': + _,_,r,x,y,k=e + if check_frames:need(cur[r]==x,'Climb source frame') + need(k==len(c['frames'][y])-len(c['frames'][x])and k>0,'Ascending paid rank');cur[r]=y;paid[k]+=1 + elif e[0]=='center': + _,r,x,y,k=e;r+=632 + if check_frames:need(cur[r]==x,'Center source frame') + need(k==abs(len(c['frames'][y])-len(c['frames'][x])),'Center paid rank');cur[r]=y;paid[k]+=1 + else:need(e[0]in('phase','adapter','residual_adapter'),'Unknown opcode') + need(cur[:632]==c['final'],'Final frames');need(not rows[632],'Owned field cleared') + return rows,paid,maxnorm + +def clear_centers(program):return [['scalar',['clear',['C',e[1]]],e[3]]if e[0]=='center'else copy.deepcopy(e)for e in program] +def error_kernel(a): + rows,paid,_=replay(a['canonical'],clear_centers(a['programs']['forward']));E=[] + for i in range(632): + err=rows[i].copy();add(err,expected(i,False),-1) + for (j,w),v in sorted(err.items()): + need(112<=i<224 and(j<112 or j>=224),'Strict triangular error block');need(not w,'Constant owner kernel') + need(a['canonical']['final'][j]==1,'Repair source final full frame');need(j<112 or a['canonical']['start'][j]==0,'Pre-repair source initial ground') + E.append((i,j,v)) + need(len(E)==12532,'Frozen error term count') + return E + diff --git a/research/native-wordram-interfaces/decoder/source/research/native-helper-query-bank/ATTRIBUTION.md b/research/native-wordram-interfaces/decoder/source/research/native-helper-query-bank/ATTRIBUTION.md new file mode 100644 index 0000000000..51041de841 --- /dev/null +++ b/research/native-wordram-interfaces/decoder/source/research/native-helper-query-bank/ATTRIBUTION.md @@ -0,0 +1,57 @@ +# Source credit and distinct addition + +The fixed source word and all its native/compiler/precision lineage are retained. +New work is Apache-2.0 with substantial OpenAI Codex assistance for Dillon / +dillona; no independent human or formal-kernel acceptance is asserted. + +- **Cao Yifan / intqwq, PR #4610**: round-three joint-helper/native-map word, + retained as `research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz` and the + source payload consumed here. +- **Dugongue / mdumitrean, PR #4929**: exact center-free producer, helper-clean + pre-compensation, explicit eight-mode code and all-width free-group proof in + `research/native-center-free-code/`. This package replays its complete forward + word; it does not claim center deletion or helper-clean endpoints as new. +- **Cinna Davis / 1337isnot1337, PRs #4694 and #4698**, and the **PR #4470** + controller/native-helper lineage: center-free cache kernel, cold-helper + observations, physical helper normalization and explicit helper-basis methods. + The present full first-departure basis is a new application of that lineage, + not a claim to invent scalar helper recoding. +- **Dillon / dillona, PR #4933**: exact real R-centralizing normalizers and their + signed phases, literal monomial lowering, physical coded interface and + all-width lift conventions in `research/coded-native-caller/`. Those K words + and the credited Clifford implementation are pinned and reused here. +- **Chris R / Clear1nsight, PR #4931**: actual helper496 paid-prefix split and + ownership discipline. It supplied the source-history positive control and + motivation for using an existing chronological response. This package's + selected112 responses need no paid split. +- **Dillon / dillona, PR #5126**: sharp standalone local-query count; its grammar + does not include this internal paid-history interface. We do not present this + interface as a counterexample to that scoped result. +- **zxv, PR #5283**: exact Gaussian cache reuse requires the matching live row, + unchanged independent returns and full costs. The present package supplies + explicit rows and return decoding for one native interface, while preserving + that distinction from a completed caller. + +The retained source proofs also credit DaysSky, Nick Petalas, Ryanson Jonathan, +Jacob Alan Sussman, zxv and the scalar, Clifford, precision, compiler and outer +construction contributors. Their attribution and notices in the unchanged +predecessor directories remain applicable. No predecessor archive is copied or +rewritten by this package. + +The distinct result is the invertible **358-by-358 matrix of actual chronological +first departures**, selecting **112 funded H1 observations of common Q** with +literal exact phases, together with **26 H5 + 6 H1** cold-return completion, +full 358-input decoding, unchanged 50-hot-helper return contract, and explicit +ordinary work and owned observation storage. The entrance-prologue extension +relocates those same children, using exact first-departure identities and +whole-field swaps with chart transport. It adds explicit storage and movement, +with the same Gaussian calls. That interface remains separate from the +still-unproved main/helper caller. + +Submission checkpoint: canonical `1ec1119972c9aefe42525172d07b332fcff81cb4`; +source-manifest baseline: `7c472563474e60185e6ca101a17622133d047e56`; +scientific source freeze: `a5df48c55ea806d7952b65acc9c76d878ff09b13`. +The sources are already retained in canonical history, and exact live file pins +are in `SOURCES.json`. Coordination and overlap were reviewed by the parent +paid-history campaign in Discussion #4930 before this package was assigned; +this subtask did not reroll the research card or take over a concurrent claim. diff --git a/research/native-wordram-interfaces/decoder/source/research/native-helper-query-bank/BANK.json b/research/native-wordram-interfaces/decoder/source/research/native-helper-query-bank/BANK.json new file mode 100644 index 0000000000..91a6c7a5f3 --- /dev/null +++ b/research/native-wordram-interfaces/decoder/source/research/native-helper-query-bank/BANK.json @@ -0,0 +1 @@ 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diff --git a/research/native-wordram-interfaces/decoder/source/research/native-helper-query-bank/PROOF.md b/research/native-wordram-interfaces/decoder/source/research/native-helper-query-bank/PROOF.md new file mode 100644 index 0000000000..7ae6b095a2 --- /dev/null +++ b/research/native-wordram-interfaces/decoder/source/research/native-helper-query-bank/PROOF.md @@ -0,0 +1,313 @@ +# A forward native paid-history interface on independent helper inputs + +## Fixed source and precise scope + +Use the center-free forward word in the pinned `CODED-WORDS.json.gz`, with +632 arbitrary independent inputs: 112 X, 112 Y and 408 helpers. Its predecessor +proves, over the rational free-group algebra of the native warp symbols, + + (X,Y,H) -> (X,Y+A X,H), + +with the original physical entrance and exit frames. Here +`A=I-MM^T/4`, `M^T M=56I`, is the center-free producer's code. This package does +not change A. The independent helper block and zero helper-to-main blocks are +essential. Our verifier regenerates and checks all 632 endpoint rows against +that identity, rather than trusting a stored prefix registry. It also checks the +6,596-instruction source offset and exact center-deleted source suffix. + +The inherited physical rule is: a normalized logical term `a H_j` with native +word W, in physical chart F, acts as + + a F W F_birth(j)^-1 H_j. + +The rational coefficient stays outside the lifted address operator. Source +`phase`, `adapter` and `residual_adapter` markers use the authenticated native +physical implementation and the predecessor theorem; they are not newly proved +by the symbolic interpreter. The source has one owned center temporary, cleared +at exit; no persistent owner is erased. + +This result concerns the **forward** word only. In particular the raw-dual +backward word, conjugated frames and the main X-only Q-squared correction are +not supplied by reversing the observation list. A future bidirectional caller +must prove those obligations separately. + +## The scalar first-departure basis + +Let J be the ordered set of 358 helper owners whose initial chart is empty. +Let the other 50 helpers be called hot only to distinguish their nonempty birth +charts; their inputs are also arbitrary and independent. + +For each j in J, stop immediately before that owner's first paid climb. Direct +source replay proves: + +1. its current chart is empty; +2. its row contains only inputs in J; +3. every native word in that row is empty. + +Write that row as `sum_k T[j,k] H_k`, with rows and columns indexed by the same +increasing list J. Thus T is an actual scalar matrix of chronological +first-departure observations; its rows need not occur at one simultaneous cut. +`BANK.json` lists every entry. Exact elimination and both product identities +prove that the entire 358-by-358 matrix is invertible. T has 2,242 nonzero +entries; its inverse has 3,206. This statement includes every cold helper input, +not merely the selected query subspace. + +The deterministic elimination uses 2,949 ADDs, 117 SCALEs and 87 swaps. Each swap +is emitted without scratch as + + a += b; b -= a; a += b; b *= -1. + +The resulting 3,210 ADDs and 204 nonzero SCALEs implement T^-1 in place. +Reversing them and reciprocating SCALE coefficients implements T. The checker +executes both literal programs on all 358 independent input columns and checks +both inverse identities. These operations preserve all input information; none +uses a productive helper as an erased temporary. The coefficients are fixed +rationals, including odd denominators. This is an ordinary scalar program, not +a claim of free exact division in the eventual integer multiplier. + +## The selected common-Q responses + +Among the first departures, exactly 198 are already funded H1 children on odd +noncharacteristic lines, and their original helper endpoints have rank nine. +Choose the earliest 112, ordered by the emitted forward event index. Their +helper owners, zero-based event indices in both words, first chart and line q +are in `BANK.json`. Every selected row is an independent row of the full T. + +Let Q be the rank-one native Gaussian C gate on the first of the nine axes, +and R the full nine-axis Gaussian. For selected slot s, use the real signed +monomial K_s inherited from the phase-correct normalizer construction, so + + K_s R K_s^-1 = R. + +Let E_s be the actual first-departure frame for that slot. Define the monomial +response map + + O_s = Q K_s^-1 E_s^-1. + +For every selected slot the verifier proves that K_s and O_s have Fourier rank +zero, compiles them into literal P/D/X/phase-only words, and checks + + O_s E_s K_s = Q + +by the signed tableau **and** the complete exact zero-column amplitude. The +latter fixes the absolute phase left undetermined by a tableau. The full +R-commutator is checked by the same exact method. No Gaussian call occurs in +these wrappers. The unselected diagonal entries of D_K are the identity. + +The input contract is 358 independent fields ξ, plus the original arbitrary +main and hot-helper fields. Before the source word: + + H_J = T^-1 D_K ξ. + +Execute the diagonal K maps, followed by the emitted T^-1 scalar program. The +selected first-departure row is then `(T H_J)_s = K_s ξ_s`. The existing paid +H1 child produces `E_s K_s ξ_s`. Immediately after that actual event, COPY the +field into a distinct owned zero field and apply O_s to that copy. It is exactly +`Q ξ_s`. The persistent native owner continues along its original paid path. +This adds **no Gaussian child and no paid split** to obtain the observation. + +In this chronological version, each response becomes available after its listed +event and may be retained until the source word finishes. The following exact +rescheduling makes every response available in an entrance prologue instead. +In both versions, observations are owned copies of existing paid history, not +independent input jobs or extra productive credit. + +## An entrance prologue with the same 112 paid children + +After the diagonal K maps, but **before** the existing T^-1 scalar program, +the cold coordinates are `w=D_K ξ`. For each selected coordinate s: + +1. Initialize a new owned raw field and COPY `w_s` into it. +2. Execute the complete adapted H1 child from the listed source event on that + field. Its physical value is `E_s w_s`. This is the original child relocated, + not a second invocation or a bare C gate without its source adapters. +3. COPY its value into the owned observation field and apply the already + compiled monomial O_s. This gives `Q ξ_s` immediately. Keep the raw field + `E_s w_s` unchanged for its later replacement cut. + +Now execute T^-1 and the source word, omitting the 112 selected child events. +At such an event the original persistent field has chart zero and value + + (T T^-1 w)_s = w_s. + +The first-departure proof establishes this identity on every original input; +it contains no main-input coefficient. SWAP that entire physical field with +its stored raw field, **transporting the chart tags with the data**. The +persistent field now has exactly the chart E_s and value E_s w_s that the +omitted original child would have produced. The owned raw slot contains the +old duplicate w_s in chart zero; CLEAR that owned slot. No persistent field is +cleared, and its input information remains in the invertibly transformed +E_s w_s. A whole-field permutation works between these two charts; it is not +the three-ADD common-chart swap used by the scalar basis program. + +All other source instructions are unchanged. Induction at the 112 replacement +cuts therefore restores the complete source state, with exactly its original +paid inventory. Completion and return decoding below apply unchanged. All +responses are available after the 112 prologue children, before the original +native operations and even before T^-1. This is an early-query interface, not +a claim that the prologue has zero cost. + +The helper arguments are fixed before the prologue and thereafter follow only +the declared basis program and source word. A caller may recode its **main** +entrance values after receiving the responses: the replacement identities hold +for arbitrary main values and have zero main coefficients. Such a recoding +changes the main input to which the producer contract applies. It does not +automatically preserve a caller's original jobs. Later interventions in the +native word, changes to helper arguments, or mutation of held raw fields require +a new integrated proof. + +[HOIST.json](HOIST.json) emits an **ordered patch recipe**, not a standalone +instruction stream. After its prologue, insert the existing BANK scalar +T^-1 entrance program. Then replay the pinned forward source in order, replacing +only the listed child events and retaining every intervening source segment. +Afterward apply the unchanged BANK completion and return decoder. The final +observation clears are obligations after the consumer's last use. +The verifier executes that program on all 632 original inputs and 225 arbitrary +owned inputs (the native center, 112 held raw fields and 112 observation fields). +It checks all 112 replacement cuts, every persistent endpoint, unchanged paid +counts, and clearing of every owned input. Observation copies are tracked in +their raw representation; the independent signed-tableau and absolute-phase +identities above verify their O_s readouts. The native word never reads those +copies, so normalizing them immediately cannot affect the replay. Wrong held +arguments and a swap that fails to transport chart tags are rejected. + +## Returning every independent helper + +At source termination, the old cold-helper target census is + + 26 H4 + 6 H8 + 326 H9. + +The other 50 helpers have targets `2 H4 + 7 H7 + 41 H8`. Rank means the dimension +increase from that helper's actual birth chart, not just its exit-frame rank. +The hot helpers remain completely unchanged in this package. + +The scalar decoder T cannot be applied while different cold fields still carry +different physical Gaussian frames. For every cold owner j of original rank +r<9, append the operator + + C_j = R F_final(j)^-1. + +The verifier compiles C_j into a monomial wrapper, one contiguous standard +Gaussian block of rank 9-r, and a monomial wrapper. It checks the exact signed +tableau and phase of the compiled word, and `C_j F_final(j)=R`. The explicit +32 recipes cost **26 H5 plus six H1**, with at most 64 monomial wrapper maps. +The 326 original H9 outputs already equal R H_j. The whole cold bank is now +uniformly `R H_J`. + +Apply the literal T program, then the diagonal K_s^-1 maps. Scalar owner maps +commute with the same R on every owner, and K_s commutes with R, so the output is + + D_K^-1 T R T^-1 D_K ξ = R ξ. + +Every one of the 358 input coordinates is returned as its independent H9 job. +No original helper information is discarded or replaced by a main input. This +changes the target contract for the cold bank to 358 H9 jobs; it does **not** +claim that the old ordered H4/H8 target list survives the mixing unchanged. +Together with the unmodified hot bank, the new target profile is +`{4:2,7:7,8:41,9:358}`. The added target rank mass and added paid rank mass are +both 136. The main coded endpoint remains exactly the source endpoint, because +its helper-to-main blocks vanish for all original helper values, and all new +exit operations act solely on helpers or owned observation copies. + +## Ownership and ordinary work + +The source retains its original persistent owners and owned center temporary. +The scalar basis programs operate reversibly in place on all 358 cold fields. +They require no additional basis scratch. The observation interface owns at +most 112 extra fields. Each is initially cleared, receives one COPY after its +specified H1 event, then receives its response monomial map. At an interface +return these fields contain the promised responses and the recipient owns them; +a completed caller must CLEAR them after their last use. The ordinary-work +invoice includes those terminal clears. A demonstration that simply clears all +responses at the end leaves only the independent original jobs, without +turning the observations into productive outputs. + +Additional field passes for the chronological version, relative to the pinned +center-free producer: + +| Operation | Count | +|---|---:| +| Scalar ADD | 6,420 | +| Scalar SCALE | 408 | +| Diagonal basis monomial maps K and K^-1 | 224 | +| Observation monomial maps | 112 | +| Completion monomial wrapper maps | at most 64 | +| Owned observation COPY | 112 | +| Owned observation initial CLEAR | 112 | +| Owned observation terminal CLEAR | 112 | +| Extra simultaneously owned fields | at most 112 | +| Paid completion children | 26 H5 + 6 H1 | + +For the entrance-prologue version, keep the same scalar, monomial and completion +counts. Replace the observation-storage rows by **224 owned COPYs, 448 owned +CLEARs, 112 whole-field SWAPs and at most 224 extra simultaneous fields**. These +totals include observation creation and the recipient's final observation +clears. Each SWAP requires ordinary movement of two complete fields. Thus the +prologue adds 112 copies, 224 clears, 112 swaps and 112 held +fields over the chronological interface, with **zero additional scalar passes +and zero additional Gaussian children**. Copying the selected w coordinates +before T^-1 avoids reconstructing the dense T rows afterward. The source's +original owned center remains separately charged as before. + +A monomial field map is the complete emitted P/D/X/phase word, not a single +machine instruction; its indexed movement and phase arithmetic must be priced +using the retained source implementation. Each rational ADD/SCALE must likewise +be implemented at the chosen precision. The lists are fixed finite programs, +so they admit width-independent algebraic suffix bounds: charge each scalar +ADD or SCALE coefficient c the bound `1+|c|`, and each unitary, whole-field SWAP +or owned COPY/CLEAR the bound one in maximum-over-fields Euclidean fiber norm. The finite +product bounds propagation of local rounding errors. This is a local existence +bound, not a complete precision allocation, optimized ordinary-work tariff or +outer multiplication budget. The new Gaussian children also require the source +Gaussian implementation and its normal costs. + +## Every positive digit width + +For f positive, evaluate the source rational free-group identity at the actual +consistent native operators on the f digit columns, as in the pinned +`CODED-PROOF.md`. The same exact first-departure rows have empty words, hence +the same scalar matrix T. All coefficients remain scalar owner coefficients; +T is **not** raised to a tensor power. + +Independently lift each one-column physical word K_s, O_s, E_s, R and C_j to its +columnwise f-fold operator, with spectator coordinates unchanged. Exact +operator composition identities lift under this tensor operation. P and X act +columnwise, diagonal Z4 phases sum over columns, and a one-column global phase +`i^gamma` becomes `i^(f*gamma)`. Keeping that phase unchanged would be wrong. +The signed-tableau plus absolute-phase checks establish the one-column +identities, and the emitted literal words fix this lift unambiguously. + +Finally evaluate the same finite scalar owner programs in the algebra of these +lifted address operators. This gives `O_s,f E_s,f K_s,f = Q_f`, and the completed +return identity `D_K,f^-1 T R_f T^-1 D_K,f = R_f` at every f. It never asserts +that tensor powers preserve sums. Thus the ABI is an all-width consequence of +explicit fixed scalar programs and inherited source semantics, not merely a +512-dimensional numerical experiment. + +The hoist uses those same evaluated first-departure identities. COPY and SWAP +move complete f-column fields, with their frames, and the relocated child is the +same lifted E_s. Hence the equality at each replacement cut and the source-state +induction hold at every f as well. Neither scalar T nor an owner sum is tensor +powered in this rescheduling argument. + +## Evidence boundaries + +The registered verifier authenticates every live source file before importing +source code. It regenerates all 632 forward rows and all 358 first departures, +checks the entire scalar basis, emits and checks 112 response words and 32 +completion words, and compares the deterministic receipt. It also rejects: +main-input contamination of a claimed helper-only departure; a singular basis; +a phase-only wrong response with the same tableau; and omission of a required +cold-H8 completion. These checks use explicit exceptions and also run under +Python `-O`. The additional hoist replay checks all 857 raw-state input columns, +the 112 matching physical replacement cuts, the unchanged Gaussian inventory, +and the two rescheduling controls described above. + +The inherited native physical compiler and multiplication analytic hypotheses +are not independently audited here. No full historical suite, selected cold +replay, hosted CI or formal-kernel acceptance is claimed. A complete caller must +still put the required main arguments into this interface without losing any +independent helper input, establish both directions actually used, clear all +owned observations, and pay storage, precision, ordinary work and the outer +budget. Until then the result is an exact reusable forward paid-history ABI, +not an admitted supplier or a new exponent. diff --git a/research/native-wordram-interfaces/decoder/source/scripts/compare_recursive_invoices.py b/research/native-wordram-interfaces/decoder/source/scripts/compare_recursive_invoices.py new file mode 100644 index 0000000000..fda2a852e9 --- /dev/null +++ b/research/native-wordram-interfaces/decoder/source/scripts/compare_recursive_invoices.py @@ -0,0 +1,218 @@ +#!/usr/bin/env python3 +# SPDX-License-Identifier: Apache-2.0 +"""Compare declared recursive invoices by exact signed concave order. + +Usage: python3 -B scripts/compare_recursive_invoices.py OLD.json NEW.json + +Each input has schema ``integer-mult-recursive-invoice/v1``, an identical +contract object with model, rank_semantics, ambient_rank and boundary, and +paid/targets objects mapping canonical positive decimal ranks to nonnegative +integer counts. Contracts are declarations, not verified mathematical premises. + +For d = (new paid - old paid) - (new targets - old targets), set +K(k) = sum_r d[r] min(r,k). The sign of K at every support knot determines +the order for every increasing concave tariff f with f(0)=0. Indeed, on the +integer ranks 0..R, write s_j=f(j)-f(j-1). Then + + sum_r d[r] f(r) = s_R K(R) + sum_(k=1..R-1) (s_k-s_(k+1)) K(k). + +All coefficients on the right are nonnegative. Conversely, the increasing +concave tariffs min(r,k) witness every required hinge. Between support knots +K is linear. For f(r)=r**t, 0= 0 for value in values): + classification, power_sign = "uniformly_worse", "strictly_positive" + else: + classification, power_sign = "inconclusive", "not_determined" + old_mass, new_mass = _masses(old), _masses(new) + return { + "schema": REPORT_SCHEMA, + "classification": classification, + "contract": old["contract"], + "delta_paid": paid, + "delta_targets": targets, + "signed_net_delta": net, + "hinges": hinges, + "rank_mass": {"old": old_mass, "new": new_mass, + "delta": {key: new_mass[key] - old_mass[key] for key in old_mass}}, + "quantity": "(new paid - new targets) - (old paid - old targets)", + "tariff_class": "increasing concave f on nonnegative ranks, with f(0)=0", + "uniform_order": "weak; some concave tariffs can give equality", + "power_moment": {"tariff": "r^t", "exponent": "0 < t < 1", + "new_minus_old_sign": power_sign}, + "assurance": { + "contract": "Exact matching user declarations; mathematical applicability is not verified.", + "input_binding": "SHA-256 identifies the exact input bytes read, when loaded by this CLI.", + "scope": "Histogram arithmetic only. Histogram correctness, circuit legality, ownership, " + "phases, precision, supplier admission and compiler endpoints are not validated.", + "inconclusive": "Mixed hinge signs do not establish a power-moment crossing or failure.", + }, + "method_credit": "Classical concave order/majorization; mightyOil's t16-moment-order-audit " + "and its retained predecessors. No new theorem claim.", + } + + +def main(argv=None): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("old", help="old invoice JSON") + parser.add_argument("new", help="new invoice JSON") + args = parser.parse_args(argv) + try: + old, old_evidence = load_invoice(args.old) + new, new_evidence = load_invoice(args.new) + report = compare_invoices(old, new) + report["inputs"] = {"old": old_evidence, "new": new_evidence} + except (OSError, ValueError, TypeError, RecursionError) as exc: + print(json.dumps({"status": "INVALID_RECURSIVE_INVOICE", "error": str(exc)}, + ensure_ascii=True), file=sys.stderr) + return 2 + print(json.dumps(report, indent=2, sort_keys=True, ensure_ascii=True)) + return 0 + + +if __name__ == "__main__": + raise SystemExit(main()) diff --git a/research/native-wordram-interfaces/decoder/three-query-terminal-result.json b/research/native-wordram-interfaces/decoder/three-query-terminal-result.json new file mode 100644 index 0000000000..1e21e15bd7 --- /dev/null +++ b/research/native-wordram-interfaces/decoder/three-query-terminal-result.json @@ -0,0 +1,74 @@ +{ + "status": "PASS_THREE_QUERY_TERMINAL_DECODER", + "original_inputs": 632, + "arbitrary_owned_inputs": 8, + "additional_owned_fields": 7, + "replacement_cuts": 3, + "paid": { + "1": 2201, + "2": 412, + "3": 510, + "4": 127, + "5": 40, + "8": 8 + }, + "ordinary": { + "owned_clear": 26, + "owned_copy": 15, + "monomial_map": 13, + "scalar_add": 13, + "physical_field_swap": 3 + }, + "basis_adds": 0, + "basis_scales": 0, + "observation_normalizers": 3, + "completion_calls": 0, + "target_abi": "exact original independent helper/main ABI", + "new_kappa": false, + "feedbacks": [ + [ + 0, + 1, + 1 + ], + [ + 1, + 2, + 1 + ], + [ + 0, + 1, + -1 + ], + [ + 1, + 2, + -1 + ] + ], + "source_query_indices": [ + 0, + 16, + 32 + ], + "first_departures_checked": 358, + "physical_checks": { + "query_identities": 3, + "completion_identities": 0 + }, + "decoder_monomial_maps_checked": 3, + "decoder_commutes_full_return": true, + "rejected_controls": [ + { + "mutation": "omit_terminal_decode", + "result": "REJECT", + "reason": "Original independent terminal endpoint" + }, + { + "mutation": "chart_swap", + "result": "REJECT", + "reason": "Replacement chart transport" + } + ] +} diff --git a/research/native-wordram-interfaces/decoder/verify_terminal.py b/research/native-wordram-interfaces/decoder/verify_terminal.py new file mode 100644 index 0000000000..a39e43c7b1 --- /dev/null +++ b/research/native-wordram-interfaces/decoder/verify_terminal.py @@ -0,0 +1,42 @@ +"""Source-bound three-query closed workspace replay; Python 3.12+, standard library.""" +from pathlib import Path +import gzip,hashlib,importlib.util,json,sys +ROOT=Path(__file__).resolve().parent +if not __debug__: raise RuntimeError('Run this certificate without Python -O') +def module(name,path): + spec=importlib.util.spec_from_file_location(name,path) + out=importlib.util.module_from_spec(spec);spec.loader.exec_module(out);return out +m=module('closed_physics',ROOT/'source/research/closed-helper-feedback/derived_replay.py') +w=module('three_query_workspace',ROOT/'source/research/closed-helper-feedback/three_query_terminal.py') +raw=gzip.decompress(m.SOURCE.read_bytes()) +m.need(hashlib.sha256(raw).hexdigest()==m.PIN,'Native decompressed payload hash') +source=json.loads(raw);bank=json.loads((m.ROOT/'research/native-helper-query-bank/BANK.json').read_text()) +result=w.check(m,source,bank) +selected={**bank,'queries':[bank['queries'][j]for j in (0,16,32)],'cold_completions':[]} +result['first_departures_checked']=m.original_departures(source,selected) +result['physical_checks']=m.check_physics(source,selected) +q=m.ce.cgate(9,1);q2=q.then(q) +m.need(m.equal(q2,m.ce.xgate(9,1)),'Exact central Pauli square') +K0=m.literal(bank['queries'][0]['input_K']['word']) +K2=m.literal(bank['queries'][32]['input_K']['word']) +O2=m.literal(bank['queries'][32]['response']['word']) +for op in [K0.adjoint().then(q2).then(K2),q2,O2.adjoint()]: + compiled,_=m.ce.monomial(op) + m.need(m.equal(compiled,op),'Literal ordinary decoder map including absolute phase') +r=m.ce.fourier(9) +B=K0.adjoint().then(q2).then(K2) +m.need(m.equal(B.then(r),r.then(B)), 'Physical terminal decoder commutes with full return') +result['decoder_monomial_maps_checked']=3 +result['decoder_commutes_full_return']=True +controls=[] +for mutation in ['omit_terminal_decode','chart_swap']: + try:w.check(m,source,bank,mutation=mutation) + except ValueError as exc:controls.append({'mutation':mutation,'result':'REJECT','reason':str(exc)}) + else:raise ValueError('Mutation accepted: '+mutation) +result['rejected_controls']=controls +# Tuples are serialized as arrays in a portable frozen receipt. +result=json.loads(json.dumps(result)) +receipt=ROOT/'three-query-terminal-result.json' +if '--emit' in sys.argv:receipt.write_text(json.dumps(result,indent=2)+'\n',encoding='utf-8') +else:m.need(result==json.loads(receipt.read_text(encoding='utf-8')),'Saved typed receipt differs') +print(json.dumps(result,indent=2)) diff --git a/research/native-wordram-interfaces/native/REPORT.txt b/research/native-wordram-interfaces/native/REPORT.txt new file mode 100644 index 0000000000..d92d03af6b --- /dev/null +++ b/research/native-wordram-interfaces/native/REPORT.txt @@ -0,0 +1,124 @@ +A concrete centre-free native producer leaf, with global address embeddings + +Positive deliverable +compile_unit.py serializes the actual centre-free native source, preserving its +full retained entrance/exit chart ABI, into named field operations with explicit +153-axis frame bases and native address-map columns. It supplies every source +record, not a CENTER_FREE_FULL placeholder. The exported UNIT0-forward.json.gz +and UNIT0-backward.json.gz contain those literal event arrays. Both orientations +have 28,047 records: the source's 28,045 plus explicit owned entry and exit clears. +This is a sufficient source-ABI leaf. It is not a compiler for the complete p19 +controller and does not assert a new multiplication kappa. + +Exact resulting contracts +For arbitrary independent data in all 632 persistent source fields, the forward +logical endpoint is (X,Y,H)->(X,Y+A X,H), and its actual raw dual is +(X-A^T Y,Y,H). There are 112 X fields, 112 Y fields, 408 independent productive +helper fields and one owned centre. The owned centre accepts arbitrary dirty +entry data and is explicitly zero on exit. No helper is borrowed or erased. +The original entrance and exit frame lists are supplied explicitly in each export. +The code A is the retained real symmetric 112-by-112 invertible matrix with +spectrum 1 (104 times), -13 (8 times), and inverse I+(A-I)/13. + +The exact paid profile is {1:2201,2:412,3:510,4:127,5:40}; there is no rank-8 centre +job. The exact productive helper profile is {4:28,7:7,8:47,9:326}. The source and +serialized traces both verify all persistent frames and every paid rank. Every forward/inverse native-map event also checks the image of its entire source frame span against its declared target span, including reused ground-to-ground instances. Direct +free-group row replay rederives the endpoint for all 632 arbitrary input rows, +including every helper, in both directions. This is the actual centre-free +28,045-record source, not the older 21,449-record predecessor with eight H8 jobs. + +The scalar primitive tariffs, including the two extra clears, are 223,444 forward +and 223,492 backward. These differ from the predecessor's 158,120/158,168 tariffs. +They are scalar-record tariffs; native address movement, monomial adapters, +precision and every caller-level resource must still be charged under the source +physical model. We do not describe them as complete TM or Word RAM running times. + +Universal relocation and spectator proof +For unit u in {0,...,18}, map local binary address axis 0 to global axis 0, and +local axes j=1,...,8 to 1+8u+(j-1). The explicit vector map is + e_u(v)=(v mod 2) XOR ((v div 2) shifted left by 1+8u). +Its nine basis images are distinct standard basis vectors. It is therefore +linear and injective. Consequently it preserves sums, intersections, independence +and dimension of every source frame; every paid rank difference is unchanged. +The 72 retained native binary address maps are supplied by complete columns, +with inverse columns checked on all 512 local addresses, and extended by identity +on all spectator axes. All original field operands are renamed injectively into +MAIN, HELPER and OWNED_CENTER namespaces. Hence no owned field collides with an +independent productive field. Source adapter records are retained and bound to +the same explicit field and axis names; their inherited physical implementation +is not replaced by an assumed new primitive. + +For one digit column the embedding identifies the local active tensor factor +with the nine selected axes. For every positive column count f, use the source's +columnwise lift on those axes and identity on every spectator coordinate. The +field index is a direct-sum role label and is not tensor-powered. Composition and +addition of the fixed source field program commute with this linear evaluation, +so its exact free-group endpoint and autonomous helpers are preserved for every +f. In particular no assertion that tensor powers preserve matrix sums is used. +The compiler's explicit clearing at entry kills any initial owned-centre value; +its exit clear returns the centre to the zero value in ground frame. Every other +field has exactly the source's arbitrary-data endpoint and is never cleared. + +Actual uncoded leaf +The verifier also serializes and replays the retained uncoded source in both +orientations. All 632 arbitrary-input rows agree with the genuine identity +cross-transfer (X,Y)->(X,Y+X), respectively raw dual (X-Y,Y). Its paid profile is +{1:2201,2:412,3:510,4:127,5:40,8:8}; its 408 helper targets are unchanged. Thus +there really is an actual C=I producer; removing its eight H8 jobs without the +owned-helper target debits or changed code would be an invalid invoice. +The centre-free source changes the transfer to A, which is why the two payloads +cannot be interchanged solely because their other rank counts agree. + +Actual checks +The verifier checks all 19 unit embeddings and both orientations. It independently +reconstructs the source error kernel, centre-free arbitrary-input endpoint, +serialized frame trace, complete paid profile and all 408 productive helper +ranks. A changed paid-rank record is rejected. Both committed compressed literal exports are required and compared as decoded JSON against regeneration. Every one of the 12,544 actual CODE.json entries is matched to the rederived arbitrary-input defect. Every consumed source is checked +against its content hash before use. The exports are generated from the literal +source events and explicit map tables, not from a substitute mathematical word. +The default run compares the retained RESULT.json and writes no output. Use +--write --emit explicitly to regenerate the receipt and two literal exports. + + python -B compile_unit.py + +Python 3.10+ and its standard library suffice. No network, installed Lean, Git, +Windows-specific executable or private path is required. Upstream source is +SOURCE_ONLY here; no fresh Lean kernel or transitive-axiom audit is claimed. + +Precise remaining p19 boundary +The normalized physical full call in the retained PHYSICAL.md includes a common +D on both outputs. The existing p19 FORWARD/REVERSE replay specifies pure query +shears instead. Its 20 FORWARD records are thin queries, while only its 19 thick +units may consume the above producer. Replacing all 39 records by this source +would both change the operator and double-charge the intended local profile. +Changing the prototype LETTER from R to D is not enough: with the actual C/C^-1 +gauges, the p1 control then differs in 57,344 entries, whereas the R control agrees. +The same controls at p2/p3 have 99,233/141,124 differences for D and zero for R. +A fresh D-based caller can still be researched; these controls only refute that +literal substitution, not every new caller. + +The PHYSICAL full-call gauge G(B)=diag(B,Q^-1 B Q) identifies the next exact +interface. Q is an f-column Gaussian. Although Q=aI+bX has a four-term ordinary +conjugation expansion at f=1, tensoring that expression has exponentially many +terms in f. It is therefore not an all-width cheap recoding theorem. We do not +use this invalid shortcut to assert the p19 compiler is complete. The source +normalizer theorem supplies normalized full F/B calls, not unpaid pure shears. + +Credit and scope +The centre-free producer and compensation are Dugongue PR4929, with retained +Cao Yifan PR4610, Cinna Davis helper/cache and the existing native/compiler +lineage. The concrete source is pinned from DaysSky PR5440 head +c0f52b5b18bba78a6a5e8057edf9571bade88549. Its new p19 operator/receipt claims are +not silently adopted as compiler evidence. SOURCES.json records all exact files, +content hashes and public revision URLs. Original work here is the explicit +source-ABI serialization, owned dirty-entry/return wrapper, resolved global +native-map tables, embedding proof and complete trace/profile replay. Substantial +OpenAI Codex assistance. Apache-2.0; retained source notices stay unchanged. + +Open next questions +1. Build a D-based caller using the actual normalized full B endpoint, with + exact productive rank census and a literal thin-query implementation. +2. Prove an all-width finite-cost implementation of the needed G(B) recodings, + or choose an endpoint gauge avoiding Q^-1 BQ. An f=1 expansion is insufficient. +3. Compose this concrete unit compiler only after every caller bridge's actual + input/output frame and ownership obligations have been established. diff --git a/research/native-wordram-interfaces/native/RESULT.json b/research/native-wordram-interfaces/native/RESULT.json new file mode 100644 index 0000000000..2b4e11bef4 --- /dev/null +++ b/research/native-wordram-interfaces/native/RESULT.json @@ -0,0 +1,921 @@ +{ + "status": "PASS_CENTER_FREE_NATIVE_UNIT_SERIALIZATION_NOT_P19_CHAIN", + "authenticated_actual_code_entries": 12544, + "local_paid": { + "1": 2201, + "2": 412, + "3": 510, + "4": 127, + "5": 40 + }, + "independent_helper_targets": { + "4": 28, + "7": 7, + "8": 47, + "9": 326 + }, + "logical_endpoints": [ + { + "direction": "forward", + "max_prefix_l1": "457", + "all_arbitrary_rows": 632 + }, + { + "direction": "backward", + "max_prefix_l1": "258", + "all_arbitrary_rows": 632 + } + ], + "serialized_units_checked": [ + { + "unit": 0, + "direction": "forward", + "events": 28047, + "paid": { + "1": 2201, + "3": 510, + "2": 412, + "4": 127, + "5": 40 + }, + "scalar_tariff": 223444, + "owned_entry_clear": true, + "owned_exit_clear": true, + "persistent_inputs": 632, + "helper_target_profile": { + "4": 28, + "7": 7, + "8": 47, + "9": 326 + } + }, + { + "unit": 0, + "direction": "backward", + "events": 28047, + "paid": { + "1": 2201, + "3": 510, + "2": 412, + "4": 127, + "5": 40 + }, + "scalar_tariff": 223492, + "owned_entry_clear": true, + "owned_exit_clear": true, + "persistent_inputs": 632, + "helper_target_profile": { + "4": 28, + "7": 7, + "8": 47, + "9": 326 + } + }, + { + "unit": 1, + "direction": "forward", + "events": 28047, + "paid": { + "1": 2201, + "3": 510, + "2": 412, + "4": 127, + "5": 40 + }, + "scalar_tariff": 223444, + "owned_entry_clear": true, + "owned_exit_clear": true, + "persistent_inputs": 632, + "helper_target_profile": { + "4": 28, + "7": 7, + "8": 47, + "9": 326 + } + }, + { + "unit": 1, + "direction": "backward", + "events": 28047, + 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Apache-2.0, Codex assistance. +""" +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +import gzip +import importlib.util +import json +from pathlib import Path +import sys + +HERE=Path(__file__).resolve().parent +ROOT=HERE/'vendor' +CENTER=632 +PROFILE={1:2201,2:412,3:510,4:127,5:40} +HELPERS={4:28,7:7,8:47,9:326} + + +def need(x,message): + if not x:raise ValueError(message) + + +def load_core(): + path=ROOT/'research/native-center-free-code/native_core.py' + spec=importlib.util.spec_from_file_location('retained_native_core',path) + mod=importlib.util.module_from_spec(spec);spec.loader.exec_module(mod) + return mod + + +def payload(): + return json.loads(gzip.decompress((ROOT/'research/native-center-free-code/CODED-WORDS.json.gz').read_bytes())) + + +def embed_vector(v,unit,units=19): + """Common axis 0, independent eight-axis unit blocks; no selected-stage powers.""" + need(type(v)is int and 0<=v<512 and 0<=unit>1)<<(1+8*unit)) + + +def role_name(role,unit): + need(0<=role<=CENTER,'Local role range') + if role<112:return ['MAIN',2*unit,role] + if role<224:return ['MAIN',2*unit+1,role-112] + if role>bit&1:result^=column + return result + inverse={apply(v):v for v in range(512)} + need(len(inverse)==512,'Native permutation map invertible') + invcols=[inverse[1<0 else native['inverse_columns'] + def apply_columns(v): + output=0 + for bit,column in enumerate(columns): + if v>>bit&1:output^=column + return output + before=program['frames'][e['source_frame'][2]] + after=program['frames'][e['target_frame'][2]] + image=[apply_columns(v) for v in before] + need(rank(image)==rank(after)==rank(image+after), + 'Actual native map sends complete source frame span to target frame span') + need([cur[tuple(r)] for r in program['persistent_roles']]==program['output_frames'],'Every exit frame') + need(cur[owned]==['FRAME',program['unit'],0],'Owned center returned blank ground frame') + need(dict(paid)=={int(k):v for k,v in source['canonical']['local_profile'].items()},'Complete serialized profile') + return {'events':len(program['events']),'paid':dict(paid),'scalar_tariff':int(scalar), + 'owned_entry_clear':True,'owned_exit_clear':True,'persistent_inputs':632, + 'helper_target_profile':HELPERS} + + +def verify_exports(data): + for direction in ('forward','backward'): + path=HERE/('UNIT0-'+direction+'.json.gz') + need(path.is_file(),'Missing required literal export '+path.name) + need(json.loads(gzip.decompress(path.read_bytes()))==serialize(0,direction,data), + 'Literal serialized export disagrees with source: '+path.name) + + +def verify(check_exports=True): + sources=json.loads((HERE/'SOURCES.json').read_text(encoding='utf-8'))['files'] + for row in sources:need(sha256((HERE/row['package_path']).read_bytes()).hexdigest()==row['sha256'],'Changed source '+row['path']) + data=payload();c=data['canonical'];V=load_core() + # Independently rederive the arbitrary-input free-group endpoint, not just frames. + original=json.loads(gzip.decompress((ROOT/'research/native-center-free-code/SOURCE-WORD.json.gz').read_bytes())) + need(sha256(gzip.decompress((ROOT/'research/native-center-free-code/SOURCE-WORD.json.gz').read_bytes())).hexdigest()==V.SOURCE_SHA,'Original native source') + E=V.error_kernel(original) + EX=[[Q(0)]*112 for _ in range(112)] + for i,j,v in E: + if j<112:EX[i-112][j]=v + source_A=[[Q(x) for x in row] for row in json.loads((ROOT/'research/native-center-free-code/CODE.json').read_text())['A']] + need(len(source_A)==112 and all(len(row)==112 for row in source_A),'Actual code dimensions') + need(all(source_A[i][j]==Q(i==j)+EX[i][j] for i in range(112) for j in range(112)), + 'All 12544 actual source code entries match the rederived endpoint') + expected_helpers=Counter(len(c['frames'][c['final'][i]])-len(c['frames'][c['start'][i]]) for i in range(224,632)) + need(dict(expected_helpers)==HELPERS,'All 408 independent helper targets') + logical=[] + for direction in ('forward','backward'): + back=direction=='backward' + p=[['scalar',['clear',['C',0]],0]]+data['programs'][direction]+[['scalar',['clear',['C',0]],0]] + rows,paid,mx=V.replay(c,p,back) + for i in range(CENTER): + expected=V.expected(i,back) + if not back and 112<=i<224: + for j,v in enumerate(EX[i-112]): + if v:V.add(expected,V.identity(j),v) + if back and i<112: + for j in range(112): + if EX[j][i]:V.add(expected,V.identity(112+j),-EX[j][i]) + need(rows[i]==expected,'Every arbitrary-input endpoint row') + need(dict(paid)==PROFILE,'Logical replay profile') + logical.append({'direction':direction,'max_prefix_l1':str(mx),'all_arbitrary_rows':632}) + checks=[] + for unit in range(19): + for direction in ('forward','backward'): + p=serialize(unit,direction,data) + # Embedding is linear, injective, and support-exact on all 512 local vectors. + need(len({embed_vector(v,unit) for v in range(512)})==512,'Injective local embedding') + need(all(embed_vector(1<(X,Y+A X,H), raw dual (X-A^T Y,Y,H), with original entrance/exit charts. Normalized full calls include D; no unpaid pure shear is inferred.'} + + +if __name__=='__main__': + result=verify(check_exports='--emit' not in sys.argv) + if '--write' in sys.argv:(HERE/'RESULT.json').write_text(json.dumps(result,indent=2)+'\n',encoding='utf-8') + else:need(json.loads((HERE/'RESULT.json').read_text())==json.loads(json.dumps(result)),'Retained unit receipt') + if '--emit' in sys.argv: + # Authoring only: literal actual events, not an unresolved macro. + for direction in ('forward','backward'): + raw=json.dumps(serialize(0,direction),sort_keys=True,separators=(',',':')).encode() + with gzip.GzipFile(filename=str(HERE/('UNIT0-'+direction+'.json.gz')),mode='wb',mtime=0) as f:f.write(raw) + verify_exports(payload()) + print(json.dumps({k:result[k] for k in ['status','local_paid','independent_helper_targets','source_files_authenticated','new_multiplication_kappa']})) diff --git a/research/native-wordram-interfaces/native/vendor/research/coded-native-caller/NORMALIZERS.json b/research/native-wordram-interfaces/native/vendor/research/coded-native-caller/NORMALIZERS.json new file mode 100644 index 0000000000..bca92c222c --- /dev/null +++ b/research/native-wordram-interfaces/native/vendor/research/coded-native-caller/NORMALIZERS.json @@ -0,0 +1,126 @@ +{ + "clifford_sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "code_sha256": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0", + "finite_checks": {"absolute_phase_mutations_rejected":112,"exact_endpoint_factor_identities":896,"gaussian_free_compiled_wrappers":896,"monomial_wrappers":896,"omitted_phase_rejections":112,"ports":112,"scalar_basis_recodings":224,"weight_congruence_addresses":57344}, + "local_gauge_bill": {"added_recursive_calls":0,"backward_extra_monomial_field_maps_upper":448,"main_wrapper_field_maps":448,"owned_fields_reused":8,"recoding_monomial_field_maps":448,"recoding_owned_clears":32,"recoding_scalar_adds":1792,"recodings":2}, + 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+ ], + "recoding_bill": {"forward_prefix_component_l1_upper":57,"forward_update_coefficient":"-1/4","inverse_output_prefix_component_l1_upper":"69/13","inverse_prefix_component_l1_upper":56,"inverse_update_coefficient":"-1/52","monomial_field_maps":224,"output_scaled_adds":448,"owned_fields":8,"owned_initial_clears":8,"owned_terminal_clears":8,"signed_mode_adds":448}, + "schema": "coded-native-real-normalizers/1", + "scope": "Exact physical central ABI and local gauges; not full-controller or multiplication admission.", + "source_payload_sha256": "cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd", + "status": "PASS_CODED_NATIVE_REAL_NORMALIZERS" +} diff --git a/research/native-wordram-interfaces/native/vendor/research/coded-native-caller/PHYSICAL.md b/research/native-wordram-interfaces/native/vendor/research/coded-native-caller/PHYSICAL.md new file mode 100644 index 0000000000..da8837ba67 --- /dev/null +++ b/research/native-wordram-interfaces/native/vendor/research/coded-native-caller/PHYSICAL.md @@ -0,0 +1,71 @@ +# Real physical normalizers for the coded producer + +This is local constructive research on canonical/pr4929, not a completed supplier or exponent claim. Source code and Gaussian conventions retain the original authors' credit. + +Let n=9 and let q be any of the source's 112 port vectors (weight 3 or 7). Let e0=1. Construct an orthogonal binary matrix G taking e0 to q. If q_0=0, use the orthogonal transvection T_(e0+q). If q_0=1, select j>0 with q_j=0 and use T_(ej+q) T_(e0+ej). Here T_v(x)=x+(v dot x)v; both v have even weight, hence T_v is orthogonal. Such j exists because q is not the all-ones vector. + +For row j of G put z_j=(wt(row_j G)-1)/2 modulo 2. Define K=Z_z P_G. It is a real signed permutation. The full Gaussian R has entries alpha*(-i)^wt(x+y), with alpha=(1+i)^9/2^9. Orthogonality gives + +wt(G^-1 d)-wt(d) = 2 z dot d (mod 4). + +Indeed the degree-two coefficients vanish modulo four because distinct columns of G^-1 have even dot product; the linear coefficient is the weight of that column minus one. Therefore K R K^-1=R exactly, including absolute phase. K also maps the central line to span(q), and its orthogonal complement to q-perp, at the canonical-frame Lagrangian level. All these statements tensor to every positive digit-column count. + +Let Q be the central C gate, D the product of the other eight C gates, so R=DQ. Let E_i and S_i be the actual retained entrance-line and exit-hyperplane frame operators. With the operator convention that rightmost applies first, use + +input X: E_i K_i Q^-1 +input Y: K_i +output X: K_i^-1 +output Y: D K_i^-1 S_i^-1. + +All four wrappers are monomial. Their Lagrangian incidences prove this for every port, and the scratch verifier checks exact tableaus and absolute phases at every one of the 112 source ports. With A from PR4929, define C_ij= A_ij K_i^-1 K_j. Then the full main endpoint is + +F = diag(D,D) [[I,0],[C Q^-1,I]]. + +C is a physically implementable fixed owner recoding: apply K_i to each owner, apply A among the owners at common physical coordinates, and apply K_i^-1. Its inverse uses A^-1=(A+12I)/13. Since each K_i is real orthogonal and A is real symmetric, C^T=C. Since K_i commutes with R, C commutes with R. The polynomial C^2+12C-13I=0 follows by similarity. The 408 independent helper jobs and every paid Gaussian child are unchanged. + +For the actual raw inverse transpose, F^-T=diag(D^-1,D^-1) [[I,-Q^-1 C],[0,I]], since Q,D are symmetric. Multiply both outputs by D^2, then conjugate the physical X bank by Q^2 (input Q^-2 and output Q^2). These are explicit monomial powers. The result is + +B = diag(D,D) [[I,-Q C],[0,I]]. + +The old source convention using Y-only Q^2 conjugation cannot simply be copied for noncommuting C. The X-only convention above is exact. + +For a prior code B0 commuting with the current D, set G(B0)=diag(B0,Q^-1 B0 Q). The following two constructive local identities hold without requiring C and Q to commute: + +(post X C) F (pre Y C) = G(C B0) F_standard G(B0)^-1, +(post X C^-1) B (pre Y C^-1) = G(C^-1 B0) B_standard G(B0)^-1. + +They use [C,DQ]=0 and [B0,D]=0. Every additional operation on the left is physically cheap fixed recoding. For disjoint fresh blocks, codes from earlier stages commute with the current D. These identities do not yet settle interstage ADD/IDLE compatibility, terminal gauges, productive jobs, or the complete moment. + +## Literal recoding and complete local bill + +The source code has an exact factorization A=I-MM^T/4 with M a 112-by-8 matrix having entries 0,+1,-1 and M^T M=56I. Each mode column has 56 nonzero entries, and each owner row has four. The mode columns are emitted in NORMALIZERS.json and all 12,544 entries are checked against the pinned CODE.json. This factorization is used here as a constructive scalar program, without relying on any common physical address chart for separate Gaussian mode transformations. + +To execute A on arbitrary independent owner fields x, allocate eight owned zero fields t. Compute t=M^T x with 448 signed ADDs; update x-=M t/4 with 448 scaled ADDs; clear the eight owned temporaries. Reading x is finished before any x is updated. Hence no input field is overwritten before its last source read. For A^-1 use the same program with coefficient -1/52, since A^-1=I-MM^T/52. Both are exact rational linear programs. The helper fields of the native producer are never used as scratch, copied as free credit, or erased. + +Conjugating this scalar program by the 112 K_i and their inverses implements C or C^-1. This pays 224 monomial field maps, 896 scalar ADDs and 16 owned CLEARs per recoding, with eight owned fields reusable sequentially. The two additional recodings in either local gauge identity therefore cost at most 448 monomial maps, 1,792 scalar ADDs and 32 CLEARs, with no recursive Gaussian child. The four actual port normalizers contribute 448 monomial maps per native invocation. The displayed backward conversion contributes at most 448 further monomial maps (112 input X powers, 112 output X powers and 224 output D-squares); fusing maps can reduce this upper bound but is not assumed. + +These are field-level operation counts. A lifted K_i is an explicit binary map on nine f-bit address blocks together with signs given by block parity. Its constants, indexed movement and phase passes use the retained native monomial implementation. It is therefore a fixed finite O(V polylog p) nonrecursive operation under that caller's precision/address ABI, not a zero-work instruction. Each fixed rational ADD is likewise charged at its actual scalar precision. In particular the inverse denominator 52 must be implemented and rounded; no free exact real-division oracle is assumed. This lemma makes no independent TM tariff or outer-budget claim. + +The maximum exact component-l1 prefix bound for the scalar A program, including its temporaries, is 57. For A^-1 it is 56 (the output-only bound is 69/13). Signed monomial maps preserve component magnitude. A fixed local sequence has a fixed suffix bound obtained by multiplying elementary bounds 1+|coefficient|; owned CLEAR has bound one. This gives a finite bound for local rounding propagation. The number of local uses, compiler precision and complete outer error allocation still belong to the caller theorem. + +The normalized producer still has its exact PR4929 paid profile + + {1:2201, 2:412, 3:510, 4:127, 5:40} + +and independent helper profile + + {4:28, 7:7, 8:47, 9:326}. + +No productive main ranks are asserted merely from the coupled central ABI. Those depend on the completed caller, its initial/final gauges and every paid correction. + +## Universal scope and reproducible evidence + +PR4929 supplies the arbitrary-input logical identity over Q[FreeGroup72] for its emitted center-free word with ground-chart helper pre-compensation. Its normalized main endpoint is L(A), its raw dual is L(A)^-T, and every one of the 408 helper endpoints is autonomous. This proof is an inherited premise with exact source pins, not a consequence of this normalizer checker. The present wrappers and owner recodings act exclusively on the 224 main fields; new scratch is explicitly owned. Thus the helper block remains autonomous and its independent inputs, requested transforms and paid profile remain unchanged. + +For every f>=1, assign the shared native letters their actual consistent invertible lifted operators. Evaluation of the source free-group algebra is a homomorphism and gives the source logical identity. Independently lift each K_i as its f-fold tensor product, retaining spectator coordinates; its signed-permutation word, the two direct frame identities and its commutation with R lift by operator composition. In every compiled monomial word, P and X act columnwise on the f-bit blocks, D sums its Z4 polynomial over the f columns, and a one-column scalar phase i^gamma becomes i^(f*gamma). Reusing the one-column global phase unchanged would be incorrect. Finally form the owner matrix C_f with entries A_ij K_i,f^-1 K_j,f. One does not tensor the whole 224-by-224 owner matrix and does not assert that tensor powers preserve sums. Instead the finite scalar owner program is evaluated directly in the algebra of these lifted address operators. This proves the central ABI and local gauge identities at every positive width. + +Run `python3 -I -B research/coded-native-caller/normalizers.py` or its optimized `-O` form. The checker authenticates the decompressed actual native payload, CODE.json and retained Clifford source before executing the latter. It verifies all 112 real signed normalizers, 57,344 explicit weight-congruence addresses, 896 forward/backward monomial wrappers and eight exact frame/block identities per port, including absolute phase. Each emitted wrapper is separately lowered to a literal P/D/X/phase-only word and checked against its defining expression by exact tableau and absolute-phase state. No C gate remains in an emitted wrapper. The independent incoming-column and outgoing-row identities imply all 5,824 nonzero off-diagonal code blocks, without sampling those pairs. It also executes the eight-mode recoding on all 112 arbitrary-input basis columns in both directions. Omitting the essential signed phase is rejected at every affected port. The default command compares a regenerated mathematical receipt and performs no writes; `--write` is the explicit authoring path. + +Source pins: canonical main 624de9dc66858af0945e5f8a0942488d62280d43, `research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz`, decompressed SHA-256 cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd; PR4929 head 361f5d4100640177d6a983dd2f336021c75bfd5e, `research/native-center-free-code/CODE.json`, SHA-256 8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0; canonical `research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py`, SHA-256 2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962. Gzip container bytes are not substituted for decompressed source identity. + +Credit Dugongue's PR4929 for the coded producer and stable code; Cinna Davis's PR4694/4698 and the original cache/helper construction; Cao Yifan's PR4610 native word; the retained zxv, Jacob Alan Sussman, Cinna Davis and Clifford/native/compiler lineage. The exact canonical-frame implementation and phase conventions are retained source material. The constructive real centralizing normalizers, their explicit lifted words, X-only raw-dual convention and costed local code gauges are the additions here. New work is Apache-2.0 and has substantial OpenAI Codex assistance; no formal-kernel or independent human acceptance is asserted. diff --git a/research/native-wordram-interfaces/native/vendor/research/native-center-free-code/CODE.json b/research/native-wordram-interfaces/native/vendor/research/native-center-free-code/CODE.json new file mode 100644 index 0000000000..03170f4a31 --- /dev/null +++ b/research/native-wordram-interfaces/native/vendor/research/native-center-free-code/CODE.json @@ -0,0 +1 @@ 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diff --git a/research/native-wordram-interfaces/native/vendor/research/native-center-free-code/CODED-PROOF.md b/research/native-wordram-interfaces/native/vendor/research/native-center-free-code/CODED-PROOF.md new file mode 100644 index 0000000000..1f28d33884 --- /dev/null +++ b/research/native-wordram-interfaces/native/vendor/research/native-center-free-code/CODED-PROOF.md @@ -0,0 +1,80 @@ +# An exact center-free native offer with an invertible eight-mode code + +Prepared for Dugongue with substantial OpenAI Codex assistance. Apache-2.0. + +Building on Cinna Davis's center-free cache kernel in PR #4694, this gives an explicit free ground-chart helper pre-compensation and an invertible eight-mode main code: all eight rank-eight center Gaussian calls disappear, all 408 independent helper jobs remain, and the main cross-transfer is an explicitly known invertible constant code. It is not the old uncoded main ABI and does not by itself prove a new κ. + +## The exact offer + +Freeze the native source payload with SHA-256 `cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd`. Its persistent logical rows are 112 X, 112 Y and 408 independent helpers H. The original normalized endpoint is `(X,Y,H) -> (X,Y+X,H)`. Physical entrance and exit charts remain exactly those of the frozen source. + +There is a completely emitted constant dyadic pre-compensation, followed by the source word with every center Gaussian operation replaced by an owned CLEAR, whose exact normalized endpoint is + +`X' = X; Y' = Y + A X; H' = H`. + +All 632 persistent inputs are arbitrary and independent; no helper is initialized, discarded, identified or counted twice. The literal backward construction has exact normalized endpoint + +`X' = X - A^T Y; Y' = Y; H' = H`, + +the raw inverse transpose of the forward endpoint. The paid profile in both directions is + +`{1:2201, 2:412, 3:510, 4:127, 5:40}`. + +The helper profile stays `{4:28,7:7,8:47,9:326}`. Relative to the source, exactly eight rank-eight children are removed and no Gaussian child is added. The pre-compensation adds 6,596 scalar ADDs with a retained scalar allowance of 32,652 primitives; all numerator magnitudes and denominators are at most 4. These finite scalar operations do not establish a better recursive exponent on their own. + +## Constructive proof + +Delete all eight center calls by replacing each with CLEAR of the owned center field in the call's destination chart. Zero has every chart, so this is a valid erasure of owned scratch, not a borrowed input overwrite. Retain every other physical instruction and every endpoint chart. + +The exact sparse replay over the rational free group algebra on the 72 native symbols gives + +`M_0 = I + S + E_X + E_H`. + +Here S is the original transfer X to Y. Both error blocks land only in Y. E_X reads X; E_H reads only 106 particular helpers, each with a ground entrance and full-frame exit. Every helper and every X output remains autonomous. All error terms have EMPTY native word: the errors are ordinary constant dyadic matrices, not uncomputed address-operator oracles. The 12,532 nonzero entries split into 5,936 in E_X and 6,596 in E_H. + +Every pairwise product of S, E_X and E_H is zero, because all three maps land in Y and none reads Y. Before executing the center-cleared word, apply `I-E_H`. Every required source and target is in the actual ground chart: the targets are Y and the sources are those 106 ground-ended helpers. The operation is the explicit list of 6,596 dyadic ADDs. + +Consequently + +`M_0 (I-E_H) = I+S+E_X`. + +Thus `A=I+E_X` on the 112 main port indices gives the claimed offer, with no helper contamination. Scalar operations in one common address chart have their exact owner-space action, so this is a physical fixed-template pre-compensation and not an abstract change of logical coordinates. + +For the backward direction, the separately emitted center-cleared source word is verified to equal `I-S^T-E_X^T-E_H^T`, with the source's distinct inverse-transpose native letters. Prepend `I+E_H^T`, again using only actual ground-chart fields. The product is `I-S^T-E_X^T`. The verifier compares all 632 independent rows in both orientations. The owned center field is empty at termination. + +## Explicit code, inverse and conditioning + +The same exact entries satisfy + +`E_X^T = E_X, E_X^2 = -14 E_X, tr(E_X) = -112`. + +Set `P=-E_X/14`. It is a real symmetric idempotent of trace 8, hence an orthogonal projection of rank 8. Therefore + +`A=I-14P`, + +with eigenvalue -13 on the eight-dimensional image of P and eigenvalue +1 on its 104-dimensional kernel. In particular + +`A^-1 = I + E_X/13`, + +and its Euclidean condition number is exactly 13. The complete main shear is I+N_A with N_A^2=0 and ||N_A||_2=13; both it and its inverse have norm at most 14, so its condition number is at most 196. Helpers are an independent identity block, and the physical boundary charts are unitary, so this same bound applies to the complete physical coded offer. Its inverse uses I-N_A and needs no 1/13 arithmetic; 1/13 appears only when separately inverting the main code A. Every diagonal entry of A is zero; its 5,824 nonzero off-diagonal entries are ±1/2. The exact checker verifies the degree-two polynomial entry by entry over rational arithmetic, so the spectrum and inverse are universal consequences of that identity rather than numerical eigenvalue observations. + +The coefficient 1/13 is part of the mathematical inverse formula. This deliverable does not call it a free dyadic SCALE, assume a division oracle, or insert A^-1 across different physical address charts without paying for the resulting adapters. + +## Arbitrary fiber widths + +The replay identities hold over Q[FreeGroup72]. Every consistently shared invertible assignment of the 72 native operators defines an evaluation homomorphism. Hence the logical word identity holds at every positive column multiplicity under the retained source native implementation. It does not rely on one-column matrix testing, erasure of central phases or tensor powers preserving sums. + +Every physical frame, native monomial and Gaussian child is retained from the authenticated source, except the eight deleted owned-center calls. The new instructions are only constant dyadic scalar operations at an explicitly common ground chart. No fresh nonmonomial address implementation is introduced. + +The exact observed maximum prefix coefficient ℓ1 norms are 457 forward and 258 backward, checked on the fixed free-symbol words. Unitary evaluation bounds intermediate exact states and perturbations at the initial input in the maximum-over-fields Euclidean fiber norm by fixed constants independent of fiber width. For discrepancies inserted at later sites, use a separate suffix bound: assign each scalar ADD or SCALE of coefficient c the bound 1+|c|, and every unitary Gaussian/monomial, owned CLEAR or owned COPY the bound 1. The product of these elementary bounds over the finite word bounds every suffix. Thus the sum of local error magnitudes times this fixed product bounds propagated rounding error; no prefix norm is substituted for a suffix norm. Entrywise infinity-norm statements require the appropriate square-root fiber-volume conversion. There is no precision-dependent epsilon and no recursive border-precision claim. + +## Integration boundary + +The old source wrapper's port-dependent entrance lines and exit hyperplanes remain. A is a constant matrix in the stated normalized logical coordinates. It must not be silently treated as a constant free recoding in every physical main chart or in a different standardized central-Q ABI. Its nonzero off-diagonal entries connect distinct entrance-line charts. A useful next step is an actual coded caller or a paid simultaneous adapter that exploits the eight-mode structure, together with complete moment, raw-dual, compiler, finite precision and outer recovery budgets. This document supplies the exact producer and its bill, not those missing consumers. + +## Predecessor overlap and credit + +Cinna Davis's PR #4694, head `2add42d1edf14a263abe90a3bcde67fc1ba30768`, already emits a center-free kernel with paid profile minus eight rank-eight calls, records its coupled cache ABI, constructs its raw dual, and proves that its 106 observed helpers start at the empty chart. The source CACHE.md was read directly. None of center deletion, the cold-helper observation or the abstract block Schur elimination is claimed here as new. PR #4698, scientific head `9079ab66ba9a1717df478a08eb957c20d84d3e61`, already emits a dyadic helper basis of 379 gates in each direction reducing observations to eight helpers, and a conditional consumer. The present deliberately dense 6,596-ADD pre-compensation is easier to audit, not a claim to a better basis count. Its changed sufficient result is the actual fixed-template helper-independent coded offer, explicit A entries, exact eight-mode spectrum/inverse/conditioning, and unchanged independent helper ABI. + + +Cao Yifan / intqwq supplies the joint-helper/native-map round-three word at canonical `research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz`, commit `624de9dc66858af0945e5f8a0942488d62280d43`. Its predecessor and refreshed public lineage includes PR #4610; the exact source package and bytes, rather than an older PR headline, bind this result. Cinna Davis, the PR #4470 native/helper/controller lineage, Dugongue's exact native and complementary-provider work, DaysSky, Nick Petalas, Ryanson Jonathan, Jacob Alan Sussman, zxv and the retained scalar, Clifford, precision, compiler and outer contributors retain predecessor credit. The common-chart pre-compensation and exact eight-mode code are the present construction. Local MathProof's Schur block elimination and low-rank composition notes motivated the representation; their source-only inspection is not a fresh Lean/kernel audit or a claim of priority for elementary projection algebra. diff --git a/research/native-wordram-interfaces/native/vendor/research/native-center-free-code/CODED-WORDS.json.gz b/research/native-wordram-interfaces/native/vendor/research/native-center-free-code/CODED-WORDS.json.gz new file mode 100644 index 0000000000..935fedd9c9 Binary files /dev/null and b/research/native-wordram-interfaces/native/vendor/research/native-center-free-code/CODED-WORDS.json.gz differ diff --git a/research/native-wordram-interfaces/native/vendor/research/native-center-free-code/SOURCE-WORD.json.gz b/research/native-wordram-interfaces/native/vendor/research/native-center-free-code/SOURCE-WORD.json.gz new file mode 100644 index 0000000000..46d929df83 Binary files /dev/null and b/research/native-wordram-interfaces/native/vendor/research/native-center-free-code/SOURCE-WORD.json.gz differ diff --git a/research/native-wordram-interfaces/native/vendor/research/native-center-free-code/coded_verify.py b/research/native-wordram-interfaces/native/vendor/research/native-center-free-code/coded_verify.py new file mode 100644 index 0000000000..90627892f6 --- /dev/null +++ b/research/native-wordram-interfaces/native/vendor/research/native-center-free-code/coded_verify.py @@ -0,0 +1,63 @@ +"""Exact center-free coded native offer; Apache-2.0, Codex assistance.""" +from pathlib import Path +import sys,json,gzip +from fractions import Fraction as Q +from collections import Counter +from hashlib import sha256 +sys.path.insert(0,str(Path(__file__).resolve().parent)) +import native_core as V +HERE=Path(__file__).resolve().parent + +def build(a,E,back=False): + c=a['canonical'];p=[] + for i,j,v in E: + if j<224:continue + dst,src,coef=(j,i,v)if back else(i,j,-v) + V.need(c['start'][dst]==0 and c['start'][src]==0,'Ground pre-compensation') + p.append(['scalar',['add',['L',dst],['L',src],coef.numerator,coef.denominator],0]) + return c,p+V.clear_centers(a['programs']['backward'if back else'forward']) + +def matrices(E): + EX=[[Q(0)]*112 for _ in range(112)] + for i,j,v in E: + if j<112:EX[i-112][j]=v + A=[[EX[i][j]+Q(i==j)for j in range(112)]for i in range(112)] + V.need(all(EX[i][j]==EX[j][i]for i in range(112)for j in range(112)),'Real symmetric defect') + V.need(sum(EX[i][i]for i in range(112))==-112,'Projection trace') + for i in range(112): + for j in range(112): + s=sum(EX[i][k]*EX[k][j]for k in range(112)) + V.need(s==-14*EX[i][j],'Exact defect minimal polynomial') + return EX,A + +def expected(i,back,EX): + r=V.expected(i,back) + if not back and 112<=i<224: + for j,v in enumerate(EX[i-112]): + if v:V.add(r,V.identity(j),v) + if back and i<112: + for j in range(112): + if EX[j][i]:V.add(r,V.identity(112+j),-EX[j][i]) + return r + +def main(): + b=gzip.decompress((HERE/'SOURCE-WORD.json.gz').read_bytes());V.need(sha256(b).hexdigest()==V.SOURCE_SHA,'Source hash');a=json.loads(b);E=V.error_kernel(a);EX,A=matrices(E);res=[] + generated={'scope':'Exact center-free coded ABI, not the old uncoded supplier','canonical':json.loads(json.dumps(a['canonical'])),'programs':{}} + generated['canonical']['local_profile']={'1':2201,'2':412,'3':510,'4':127,'5':40} + for back in(False,True): + c,p=build(a,E,back);generated['programs']['backward'if back else'forward']=p;rows,paid,mx=V.replay(c,p,back) + V.need(all(rows[i]==expected(i,back,EX)for i in range(632)),'All arbitrary coded endpoints') + V.need(paid==Counter({1:2201,2:412,3:510,4:127,5:40}),'Complete center-free profile') + res.append({'backward':back,'paid':dict(paid),'max_prefix_l1':str(mx),'events':len(p)}) + V.need((HERE/'CODED-WORDS.json.gz').is_file(),'Missing frozen emitted words') + frozen=json.loads(gzip.decompress((HERE/'CODED-WORDS.json.gz').read_bytes()));V.need(frozen==generated,'Frozen emitted words') + V.need((HERE/'CODE.json').is_file(),'Missing frozen code') + V.need(json.loads((HERE/'CODE.json').read_text())=={'A':[[str(v)for v in row]for row in A]},'Frozen code entries') + # Actual signed pre-compensation corruption must leave helper-dependent error. + c,p=build(a,E,False);p[0][1][3]*=-1;rows,_,_=V.replay(c,p,False) + V.need(any(rows[i]!=expected(i,False,EX)for i in range(632)),'Pre-compensation mutation rejected') + EH=[v for i,j,v in E if j>=224] + tariff=lambda v:3+abs(v.numerator).bit_length()-1+abs(v.numerator).bit_count()+v.denominator.bit_length()-1 + out={'status':'PASS_CENTER_FREE_CODED_SUPPLIER','source_payload_sha256':V.SOURCE_SHA,'precompensation_ADDs':len(EH),'precompensation_scalar_primitive_allowance':sum(tariff(v)for v in EH),'symmetric_defect_rank':8,'code_spectrum':{'1':104,'-13':8},'code_inverse':'I+E_X/13','condition_number_2':13,'all_632_arbitrary_rows':True,'new_kappa':None,'runs':res} + print(json.dumps(out,sort_keys=True)) +if __name__=='__main__':main() diff --git a/research/native-wordram-interfaces/native/vendor/research/native-center-free-code/native_core.py b/research/native-wordram-interfaces/native/vendor/research/native-center-free-code/native_core.py new file mode 100644 index 0000000000..5d8a8f0a63 --- /dev/null +++ b/research/native-wordram-interfaces/native/vendor/research/native-center-free-code/native_core.py @@ -0,0 +1,73 @@ +"""Exact source-bound coded-supplier replay core. Apache-2.0; Codex assistance. +Frozen source: Cao Yifan #4610 and retained Cinna Davis/Dugongue lineage. +""" +from pathlib import Path +from fractions import Fraction as Q +from collections import Counter +from hashlib import sha256 +import gzip,json,copy,importlib.util,sys +HERE=Path(__file__).resolve().parent +SOURCE_SHA='cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd' +def need(c,m): + if not c:raise ValueError(m) +def identity(i):return {(i,()):Q(1)} +def add(dst,src,a): + for k,v in tuple(src.items()): + z=dst.get(k,Q(0))+a*v + if z:dst[k]=z + else:dst.pop(k,None) +def warp(row,op,back): + s=(1 if op>0 else -1)*(abs(op)+(1000000 if back else 0));out={} + for (v,w),a in row.items(): + ww=w[1:]if w and w[0]==-s else(s,)+w;out[v,ww]=out.get((v,ww),Q(0))+a + return {k:a for k,a in out.items()if a} +def expected(i,back): + r=identity(i) + if back and i<112:add(r,identity(i+112),-1) + if not back and 112<=i<224:add(r,identity(i-112),1) + return r + +def replay(c,program,back=False,check_frames=True): + rows={i:identity(i)for i in range(632)};rows[632]={};cur=c['start'][:]+[None];paid=Counter();maxnorm=Q(1) + for e in program: + if e[0]=='scalar': + g,f=e[1:];r=g[1][1]+(632 if g[1][0]=='C'else 0) + if g[0]=='clear':need(r==632,'Borrowed erasure');rows[r]={};cur[r]=f + else: + if check_frames:need(cur[r]==f,'Scalar target frame') + if g[0]in('add','copy'): + v=g[2][1]+(632 if g[2][0]=='C'else 0) + if check_frames:need(cur[v]==f,'Scalar source frame') + if g[0]=='copy':need(r==632,'Borrowed overwrite');rows[r]=rows[v].copy() + else:need(r!=v,'Self add');add(rows[r],rows[v],Q(g[3],g[4])) + elif g[0]=='scale':rows[r]={k:Q(g[2],g[3])*v for k,v in rows[r].items()} + else:raise ValueError('Scalar opcode') + maxnorm=max(maxnorm,sum(map(abs,rows[r].values()),Q(0))) + elif e[0]=='warp': + _,r,op,x,y=e;r=r[1]+(632 if r[0]=='C'else 0) + if check_frames:need(cur[r]==x,'Warp source frame') + rows[r]=warp(rows[r],op,back);cur[r]=y + elif e[0]=='climb': + _,_,r,x,y,k=e + if check_frames:need(cur[r]==x,'Climb source frame') + need(k==len(c['frames'][y])-len(c['frames'][x])and k>0,'Ascending paid rank');cur[r]=y;paid[k]+=1 + elif e[0]=='center': + _,r,x,y,k=e;r+=632 + if check_frames:need(cur[r]==x,'Center source frame') + need(k==abs(len(c['frames'][y])-len(c['frames'][x])),'Center paid rank');cur[r]=y;paid[k]+=1 + else:need(e[0]in('phase','adapter','residual_adapter'),'Unknown opcode') + need(cur[:632]==c['final'],'Final frames');need(not rows[632],'Owned field cleared') + return rows,paid,maxnorm + +def clear_centers(program):return [['scalar',['clear',['C',e[1]]],e[3]]if e[0]=='center'else copy.deepcopy(e)for e in program] +def error_kernel(a): + rows,paid,_=replay(a['canonical'],clear_centers(a['programs']['forward']));E=[] + for i in range(632): + err=rows[i].copy();add(err,expected(i,False),-1) + for (j,w),v in sorted(err.items()): + need(112<=i<224 and(j<112 or j>=224),'Strict triangular error block');need(not w,'Constant owner kernel') + need(a['canonical']['final'][j]==1,'Repair source final full frame');need(j<112 or a['canonical']['start'][j]==0,'Pre-repair source initial ground') + E.append((i,j,v)) + need(len(E)==12532,'Frozen error term count') + return E + diff --git a/research/native-wordram-interfaces/precision/CODE.json b/research/native-wordram-interfaces/precision/CODE.json new file mode 100644 index 0000000000..03170f4a31 --- /dev/null +++ b/research/native-wordram-interfaces/precision/CODE.json @@ -0,0 +1 @@ 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diff --git a/research/native-wordram-interfaces/precision/RECODING-PROOF.txt b/research/native-wordram-interfaces/precision/RECODING-PROOF.txt new file mode 100644 index 0000000000..159eb56740 --- /dev/null +++ b/research/native-wordram-interfaces/precision/RECODING-PROOF.txt @@ -0,0 +1,64 @@ +Actual producer inverse recoding: shared rounded quotients and counted Word RAM + +This component binds directly to the selected source's scalar owner code, rather than a hypothetical residual. It supplies a local sufficient realization and precision theorem for the code A^-1=I-MM^T/52 in canonical research/coded-native-caller/PHYSICAL.md. It does not replace the missing complete p19 native event compiler or establish a new multiplier kappa. + +1. Authenticated actual matrix and universal operator norms. +CODE.json is retained byte-for-byte from canonical main 32890bc5de034ab8fc93ac88ead7279a6a416d04, SHA-256 8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0. The eight 112-entry signed columns M are extracted from that snapshot's NORMALIZERS.json (SHA-256 ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da). The verifier checks every one of the 12,544 entries of A=I-MM^T/4 against the actual CODE.json. Each M column has 56 nonzeros, each row has four, and M^T M=56 I_8, checked exactly. + +Putting X=MM^T gives X^2=56X. Consequently + (I-X/4)(I-X/52)=I, +so A^-1=I-X/52=(A+12I)/13, without a numerical inverse or new hypothesis. The exact absolute row sums of A are all 26; its diagonal is zero. Thus the exact absolute row sums of A^-1 are (26+12)/13=38/13. The checker validates all rows independently. These are exact induced infinity norms, stronger output bounds than the source's conservative 57/56/69-over-13 prefix bounds. Prefix bounds still matter for intermediate overflow. + +The physical owner recodings are C_f=diag(K_i,f^-1) A diag(K_i,f), and similarly for their inverses, where each K_i,f is a real signed permutation. Such operators are exact infinity-norm isometries. Hence for EVERY positive physical field width f, + ||C_f||_infinity=26, + ||C_f^-1||_infinity=38/13. +No square root of the physical payload dimension is present. This uses the actual source's signed-permutation wrappers, not a claim that tensor powers preserve sums of owner matrices. + +2. Hoisted quotient program and precision theorem. +For every coordinate of arbitrary independent owner fields, form t=M^T x exactly. Replace each of the eight t_j in its owned buffer by RN_h(t_j/52), then compute y=x-M t. Here RN_h rounds to the h lattice with ties to even. Entry/exit clearing owns the eight mode buffers. Only eight divisions/roundings are performed, compared with repeating the same quotient in each of 448 nonzero output updates. The 448 mode signed additions and 448 output signed additions remain explicit. + +For nearest ties to even, RN_h(-z)=-RN_h(z), including ties. Therefore this hoisting produces exactly the same rounded output as 448 independently rounded signed quotients. It is not valid to make this same-output claim for every tie convention: floor(z/h+1/2) is not odd at z=h/2; the executable rejection control demonstrates this distinction. + +Each mode quotient rounding has absolute error at most h/2. Each output row uses four signed modes. Therefore + ||y-A^-1 x||_infinity <= 2h. +For approximate input x_tilde with ||x_tilde-x||_infinity<=E, + ||computed(x_tilde)-A^-1 x||_infinity <= (38/13)E+2h. +The corresponding forward program has <=26E+2h if it also rounds the eight divided modes. For forward division by four, two additional fractional bits make this division exact on dyadic inputs, eliminating that local rounding term. + +Signed-permutation wrapper composition preserves these error bounds. This closes a concrete local scalar precision interface, uniformly in physical field width, given the actual source's exact wrappers. It does not by itself allocate the error of a whole caller containing Gaussians, every intermediate cut and every decoder. + +3. Literal finite-word implementation with no division instruction. +The actual interpreter admits only one, add, sub, bltz and accept, with 64-bit modular words, signed comparisons and charged halting. No high-level division, multiplication, nearest function or arbitrary-precision arithmetic is an interpreted instruction. Fractions appear only in the independent mathematical oracle. + +Fix an integer numerator bound |n_i|<=2^k, with 1<=k<=56, for x_i=h n_i. Each mode numerator t_j is an exact signed integer with |t_j|<=56*2^k<2^62. Its absolute value is obtained by a signed branch. Unsigned division by 52 is implemented by descending greedy tests/subtractions of 52*2^j for j=k,...,0, accumulating quotient bits. Since |t_j|<52*2^(k+1), this yields the exact quotient and a remainder in [0,51]. At each step, the invariant is 0<=remainder<52*2^(j+1); after conditional subtraction it is <52*2^j. The last quotient bit records its parity. Compare the final remainder with 26: increment when it exceeds 26 or equals 26 with an odd quotient. Finally restore the sign. This is exactly nearest ties to even and uses only the admitted instructions. + +Every threshold and tentative signed difference has magnitude below 2^62, so the signed comparisons are correct under modular 64-bit semantics. Mode accumulation is bounded by 56*2^k. Output-update prefixes are bounded by (69/13)*2^k+2, below 2^63 throughout the admitted range. Thus there is no hidden signed overflow. Constants are constructed at runtime using one/add instructions, never inserted for free. + +The shared program computes all eight modes before changing any owner output, so it preserves the source's read-before-write requirement. The source-ABI variant updates the 112 owners in place. A fresh-output variant additionally preserves all 112 inputs at a charge of exactly 112 copying instructions. Both variants have the same explicit owned scratch region as their duplicate-quotient control. No meaningful read depends on dirty owned entry data; final self-subtractions also zero any unused scratch, and every owned scratch/constant word is cleared at exit; arbitrary exterior memory remains unchanged. The final accept is charged. + +4. Fully charged same-output savings. +A division block has exactly 4k+24 static instructions and between 2k+12 and 4k+24 executed instructions. The lower bound counts the unavoidable absolute/sign setup, two instructions per quotient bit, final remainder comparison and sign output; optional updates and tie handling can only add instructions. The upper bound is the static block length because every branch is forward. + +The duplicate program divides each of the eight identical mode numerators once per nonzero contact, 56 times per mode. The shared program divides it once. All other setup, signed additions, output copies, owned clearing and halt instructions are identical. Thus the exact dynamic saving is + 55 sum_(j=1)^8 D_j, +where D_j is the literal execution length for dividing that mode numerator. In particular the savings lie between + 440(2k+12) and 440(4k+24). +The exact static saving is 440(4k+24). This is a same-source, same-rounded-output, same-scratch-ABI comparison against the stated repeated-quotient control; it is not a comparison with every existing optimized compiler. + +At k=4 (|integer numerators|<=16), the input-preserving program has 1,441 static instructions versus 19,041 for its duplicate control; the source in-place variant has 1,329 versus 18,929. Both own 29 scratch/constant words. The 136 primary tests include every one of the 112 independent owner basis columns, all-zero, all-positive/negative, alternating sign and 20 deterministic random inputs. Shared execution ranges from 1,285 to 1,318 instructions and saves 9,020 to 10,835 on these controls. Eight additional boundary cases exercise k=1,8,31,56 and both signs against exact rational quotient oracles. Four in-place controls match the input-preserving output exactly. An isolated literal division program is also checked exhaustively on all 1,793 signed numerators from -896 through 896, including every nearest-even tie in that range. These finite checks support, and do not replace, the universal proofs above. + +For V physical coordinates the coordinatewise scalar work repeats V times. The exact wrapper movements K_i,f and the outer memory traversal must still be implemented and charged; they are not free instructions here. If dyadic numerators exceed the stated word bound, charged multiword arithmetic is required. The local all-width norm theorem does not assert that an arbitrarily large physical address space fits a fixed 64-bit machine. + +5. Consequence for the p19 proof obligation. +The p19 macro source records 77 recodings and 68,992 scalar additions. This concrete quotient-hoisting implementation changes the realization of scalar scaling and supplies its sufficient uniform local error bound. It leaves those scalar-add counts, recursive ranks, native producer/helper profile and target histogram unchanged. It does not serialize the 259 p19 macros into the retained native event language, settle every wrapper frame or global erasure schedule, or supply the complete ordinary compiler/precision tariff. Consequently there is no justified substitution into the outer kappa equation yet. This closes one local constructive interface rather than relabeling all remaining native hypotheses as inherited. + +Independent model review. The joint p19/#5421 supplier arithmetic verifier was independently rerun successfully. Its exact model endpoint is 4821763/1400000000, and it correctly preserves FINDING_PRECOMPILATION_CONTRACT_MISSING. The present local result does not discharge that finding. In particular it supplies neither full native Gaussian event chronology nor a global output recovery/ordinary supplier theorem. + +Reproduce: + python -B native_recoding.py + +Credit. The actual code and eight-mode decomposition come from Dugongue's PR4929 producer and the retained coded-native-caller work, with Cinna Davis's PR4694/4698/cache-helper, Cao Yifan's PR4610 native word, and zxv/Jacob Alan Sussman/compiler lineage retained. Their source already supplies the scalar factorization, constructive modes and conservative prefix bounds; no novelty is claimed for those facts. The prior Word RAM kernel supplies the explicit ISA/interpreter discipline based on tcslib and Anthropic/formal-math attribution retained there. mpfx supplies strict nearest-lattice recovery and FastPoly the fixed-syntax sharing precedent. The exact row-norm calculation, quotient-hoisting realization, tie-aware same-output comparison and literal greedy-division program are this scoped extension, prepared with substantial OpenAI Codex assistance. Original work is Apache-2.0; original source notices remain applicable. + + +Selected-profile boundary. PR 5438's actual selected #5413 body/#5402 provider grid check reports no odd denominators, whereas this local implementation specifically consumes the older coded-native-caller inverse denominator 52 used by the p19 source. The quotient-hoisting result therefore must not be presented as removal of an existing selected #5413 division-by-52 charge. Its current applicable producer is the authenticated coded owner recoding. A selected paid-profile change needs its own literal packet/census rewrite or an independently proved replacement of its actual ordinary-cost majorant; changing these finite instruction counts does not automatically change the recursive rank moment. + diff --git a/research/native-wordram-interfaces/precision/RECODING-RESULT.json b/research/native-wordram-interfaces/precision/RECODING-RESULT.json new file mode 100644 index 0000000000..97f1fce90c --- /dev/null +++ b/research/native-wordram-interfaces/precision/RECODING-RESULT.json @@ -0,0 +1,46 @@ +{ + "status": "PASS_ACTUAL_INVERSE_MODE_SHARING", + "source": { + "canonical_commit": "32890bc5de034ab8fc93ac88ead7279a6a416d04", + "path": "research/coded-native-caller/NORMALIZERS.json", + "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da", + "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/32890bc5de034ab8fc93ac88ead7279a6a416d04/research/coded-native-caller/NORMALIZERS.json" + }, + "exact_component_infinity_norms": { + "4": "26", + "52": "38/13" + }, + "mode_matrix_shape": [ + 112, + 8 + ], + "uniform_local_error_in_lattice_steps": "2", + "rounding": "nearest ties to even", + "word_bound": "|input integer numerator|<=2^k; 1<=k<=56; program instances tested k=4", + "tested_pairs": 136, + "exhaustive_signed_division_cases": 1793, + "additional_word_boundary_cases": 8, + "source_all_input_columns": 112, + "static_shared": 1441, + "static_control": 19041, + "inplace_static_shared": 1329, + "inplace_static_control": 18929, + "inplace_checked_cases": 4, + "dynamic_shared_min": 1285, + "dynamic_shared_max": 1318, + "dynamic_saving_min": 9020, + "dynamic_saving_max": 10835, + "owned_words": 29, + "rounded_divisions_shared": 8, + "rounded_divisions_control": 448, + "signed_add_subtractions_for_modes_and_updates": 896, + "max_observed_error_lattice_steps": "43/26", + "instructions": [ + "one", + "add", + "sub", + "bltz", + "accept" + ], + "scope": "One actual scalar inverse recoding coordinate with full instruction/setup/cleanup counts; no p19 full native compiler, monomial wrappers, all-size precision tariff or kappa claim" +} diff --git a/research/native-wordram-interfaces/precision/REPORT.txt b/research/native-wordram-interfaces/precision/REPORT.txt new file mode 100644 index 0000000000..ef661e111a --- /dev/null +++ b/research/native-wordram-interfaces/precision/REPORT.txt @@ -0,0 +1,71 @@ +All-width strict recovery from a weighted infinity transfer certificate + +Scope and result. +This note gives a sufficient all-width exact-recovery theorem in the complete physical transfer contract of PR 5441/5451. Its finite rational certificate uses a weighted induced infinity norm. Unlike an unconditioned Euclidean operator bound, it directly consumes a coordinate bound on integer digits, without multiplying by the square root of the physical dimension. It also supplies a closed-form sufficient bit budget for the shared fixed-point FFT at every power-of-two length. These results do not establish a changed selected paid profile, a selected residual table, or a new kappa. + +1. Complete weighted infinity transfer theorem. +Let T[y,x] be D-by-D real matrices for every local physical input x and output y in {0,...,d-1}, let F be a p-by-D left boundary and B a D-by-q right boundary. For width f define the full physical endpoint + E_f[i,y_1...y_f ; j,x_1...x_f]=(F T[y_1,x_1] ... T[y_f,x_f] B)[i,j]. +Supply strictly positive rational virtual weights w_v and nonnegative bounds a,b,rho satisfying + (A) for each output role i, sum_v |F[i,v]| w_v <= a; + (B) for each virtual v, sum_j |B[v,j]| <= b w_v; + (C) for every output letter y and virtual v, + sum_(x,u) |T[y,x][v,u]| w_u <= rho w_v. +Then for every positive integer f, + ||E_f||_infinity <= a b rho^f. +Here ||M||_infinity is the maximum absolute row sum, the induced norm on coordinatewise bounded input vectors. In particular, for every input with max_j |z_j|<=H, every output coordinate of E_f z has magnitude at most a b rho^f H. + +Proof. Give a virtual/physical array the norm max_(v,inputword) |z[v,inputword]|/w_v. Condition B bounds the right-boundary map from input infinity norm by b. Condition C bounds each local map from virtual+input-letter to virtual+output-letter by rho: take absolute values, apply the input bound w_u times the norm, and sum over EVERY input letter x and virtual index u. Identity factors on other physical columns preserve this weighted infinity norm. Compose the maps in column order f,...,1; this produces exactly the displayed matrix product. Condition A bounds the final left boundary by a. Multiplying the bounds proves the theorem. All cross-input contributions and all input/output roles remain in the contract. This is a sufficient contract; cancellation can make an uncertifiable representation stable, so certificate failure is not an instability theorem. + +2. Exact lattice recovery. +Suppose an exact target operator A_f has outputs on h Z, where h>0, and an implemented endpoint is A_f+E_f with E_f represented by the complete table above. If every input coordinate is bounded in absolute value by H and + a b rho^f H < h/2, +then coordinatewise nearest-h-lattice rounding of the implemented output recovers A_f z exactly. If rho<=1, the width-uniform sufficient condition a b rho H=1. + +Proof. The transfer theorem bounds each coordinate error strictly below h/2. Write the exact output as h m with m an integer. Then |(computed/h)-m|<1/2, which gives m<=computed/h+1/2=1, and exact input digit magnitudes be at most an integer D>=1. Use fixed-point complex arithmetic with Q=2^b, exact unbounded integer intermediate products and additions, and nearest complex-product component rounding. Suppose the actual twiddle table is independently certified to Euclidean error at most delta=1/Q. For each stage use one shared twiddle product for its two butterfly outputs. Then the uniform sufficient choice + Q >= 4 N^2 A, A=(5D^2+2D)L+8D+8, +gives final coefficient error at most 1/4, and thus exact integer convolution recovery whenever zero padding removes cyclic wrap. + +Proof. Write M_s,E_s for exact magnitudes and approximation errors. A butterfly gives M_(s+1)<=2M_s and + E_(s+1)<=(2+delta)E_s+delta M_s+delta. +The product term includes twiddle/input error interaction delta E_s. Set e_s=E_s/2^s. Since delta L<=1, the amplification (1+delta/2)^L is at most 2. For completeness, expand the binomial and bound binomial(L,k)<=L^k; the result is at most the geometric sum 1/(1-L delta/2)<=2. Starting from M_0=D,E_0=0 and summing the geometric 2^(-s) terms gives + E_forward <= N delta K, K=DL+2. +Exact forward magnitudes are at most ND. The pointwise product error is at most + E_product <= 2ND E_forward+E_forward^2+delta. +The proposed Q ensures delta K<=1, so + E_product <= N^2 delta (2D+1)K+delta. +For the unnormalized inverse start at magnitude N^2 D^2 and error E_product. The same rescaled recurrence, divided by N at the end, gives + final_error <= 2E_product+delta N^2 D^2 L+2delta + <= delta N^2 [2(2D+1)K+D^2L+4] + = delta N^2 [(5D^2+2D)L+8D+8] + <= 1/4. +The conditions delta L<=1 and delta K<=1 used above follow immediately from Q>=4N^2 A. Strict half-unit recovery then gives exact integer coefficients. This proof uses no empirical error estimate and includes every forward, pointwise and inverse rounding contribution. + +For D=15, b=ceil(log2(4 N^2 (1155L+128))) suffices. Examples: L=9 -> b=34, L=16 -> b=49, L=32 -> b=82. The earlier exact finite recurrence can certify 31 bits at N=512; the simpler closed form is intentionally conservative. Fixed 31 bits does NOT cover growing N. The exact checker independently evaluates the unsimplified rational recurrence for 96 choices L=1,...,32 and D=1,15,255 and verifies the 1/4 bound. These controls support the formula; the algebra above proves it universally. + +A certified root table remains an explicit premise, obtainable by sufficiently refining exact transcendental interval bounds; the earlier fixed-degree/fixed-pi-precision generator is not claimed to work unchanged at arbitrary N or b. This is a precision theorem, not an all-size complexity theorem: table generation, multiword products, normalization, input/output conversions, storage, and the selected paid-profile interface still require charges. There is no unit-cost 64-bit approximation of unrestricted multiword arithmetic. + +5. Consequences for the actual frontier. +The freshly read PR 5440 at c0f52b5b18bba78a6a5e8057edf9571bade88549 gives a conditional complex supplier near 0.007578535190 but says its admitted BIT saving 17/5000 binds the advertised candidate 951999/280000000. It explicitly records a missing chain-to-event compiler and physical_attachment CONDITIONAL. Our recovery certificate alone changes neither the admitted BIT supplier nor the complete p19 native program. Therefore it cannot be used as an arithmetic excuse to raise that kappa. + +Likewise, the selected PR 5413 remains the authoritative conditional record unless its own complete paid profile, physical source binding and outer ledger are improved. Replacing a crude intermediate-height estimate by an exact grid is useful but cannot on its own change a leading tariff; width-independent bit savings can be lower-order. Current autoresearch.md explicitly says more digits of the same root do not count as a hill-climbing step, and requires a changed complete paid profile. No changed selected frontier, selected consumer recovery theorem or project-best claim is made here. + +Open next questions. +1. Extract a complete residual table of one selected native physical consumer, including every return and dirty role, and check A-C with a rational weight vector. First step: preserve its exact table/role source hash and derive the row sums. Blocker: no selected complete residual is present in the cited packages. +2. Prove the actual input coordinate bound H and decoder infinity norm for that consumer. First step: use the literal source row forms and coefficient ranges, rather than infer H from the exact grid. Blocker: an exact denominator exponent does not bound coordinate magnitudes or conditioning. +3. If the resulting precision bill is genuinely smaller in its leading term, reprice the complete selected invoice and every outer predicate. First step: expose a before/after precision tariff in the selected source. Blocker: no such invoice replacement is established by the present theorem. + +Credit. +Ali Romman and retained contributors supply PR 5451's complete transfer contract, rational metric checker and parity/noncommuting examples; zxv's PR 5441 supplies the preceding physical-table lifting and approximation handoff. Matarener supplies PR 5438's exact grid, with Clear1nsight (#5413), dillona (#5402), Ali Romman (#5383,#5398), Cao Yifan (#4610), Ross Richardson's Clifford denominator lemma and zxv (#5428) explicitly retained there. The p19 word retains its PR 4940/4929 controller/producer and PR 4470/4610 native lineage. bksaiki/mpfx-lean supplies the strict lattice-recovery precedent; thomasahle/fast-polynomials supplies fixed-syntax sharing. Induced matrix norms, geometric-series FFT inversion and strict-half recovery are classical. This scoped combination and exact checker were prepared with substantial OpenAI Codex assistance; Apache-2.0. diff --git a/research/native-wordram-interfaces/precision/RESULTS.json b/research/native-wordram-interfaces/precision/RESULTS.json new file mode 100644 index 0000000000..0344218631 --- /dev/null +++ b/research/native-wordram-interfaces/precision/RESULTS.json @@ -0,0 +1,35 @@ +{ + "status": "PASS", + "weighted_infinity_contracts": 2, + "literal_endpoints": 12, + "literal_lattice_recovery_cases": 12, + "universal_precision_instantiations": 96, + "fft_precision_examples": [ + { + "log2_N": 9, + "digit_abs_bound": 15, + "sufficient_bits": 34 + }, + { + "log2_N": 16, + "digit_abs_bound": 15, + "sufficient_bits": 49 + }, + { + "log2_N": 32, + "digit_abs_bound": 15, + "sufficient_bits": 82 + } + ], + "selected_grid_endpoint": { + "controller_grid_bits": 74, + "digit_abs_bound": 15, + "sufficient_residual_scale": "2^(-79)", + "status": "sufficient example for the cited parity transfer; 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b/research/native-wordram-interfaces/precision/native_recoding.py new file mode 100644 index 0000000000..dab6d4d56d --- /dev/null +++ b/research/native-wordram-interfaces/precision/native_recoding.py @@ -0,0 +1,187 @@ +"""Literal 64-bit scalar recoding for the source 112-owner inverse code. +One coordinate of the field; arbitrary field-width repetition is explicit. +ISA subset and interpreter adapted from the preceding Word RAM kernel. +""" +from fractions import Fraction as F +from pathlib import Path +from collections import Counter +import hashlib,json,random + +MASK=(1<<64)-1 +ZERO,ONE,NEG,ABS,SIGN,QUOT,PARITY,TMP,NTMP,SHARED=range(10,20) +OWNED=set(range(10,20))|set(range(3000,3008)) + +def need(ok,message): + if not ok: raise ValueError(message) + +def signed(x): return x if x<(1<<63) else x-(1<<64) + +def execute(code,initial): + m={a:v&MASK for a,v in initial.items()};pc=steps=0;writes=set() + while steps<=len(code): + op,*args=code[pc];steps+=1;pc+=1 + if op=='accept':return m,steps,writes + if op=='bltz': + if signed(m.get(args[0],0))<0:pc=args[1] + else: + dst=args[0];writes.add(dst) + if op=='one':v=1 + elif op=='add':v=m.get(args[1],0)+m.get(args[2],0) + elif op=='sub':v=m.get(args[1],0)-m.get(args[2],0) + else:raise ValueError('not an admitted ISA instruction') + m[dst]=v&MASK + raise ValueError('nonhalting program') + +class Builder: + def __init__(self):self.code=[];self.labels={};self.fixups=[];self.constants={};self.owned=set(OWNED) + def emit(self,*args):self.code.append(args) + def label(self,name):self.labels[name]=len(self.code) + def branch(self,cell,label):self.fixups.append((len(self.code),label));self.emit('bltz',cell,-1) + def jump(self,label):self.branch(NEG,label) + def constant(self,n): + if n not in self.constants: + a=4000+len(self.constants);self.constants[n]=a;self.owned.add(a) + self.emit('one',a) + for bit in bin(n)[3:]: + self.emit('add',a,a,a) + if bit=='1':self.emit('add',a,a,ONE) + return self.constants[n] + def divide52(self,src,dst,k): + tag=f'div{len(self.code)}';self.emit('add',ABS,src,ZERO);self.emit('add',SIGN,src,ZERO) + self.branch(SIGN,tag+'negative');self.jump(tag+'absdone') + self.label(tag+'negative');self.emit('sub',ABS,ZERO,ABS);self.label(tag+'absdone') + self.emit('sub',QUOT,ZERO,ZERO);self.emit('sub',PARITY,ZERO,ZERO) + for j in range(k,-1,-1): + threshold=self.constants[52*(1<x.denominator or (2*r==x.denominator and q%2==1)) + +def verify(): + here=Path(__file__).resolve().parent + data=json.loads((here/'mode_columns.json').read_text(encoding='utf-8'));M=data['mode_columns'] + need(len(M)==8 and all(len(c)==112 for c in M),'matrix dimensions') + need(all(x in (-1,0,1) for c in M for x in c),'signed modes') + need(all(sum(x!=0 for x in c)==56 for c in M),'56 per mode') + need(all(sum(c[i]!=0 for c in M)==4 for i in range(112)),'four per row') + need(all(sum(M[i][k]*M[j][k] for k in range(112))==56*(i==j) for i in range(8) for j in range(8)),'mode Gram') + code_raw=(here/'CODE.json').read_bytes() + need(hashlib.sha256(code_raw).hexdigest()=='8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0','pinned actual producer code') + source_A=[[F(x) for x in row] for row in json.loads(code_raw)['A']] + need(all(source_A[i][j]==F(i==j)-sum(F(c[i]*c[j],4) for c in M) for i in range(112) for j in range(112)),'all 12544 actual code entries') + norms={} + for den in (4,52): + A=[[F(i==j)-sum(F(c[i]*c[j],den) for c in M) for j in range(112)] for i in range(112)] + values={sum(abs(x) for x in row) for row in A} + need(values=={F(26) if den==4 else F(38,13)},'exact output row norms') + norms[str(den)]=str(next(iter(values))) + shared,owned=program(M);control,owned_control=program(M,shared=False) + need(owned==owned_control,'same scratch ABI') + rng=random.Random(20261024) + tests=[[0]*112,[15]*112,[-15]*112,[15*(-1)**i for i in range(112)]] + tests += [[int(i==j) for i in range(112)] for j in range(112)] + tests += [[rng.randrange(-16,17) for _ in range(112)] for _ in range(20)] + dynamic=[];maxerror=F(0) + for values in tests: + initial={1000+i:x for i,x in enumerate(values)} + initial.update({a:rng.randrange(1<<64) for a in owned}) + initial.update({-999:12345,999999:(1<<64)-1}) + a,sa,wa=execute(shared,initial);b,sb,wb=execute(control,initial) + ta=[sum(c[i]*values[i] for i in range(112)) for c in M] + exact=[F(values[i])-sum(F(M[j][i]*ta[j],52) for j in range(8)) for i in range(112)] + expected=[values[i]-sum(M[j][i]*nearest_even(F(ta[j],52)) for j in range(8)) for i in range(112)] + for i in range(112): + need(signed(a[2000+i])==signed(b[2000+i])==expected[i],'shared/control output') + maxerror=max(maxerror,abs(F(expected[i])-exact[i])) + need(all(a[x]==b[x]==0 for x in owned),'owned cleanup') + need(all(a[x]==b[x]==v&MASK for x,v in initial.items() if x not in owned),'input/exterior frame') + need(wa<=owned|set(range(2000,2112)) and wb<=owned|set(range(2000,2112)),'write frame') + dynamic.append({'shared':sa,'control':sb,'saving':sb-sa}) + need(maxerror<=2,'uniform local 2h error bound') + db=Builder();db.emit('one',ONE);db.emit('sub',ZERO,ONE,ONE);db.emit('sub',NEG,ZERO,ONE) + for j in range(4,-1,-1):db.constant(52*(1<0 and D>0,'empty contract') + need(all(w>0 for w in weights),'strictly positive virtual weights required') + need(a>=0 and b>=0 and rho>=0,'nonnegative bounds required') + need(all(len(r)==D for r in left),'left dimension') + need(len(right)==D and len(right[0])>0,'right dimension') + q=len(right[0]); need(all(len(r)==q for r in right),'right dimension') + for row in left: + need(sum(abs(row[j])*weights[j] for j in range(D))<=a,'left bound') + for i in range(D): + need(sum(abs(x) for x in right[i])<=b*weights[i],'right bound') + for y in range(d): + need(len(transitions[y])==d,'input dimension') + for x in range(d): + need(len(transitions[y][x])==D and all(len(r)==D for r in transitions[y][x]),'virtual dimension') + for i in range(D): + value=sum(abs(transitions[y][x][i][j])*weights[j] for x in range(d) for j in range(D)) + need(value<=rho*weights[i],'full coherent row bound') + return True + + +def matmul(a,b): + return [[sum((a[i][k]*b[k][j] for k in range(len(b))),Q(0)) for j in range(len(b[0]))] for i in range(len(a))] + + +def literal_endpoint(T,F,B,f): + d=len(T); D=len(B); p=len(F); q=len(B[0]); dimension=d**f + out=[[Q(0) for _ in range(q*dimension)] for _ in range(p*dimension)] + def digits(n): + result=[] + for _ in range(f): result.append(n%d); n//=d + return result[::-1] + words=[digits(i) for i in range(dimension)] + for yy,y in enumerate(words): + for xx,x in enumerate(words): + product=F + for yi,xi in zip(y,x): product=matmul(product,T[yi][xi]) + product=matmul(product,B) + for i in range(p): + for j in range(q): out[i*dimension+yy][j*dimension+xx]=product[i][j] + return out + + +def infinity_norm(a): return max(sum(abs(x) for x in row) for row in a) + + +def nearest(x): return (2*x.numerator+x.denominator)//(2*x.denominator) + + +def recover(y,step): + need(step>0,'positive lattice step') + return step*nearest(y/step) + + +def fft_sufficient_bits(L,D): + need(isinstance(L,int) and L>=1 and isinstance(D,int) and D>=1,'L,D positive integers') + # Q >= 4*N^2*((5D^2+2D)*L+8D+8), exact ceil(log2()) by bit length. + n=1<