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Historical receipt paths and producer hashes remain original; selected entrypoints are replayed through the explicit source-byte loader.", + "original_run": "kappa-four-coordinate-20261019T0717Z", + "path_adaptations": [ + { + "adapted_sha256": "b4291b2868f91f6e77058e58e936b2efe965a9d9ae58095745fa2dad8c1d5c68", + "change": "Three source locations only: package-local BASE and immutable CE/BOUND locations. No arithmetic, assertions, constants or coverage changed.", + "original_sha256": "6397a86bd3d1461be182fcfa8602b0c70c489964a8c14f12436ba2506e11d9e3", + "path": "source/native-frames/native_model.py" + } + ], + "schema_version": 1, + "scientific_base": "20ecf2891d80b5acf18d980b2164fb44ea7faa90" +} diff --git a/research/two-pivot-caller-readers/EVIDENCE-INDEX.md b/research/two-pivot-caller-readers/EVIDENCE-INDEX.md new file mode 100644 index 0000000000..675eee7d8e --- /dev/null +++ b/research/two-pivot-caller-readers/EVIDENCE-INDEX.md @@ -0,0 +1,170 @@ +# Evidence index + +Start with the [README](README.md), the [all-q proof](source/caller/HANDOFF-FAMILY-PROOF.md), +the [tail proof](source/native-frames/HANDOFF-FAMILY-TAIL-PROOF.md), and the +[fixed-chart proof](FIXED-CHART-PROOF.md). Then read [verify.py](verify.py) and +the replay dependencies below. Large historical receipts need not be read as +new proofs to review this package. + +This index describes the unchanged verifier and frozen evidence first published +at `896e2a2e89fd2b54d4defafaef3b91bb4b33b493`. It is a reading guide, not a new +manifest or a change to verification coverage. The classifications follow the +six entrypoints at the end of `verify.py`, their transitive calls, and an observed +direct replay. They do not describe every optional historical script entrypoint. + +## Required files versus replay coverage + +**Keep every file in [BINDINGS.json](BINDINGS.json).** Before doing mathematics, +`verify.py` checks all 59 retained files against their SHA-256 pins. A missing or +changed archival file fails this integrity gate too. “Archival-only” below means +its mathematical contents are not consumed by the registered replay; it does +not mean optional for running or exporting this package. No frozen receipt, +source, original, notice, or pin was changed to add this index. + +The 29 retained JSON files divide as follows. Line counts describe frozen bytes; +the five top-level JSON metadata files are outside this table. + +| Role in the registered replay | Files | Lines | Bytes | +|---|---:|---:|---:| +| Mathematical inputs, expected receipts, or fixed certificates | 14 | 151,471 | 2,570,030 | +| Status-only dependency, not a replay of its mathematical body | 1 | 36,969 | 611,360 | +| Archival-only mathematical receipts, checked for byte integrity | 12 | 83,356 | 1,477,217 | +| Attribution/provenance JSON, checked for byte integrity | 2 | 181 | 7,146 | + +Hashes establish retention relative to this publication, not correctness or +independent authentication. A saved `PASS` status is not a fresh proof. The +written all-q argument, finite fixture replay, fixed-chart certificate and +supplier-admission obligations remain distinct. No new κ is claimed. + +## Replay entrypoints + +All paths below are relative to this package. In the inventories, **input** means +mathematical fields are consumed, **expected** means the replayed result is +compared with the saved mathematical body, and **certificate** means fixed +choices or witnesses are checked. A file can have more than one role. + +| Entry in `verify.py` | Main implementation | What the replay checks | +|---|---|---| +| `replay('handoff_family', 'prove', ...)` | [handoff_family.py](source/caller/handoff_family.py) | Reconstructs the retained family fixtures and compares the mathematical receipt. The written induction supplies the all-q claim. | +| `replay('review_handoff_family', 'run', ...)` | [review_handoff_family.py](source/root-chronology/review_handoff_family.py) | Combines the saved family prefixes and tails for q=2,3,4; checks all original columns, inverse orders, paid-progress control and full-stock-plus-8f bills. | +| `charts()` | [native_chart_search.py](source/root-chronology/native_chart_search.py), [signed_chart_optimization.py](source/root-chronology/signed_chart_optimization.py), [batch_paid_progress.py](source/root-chronology/batch_paid_progress.py) | Recompiles fixed signed choices for six/eight banks, checks equivalent complete words and bills 72f/128f; rebuilds the six-bank graph and checks 36 edge-disjoint odd Eulerian subgraphs and a duplicate-cycle rejection. | +| `replay('audit_encoded_complete', 'run', ...)` | [audit_encoded_complete.py](source/root-chronology/audit_encoded_complete.py) | Decodes the triangular prefix/tail literal circuits; checks each unary rank, full target, inverse orders and omitted-Q rejection; compares the retained receipt reporting 138f. The total 138f is a literal in this producer, not a recomputed sum. | +| `replay('balanced_physical_replay', 'produce', ...)` | [balanced_physical_replay.py](source/caller/balanced_physical_replay.py) | Constructs the balanced word using a regenerated prefix and saved tail; checks literal phases/ranks, full target, inverse orders and the 138f receipt. | +| `saved_quadratic()` | [quadratic_charts.py](source/root-chronology/quadratic_charts.py), [audit_encoded_complete.py](source/root-chronology/audit_encoded_complete.py) | Recompiles both saved quadratic choices; checks serialized events, target, inverse orders, rank mass 130f and omitted-query rejection. | + +`replay()` compares the entire mathematical body after removing only the +explicitly enumerated provenance keys in `verify.py`; raw input bytes are checked +separately. The certificate routines check their stated fields and properties, +not every historical claim in their JSON. No optimization search is rerun or +solver bound trusted. Historical absolute paths are provenance labels resolved +through `BINDINGS.json`, not directories a reviewer must recreate. + +## JSON used by mathematical replay + +These are the 14 mathematical dependencies, including expected outputs. Each is +also hashed by the initial integrity pass. + +| File | Role and consumer | +|---|---| +| [caller/HANDOFF-FAMILY.json](source/caller/HANDOFF-FAMILY.json) | **Expected** for `handoff_family.prove`; **input** prefixes for `review_handoff_family.run`. | +| [native-frames/HANDOFF-FAMILY-TAIL.json](source/native-frames/HANDOFF-FAMILY-TAIL.json) | **Input** tails for `review_handoff_family.run`. | +| [root-chronology/INDEPENDENT-HANDOFF-FAMILY.json](source/root-chronology/INDEPENDENT-HANDOFF-FAMILY.json) | **Expected** complete-family receipt for `review_handoff_family.run`. | +| [root-chronology/INDEPENDENT-HANDOFF-SIX.json](source/root-chronology/INDEPENDENT-HANDOFF-SIX.json) | **Input** six-bank source word for `charts()`, including its cycle graph. | +| [root-chronology/HANDOFF-COMPLETE-Q3.json](source/root-chronology/HANDOFF-COMPLETE-Q3.json) | **Input** eight-bank source word for `charts()`. | +| [root-chronology/SIGNED-CHART-HANDOFF-SIX.json](source/root-chronology/SIGNED-CHART-HANDOFF-SIX.json) | **Certificate** of fixed six-bank choices/events and matching 72f bill, checked by `charts()`. | +| [root-chronology/SIGNED-CHART-HANDOFF-Q3.json](source/root-chronology/SIGNED-CHART-HANDOFF-Q3.json) | **Certificate** of fixed eight-bank choices/events and matching 128f bill, checked by `charts()`. | +| [root-chronology/CHART-CYCLE-PACK-HANDOFF-SIX.json](source/root-chronology/CHART-CYCLE-PACK-HANDOFF-SIX.json) | **Certificate** of 36 odd Eulerian subgraphs, checked by `charts()`; the written fixed-chart proof supplies the general cost implication. | +| [caller/ENCODED-PHYSICAL-PREFIX.json](source/caller/ENCODED-PHYSICAL-PREFIX.json) | **Input** literal triangular prefix for `audit_encoded_complete.run`; also read for provenance hashes by the balanced producer. | +| [native-frames/ENCODED-STAGE-TAIL.json](source/native-frames/ENCODED-STAGE-TAIL.json) | **Input** literal tail for `audit_encoded_complete.run` and `balanced_physical_replay.produce`. | +| [root-chronology/INDEPENDENT-ENCODED-COMPLETE.json](source/root-chronology/INDEPENDENT-ENCODED-COMPLETE.json) | **Expected** for `audit_encoded_complete.run`; **input** original triangular word for `saved_quadratic()`. | +| [caller/BALANCED-PHYSICAL-REPLAY-Q3.json](source/caller/BALANCED-PHYSICAL-REPLAY-Q3.json) | **Expected** for `balanced_physical_replay.produce`; **input** original balanced word for `saved_quadratic()`. | +| [root-chronology/CLUSTER-INDEPENDENT-ENCODED-COMPLETE-ALLPAIRS.json](source/root-chronology/CLUSTER-INDEPENDENT-ENCODED-COMPLETE-ALLPAIRS.json) | **Certificate** of saved triangular quadratic choices/events and 130f bill, checked by `saved_quadratic()`. | +| [root-chronology/CLUSTER-BALANCED-PHYSICAL-REPLAY-Q3-ALLPAIRS.json](source/root-chronology/CLUSTER-BALANCED-PHYSICAL-REPLAY-Q3-ALLPAIRS.json) | **Certificate** of saved balanced quadratic choices/events and 130f bill, checked by `saved_quadratic()`. | + +### Status-only dependency + +[caller/ENCODED-STAGE.json](source/caller/ENCODED-STAGE.json) is parsed by +`encoded_physical.produce`, called by the balanced producer, solely to require +its saved `status` to equal `PASS_NATIVE_ZERO_ENCODED_STAGE_ALL_COLUMNS_ALL_F`. +Its bytes are also hashed. The registered replay **does not rerun +`encoded_stage.prove` or compare this receipt's mathematical body**. The complete +triangular and balanced physical words receive the separate direct checks above. +This 36,969-line file must not be counted as 36,969 lines of freshly replayed +evidence merely because the package passes. + +## Archival-only mathematical receipts + +These 12 receipts are retained unchanged and hashed, but their JSON mathematical +contents are not parsed or compared by the registered commands. Their original +statuses, scope limits and provenance remain historical evidence. + +| File | Retained context; current replay distinction | +|---|---| +| [caller/BALANCED-STAGE-TRIAL.json](source/caller/BALANCED-STAGE-TRIAL.json) | Earlier balanced-prefix trial. The balanced producer also reads its bytes to report a provenance hash; it does not replay this trial. | +| [caller/NESTED-FAMILY.json](source/caller/NESTED-FAMILY.json) | Earlier nested-family receipt; the complete handoff-family receipts above are checked instead. | +| [caller/NESTED-SIX.json](source/caller/NESTED-SIX.json) | Earlier six-bank prefix receipt. | +| [caller/PIVOT-PLANE-PROBE.json](source/caller/PIVOT-PLANE-PROBE.json) | Bounded source-retraction screen. Its Python helper is imported, but this saved screen is not read. | +| [caller/QUADRATIC-MODEL-REVIEW.json](source/caller/QUADRATIC-MODEL-REVIEW.json) | Separate model-audit receipt. Only helper functionality from its producer is used; that producer's complete audit is not rerun. | +| [root-chronology/CHRONOLOGY.json](source/root-chronology/CHRONOLOGY.json) | Restricted local chronology screen. Algebra functions from `chronology.py` are used, not this receipt. | +| [root-chronology/ENCODED-COMPLETE-Q3.json](source/root-chronology/ENCODED-COMPLETE-Q3.json) | Earlier serialized complete encoded word; current direct checks assemble the prefix/tail and compare `INDEPENDENT-ENCODED-COMPLETE.json`. | +| [root-chronology/EXACT-CHART-RESULTS.json](source/root-chronology/EXACT-CHART-RESULTS.json) | Earlier chart-validation summary. Current `charts()` checks the underlying words/cycle witness directly; it does not compare this summary. | +| [root-chronology/INDEPENDENT-COMPLETE-SIX.json](source/root-chronology/INDEPENDENT-COMPLETE-SIX.json) | Earlier complete six-bank caller receipt. | +| [root-chronology/INDEPENDENT-SHARED-CALLER.json](source/root-chronology/INDEPENDENT-SHARED-CALLER.json) | Earlier complete four-bank shared-tail receipt. | +| [root-chronology/PAID-PROGRESS-BATCHING.json](source/root-chronology/PAID-PROGRESS-BATCHING.json) | Earlier batching receipt; current family replay calls the batching implementation directly. | +| [root-chronology/SAVED-QUADRATIC-WORDS-VALIDATION.json](source/root-chronology/SAVED-QUADRATIC-WORDS-VALIDATION.json) | Earlier saved-word validation summary. Current `saved_quadratic()` checks the two underlying certificates directly. | + +## Retained Python sources + +The 19 source modules below are loaded by the registered verifier. Loading a +module does not imply that its standalone driver, search or complete audit ran. +The source-byte loader authenticates and compiles the same bytes with +`optimize=0`, including when the parent verifier is run with `-O`. + +| Functionality | Loaded source files | +|---|---| +| Handoff construction and algebra dependencies | [handoff_family.py](source/caller/handoff_family.py), [nested_family.py](source/caller/nested_family.py), [nested_prefix.py](source/caller/nested_prefix.py), [free_ops.py](source/caller/free_ops.py), [plane_group.py](source/caller/plane_group.py), [pivot_plane_probe.py](source/caller/pivot_plane_probe.py) | +| Complete family replay and signed charts | [review_handoff_family.py](source/root-chronology/review_handoff_family.py), [chronology.py](source/root-chronology/chronology.py), [batch_paid_progress.py](source/root-chronology/batch_paid_progress.py), [native_chart_search.py](source/root-chronology/native_chart_search.py), [signed_chart_optimization.py](source/root-chronology/signed_chart_optimization.py) | +| Physical and quadratic replay | [audit_encoded_complete.py](source/root-chronology/audit_encoded_complete.py), [quadratic_charts.py](source/root-chronology/quadratic_charts.py), [balanced_physical_replay.py](source/caller/balanced_physical_replay.py), [encoded_physical.py](source/caller/encoded_physical.py), [quadratic_model_review.py](source/caller/quadratic_model_review.py) | +| Native model and inherited exact helpers | [native_model.py](source/native-frames/native_model.py), [clifford_exact.py](source/vendor/clifford_exact.py), [full_stabilizer_bound.py](source/vendor/full_stabilizer_bound.py) | + +The remaining six retained Python files are **not loaded** by these entrypoints: + +| File | Retention role | +|---|---| +| [caller/encoded_stage.py](source/caller/encoded_stage.py) | Historical stage producer; additionally hashed for producer provenance. Its proof routine is not executed. | +| [caller/nested_six.py](source/caller/nested_six.py) | Historical prefix producer. | +| [native-frames/lifted_algebra.py](source/native-frames/lifted_algebra.py) | Historical lifted-algebra implementation. | +| [root-chronology/verify_chart_results.py](source/root-chronology/verify_chart_results.py) | Original chart-verification driver; the portable adapter uses `charts()`. | +| [root-chronology/verify_saved_quadratic_words.py](source/root-chronology/verify_saved_quadratic_words.py) | Original saved-word driver; the portable adapter uses `saved_quadratic()`. | +| [original/native-frames/native_model.py](original/native-frames/native_model.py) | Original before the three path-only adaptations recorded in `BINDINGS.json`; retained for comparison, not execution. | + +## Proofs, attribution and package controls + +The two retained written proofs are +[HANDOFF-FAMILY-PROOF.md](source/caller/HANDOFF-FAMILY-PROOF.md) and +[HANDOFF-FAMILY-TAIL-PROOF.md](source/native-frames/HANDOFF-FAMILY-TAIL-PROOF.md). +They are hashed, not machine-checked written arguments. The package-level +[FIXED-CHART-PROOF.md](FIXED-CHART-PROOF.md) is likewise a written proof, separate +from the finite cycle-certificate checks. + +Five retained credit/provenance files complete the 59-file binding inventory: +[NOTICE.md](source/vendor/credits/NOTICE.md), +[PR533-NOTICE.md](source/vendor/credits/PR533-NOTICE.md), +[PR531 NOTICE.md](source/vendor/credits/vendor/pr531/NOTICE.md), +[PR531 SOURCES.json](source/vendor/credits/vendor/pr531/SOURCES.json), and +[PR523-ANCESTRY.json](source/vendor/credits/vendor/pr531/inputs/PR523-ANCESTRY.json). +They are hashed, not mathematical replay inputs. Preserve all source-specific +credit and license obligations regardless of replay role. + +At package level, [BINDINGS.json](BINDINGS.json) controls retained-file hashes +and original-to-portable path mappings; [VERIFY.json](VERIFY.json) registers +normal and optimized replay; [SOURCES.json](SOURCES.json) pins Git provenance; +[TASK.json](TASK.json) records the assigned/changed scope and open questions; +[RELATED-WORK.json](RELATED-WORK.json) records overlap and prior publication. +[LICENSE](LICENSE) and [NOTICE.md](NOTICE.md) retain the package's license and +credit. These controls and the written proofs are not substitutes for each other. + +Use the two commands in [README: Reproduce](README.md#reproduce) for registered +replay and committed-source/history checks. The registered commands consume the +complete package, including the archival files; this index is not a reduced +export recipe and does not authorize regenerating or pruning frozen evidence. diff --git a/research/two-pivot-caller-readers/FIXED-CHART-PROOF.md b/research/two-pivot-caller-readers/FIXED-CHART-PROOF.md new file mode 100644 index 0000000000..848e3c63fc --- /dev/null +++ b/research/two-pivot-caller-readers/FIXED-CHART-PROOF.md @@ -0,0 +1,63 @@ +# Exact rank mass of the fixed native-product chart compiler + +This proves the physical-word-to-signed-graph implication used by the n=6 +certificate. It concerns the literal compiler in +`source/root-chronology/native_chart_search.py`, with its fixed input ADD, +ADDRESS and bank-SWAP skeleton. It makes no claim about other compilers. + +For each bank retain a pending product of the commuting native plane +operators. A bit `s_j` records whether plane j occurs. The exact signed +plane algebra has `N_j^2=-I`; its Gaussian unit is retained separately. +It contributes zero native rank, although its physical scan remains paid. +The compiler invariant is that the old logical bank equals its pending +native product times the current retimed physical bank. + +Initially every s_j is zero. A native/ADDRESS unary with native mask t +and plane permutation pi replaces the pending mask by `t xor pi(s)`. +The literal ADDRESS is emitted, and the exact scalar sign is retained. +A bank-SWAP exchanges the pending masks. Neither case introduces a new +binary choice in this compiler. + +Immediately before a literal scalar ADD, source and destination must use +one common chart r. The compiler permits every native-product r, with +one independent bit r_j per plane. It emits alignment products with +masks `s_source xor r` and `s_destination xor r`, then performs the +unchanged scalar ADD. Each differing bit pays native rank 2f. The final +restoration aligns each bank with chart zero and has the same cost rule. +Splitting an alignment into contracting pieces preserves this rank mass. + +Represent every current bit as `x_v xor c`, where x_0 is the fixed zero +variable, and c is a constant. At an ADD introduce a new variable x_w for +each common-chart bit. The two alignments contribute edges `(v,w,c)`. +Their violation bits are `x_v xor x_w xor c`. Unary events only move +the labels and toggle c; bank-SWAPs exchange them. Final restoration +contributes `(v,0,c)`. This is exactly the chronological construction in +`source/root-chronology/signed_chart_optimization.py::graph`. + +Therefore, for every binary assignment of all chart choices, not merely +an optimizer-produced assignment, the compiled native rank mass is +`2f * sum_edges (x_u xor x_v xor c_edge)`. The same identity holds for +every scalar ADD coefficient in the fixed skeleton. Additional physical +scan costs cannot lower this expression. + +On an Eulerian edge subgraph, every variable occurs an even number of +times, so XOR of all its edge violation bits equals XOR of its edge +signs. An odd signed Eulerian subgraph must contain a violated edge. +The retained certificate contains 36 such subgraphs with disjoint edge +sets. Every assignment therefore has at least 36 violations, and native +mass at least 72f. The retained six-bank word has exactly 72f, proving +equality for this compiler. Its stock is also 72f. + +The verifier reconstructs the graph from the complete retained word, +checks every edge index, even vertex degree, odd sign sum and global +edge disjointness, and replays the matching compiled word on every +original input column in both literal inverse orders. A repeated cycle +is a rejected control. Numerical optimizer bounds are not used. + +For b>0 and any strictly smaller recursive rank rm^(-b) r`. Thus a complete word in this fixed compiler with +rank mass at least n*m cannot meet a favorable positive-b moment +against n full-size banks. This is a scoped moment consequence, not a +global caller, native-alphabet or multiplication-exponent lower bound. + +Ross Richardson with substantial OpenAI Codex assistance. Apache-2.0. diff --git a/research/two-pivot-caller-readers/LICENSE b/research/two-pivot-caller-readers/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/two-pivot-caller-readers/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/two-pivot-caller-readers/NOTICE.md b/research/two-pivot-caller-readers/NOTICE.md new file mode 100644 index 0000000000..9b2e471c3f --- /dev/null +++ b/research/two-pivot-caller-readers/NOTICE.md @@ -0,0 +1,19 @@ +# Attribution and scope + +Copyright 2026 Ross Richardson. New caller derivations, exact replay adapter +and packaging: Ross Richardson with substantial OpenAI Codex assistance. +Apache-2.0, under the included LICENSE. + +The exact inherited Gaussian-dyadic compiler is not new work. The unchanged +kernel92/PR531 notices, source manifest and PR523 ancestry remain under +source/vendor/credits/. Their source authors and AI disclosures are retained. +The locally frozen predecessor proofs and mathematical scripts are retained +with original bytes and original AI assistance notices, except the explicitly +identified read-only path adaptations whose originals are also retained. + +PR3987 (Chris R / Clear1nsight) and PR4002 (ToikY) retain generic signed-lift +and phase-normalization credit. PR3989/4045 retain their separate interface +and physical-volume theorems. Separate BIT PR4021/4023 and older Ross-authored +PR3630/3632/3645/3649/3655 are prior publications, not unpublished new results. +No arithmetic, κ, selected-record or scientific-acceptance claim is imported +from a PR title, publication state, archive or source-integrity check. diff --git a/research/two-pivot-caller-readers/README.md b/research/two-pivot-caller-readers/README.md new file mode 100644 index 0000000000..cae04d61b8 --- /dev/null +++ b/research/two-pivot-caller-readers/README.md @@ -0,0 +1,127 @@ +# Complete two-pivot caller readers and exact retiming bills + +**Scoped caller result; no new κ or selected-frontier change.** + +**Reviewer guide:** the [evidence index](EVIDENCE-INDEX.md) maps each retained +receipt to its replay role, distinguishes mathematical inputs and status-only +dependencies from archival-only receipts, and lists the loaded source modules. +All retained files, including archival evidence, remain required by the hash gate. + +## Result + +For every integer `q>=2` and `f>=1`, the displayed complete caller on +`n=2q+2` independent arbitrary banks has ambient arity `m=(4q+4)f` and +`H_(2f)=n^2+2, H_(4f)=1`. Its rank mass is exactly full stock plus `8f`. +Both dirty pivot inputs and every public-input reader are included. This +repairs the tempting prefix-only invoice, whose `2qf` deficit is consumed +by its complete tail. + +Within the fixed ordinary native-product chart compiler, a six-bank word +has matching mass/stock `72f`. A certificate of 36 edge-disjoint odd +Eulerian subgraphs proves its all-chart lower bound `72f`. An eight-bank +word has matching mass/stock `128f`; no general n=8 lower bound is claimed. + +Separate triangular and balanced changed eight-bank words have complete +baseline mass `138f` against stock `128f`. Saved exact quadratic choices +reduce each to `130f`. This is a useful local rank reduction, still an +unfavorable invoice. No optimizer is imported or trusted by replay. + +## Proof and exact coverage + +The [all-q construction and complete reader proof](source/caller/HANDOFF-FAMILY-PROOF.md) +uses a noncommutative scalar invariant, including raw-a repair, actual +source swaps and the two affine pivot readers. The +[tail derivation](source/native-frames/HANDOFF-FAMILY-TAIL-PROOF.md) retains +the ordinary factory supports. The registered command reconstructs q=2,3,4 +fixtures on all original independent columns and checks both literal +inverse orders. The written induction supplies all q; finite fixtures +alone do not quantify over q. + +The [fixed-compiler proof](FIXED-CHART-PROOF.md) derives the complete +chronological physical-word-to-graph cost identity for every chart choice. +The exact signed chart certificate checks every declared graph edge, +odd parity, Eulerian degree and global edge disjointness. A duplicate-cycle +mutant rejects. Triangular and balanced source circuits are independently +decoded into exact affine X-character monomials with Z4 phases. All four +f residue classes are retained, including the once-per-bank global phase. +Every saved retiming is recompiled from its fixed choices, compared with +the complete target, and checked in both inverse orders. Omitting a paid +query rejects. No broad search is rerun. + +## Limits + +The n=6 floor concerns exactly the retained ADD/ADDRESS/bank-SWAP +skeleton and native-product chart compiler. It is not a lower bound on +changed callers, source handoffs or nonmonomial charts. The retimed arity +invoices still need literal selected-native lowerings, contracting splits, +precision, source/COPY scans, chronological integral owners, storage and +fixed-tape realization before recursive supplier admission. + +## Reproduce + +From the repository root, on Python 3.12: + +```sh +python3.12 -B scripts/research_package.py --package research/two-pivot-caller-readers +python3.12 -B scripts/check_research_commit.py --package research/two-pivot-caller-readers --check-source-history +``` + +The registered manifest runs `verify.py` normally and with `-O`. Its direct +portable equivalent is `python3 -B verify.py` (or `python3 -O -B verify.py`) +from this package. The direct command needs only standard-library Python, +no Git/network and no original Ross-specific directory. `--json` prints the +complete replay summary. It writes no package files. + +[BINDINGS.json](BINDINGS.json) retains every consumed original source/data +byte hash and explicitly records the path-only adaptations. Original versions +of adapted scripts remain under `original/`. Other source bytes and historical +receipts remain unchanged. Those receipts retain their old absolute provenance +paths; they are data, not required filesystem locations. The replay adapter +resolves only the explicitly retained original source inventory. Original lane +notes are archival and keep their original scope and attribution. + +The source loader hashes and compiles the **same bytes**, never loads `.pyc`, +and compiles historical implementations with `optimize=0` in both parent +Python modes, preserving inherited assertions. Mathematical receipt comparison +omits only the enumerated provenance fields in `verify.py`; all such retained +input bytes are checked separately. A changed-source control rejects. Hashes +provide integrity against the trusted publication, not external authentication +or mathematical correctness. Git/source-history, export integrity, finite +replay, written proof, hosted CI and supplier admission remain separate. + +## Related work and credit + +Ross Richardson with substantial OpenAI Codex assistance, including separate +mathematical checking contexts and this packaging adapter. No independent +human or formal-kernel review is claimed. New work is Apache-2.0. + +The Gaussian-dyadic compiler is inherited unchanged from icekylinx's PR531 +through Rohan Arun's kernel92 composition. The exact original notices and +source ancestry are retained in `source/vendor/credits/`; they preserve +DreamingOfClouds, Dugongue, eumemic and the geometry/compiler lineage. + +Chris R / Clear1nsight's PR3987 and ToikY's PR4002 retain credit for generic +native-lift phase/cocycle normalization and the need for exact signed/global +phase witnesses. This package makes no generic normalization priority claim. +Chris R's PR3989 and PR4045 are related explicit interface/volume-cost results; +their different fixed sources and theorems are neither imported nor claimed +as new here. These named overlaps were read at exact heads: + +| PR | Exact head | Contributor | +|---|---|---| +| [#3987](https://github.com/CrocSwap/integer-mult-bounds/pull/3987) | `fc536202fdaa924158789a5ef59ac079bbe21922` | Clear1nsight | +| [#4002](https://github.com/CrocSwap/integer-mult-bounds/pull/4002) | `d593941ea0a4926021cba9d01fe60500579e464f` | ToikY | +| [#3989](https://github.com/CrocSwap/integer-mult-bounds/pull/3989) | `7b6dda7ab6ed10d608ecba357ac2f6924166d38b` | Clear1nsight | +| [#4045](https://github.com/CrocSwap/integer-mult-bounds/pull/4045) | `91afbb643f7f4ccf6f34b685ecd959eb790a0f94` | Clear1nsight | + +[RELATED-WORK.json](RELATED-WORK.json) separately inventories the already +published PRs 3630/3632/3645/3649/3655 and separate BIT PRs 4021/4023. +Their publication is not supplier admission. This contribution neither +constructs BIT nor duplicates those results. The recent-PR/live-discussion +overlap has explicit partial coverage, not a proof of novelty. + +## Open next questions + +Can an explicitly completed changed pivot/factory/reader word remove the unfavorable rank mass without granting a free original-input reader? Keep every original bank independent and write the complete H/L terminal map before optimizing its paid native word. No favorable complete changed caller, compatible positive BIT supplier or complete joint outer transfer is supplied here. +The same question, relevance, feasible first step and blockers are in +[TASK.json](TASK.json). diff --git a/research/two-pivot-caller-readers/RELATED-WORK.json b/research/two-pivot-caller-readers/RELATED-WORK.json new file mode 100644 index 0000000000..411c6f4f54 --- /dev/null +++ b/research/two-pivot-caller-readers/RELATED-WORK.json @@ -0,0 +1,95 @@ +{ + "scientific_base": "20ecf2891d80b5acf18d980b2164fb44ea7faa90", + "priority_revision": 6, + "coverage": "Exact named PR head/body reads plus parent recent80-open-PR and partial live Discussion delta; not exhaustive code/closed/unpublished overlap.", + "pull_requests": [ + { + "number": 3987, + "title": "Audit staged544 native phases and expose the binary-inverse lift defect", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3987", + "head": "fc536202fdaa924158789a5ef59ac079bbe21922", + "author": "Clear1nsight", + "scope": "Related phase/interface result; not rerun or claimed here." + }, + { + "number": 4002, + "title": "Derive explicit native-lift phase tags and signed-word certificates", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4002", + "head": "d593941ea0a4926021cba9d01fe60500579e464f", + "author": "ToikY", + "scope": "Related phase/interface result; not rerun or claimed here." + }, + { + "number": 3989, + "title": "Construct selected rank-two Pauli fusion and bound its uniform transfer bill", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3989", + "head": "7b6dda7ab6ed10d608ecba357ac2f6924166d38b", + "author": "Clear1nsight", + "scope": "Related phase/interface result; not rerun or claimed here." + }, + { + "number": 4045, + "title": "research: bind joint-child batching to the staged544 native rank interface", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4045", + "head": "91afbb643f7f4ccf6f34b685ecd959eb790a0f94", + "author": "Clear1nsight", + "scope": "Related phase/interface result; not rerun or claimed here." + }, + { + "number": 4021, + "title": "Verify five rank-four BIT terminals and their fixed-controller cost bound", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4021", + "head": "c01f97ecfc7fa64847f6abd8f7b231e1df8c7b70", + "author": "RossRichardson", + "scope": "Already published separate BIT/prior lineage; excluded from this new contribution." + }, + { + "number": 4023, + "title": "Prove sharp fixed-support unary-query bounds with restored dirty banks", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4023", + "head": "9124007ea9029a9a3b88898bb4c350ddb27ffa58", + "author": "RossRichardson", + "scope": "Already published separate BIT/prior lineage; excluded from this new contribution." + }, + { + "number": 3630, + "title": "Bound staged-supplier packing for every replica count", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3630", + "head": "bcac7fe04b9b7f7f5d3c27d620561f96c4ae5608", + "author": "RossRichardson", + "scope": "Already published separate BIT/prior lineage; excluded from this new contribution." + }, + { + "number": 3632, + "title": "Correct the selected P112 scatter covariance and dirty restoration", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3632", + "head": "7e7a889cbf6da2c4461af806fe52a888c621a7e7", + "author": "RossRichardson", + "scope": "Already published separate BIT/prior lineage; excluded from this new contribution." + }, + { + "number": 3645, + "title": "Reduce R438 to 429 helpers with three source snapshots", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3645", + "head": "99b901c9b5ac70cf441b3d7e585cc7b8744b5359", + "author": "RossRichardson", + "scope": "Already published separate BIT/prior lineage; excluded from this new contribution." + }, + { + "number": 3649, + "title": "Classify sharp noncubic ranks of the H6 odd-Gram family", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3649", + "head": "f8768756d8ac4abb263295170a436ba54562fdcd", + "author": "RossRichardson", + "scope": "Already published separate BIT/prior lineage; excluded from this new contribution." + }, + { + "number": 3655, + "title": "Classify H6 dyadic Smith factors and sharp physical-row repair", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3655", + "head": "7bf23e128e58a33c019268f57129629f603547f7", + "author": "RossRichardson", + "scope": "Already published separate BIT/prior lineage; excluded from this new contribution." + } + ] +} diff --git a/research/two-pivot-caller-readers/SOURCES.json b/research/two-pivot-caller-readers/SOURCES.json new file mode 100644 index 0000000000..68bddcb9b4 --- /dev/null +++ b/research/two-pivot-caller-readers/SOURCES.json @@ -0,0 +1,60 @@ +{ + "schema_version": 1, + "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81", + "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "67f085acd86acd7d4e03922d9cf4b26bca66fed5", + "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0" + }, + { + "path": "research/kernel92-frame-composition/vendor/pr531/vendor/clifford/clifford_exact.py", + "usage": "provenance", + "git_blob": "166841a037f069249f6f7f6dedb89248812f59e2", + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962" + }, + { + "path": "research/kernel92-frame-composition/NOTICE.md", + "usage": "provenance", + "git_blob": "8d3c3349e13774de4f992591c3a0b9e74029f761", + "sha256": "538e7634331d7e24791be08dedd737bf458f35a3b46ce651e6aacd905f3dee6e" + }, + { + "path": "research/kernel92-frame-composition/PR533-NOTICE.md", + "usage": "provenance", + "git_blob": "6e6d0042d1cf618308e7e57df3e7e8b6958991d0", + "sha256": "2c1961a07b0976e29e8e6f4da14a9aaeb2f961a3a78d842488065aa433fa2f98" + }, + { + "path": "research/kernel92-frame-composition/vendor/pr531/NOTICE.md", + "usage": "provenance", + "git_blob": "f7a8f861be860edd5a78114c5225dec90effa029", + "sha256": "a92f49c5ced455160fbedcc8954e3c9255e3605e88ad12ae5a84f1c4302986f1" + }, + { + "path": "research/kernel92-frame-composition/vendor/pr531/SOURCES.json", + "usage": "provenance", + "git_blob": "78244052aae4866ae9e8e2d2e4c10180870a0fc4", + "sha256": "9e8182e6e659f4671fe0873e324b622cc871df7344157093df40476c8687be5f" + }, + { + "path": "research/kernel92-frame-composition/vendor/pr531/inputs/PR523-ANCESTRY.json", + "usage": "provenance", + "git_blob": "385a202fbc485ceaed1b604d6c21eb3486caa600", + "sha256": "0bfce40d86c849f18e8872ee9e8462b0a69a34ed04e01e942a6614645f686f4b" + }, + { + "path": "LICENSE", + "usage": "provenance", + "git_blob": "261eeb9e9f8b2b4b0d119366dda99c6fd7d35c64", + "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4" + } + ] +} diff --git a/research/two-pivot-caller-readers/TASK.json b/research/two-pivot-caller-readers/TASK.json new file mode 100644 index 0000000000..ceac2be4c8 --- /dev/null +++ b/research/two-pivot-caller-readers/TASK.json @@ -0,0 +1,79 @@ +{ + "schema_version": 1, + "task_id": "joint-query-controller", + "priority_revision": 6, + "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90", + "original_card": { + "id": "joint-query-controller", + "question": "Can a literal QQ16 producer meet the proposed completed-output error budgets with dirty helpers and an affordable physical consumer?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/joint-query/README.md", + "research/joint-query/evidence/QQ16-SELECTED-WITNESS.md", + "research/joint-query/evidence/JOINT-QUERY-TRANSFER.md", + "docs/research/community-efficient1000-review.md", + "research/qq16-producer-defect-transfer/README.md" + ], + "methods": [ + "Derive one literal producer's completed-output defects and intermediate dirty-helper bounds, with its physical bill.", + "Design or audit one consumer, retention or hosting boundary and its complete cost for the pinned producer/decoder." + ], + "acceptance_gate": "Name the changed premise of the fixed F0/B1 observation obstruction. Show exactly which query is recovered, legal native reads and restoration, and a full favorable budget including cover maps, helpers and endpoints. Local inverse identities alone do not close the global controller. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read the revision-6 family record and #2965 producer-defect transfer after the local QQ16 decoder contract. Its author-checked output-error estimate does not implement producer interiors, bound dirty helpers, or pay for the consumer; independently check the implication used.", + "scope": "Source-bound orientation only. Read the named package and review before relying on its local evidence; this command is not its replay or supplier admission." + }, + "first_experiment": "Pin one literal F0/B1 producer and its native-child contracts; derive the actual intermediate magnitude ledger and completed-output defects, including dirty helpers and correlations. Compare with #2965 budgets and price storage, movement, cleanup and F17 consumption. Stop with a precise missing bound if no producer contract supplies it; do not optimize another decoder precision constant in isolation.", + "bottleneck_link": "The native local words exist; retained query information and its physical access are the missing link to a composed recursive interface.", + "allowed_variations": [ + "One paid query, one changed first pair, or one precisely specified affine helper state.", + "A counterexample or lower bound for that exact proposed repair.", + "One unresolved obligation of a newer local decoder, with exact source heads and a distinct claim/domain." + ], + "scope_change_triggers": [ + "Retaining the fixed first pair and ordinary schedule while allowing only homogeneous selected-only control, already excluded by the witness.", + "Treating cover-map counts as zero-cost physical address operations.", + "Recreating the pending complete local decoder or early-record/output-bank coalescing already under investigation without a distinct audit or changed premise.", + "Treating a completed-output defect inequality as a producer-interior, dirty-range or physical-cost certificate." + ], + "overlap_terms": [ + "QQ16", + "joint-query", + "changing-chart controller", + "selected observation", + "1969", + "2540", + "early record", + "output-bank retention", + "complete native decoder", + "2965", + "producer defect", + "dirty-helper range", + "F17 consumer" + ] + }, + "scope_status": "changed", + "actual_scope": "Construct the complete scalable two-pivot source-handoff caller with both original-input readers; certify fixed-chart break-even words and the n=6 compiler floor; bind the triangular/balanced eight-bank words and saved quadratic retimings to their actual source circuits.", + "scope_change_reason": "Explicit donor-assigned caller investigation and authorized publication of the frozen preceding-run results; this is not a claim to solve the full original card.", + "bottleneck_link": "Complete native caller charge and original-input reader/cleanup obligations. No selected result or new kappa.", + "budget_minutes": 240, + "stop_rule": "Publish only exact complete local identities, scoped proofs or explicitly archived finite screens. Stop favorable-supplier claims at the unresolved full-bill and physical-admission boundaries.", + "outcome": "partial", + "evidence": "README.md; source proof links; BINDINGS.json; explicit normal/optimized VERIFY.json commands.", + "author": "Ross Richardson", + "ai_assistance": "Substantial OpenAI Codex assistance across the original construction, separate mathematical checking contexts, and publication packaging. AI review is not independent human or formal-kernel acceptance.", + "open_questions": [ + { + "question": "Can an explicitly completed changed pivot/factory/reader word remove the unfavorable rank mass without granting a free original-input reader?", + "why_it_matters": "This is the remaining constructive gap between the scoped result and a useful complete caller.", + "first_step": "Keep every original bank independent and write the complete H/L terminal map before optimizing its paid native word.", + "blocked_by": "No favorable complete changed caller, compatible positive BIT supplier or complete joint outer transfer is supplied here." + } + ] +} diff --git a/research/two-pivot-caller-readers/VERIFY.json b/research/two-pivot-caller-readers/VERIFY.json new file mode 100644 index 0000000000..dcd98d89ff --- /dev/null +++ b/research/two-pivot-caller-readers/VERIFY.json @@ -0,0 +1,28 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 600, + "checks": "Complete listed operator/receipt replays and named rejecting controls; source-bound exact bytes with historical assertions enabled." + }, + { + "argv": [ + "{python}", + "-O", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 600, + "checks": "Same mathematical coverage under optimized parent Python; historical source assertions deliberately retained by optimize=0 compilation." + } + ] +} diff --git a/research/two-pivot-caller-readers/original/native-frames/native_model.py b/research/two-pivot-caller-readers/original/native-frames/native_model.py new file mode 100644 index 0000000000..03925dd36e --- /dev/null +++ b/research/two-pivot-caller-readers/original/native-frames/native_model.py @@ -0,0 +1,67 @@ +"""Pinned Gaussian Clifford model for common2/fresh2 native bridges. +Apache-2.0; substantial OpenAI Codex assistance. Frozen imports are read only. +""" +from pathlib import Path +import hashlib,importlib.util,sys +sys.dont_write_bytecode=True +BASE=Path('/Users/ross/git/math') +PIN='20ecf2891d80b5acf18d980b2164fb44ea7faa90' +CE_PATH=BASE/'integer-mult-bounds/research/kernel92-frame-composition/vendor/pr531/vendor/clifford/clifford_exact.py' +CE_SHA='2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962' +BOUND_PATH=BASE/'.research-automation/runs/kappa-changed-endpoints-20261019T0153Z/stabilizer-escape/full_stabilizer_bound.py' +BOUND_SHA='f073a00ad4831616e873eb110fd33ad7226010a7c2f6cfa6a6b63167bf58ef75' +def need(ok,why): + if not ok:raise ValueError(why) +def load(name,path,sha): + need(hashlib.sha256(path.read_bytes()).hexdigest()==sha,'source pin '+str(path)) + spec=importlib.util.spec_from_file_location(name,path);mod=importlib.util.module_from_spec(spec);sys.modules[name]=mod;spec.loader.exec_module(mod);return mod +ce=load('native_frames_pinned_clifford',CE_PATH,CE_SHA) +b=load('native_frames_frozen_independent',BOUND_PATH,BOUND_SHA) +def mul(*ops):return b.standard_product(ce,*ops) +def same(a,c,why,phase=True): + need(a.tab==c.tab,why+' signed tableau') + if phase:need(b.sparse_column(a)==b.sparse_column(c),why+' actual Gaussian phase') +def phase(n,p):return ce.Op(n,ce.identity(n),[('phase',p%4)]) +def symplectic_defect_rank(op): + return b.binary_rank(x^y for x,y in zip(b.binary_tableau(op),b.binary_tableau(ce.ident(op.n)))) +def pauli(n,x=0,z=0,p=0): + out=ce.diag(n,[0]*n,[2*((z>>j)&1)for j in range(n)]) + return mul(phase(n,p),ce.xgate(n,x),out) +def conjugated_pauli(op,x=0,z=0,p=0): + triple=ce.apply(op.tab,(x,z,p));return pauli(op.n,*triple),triple +class Model: + def __init__(self,f=1,stages=4): + need(f>=1 and stages>=1,'positive chunk/stages');self.f=f;self.stages=stages;self.n=(2+2*stages)*f;self.I=ce.ident(self.n) + self.N=self.Npair(0,1);self.U=self.Hp(0);self.V=mul(self.N,self.U.adjoint()) + self.P=[self.swap_pair(s+1)for s in range(stages)];self.T=[self.Npair(2+2*s,3+2*s)for s in range(stages)] + self.Q=ce.xgate(self.n,1) + def Hp(self,chunk): + out=self.I + for j in range(self.f): + bit=chunk*self.f+j;alpha=[0]*self.n;alpha[bit]=2 + out=mul(ce.diag(self.n,[0]*self.n,alpha),ce.cgate(self.n,1<=4,'pqqp uses4 stages');gs=[self.I,self.I];controls=[];F=self.I + for s,(kind,W) in enumerate(zip('FGFG',[self.U,self.V,self.V,self.U])): + required=self.phi(gs[1])if kind=='F'else mul(W,self.N.adjoint(),gs[1],self.N,W.adjoint()) + L=mul(required,gs[0].adjoint());controls.append(L);gs[0]=required + if kind=='F':gs=[gs[0],mul(W,self.P[s],gs[1],W.adjoint())] + else:gs=[mul(W.adjoint(),gs[0],W),mul(self.P[s],gs[1])] + F=mul(self.T[s],F) + return gs,controls diff --git a/research/two-pivot-caller-readers/source/caller/BALANCED-PHYSICAL-REPLAY-Q3.json b/research/two-pivot-caller-readers/source/caller/BALANCED-PHYSICAL-REPLAY-Q3.json new file mode 100644 index 0000000000..be50443f87 --- /dev/null +++ b/research/two-pivot-caller-readers/source/caller/BALANCED-PHYSICAL-REPLAY-Q3.json @@ -0,0 +1,30327 @@ +{ + "D": -10, + "all_f_phase_binding": "Every literal P/C/even-linear-D/unit circuit is evaluated independently on X characters. 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complete negative budget result +for its displayed cleanup. It does not establish a new multiplication exponent. + +## Domain and conventions + +Fix integers `q>=2` and `f>=1`. There are `n=2q+2` independent, arbitrary +field inputs, in banks + +``` +(a,t,b1,c1,b2,c2,...,bq,cq). +``` + +Write the original inputs as `a,t0,b1,k0,b2,C2,...,bq,Cq` and put `C1=0`. +The two distinguished dirty input directions are `t0,k0`; neither is initialized. +Every final bank, including these two directions, is eventually transformed. +All operators below act on the LEFT. Products are applied rightmost first. + +In the free-operator calculation `N^2=-I`, and `P_j` are arbitrary independent, +invertible, noncommuting operators. The physical instance has common plane 0, +fresh planes `1,...,k`, `k=2q+1`, each of arity `2f`. Operators `N_i` satisfy +`N_i^2=-I`, commute on distinct planes, and are conjugated by actual ADDRESS +plane permutations. Set `N=N_0`, `P_j=S_(0,j)`, and + +``` +F_s=N_s ... N_1, E=N_0 F_k. +``` + +All native phases are the exact global normalizations inherited from the +minimal-carrier interface. They are retained by the signed plane algebra. +`E` commutes with every native plane and every whole-plane ADDRESS permutation. +The physical public target is `diag(E,...,E)`, of arity `m=2(k+1)=4q+4`. +The displayed formula with formal `P_j` does not, by itself, admit a different +physical chart or postcode. + +A raw stage pays `N_0` on its source and `N_j` on every other bank. It applies +the ADDRESS swap `S_(0,j)` on the source. The fresh-progress count is therefore +`n` calls of arity 2 per stage, including the source call; no inactive bank +is free. A before/after bank SWAP changes which arbitrary value receives the +source ADDRESS operation. Every such SWAP is in the event list. + +## Base on the original independent inputs + +Put + +``` +S = a + sum_(l=1..q) b_l, +A_r = a + sum_(l=r..q) b_l, +Q1 = N^-1 P1 N, +J = [[P2+Q1-I, I-P2], [Q1-I, I]]. +``` + +The first three source stages, followed by scalar entrances, give the following +exact original-input rows: + +``` +u = P3 [N k0 + (P1-I)(N t0+S) - A2], +v = (P2+Q1-I)t0 + (I-P2)k0 + (2N-N P1-P2 N)S. +``` + +At the entrance to pair `r=2`, in the common retarded frame `F_3`, the rows are + +``` +bank a = a, +bank t = u + C2, +bank b1 = N b1 - v, +bank c1 = N u, +bank b_r = b_r (r>=2), +bank c2 = -v-N A2, +bank c_l = (C_l-C2)-v-N A2 (l>2). +``` + +This is a matrix identity on all `2q+2` original columns. In particular, `u,v` +are not clean states or promised copies of one another. + +Here is an algebraic specification of the base word, sufficient to obtain the +rows by direct substitution. At raw ZERO apply `c_r+=c1` for `r>=2`, then the +shared encoder `b1+=N t`. This encoder uses one actual `N` exposure and its +literal inverse. For `r=q,...,1`, apply `c_r-=t; a+=b_r`. The three queries have +source/target pairs `(a,t),(t,b1),(b1,c1)`. Their normalized source-retraction +columns are respectively + +``` +u1=e_a+e_b1, +u2=e_t+sum_(r=1..q)e_c_r, +u3=e_b1-N sum_(r=2..q)e_c_r. +``` + +For a source `s`, the retraction is the invertible shear +`G=I+(u_i-e_s)e_s^T`; `G^-1` is obtained by negating the off-source entries. +Use `G^-1`, then the raw query with source diagonal `P_i` and target cross `N`, +then `G`. At the third source retain the actual `N` continuation, so its source +diagonal is `N P3`. Its `N`-valued entry fanouts use the existing source query; +its `N`-valued exit fanouts precede the continuation using `N(N P3)=-P3`. +The intervening bridges are + +``` +a-=b1; t+=c1; [between stages 1 and 2] +t-=c1; [between stages 2 and 3] +b1+=a; c1+=t; t-=c1; SWAP(b1,c1); +a-=b2; t+=c2; c_r-=t for r>=2. +``` + +Finally restore `a-=sum_(r=3..q)b_r`, and apply +`c1-=a+sum_(r=2..q)b_r`. The raw-a restoration is necessary: without it the +deeper response entrance leaves those independent future `b_r` inputs on `a`. +The saved defect control omitting it changes completed public columns. +This base pays `3n+3` arity-2 calls: three complete raw stages, the shared input +exposure and inverse, and the third-source continuation. All other operations +are explicitly paid finite scalar/ADDRESS scans. + +## One pair: the scalar invariant and its proof + +Suppose pair `r`, `2<=r<=q`, has the entrance + +``` +t=u+delta C_r, c1=N u, +b1=N b1raw-v, c_r=-v-N A_r, +c_l=(C_l-C_r)+c_r (l>r), b_l=b_lraw (l>=r), +a=a_raw, +``` + +where `delta C_r=C_r-C_(r-1)` and every displayed future raw input remains +independent. Earlier completed public outputs may be retained unchanged. +There are two raw stages `e=2r`, `o=2r+1`. + +At the even stage: + +1. Query `N(t)` and perform `t-=c1`. This gives `N delta C_r` on `t`. +2. SWAP `t,c1` before the source ADDRESS operation. The source now holds `N u`. +3. Apply its literal `S_(0,e)` and fresh `N_e` to all non-source banks. +4. SWAP `c1,c_r`. + +After removing the common fresh prefix, the source row is `U=P_e u`, the +completed `c_r` row is `N delta C_r`, and `c1` is the old dirty row `-v-N A_r`. +The elementary identity used here is `N_e^-1 S_(0,e)=S_(0,e) N^-1`. +It explains the retarded source postfactor `P_e N^-1`; this factor is not an +additional unpaid native query. + +At the odd stage: + +1. Query `N(b_r)`. Add that exposed source to every future `c_l`. +2. Perform `c1+=b_r`, and SWAP `b_r,c1` before the source ADDRESS operation. + The new source is + `-v-N A_(r+1)=N(Nv-A_(r+1))`. +3. Subtract that source from `b1` and every future `c_l`. +4. Apply source ADDRESS `S_(0,o)` and fresh `N_o` to every non-source bank. + +The resulting rows are exactly + +``` +U=P_e u, V=P_o(Nv-A_(r+1)), +b_r=N b_rraw, c_r=N delta C_r, +b1=N(b1raw+A_(r+1)), c_l=C_l-C_r (l>r). +``` + +The future-c calculation retains all cross terms: + +``` +(C_l-C_r)-v-N A_r + N b_r -[-v-N A_(r+1)] = C_l-C_r. +``` + +If `r=q`, stop this loop and SWAP the finished `b_r` into its public slot. +If another pair remains, perform the following scalar re-encoding BEFORE the +one retained odd-source continuation: + +``` +b1+=U; +c_l-=c_(r+1); c_l+=U for l>r+1; +SWAP(t,c_(r+1)); +t+=V; +N(V); [one actual arity-2 continuation] +SWAP(source b_r,c1). +``` + +Define + +``` +u_next=V, +v_next=-U-N A_(r+1). +``` + +Then `b1=N b1raw-v_next`, the next dirty `c_(r+1)` row is +`U=-v_next-N A_(r+1)`, the next `t` row is +`u_next+delta C_(r+1)`, and the held row is `N u_next`. +The future-c rows become `(C_l-C_(r+1))+U`, exactly the next invariant. +This proves the induction for every `q`; no fitted finite pattern is used. +The one-source continuation and all scalar re-encoding reads occur at their +actual shared fresh cut. Moving them elsewhere requires a new intertwiner. + +At the end, query `N(a)` once and subtract it from `b1`. Decode completed c +outputs triangularly by `c_r+=c_(r-1)` for `r=3,...,q`. These operations finish +`a,b1,...,bq,C2,...,Cq` as full independent native outputs. The two carrier rows +remain + +``` +U=P_(2q) u_(q-1), +V=P_(2q+1)(N v_(q-1)-a). +``` + +## Both the homogeneous defect and every public reader + +The base homogeneous dependence on the two original dirty inputs is + +``` +u1 = P3 N * (second row of J) + P3[(P1-2I)S+b1], +v1 = (first row of J) + (2N-NP1-P2N)S. +``` + +For each nonfinal pair the full affine recurrence is + +``` +u_next = P_o(N v-A), +v_next = -P_e u-N A, A=A_(r+1). +``` + +Consequently the homogeneous update is the invertible anti-diagonal matrix +`[[0,P_o N],[-P_e,0]]`. A terminal bank permutation aligns its two monomial +factors with the two rows of `J`. This is an explicit bank-rank-two defect; +it does not prove constant native cleanup. + +To include all readers, put `h=Nv`. The exact same recurrence becomes + +``` +u_next=P_o(h-A), +h_next=-N P_e u+A. +``` + +This form gives a literal inverse at the completed full-native cut: + +``` +h_next-=A; +N(h_next); +P_e^-1(h_next); [this register is now u] +P_o^-1(u_next); u_next+=A; [this register is now h] +SWAP the two carrier roles. +``` + +There is one native `N` call, two ADDRESS scans, the displayed completed-public +reader ADDs and one bank SWAP. No independent public-native query is hidden. +`A` is available at this cut because every public output is already complete. + +For clarity, the final physical prefix is `F_k` times the retarded carrier +rows, while its public rows are `E` times their inputs. Two leading common +queries on the carrier banks convert those rows to the completed `E` chart; +`E` commutes with every actual plane permutation. Invert the final factory +ADDRESS operations, restore its public `+a`, and run the inverse recurrence +above for pairs `q-1,...,2`. Then `P3^-1 u=y1` and `h=Nv1`. +The remaining original-input core has a shared two-carrier cleanup. In carrier +coordinates `(p,q)=(h,y1)`, its complete word is + +``` +p-=q; p+=b1; +Q2^-1(p); Q2^-1=N^-1 P2^-1 N +p-=S; +q+=p; q+=2S-b1; +P1^-1(q); +q-=S; q-=p; p+=q; +N^-1(p); N^-1(q). +``` + +The postponed `-P2 N S` and `-P1 S` reader contributions cancel immediately +after their corresponding shared operator exposure. This word therefore +retains all original public columns; it is not merely an inversion of `H`. +`Q2^-1` has actual native arity 4, with phase-complete monomial adapters. + +## Complete cost and precise scope + +The prefix has `k=2q+1` raw stages, `q-1` retained continuations, the two shared +input calls and the final common call. Thus + +``` +H2_prefix = n k + q+2, +m=4q+4=2n, public stock=m n=2n^2, +D_prefix=2q. +``` + +The complete reader tail has two leading native calls, `q-2` recurrence calls, +two final native exits and one arity-4 query: + +``` +H2_tail=q+2, H4_tail=1, tail mass=2q+8. +H2_total=n^2+2, H4_total=1, total mass=2n^2+8, +D_total=-8. +``` + +This is a complete constructive invoice. Legal wide batching may change +positive-exponent pressure but leaves this rank mass unchanged. No public +output, helper, idling field, source postcode, factory reader or native phase +is discarded. There are no initialized fields, extra private fields or +unrestored helpers in the complete word. The inverse is obtained by reversing +every elementary event with its literal inverse, including all bank swaps. + +For ordinary swaps, the two aligned homogeneous factory supports are exactly +`{5,9,13,...<=2q+1}` and `{3,7,11,...<=2q+1}`, of sizes `floor(q/2)` and +`ceil(q/2)`. This follows by substituting the homogeneous anti-diagonal update: +the new odd native plane enters the alternating factory and is distinct from +all earlier planes. In particular the support weight is `q`, not bounded. +The two direct `D_i^-1 N` arities sum to `2q+4`; the shared core adds 4. +This explains the displayed tariff, not a lower bound on all possible callers. + +The proven negative scope is the ordinary source-handoff family and this +explicit complete tail. It does not exclude changed held-coordinate encoders, +operator-valued bridges, source-hole relocation, changed delivery kernels, +nonmonomial factory charts, or a different joint terminal word. A retarded +operator `F^-1 M F` cannot be replaced by the physical monomial `M` in such a +proposal. Every changed input chart and right ADDRESS code must be retained. + +## Evidence and independent checks + +- `handoff_family.py` / `HANDOFF-FAMILY.json`: free noncommutative and actual + signed-plane all-column witnesses for q=2,3,4; both literal inverse orders. + Normal and Python `-O` replay both pass. The written invariant above is the + all-parameter proof, separate from these finite checks. +- `../q4-pauli-fusion/handoff_family_independent.py` / + `INDEPENDENT-HANDOFF-FAMILY.json`: independently reconstructed first-three + word and pair loop, opposite right-normal algebra, complete public-column + and literal reversed-event checks for q=2,3,4,5,6,8,12,16. Its paid-progress + intervals respect source/target reads, unary noncommutation and bank SWAPs. + The omitted raw-a repair is a rejected defect control. +- `../native-frames/handoff_family_tail.py` / `HANDOFF-FAMILY-TAIL.json`: + independently serialized full affine-reader tail, physical prefix replay, + complete endpoint and both inverse orders for q=2,3,4; all-q inverse recurrence + and exact ordinary factory-support proof. Omitting the final `a` reader fails. + +These are exact finite computations plus written all-parameter proofs with +actual all-f operator bindings. They are not formal-kernel proofs, joint BIT +admission, numerical-error theorems, stock-owner allocations, fixed-tape +realizations or verified multiplication-exponent claims. diff --git a/research/two-pivot-caller-readers/source/caller/HANDOFF-FAMILY.json b/research/two-pivot-caller-readers/source/caller/HANDOFF-FAMILY.json new file mode 100644 index 0000000000..e10151cab4 --- /dev/null +++ b/research/two-pivot-caller-readers/source/caller/HANDOFF-FAMILY.json @@ -0,0 +1,14912 @@ +{ + "all_pair_invariant": { + "continuations": "Only query3 and odd handoffs before the last pair: q-1 total.", + "entrance": "t=u+delta C_r; held=N*u; b1=N*b1raw-v; c_r=-v-N*A_r; c_l=(C_l-C_r)+c_r for l>r; A_r=a+sum_(l>=r)b_l", + "literal_cost": "k=2q+1, n=2q+2, m=4q+4, H2=n*k+q+2 (two input exposures and one final common query included), D_before_tail=2q.", + "next_pair_encoder": "b1+=U; later c_l-=next raw delta C and +=U; swap t with next c; t+=V; continue source N; u_next=V, v_next=-U-N*A_next", + "two_handoff_exit": "U=P_even*u; V=P_odd*(N*v-A_next); public b_r=N*b_rraw, c_r=N*delta C_r; b1=N*(b1raw+A_next)" + }, + "fixtures": [ + { + "D_before_tail": 4, + "H": [ + [ + [ + { + "coefficient": "-1", + "word": [ + "P4", + "P3", + "N" + ] + }, + { + "coefficient": "1", + "word": [ + "P4", + "P3", + "P1", + "N" + ] + } + ], + [ + { + "coefficient": "1", + "word": [ + "P4", + "P3", + "N" + ] + } + ] + ], + [ + [ + { + "coefficient": "-1", + "word": [ + "P5", + "N" + ] + }, + { + "coefficient": "1", + "word": [ + "P5", + "N", + "P2" + ] + }, + { + "coefficient": "1", + "word": [ + "P5", + "P1", + "N" + ] + } + ], + [ + { + "coefficient": "1", + "word": [ + "P5", + "N" + ] + }, + { + "coefficient": "-1", + "word": [ + "P5", + "N", + "P2" + ] + } + ] + ] + ], + "L": [ + [ + [ + { + "coefficient": "-2", + "word": [ + "P4", + "P3" + ] + }, + { + "coefficient": "1", + "word": [ + "P4", + "P3", + "P1" + ] + } + ], + [ + { + "coefficient": "-1", + "word": [ + "P4", + "P3" + ] + }, + { + "coefficient": "1", + "word": [ + "P4", + "P3", + "P1" + ] + } + ], + [ + { + "coefficient": "-2", + "word": [ + "P4", + "P3" + ] + }, + { + "coefficient": "1", + "word": [ + "P4", + "P3", + "P1" + ] + } + ], + [] + ], + [ + [ + { + "coefficient": "-3", + "word": [ + "P5" + ] + }, + { + "coefficient": "-1", + "word": [ + "P5", + "N", + "P2", + "N" + ] + }, + { + "coefficient": "1", + "word": [ + "P5", + "P1" + ] + } + ], + [ + { + "coefficient": "-2", + "word": [ + "P5" + ] + }, + { + "coefficient": "-1", + "word": [ + "P5", + "N", + "P2", + "N" + ] + }, + { + "coefficient": "1", + "word": [ + "P5", + "P1" + ] + } + ], + [ + { + "coefficient": "-2", + "word": [ + "P5" + ] + }, + { + "coefficient": "-1", + "word": [ + "P5", + "N", + "P2", + "N" + ] + }, + { + "coefficient": "1", + "word": [ + "P5", + "P1" + ] + } + ], + [] + ] + ], + "ambient_arity": 12, + "banks": 6, + "events": [ + { + "coefficient": "1", + "dst": 5, + "kind": "ADD", + "label": "raw c-basis", + "src": 3 + }, + { + "bank": 1, + "kind": "NATIVE", + "label": "shared input N exposure", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 0 + ], + "sign": 1 + } + }, + { + "coefficient": "1", + "dst": 2, + "kind": "ADD", + "label": "shared input fanout", + "src": 1 + }, + { + "bank": 1, + "kind": "NATIVE", + "label": "shared input N inverse", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 0 + ], + "sign": -1 + } + }, + { + "coefficient": "-1", + "dst": 5, + "kind": "ADD", + "label": "initial nested scalar bridge", + "src": 1 + }, + { + "coefficient": "1", + "dst": 0, + "kind": "ADD", + "label": "initial nested scalar bridge", + "src": 4 + }, + { + "coefficient": "-1", + "dst": 3, + "kind": "ADD", + "label": "initial nested scalar bridge", + "src": 1 + }, + { + "coefficient": "1", + "dst": 0, + "kind": "ADD", + "label": "initial nested scalar bridge", + "src": 2 + }, + { + "coefficient": "-1", + "dst": 2, + "kind": "ADD", + "label": "query1 scalar entrance", + "src": 0 + }, + { + "bank": 0, + "kind": "NATIVE", + "label": "query1 source common", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 0 + ], + "sign": 1 + } + }, + { + "coefficient": "1", + "dst": 1, + "kind": "ADD", + "label": "query1 delivery", + "src": 0 + }, + { + "bank": 0, + "kind": "ADDRESS_OR_UNIT", + "label": "query1 source swap", + "operator": { + "block_permutation": [ + 1, + 0, + 2, + 3, + 4, + 5 + ], + "native_arity": 0, + "native_blocks": [], + "sign": 1 + } + }, + { + "bank": 1, + "kind": "NATIVE", + "label": "query1 target fresh", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 1 + ], + "sign": 1 + } + }, + { + "bank": 2, + "kind": "NATIVE", + "label": "query1 inactive fresh progress", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 1 + ], + "sign": 1 + } + }, + { + "bank": 3, + "kind": "NATIVE", + "label": "query1 inactive fresh progress", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 1 + ], + "sign": 1 + } + }, + { + "bank": 4, + "kind": "NATIVE", + "label": "query1 inactive fresh progress", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 1 + ], + "sign": 1 + } + }, + { + "bank": 5, + "kind": "NATIVE", + "label": "query1 inactive fresh progress", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 1 + ], + "sign": 1 + } + }, + { + "coefficient": "1", + "dst": 2, + "kind": "ADD", + "label": "query1 scalar exit", + "src": 0 + }, + { + "coefficient": "-1", + "dst": 0, + "kind": "ADD", + "label": "initial nested scalar bridge", + "src": 2 + }, + { + "coefficient": "1", + "dst": 1, + "kind": "ADD", + "label": "initial nested scalar bridge", + "src": 3 + }, + { + "coefficient": "-1", + "dst": 3, + "kind": "ADD", + "label": "query2 scalar entrance", + "src": 1 + }, + { + "coefficient": "-1", + "dst": 5, + "kind": "ADD", + "label": "query2 scalar entrance", + "src": 1 + }, + { + "bank": 1, + "kind": "NATIVE", + "label": "query2 source common", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 0 + ], + "sign": 1 + } + }, + { + "coefficient": "1", + "dst": 2, + "kind": "ADD", + "label": "query2 delivery", + "src": 1 + }, + { + "bank": 1, + "kind": "ADDRESS_OR_UNIT", + "label": "query2 source swap", + "operator": { + "block_permutation": [ + 2, + 1, + 0, + 3, + 4, + 5 + ], + "native_arity": 0, + "native_blocks": [], + "sign": 1 + } + }, + { + "bank": 0, + "kind": "NATIVE", + "label": "query2 inactive fresh progress", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 2 + ], + "sign": 1 + } + }, + { + "bank": 2, + "kind": "NATIVE", + "label": "query2 target fresh", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 2 + ], + "sign": 1 + } + }, + { + "bank": 3, + "kind": "NATIVE", + "label": "query2 inactive fresh progress", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 2 + ], + "sign": 1 + } + }, + { + "bank": 4, + "kind": "NATIVE", + "label": "query2 inactive fresh progress", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 2 + ], + "sign": 1 + } + }, + { + "bank": 5, + "kind": "NATIVE", + "label": "query2 inactive fresh progress", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 2 + ], + "sign": 1 + } + }, + { + "coefficient": "1", + "dst": 3, + "kind": "ADD", + "label": "query2 scalar exit", + "src": 1 + }, + { + "coefficient": "1", + "dst": 5, + "kind": "ADD", + "label": "query2 scalar exit", + "src": 1 + }, + { + "coefficient": "-1", + "dst": 1, + "kind": "ADD", + "label": "initial nested scalar bridge", + "src": 3 + }, + { + "bank": 2, + "kind": "NATIVE", + "label": "query3 source common", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 0 + ], + "sign": 1 + } + }, + { + "coefficient": "1", + "dst": 5, + "kind": "ADD", + "label": "query3 source fanout", + "src": 2 + }, + { + "coefficient": "1", + "dst": 3, + "kind": "ADD", + "label": "query3 delivery", + "src": 2 + }, + { + "bank": 2, + "kind": "ADDRESS_OR_UNIT", + "label": "query3 source swap", + "operator": { + "block_permutation": [ + 3, + 1, + 2, + 0, + 4, + 5 + ], + "native_arity": 0, + "native_blocks": [], + "sign": 1 + } + }, + { + "bank": 0, + "kind": "NATIVE", + "label": "query3 inactive fresh progress", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 3 + ], + "sign": 1 + } + }, + { + "bank": 1, + "kind": "NATIVE", + "label": "query3 inactive fresh progress", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 3 + ], + "sign": 1 + } + }, + { + "bank": 3, + "kind": "NATIVE", + "label": "query3 target fresh", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 3 + ], + "sign": 1 + } + }, + { + "bank": 4, + "kind": "NATIVE", + "label": "query3 inactive fresh progress", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 3 + ], + "sign": 1 + } + }, + { + "bank": 5, + "kind": "NATIVE", + "label": "query3 inactive fresh progress", + "operator": { + "block_permutation": [ 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H and L have not been cleared or given the five-factory tail schema.", + "The complete invoice is not the optimistic two-continuation planning case: stages3,4,6 are all explicitly paid.", + "No source exposure sharing or three-stage public touch window is assumed.", + "The exact signed group algebra proves positive identities for every f; it is not a formal-kernel certificate." + ], + "mandatory_nondeferred_touches": { + "0": [ + 5, + 7, + 8, + 9, + 10, + 11, + 17, + 18, + 44, + 48, + 76, + 82, + 83, + 90, + 93, + 94, + 95, + 96, + 102 + ], + "1": [ + 1, + 2, + 3, + 4, + 6, + 10, + 19, + 20, + 21, + 22, + 23, + 24, + 30, + 31, + 32, + 45, + 46, + 49, + 50, + 51, + 52, + 53, + 54, + 55, + 61, + 62, + 63, + 64, + 65, + 77, + 78, + 80, + 81, + 82, + 83, + 84, + 90, + 91, + 92, + 95, + 102 + ], + "2": [ + 2, + 7, + 8, + 17, + 18, + 23, + 33, + 34, + 35, + 36, + 42, + 43, + 44, + 47, + 80, + 92, + 94 + ], + "3": [ + 0, + 6, + 19, + 20, + 30, + 32, + 35, + 45, + 46, + 47, + 52, + 61, + 66, + 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mode 100644 index 0000000000..9f5bfe890e --- /dev/null +++ b/research/two-pivot-caller-readers/source/caller/PIVOT-PLANE-PROBE.json @@ -0,0 +1,13 @@ +{ + "candidate_pairs": 729, + "dimension_failures": 0, + "native_invoice_if_admitted": "Same five raw carriers plus full global fresh progress; constant bank GL source changes only. Any N-dependent initial plane encoder and terminal correction remain paid/open.", + "scope": "Old n4 five-shear ideal topology only; arbitrary real source-retraction columns allowed at later queries. Source-code algebra, native encoder and actual correction are not inferred.", + "solutions": [], + "source_tail_alphabet": [ + -1, + 0, + 1 + ], + "status": "BOUNDED_EXACT_SOURCE_RETRACTION_SCREEN" +} diff --git a/research/two-pivot-caller-readers/source/caller/QUADRATIC-MODEL-REVIEW.json b/research/two-pivot-caller-readers/source/caller/QUADRATIC-MODEL-REVIEW.json new file mode 100644 index 0000000000..44a2952c45 --- /dev/null +++ b/research/two-pivot-caller-readers/source/caller/QUADRATIC-MODEL-REVIEW.json @@ -0,0 +1,46 @@ +{ + "compile_controls": { + "SCALE_scans_checked": 2, + "compiled_native_rank_mass": 19, + "complete_input_columns_f1_f2": 216, + "missing_alignment_negative_control": "REJECTED", + "one_coordinate_arity": 3, + "toy_banks": 3 + }, + "finite_core_controls": { + "complete_Walsh_rows": 512, + "complete_composition_points": 512, + "complete_polar_forms": 64, + "complete_transport_points": 512 + }, + "no_new_kappa": true, + "producer_sha256": "60f2035b5278b89eab13fd6f8a87b7018455da808ffc7a3acf33de1933e1209a", + "scope": [ + "Exact model and phase review; no bounded-search optimality claim.", + "For these X-character monomial tensor families, polar rank is exactly the physical Clifford B rank per coordinate.", + "The exact all-f closure is an algebraic tensor/phase argument; finite matrix tests are defect controls.", + "Every nonzero rank child still needs selected-native lowering, all-f adapters and contraction-cap splitting before supplier admission.", + "No source-read, precision, owner, COPY, finite-tape or joint BIT contract is supplied." + ], + "source_family_binding": { + "f_residues": [ + 1, + 2, + 3, + 4 + ], + "global_phase_negative_control": { + "correct_phase": 1, + "event_index": 2, + "f": 2, + "tensoring_the_global_i_phase": 2 + }, + "points_per_event": 140, + "source_path": "/Users/ross/git/math/.research-automation/runs/kappa-four-coordinate-20261019T0717Z/root-chronology/ENCODED-COMPLETE-Q3.json", + "source_sha256": "0c641bd3feeb6198dc36f1cb54020cc50991759de5f9f8d684a92d5180a9f2d2", + "unary_events": 82 + }, + "source_path": "/Users/ross/git/math/.research-automation/runs/kappa-four-coordinate-20261019T0717Z/root-chronology/quadratic_charts.py", + "source_sha256": "de2a36f6a6b567360c90477b58da44e2f1b618fd006d058ab1ea04e983952c3f", + "status": "PASS_SCOPED_INDEPENDENT_QUADRATIC_CHART_MODEL_REVIEW" +} diff --git a/research/two-pivot-caller-readers/source/caller/balanced_physical_replay.py b/research/two-pivot-caller-readers/source/caller/balanced_physical_replay.py new file mode 100644 index 0000000000..63ce911ced --- /dev/null +++ b/research/two-pivot-caller-readers/source/caller/balanced_physical_replay.py @@ -0,0 +1,131 @@ +#!/usr/bin/env python3 +"""Fast exact physical replay of the separate balanced eight-bank trial. + +The complete literal source circuits are converted independently into exact +X-character monomials, retaining their once-per-field Gaussian phases. +Apache-2.0; substantial OpenAI Codex assistance. +""" +from pathlib import Path +from fractions import Fraction as F +import argparse, copy, hashlib, importlib.util, json, sys +sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent +ROOT=HERE.parent/'root-chronology' +from encoded_physical import produce as prefix_source +from quadratic_model_review import qc, literal_x_action + +def need(ok,msg): + if not ok:raise ValueError(msg) + +def bridge(left,right,middle,label): + return [{'kind':'ADD','dst':left,'src':right,'coefficient':'1','label':label+' Hinv sum'}, + {'kind':'SCALE','bank':right,'coefficient':'-2','label':label+' Hinv difference scale'}, + {'kind':'ADD','dst':right,'src':left,'coefficient':'1','label':label+' Hinv difference'}, + {'kind':'SCALE','bank':left,'coefficient':'1/2','label':label+' Hinv left half'}, + {'kind':'SCALE','bank':right,'coefficient':'1/2','label':label+' Hinv right half'},middle, + {'kind':'ADD','dst':left,'src':right,'coefficient':'1','label':label+' H sum'}, + {'kind':'SCALE','bank':right,'coefficient':'-2','label':label+' H difference scale'}, + {'kind':'ADD','dst':right,'src':left,'coefficient':'1','label':label+' H difference'}] + +def bind(e,n): + if e['kind']in('ADD','SCALE','BANK_SWAP'):return + op=e.get('exact_operator',e.get('operator')) + circuit=op.get('one_coordinate_literal_circuit',op.get('one_bit_circuit')) + need(circuit is not None,'every balanced unary retains a complete literal circuit') + off,basec=literal_x_action(circuit,n,0) + cols=[literal_x_action(circuit,n,1<>i)&1)<>j&1 else 0)for j in range(model.n)] + R=ce.perm(model.n,rows) + addition=[{'kind':'ADD','dst':1,'src':4,'coefficient':'-1','label':'changed cut5 U-=V'}, + {'kind':'ADDRESS_LINEAR','bank':4,'operator':{'address_rows':rows,'native_arity':0},'label':'changed cut5 partial-plane reflection R'}, + {'kind':'ADD','dst':1,'src':4,'coefficient':'1','label':'changed cut5 U+=V'}] + where=next(i for i,e in enumerate(base)if e['label']=='query5 retain other carrier in b accumulator') + need(all('query5'not in e['label']or e['kind']!='NATIVE' or 'continuation'not in e['label']for e in base[:where]), + 'encoded bridge precedes the continuation') + events=copy.deepcopy(base[:where]+addition+base[where:]) + need(events[:where]+events[where+3:]==base,'removing the three declared free events recovers exact baseline trace') + for index,e in enumerate(events): + e['event_index']=index + if e['kind'] in('ADD','BANK_SWAP'):continue + if e['kind']=='ADDRESS_LINEAR':op=R;exponent=0;global_sign=1 + else: + data=e['operator'];global_sign=data['sign'];exponent=len(data['native_blocks']);op=model.I + for j in data['native_blocks']:op=mul(op,model.N if j==0 else model.T[j-1]) + p=data['block_permutation'];rr=[] + for out in range(k+1): + inp=p.index(out) + rr.extend((1<<(2*inp),1<<(2*inp+1))) + # The event's p maps input plane to output plane; perm uses rows. + op=mul(op,ce.perm(model.n,rr)) + e['exact_operator']={'one_coordinate_tableau':[list(x)for x in op.tab], + 'one_coordinate_literal_circuit':op.circuit, + 'tensor_lift':'global_sign * i^(phase_exponent*(1-f)) * op_1^(tensor f)', + 'global_sign':global_sign,'phase_exponent':exponent, + 'f1_native_arity':ce.rank(x for x,z,p in op.tab[model.n:])} + need(e['exact_operator']['f1_native_arity']==e['operator']['native_arity'],'serialized physical operator rank') + source=HERE/'ENCODED-STAGE.json' + need(json.loads(source.read_text())['status']=='PASS_NATIVE_ZERO_ENCODED_STAGE_ALL_COLUMNS_ALL_F','exact source matrix proof exists') + return {'status':'PASS_FULL_PHYSICAL_ENCODED_PREFIX_EVENT_INTERFACE', + 'scientific_pin':'20ecf2891d80b5acf18d980b2164fb44ea7faa90', + 'banks':n,'query_stages':k,'ambient_arity':16,'events':events, + 'native_histogram':{'2':61},'rank_mass':122,'stock_if_carriers_finish':128,'D_before_tail':6, + 'changed_cut':{'after_stage':5,'before_event':base[where]['label'],'banks':[1,4], + 'actual_word':['ADD1-=4','ADDRESS R on4','ADD1+=4'], + 'R_rows':rows,'retarded_word':'N^-1 R N onbank4 between the two ADDs', + 'phase':'R is plain ADDRESS for support3p/1q; no Gaussian phase is dropped'}, + 'covered_binding':'The original full physical source/fresh trace is pinned by HANDOFF-FAMILY; the only new three events have exactly the cut intertwiner verified in ENCODED-STAGE. The all-f public matrix and full literal inverse are proved there. This file emits actual event operators for independent full replay and retiming.', + 'limits':['This prefix has no cleanup included.','No retiming, extra child fusion or tail saving is claimed.','Any complete trace must include the actual native lowering of the encoded inverse stage and every public reader.'], + 'source_pins':[{'path':str(p),'sha256':hashlib.sha256(p.read_bytes()).hexdigest()}for p in(HERE/'handoff_family.py',HERE/'HANDOFF-FAMILY.json',HERE/'encoded_stage.py',source,HERE.parent/'native-frames'/'native_model.py')], + 'no_new_kappa':True} + + +def main(): + ap=argparse.ArgumentParser(description=__doc__);ap.add_argument('--write',action='store_true');args=ap.parse_args() + out=produce();out['producer_sha256']=hashlib.sha256(Path(__file__).read_bytes()).hexdigest();out=json.loads(json.dumps(out));p=HERE/'ENCODED-PHYSICAL-PREFIX.json' + if args.write:p.write_text(json.dumps(out,indent=2,sort_keys=True)+'\n') + else:need(json.loads(p.read_text())==out,'saved physical encoded trace differs') + print(out['status']) +if __name__=='__main__':main() diff --git a/research/two-pivot-caller-readers/source/caller/encoded_stage.py b/research/two-pivot-caller-readers/source/caller/encoded_stage.py new file mode 100644 index 0000000000..b78671dcda --- /dev/null +++ b/research/two-pivot-caller-readers/source/caller/encoded_stage.py @@ -0,0 +1,151 @@ +#!/usr/bin/env python3 +"""One genuine partial-plane encoded stage in the all-pair caller. + +The actual native-zero bridge mixes both dirty carrier banks. Its retarded +operator is N^-1 R N, not the physical ADDRESS R. No terminal tariff is +asserted. Exact tensor/phase-polynomial algebra covers every f>=1. +Apache-2.0; substantial OpenAI Codex assistance. +""" +from pathlib import Path +from fractions import Fraction +import argparse,hashlib,json,sys +sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent +NATIVE=HERE.parent/'native-frames' +sys.path.insert(0,str(NATIVE)) +import lifted_algebra as L +from native_model import ce,mul,need +from nested_prefix import skeleton +from nested_family import retraction + + +def build(q=3,encode=True,wrong_chart=False,encoder='triangular'): + need(q>=3,'one nonfinal handoff is required') + a=L.Algebra(2*q+1);n=2*q+2 + one,N=a.one,a.N;M=a.mat_identity(n);Mi=a.mat_identity(n);events=[];s=0 + def app(B,Bi,event): + nonlocal M,Mi + M=a.mat_product(B,M);Mi=a.mat_product(Mi,Bi);events.append(event) + def add(d,src,c,label): + if not c:return + B=a.mat_identity(n);Bi=a.mat_identity(n) + B[d][src]=a.add(B[d][src],a.scale(c,1));Bi[d][src]=a.add(Bi[d][src],a.scale(c,-1)) + app(B,Bi,{'op':'ADD','dst':d,'src':src,'label':label}) + def scalar(d,src,c,label):add(d,src,a.scale(one,c),label) + def unary(bank,op,label):app(a.diagonal(n,bank,op),a.diagonal(n,bank,a.adjoint(op)),{'op':'UNARY','bank':bank,'label':label}) + def swap(i,j,label): + B=a.mat_identity(n);B[i],B[j]=B[j],B[i];app(B,B,{'op':'SWAP','banks':[i,j],'label':label}) + def ec(z):return a.add(a.scale(one,z[0]),a.scale(N,z[1])) + # Partial-plane source normalizer, bitwise in every tensor coordinate. + # Typed D^-1 P_A D phases cancel for this 3p/1q support. + v=sum(1<>j&1 else 0)for j in range(a.m)] + physicalR=ce.perm(a.m,rows);R=a.lift(physicalR) + old=a.product(a.product(N,a.T[0]),a.T[1]) + need(a.product(R,R)==one,'actual reflection involution every f') + need(a.product(R,old)==a.product(old,R),'actual full-three-plane commutation every f') + logicalR=R if wrong_chart else a.product(a.product(a.adjoint(N),R),N) + retarded_actual=mul(a.model.prefix(5).adjoint(),physicalR,a.model.prefix(5)) + if not wrong_chart:need(a.lift(retarded_actual)==logicalR,'physical cut5 to literal retarded source chart') + for r in range(2,q+1):scalar(2*r+1,3,1,'raw c-basis') + _,ops=skeleton(q,[1]+[0]*(q-1)) + for typ,d,src,z in ops: + if typ=='a':add(d,src,ec(z),'initial nested bridge') + elif typ=='s':swap(d,src,'initial nested bank permutation') + else: + s+=1;u=retraction(q,s) + if s==4: + for j,(aa,bb)in enumerate(u): + if j!=src:scalar(j,src,-aa,'query4 scalar entrance') + break + for j,z in enumerate(u): + if j!=src:add(j,src,a.scale(ec(z),-1),f'query{s} retraction entrance') + add(d,src,N,f'query{s} target cross') + P=a.P[s-1];P=a.product(N,P)if s==3 else P + unary(src,P,f'query{s} retained source code') + for j,z in enumerate(u): + if j!=src:add(j,src,ec(z),f'query{s} retraction exit') + for r in range(3,q+1):scalar(0,2*r,-1,'restore raw a') + scalar(3,0,-1,'held source subtract raw a') + for r in range(2,q+1):scalar(3,2*r,-1,'held source subtract future raw b') + for r in range(2,q+1): + e,o,b,c=2*r,2*r+1,2*r,2*r+1 + unary(1,N,f'query{e} source common');scalar(1,3,-1,'isolate c difference');swap(1,3,'even handoff') + unary(1,a.product(a.P[e-1],a.adjoint(N)),'even retarded source post');swap(3,c,'finished c move') + unary(b,N,f'query{o} source common') + for ell in range(r+1,q+1):scalar(2*ell+1,b,1,'future c first fanout') + scalar(3,b,1,'odd delivery');swap(b,3,'odd handoff');scalar(2,b,-1,'b accumulator') + for ell in range(r+1,q+1):scalar(2*ell+1,b,-1,'future raw c restoration') + unary(b,a.product(a.P[o-1],a.adjoint(N)),'odd retarded source post') + if r=2,'handoff family starts with two new pairs') + n,k=2*q+2,2*q+1 + A=Algebra(k+1)if physical else None + I=A.I if physical else F.I + Z=A.Z if physical else F.Z + eye=A.eye if physical else F.eye + mm=A.mm if physical else F.mm + inv=A.inv if physical else F.inv + es=A.es if physical else F.es + mul=A.mul if physical else F.mul + N=A.n(0)if physical else F.N + M=eye(n);Mi=eye(n);events=[];stage=0 + def app(B,Bi,e): + nonlocal M,Mi + F.need(mm(B,Bi)==mm(Bi,B)==eye(n),'every literal event has its full inverse') + M=mm(B,M);Mi=mm(Mi,Bi);events.append(e) + def add(d,s,c,label): + if not c:return + op=A.mono(coefficient=c)if physical else F.mono((),c) + nop=A.mono(coefficient=-c)if physical else F.mono((),-c) + app(es(n,d,s,op),es(n,d,s,nop),{'kind':'ADD','dst':d,'src':s,'coefficient':str(c),'label':label}) + def opadd(d,s,c,label): + F.need(not physical,'operator ADD belongs only to the retarded formal proof') + app(es(n,d,s,c),es(n,d,s,F.neg(c)),{'kind':'FORMAL_ADD','dst':d,'src':s,'label':label}) + def unary(b,g,label,native=False): + B=eye(n);Bi=eye(n);B[b][b]=g;Bi[b][b]=inv(g) + if physical: + ((bits,p),c),=g.items() + op={'sign':int(c),'native_blocks':[j for j in range(k+1)if bits>>j&1], + 'block_permutation':list(p),'native_arity':A.native_arity(g)} + e={'kind':'NATIVE'if native else'ADDRESS_OR_UNIT','bank':b,'operator':op,'label':label} + else:e={'kind':'FORMAL_UNARY','bank':b,'operator':F.serial(g),'label':label} + app(B,Bi,e) + def swap(b,c,label): + B=eye(n);B[b],B[c]=B[c],B[b] + app(B,B,{'kind':'BANK_SWAP','banks':[b,c],'label':label}) + def progress(src,s,dst=None): + if physical: + for b in range(n): + if b!=src:unary(b,A.n(s),f'query{s} target fresh'if b==dst else f'query{s} inactive fresh progress',True) + # Initial direct prefix through the scalar entrance of query4. Its + # three source retractions are the independently pinned direct ones. + for r in range(2,q+1):add(2*r+1,3,1,'raw c-basis') + if physical: + unary(1,N,'shared input N exposure',True);add(2,1,1,'shared input fanout');unary(1,inv(N),'shared input N inverse',True) + _,ops=skeleton(q,[1]+[0]*(q-1)) + for typ,d,s,z in ops: + if typ=='a': + if physical: + if z[1]: + F.need(stage==0 and d==2 and s==1 and z[1]==1,'shared input is the only early N ADD') + else:add(d,s,z[0],'initial nested scalar bridge') + else:opadd(d,s,ec(z),'initial nested bridge') + elif typ=='s':swap(d,s,'initial nested permutation') + else: + stage+=1;u=retraction(q,stage) + if stage==4: + for b,(aa,bb)in enumerate(u): + if b!=s:add(b,s,-aa,'query4 scalar source entrance') + break + if physical: + for b,(aa,bb)in enumerate(u): + if b!=s:add(b,s,-aa,f'query{stage} scalar entrance') + unary(s,N,f'query{stage} source common',True) + for b,(aa,bb)in enumerate(u): + if b!=s:add(b,s,-bb,f'query{stage} source fanout') + add(d,s,1,f'query{stage} delivery') + unary(s,A.swap(0,stage),f'query{stage} source swap') + progress(s,stage,d) + if stage==3: + for b,(aa,bb)in enumerate(u): + if b!=s:add(b,s,-bb,'query3 pre-continuation fanout') + unary(s,N,'query3 retained source continuation',True) + for b,(aa,bb)in enumerate(u): + if b!=s:add(b,s,aa,f'query{stage} scalar exit') + else: + for b,z in enumerate(u): + if b!=s:opadd(b,s,F.neg(ec(z)),f'query{stage} source entrance') + P=F.mono((stage,));P=F.mul(N,P)if stage==3 else P + opadd(d,s,N,f'query{stage} cross');unary(s,P,f'query{stage} source code') + for b,z in enumerate(u): + if b!=s:opadd(b,s,ec(z),f'query{stage} source exit') + # The deeper response entrances left future raw b fields on a. + # Remove them before using a as the independent raw public input. + for r in range(3,q+1):add(0,2*r,-1,'restore raw a from deeper response entrance') + # Hold N*u without the raw A_r part. All its input fields are kept. + add(3,0,-1,'held source subtract raw a') + for r in range(2,q+1):add(3,2*r,-1,'held source subtract future raw b') + for r in range(2,q+1): + even,odd=2*r,2*r+1;b=2*r;c=2*r+1 + unary(1,N,f'query{even} source common',physical) + add(1,3,-1,f'query{even} isolate raw c difference') + swap(1,3,f'query{even} source handoff') + if physical:unary(1,A.swap(0,even),f'query{even} source swap') + else:unary(1,F.prod(F.mono((even,)),inv(N)),f'query{even} retarded source post') + progress(1,even,3) + swap(3,c,f'query{even} move finished c difference') + unary(b,N,f'query{odd} source common',physical) + for ell in range(r+1,q+1):add(2*ell+1,b,1,f'query{odd} future c first fanout') + add(3,b,1,f'query{odd} delivery') + swap(b,3,f'query{odd} source handoff') + add(2,b,-1,f'query{odd} finish current b accumulator') + for ell in range(r+1,q+1):add(2*ell+1,b,-1,f'query{odd} restore future raw c differences') + if physical:unary(b,A.swap(0,odd),f'query{odd} source swap') + else:unary(b,F.prod(F.mono((odd,)),inv(N)),f'query{odd} retarded source post') + progress(b,odd,3) + if rr; A_r=a+sum_(l>=r)b_l', + 'two_handoff_exit':'U=P_even*u; V=P_odd*(N*v-A_next); public b_r=N*b_rraw, c_r=N*delta C_r; b1=N*(b1raw+A_next)', + 'next_pair_encoder':'b1+=U; later c_l-=next raw delta C and +=U; swap t with next c; t+=V; continue source N; u_next=V, v_next=-U-N*A_next', + 'continuations':'Only query3 and odd handoffs before the last pair: q-1 total.', + 'literal_cost':'k=2q+1, n=2q+2, m=4q+4, H2=n*k+q+2 (two input exposures and one final common query included), D_before_tail=2q.'}, + 'limits':['Two raw terminal carriers retain every source swap and every public reader. Their cleanup is not included.', + 'The native cost or moment of the terminal carrier factories is not asserted bounded.', + 'The finite all-column checks q2..4 are separate from the written all-pair invariant and are not a formal-kernel proof.'], + 'source_pins':[{'path':str(HERE/p),'sha256':hashlib.sha256((HERE/p).read_bytes()).hexdigest()}for p in('nested_family.py','nested_prefix.py','free_ops.py','plane_group.py')], + 'no_new_kappa':True} + + +def main(): + ap=argparse.ArgumentParser(description=__doc__);ap.add_argument('--write',action='store_true');args=ap.parse_args() + out=prove();out['producer_sha256']=hashlib.sha256(Path(__file__).read_bytes()).hexdigest();out=json.loads(json.dumps(out));p=HERE/'HANDOFF-FAMILY.json' + if args.write:p.write_text(json.dumps(out,indent=2,sort_keys=True)+'\n') + else:F.need(json.loads(p.read_text())==out,'saved handoff family receipt differs') + print(out['status']) +if __name__=='__main__':main() diff --git a/research/two-pivot-caller-readers/source/caller/nested_family.py b/research/two-pivot-caller-readers/source/caller/nested_family.py new file mode 100644 index 0000000000..76e5827c61 --- /dev/null +++ b/research/two-pivot-caller-readers/source/caller/nested_family.py @@ -0,0 +1,181 @@ +#!/usr/bin/env python3 +"""Explicit nested source-retraction family and its one-coordinate cocycle. + +The native implementation still pays 2q-1 continuations. Algebraic +telescoping alone is not permission to remove these queries. +Apache-2.0; substantial OpenAI Codex assistance. +""" +from pathlib import Path +import argparse +import hashlib +import json +import sys +sys.dont_write_bytecode=True +from fractions import Fraction +import free_ops as F +from nested_prefix import skeleton, prefixes, Z, I, N, add, neg, mul, mm + +HERE=Path(__file__).resolve().parent + + +def ec(z):return F.add(F.mono((),z[0]),F.mono((0,),z[1])) + + +def retraction(q,s): + n=2*q+2;u=[Z]*n + if s==1: + u[0]=I;u[2]=I + elif s==2: + u[1]=I + for r in range(1,q+1):u[2*r+1]=I + elif s==2*q+2: + u[1]=I;u[0]=N;u[2]=neg(I) + elif s==2*q+3: + u[0]=I;u[2]=N + elif s%2: + r=(s-1)//2;u[2*r]=I + for j in range(1,r):u[2*j+1]=I + for j in range(r+1,q+1):u[2*j+1]=neg(N) + else: + r=(s-2)//2;u[1]=I;u[2*(r+1)]=N + for j in range(1,r+1):u[2*j+1]=N + for j in range(r+1,q+1):u[2*j+1]=I + return u + + +def coordinates(q,s): + if s==1:return(neg(N),neg(N)),(N,Z) + if s==2:return(neg(I),Z),(neg(I),I) + if s==2*q+2:return(I,Z),(I,Z) + if s==2*q+3:return(neg(N),Z),(N,Z) + if s%2:return(Z,neg(N)),(Z,N) + return(Z,I),(Z,I) + + +def continued(q,s): + return (3<=s<=2*q and s!=2)or s==2*q+2 + + +def formal(q): + n,ops=skeleton(q,[1]+[0]*(q-1));M=F.eye(n);Mi=F.eye(n);s=0;sources=[] + def app(A,Ai): + nonlocal M,Mi + F.need(F.mm(A,Ai)==F.mm(Ai,A)==F.eye(n),'each event has its full inverse') + M=F.mm(A,M);Mi=F.mm(Mi,Ai) + def a(d,src,c):app(F.es(n,d,src,c),F.es(n,d,src,F.neg(c))) + for r in range(2,q+1):a(2*r+1,3,F.I) + for typ,d,src,z in ops: + if typ=='a':a(d,src,ec(z)) + elif typ=='s': + B=F.eye(n);B[d],B[src]=B[src],B[d];app(B,B) + else: + s+=1;u=retraction(q,s) + F.need(u[src]==I,'source normalization') + for j,z in enumerate(u): + if j!=src and z!=Z:a(j,src,F.neg(ec(z))) + P=F.mono((s,));P=F.mul(F.N,P)if continued(q,s)else P + A=F.mm(F.unary(n,src,P),F.es(n,d,src,F.N)) + Ai=F.mm(F.es(n,d,src,F.neg(F.N)),F.unary(n,src,F.inv(P))) + app(A,Ai) + for j,z in enumerate(u): + if j!=src and z!=Z:a(j,src,ec(z)) + sources.append({'stage':s,'src':src,'dst':d,'u':[[str(a),str(b)]for a,b in u], + 'source_code':('N P'if continued(q,s)else'P')+str(s)}) + for r in range(2,q+1):a(2*r+1,3,F.neg(F.I)) + F.need(F.mm(M,Mi)==F.mm(Mi,M)==F.eye(n),'all-column literal inverse in both orders') + public=[i for i in range(n)if i not in(1,3)] + F.need(all(M[i]==[F.N if j==i else F.Z for j in range(n)]for i in public), + 'all n-2 public outputs are exactly N times independent inputs') + H=[[M[i][j]for j in(1,3)]for i in(1,3)];L=[[M[i][j]for j in public]for i in(1,3)] + P={j:F.mono((j,))for j in range(1,2*q+4)} + A3=F.prod(*(P[j]for j in range(2*q+1,2,-1))) + if(q-1)%2:A3=F.neg(A3) + Q1=F.prod(F.inv(F.N),P[1],F.N) + J=[[F.add(F.add(P[2],Q1),F.neg(F.I)),F.add(F.I,F.neg(P[2]))], + [F.add(Q1,F.neg(F.I)),F.I]] + D=[[F.neg(F.mul(P[2*q+3],P[2*q+2])),F.Z],[F.Z,F.mul(A3,F.N)]] + F.need(H==F.mm(D,J),'five-factory H factor for the explicit family') + # Independently rebuild H using only the two-dimensional source-coordinate updates. + B=F.eye(2) + for s in range(1,2*q+4): + w,r=coordinates(q,s);w=list(map(ec,w));r=list(map(ec,r)) + Ptilde=F.mul(F.N,P[s])if continued(q,s)else P[s] + T=[[F.add(F.I if i==j else F.Z,F.prod(w[i],F.add(Ptilde,F.neg(F.I)),r[j]))for j in range(2)]for i in range(2)] + B=F.mm(T,B) + F.need(H==[[F.mul(F.N,x)for x in row]for row in B], + 'two-coordinate update proof independently reconstructs H') + return {'q':q,'banks':n,'raw_calls':2*q+3,'public_rows':public,'pivot_rows':[1,3], + 'source_retractions':sources,'complete_matrix':F.sm(M),'complete_inverse':F.sm(Mi), + 'H':F.sm(H),'L':F.sm(L),'D':F.sm(D),'J':F.sm(J),'A3':F.serial(A3), + 'continuations':[s for s in range(1,2*q+4)if continued(q,s)], + 'separate_progress_profile':{'H2':n*(2*q+3)+2*q+1,'ambient':4*q+8, + 'rank_deficit_before_tail':2}} + + +def prefix_coordinates(q): + n=2*q+2;_,pre=prefixes(q,[1]+[0]*(q-1)) + V=[[I if i==1 else Z,I if i>=3 and i%2 else Z]for i in range(n)] + for s,(M,src,dst)in enumerate(pre,1): + B=mm(M,V);w,r=coordinates(q,s) + F.need([add(mul(row[0],w[0]),mul(row[1],w[1]))for row in B]==retraction(q,s), + 'displayed normalized source column lies in the transported fixed plane') + F.need(tuple(B[src])==r,'displayed source functional on both pivot coordinates') + + +def cocycle(): + # Columns(z,A,c,d,b) are independent fields. Po and Pe do not commute. + ZR=[F.I,F.Z,F.Z,F.Z,F.Z];AR=[F.Z,F.I,F.Z,F.Z,F.Z] + CR=[F.Z,F.Z,F.I,F.Z,F.Z];DR=[F.Z,F.Z,F.Z,F.I,F.Z];BR=[F.Z,F.Z,F.Z,F.Z,F.I] + def plus(*rows):return[F.summ(row[j]for row in rows)for j in range(5)] + def left(a,row):return[F.mul(a,x)for x in row] + Po,Pe=F.mono((1,)),F.mono((2,)) + y=plus(left(F.N,ZR),left(F.neg(F.I),AR),left(F.N,CR)) + fodd=plus(left(F.neg(F.I),AR),left(F.N,CR)) + zodd=plus(left(F.mul(Po,F.N),ZR),left(F.add(Po,F.N),fodd)) + even_source=plus(zodd,left(F.N,AR),DR) + F.need(even_source==plus(left(Po,y),DR,left(F.neg(F.I),CR)), + 'next source is the old source through one ADDRESS plus the raw c difference') + feven=plus(left(F.N,AR),DR) + zeven=plus(left(F.mul(F.N,Pe),zodd),left(F.add(F.mul(F.N,Pe),F.neg(F.I)),feven)) + ynext=plus(left(F.N,zeven),left(F.N,DR),left(F.neg(F.I),AR),BR) + rhs=plus(left(F.neg(F.mul(Pe,Po)),y),BR,left(Pe,CR),left(F.neg(Pe),DR)) + F.need(ynext==rhs,'middle two-call affine ADDRESS cocycle on every independent public/pivot column') + return {'source_y':'y_r=N z-A_r+N c_r, A_r=a+sum_(l>r)b_l; c1 means zero public reader', + 'next_even_source':'P_o y_r+c_(r+1)-c_r', + 'next_y':'-P_e P_o y_r+b_(r+1)+P_e(c_r-c_(r+1))', + 'independent_columns':['z','A_r','c_r','c_(r+1)','b_(r+1)'], + 'covered_domain':'Arbitrary independent invertible noncommuting Po,Pe; N^2=-I; literal affine operator identity.', + 'not_native_admission':'The virtual coordinate is a literal source at the odd cut. Holding its chart through the even cut still requires an explicit invertible bank encoder, all public readers at actual frames, and restoration of the other independent dirty field.'} + + +def prove(): + for q in range(1,9):prefix_coordinates(q) + fixtures=[formal(q)for q in(1,2,3,4)] + from nested_six import formal_word + M,Mi,_,_,_=formal_word() + F.need(fixtures[1]['complete_matrix']==F.sm(M)and fixtures[1]['complete_inverse']==F.sm(Mi), + 'q2 direct family agrees exactly with independently compiled NESTED-SIX') + return {'status':'PASS_EXPLICIT_NESTED_SOURCE_FAMILY_AND_ONE_COORDINATE_AFFINE_COCYCLE', + 'scientific_pin':'20ecf2891d80b5acf18d980b2164fb44ea7faa90','fixtures':fixtures,'affine_cocycle':cocycle(), + 'all_parameter_proof':'The ideal nested response skeleton gives N on every field after its output isolation. Its two transported pivot columns obey the displayed source-functional/retraction table. Conjugated source-code insertions therefore act by 2x2 updates I+w(Ptilde-I)r. The first two updates multiply to J(P2,Q1); all middle updates are on only the second coordinate and telescope to Ad_(N^-1)(A3), A3=(-1)^(q-1)P_(2q+1)...P3; the last two updates give the first diagonal factor. Left multiplication by the ideal final N yields H=diag(-P_last P_penult,A3 N)J. No source code or public coupling is discarded.', + 'initial_basis':'At raw ZERO, c_r+=c1 for r>=2. One common N/N^-1 exposure fanouts b1+=N*t only. The inverse c-basis is applied after the last query; its other public rows are retained.', + 'finite_checks':'Every free-operator matrix column and both inverse orders for q1..4. Exact transported-plane/source-functional table for q1..8. q2 entire matrix agrees with NESTED-SIX.', + 'native_invoice':'With the current literal compiler c=2q-1 retained N continuations, two shared input N calls and all separate fresh progress: H2=(2q+2)(2q+3)+2q+1, m=4q+8, n=2q+2, D_before_tail=2. Wide batching changes moment pressure, not this mass. No amortized query removal is asserted.', + 'limits':['H has a bounded five-factory form, but the complete L readers and their native cuts remain part of the contract.', + 'The affine ADDRESS cocycle is an algebraic grouping target, not an implemented shared-native controller.', + 'The finite checks and written all-parameter recurrence are not a formal-kernel proof.'], + 'source_pins':[{'path':str(HERE/p),'sha256':hashlib.sha256((HERE/p).read_bytes()).hexdigest()} + for p in('nested_prefix.py','nested_six.py','NESTED-SIX.json','free_ops.py')], + 'no_new_kappa':True} + + +def main(): + ap=argparse.ArgumentParser(description=__doc__);ap.add_argument('--write',action='store_true');args=ap.parse_args() + out=prove();out['producer_sha256']=hashlib.sha256(Path(__file__).read_bytes()).hexdigest();path=HERE/'NESTED-FAMILY.json' + out=json.loads(json.dumps(out)) + if args.write:path.write_text(json.dumps(out,indent=2,sort_keys=True)+'\n') + else:F.need(json.loads(path.read_text())==out,'saved nested-family receipt differs') + print(out['status']) + + +if __name__=='__main__':main() diff --git a/research/two-pivot-caller-readers/source/caller/nested_prefix.py b/research/two-pivot-caller-readers/source/caller/nested_prefix.py new file mode 100644 index 0000000000..d7e424e224 --- /dev/null +++ b/research/two-pivot-caller-readers/source/caller/nested_prefix.py @@ -0,0 +1,113 @@ +"""Exact ideal prefixes for nested three-response replacements. + +This is a construction helper, not a native admission or a receipt. +Apache-2.0; substantial OpenAI Codex assistance. +""" +from fractions import Fraction as F +from itertools import combinations +from pivot_plane_probe import Z, I, N, add, neg, mul, inv, eye, mm, es, null, summ + + +def skeleton(q, betas=None): + n = 2*q+2 + out = [] + def a(d,s,c=I): out.append(('a',d,s,c)) + def query(d,s,depth): + if depth == 0: + out.append(('q',d,s,N)) + return + b,c = 2*depth, 2*depth+1 + a(c,d,neg(I));a(s,b) + query(d,s,depth-1) + a(s,b,neg(I));a(d,c) + out.append(('q',b,d,N)) + a(d,c,neg(I)) + out.append(('q',c,b,N)) + a(b,s);a(c,d);a(d,c,neg(I)) + out.append(('s',b,c,I)) + # All independent incoming b fields use the same paid input exposure. + betas=[F(1)]*q if betas is None else list(map(F,betas)) + for j in range(1,q+1):a(2*j,1,(F(0),betas[j-1])) + query(1,0,q) + out.append(('q',0,1,N));out.append(('q',1,0,N)) + out.append(('s',0,1,I)) + for j in range(1,q+1):a(2*j,1,(F(0),-betas[j-1])) + return n,out + + +def prefixes(q,betas=None): + n,ops=skeleton(q,betas) + M=eye(n);out=[] + for typ,d,s,c in ops: + if typ=='s': + M=[list(row) for row in M] + M[d],M[s]=M[s],M[d] + else: + M=mm(es(n,d,s,c),M) + if typ=='q':out.append((M,s,d)) + target=[[N if i==j else Z for j in range(n)]for i in range(n)] + if M!=target:raise ValueError('nested ideal skeleton not full N') + return ops,out + + +def rref_null(A): + return null(A) + + +def source_choice(B,src,prefer_real=True): + """Choose E-column coefficients with source1, minimizing N-row support. + + B has two E-columns. The search is only the finitely many possible + active constraints of its at-most-two-dimensional affine solution. + """ + n=len(B) + # c_j=a_j+N*b_j. Source normalization is exact (real1,N0). + realrows=[];imagrows=[] + for row in B: + realrows.append([z for x in row for z in (x[0],-x[1])]) + imagrows.append([z for x in row for z in (x[1],x[0])]) + def solve(A,b): + m=len(A);k=4;A=[list(row)+[rhs]for row,rhs in zip(A,b)];r=0;p=[] + for j in range(k): + h=next((h for h in range(r,m)if A[h][j]),None) + if h is None:continue + A[r],A[h]=A[h],A[r];v=A[r][j];A[r]=[x/v for x in A[r]] + for h in range(m): + if h!=r and A[h][j]: + v=A[h][j];A[h]=[x-v*y for x,y in zip(A[h],A[r])] + p.append(j);r+=1 + if any(not any(row[:k]) and row[k]for row in A):return None + x=[F(0)]*k + for h,j in enumerate(p):x[j]=A[h][k] + return x + candidates=[] + # Two normalization constraints leave at most two independent choices. + for count in range(3): + for chosen in combinations(range(n),count): + A=[realrows[src],imagrows[src]]+[imagrows[i]for i in chosen] + x=solve(A,[F(1),F(0)]+[F(0)]*count) + if x is None:continue + u=[summ(mul(z,(x[2*j],x[2*j+1]))for j,z in enumerate(row))for row in B] + if u[src]!=I:raise ValueError('source normalization') + key=(sum(z[1]!=0 for z in u),sum(z!=Z for z in u),sum(abs(z[0])+abs(z[1])for z in u)) + candidates.append((key,u,x)) + if not candidates:return None + return min(candidates,key=lambda t:t[0]) + + +def probe(q,c_weights=None,betas=None): + n=2*q+2;ops,pre=prefixes(q,betas) + weights=[1]*q if c_weights is None else c_weights + V=[[I if i==1 else Z, (F(weights[(i-3)//2]),F(0))if i>=3 and i%2 else Z]for i in range(n)] + rows=[] + for M,src,dst in pre: + answer=source_choice(mm(M,V),src) + rows.append((src,dst,answer)) + return rows + + +if __name__=='__main__': + for q in(1,2,3): + print('q',q) + for src,dst,res in probe(q): + print(src,'->',dst, None if res is None else (res[0],res[1])) diff --git a/research/two-pivot-caller-readers/source/caller/nested_six.py b/research/two-pivot-caller-readers/source/caller/nested_six.py new file mode 100644 index 0000000000..56d90d15b0 --- /dev/null +++ b/research/two-pivot-caller-readers/source/caller/nested_six.py @@ -0,0 +1,207 @@ +#!/usr/bin/env python3 +"""Literal six-bank nested caller prefix with its paid source continuations. + +All six input columns are independent. Four public rows finish; two pivot +rows retain the displayed H/L. This is an expensive first recursive prefix, +not a claimed complete supplier or a promised constant terminal tail. +Apache-2.0; substantial OpenAI Codex assistance. +""" +from pathlib import Path +from fractions import Fraction +from collections import Counter +import argparse +import hashlib +import json +import sys +sys.dont_write_bytecode = True +import free_ops as F +from plane_group import Algebra +from nested_prefix import skeleton, probe + +HERE = Path(__file__).resolve().parent + + +def ec(z): + return F.add(F.mono((), z[0]), F.mono((0,), z[1])) + + +def formal_word(): + q,n=2,6 + _,ops=skeleton(q,(1,0)) + choices=probe(q,(1,1),(1,0)) + F.need(all(c is not None for _,_,c in choices), 'every normalized source retraction exists') + M=F.eye(n);Mi=F.eye(n);s=0 + def app(A,Ai): + nonlocal M,Mi + F.need(F.mm(A,Ai)==F.mm(Ai,A)==F.eye(n),'formal event inverse') + M=F.mm(A,M);Mi=F.mm(Mi,Ai) + def a(d,src,c):app(F.es(n,d,src,c),F.es(n,d,src,F.neg(c))) + a(5,3,F.I) # inverse of the final constant c-basis change + source_rows=[] + for typ,d,src,z in ops: + if typ=='a':a(d,src,ec(z)) + elif typ=='s': + P=F.eye(n);P[d],P[src]=P[src],P[d];app(P,P) + else: + s+=1;u=choices[s-1][2][1] + cont=(s!=7 and any(v[1] for v in u)) + # G E(N) G^-1=E(N), because source functional is fixed, + # target differs from source, and every coefficient lies in E. + for j,v in enumerate(u): + if j!=src and v!=(0,0):a(j,src,F.neg(ec(v))) + P=F.mono((s,)) + if cont:P=F.mul(F.N,P) + A=F.mm(F.unary(n,src,P),F.es(n,d,src,F.N)) + Ai=F.mm(F.es(n,d,src,F.neg(F.N)),F.unary(n,src,F.inv(P))) + app(A,Ai) + for j,v in enumerate(u): + if j!=src and v!=(0,0):a(j,src,ec(v)) + source_rows.append({'stage':s,'src':src,'dst':d, + 'u':[[str(x),str(y)]for x,y in u], + 'source_code':('N P'if cont else'P')+str(s), + 'continued':cont}) + a(5,3,F.neg(F.I)) + F.need(F.mm(M,Mi)==F.mm(Mi,M)==F.eye(n),'formal literal inverse both orders') + public=(0,2,4,5);pivots=(1,3) + for i in public: + F.need(M[i]==[F.N if j==i else F.Z for j in range(n)], + 'every independent finished public row is exactly N times its own input') + H=[[M[i][j]for j in pivots]for i in pivots] + L=[[M[i][j]for j in public]for i in pivots] + return M,Mi,source_rows,H,L + + +def evaluate(q,A): + out=A.Z + for w,c in q.items(): + term=A.mono(coefficient=c) + for k in w: + op=A.n(0)if k==0 else A.swap(0,abs(k)) + term=A.mul(term,A.inv(op)if k<0 else op) + out=A.add(out,term) + return out + + +def physical_word(wrong_continuation_sign=False): + banks,planes=6,8 + A=Algebra(planes);M=A.eye(banks);Mi=A.eye(banks);events=[];s=0 + _,ops=skeleton(2,(1,0));choices=probe(2,(1,1),(1,0)) + def app(B,Bi,e): + nonlocal M,Mi + F.need(A.mm(B,Bi)==A.mm(Bi,B)==A.eye(banks),'physical event inverse') + M=A.mm(B,M);Mi=A.mm(Mi,Bi);events.append(e) + def add(d,src,c,label): + if not c:return + app(A.es(banks,d,src,A.mono(coefficient=c)), + A.es(banks,d,src,A.mono(coefficient=-c)), + {'kind':'ADD','dst':d,'src':src,'coefficient':str(c),'label':label}) + def unary(i,g,kind,label): + B=A.eye(banks);B[i][i]=g;Bi=A.eye(banks);Bi[i][i]=A.inv(g) + ((bits,p),c),=g.items() + F.need(c in(-1,1),'native/ADDRESS operator is a Gaussian unit word') + op={'sign':int(c),'native_blocks':[j for j in range(planes)if bits>>j&1], + 'block_permutation':list(p),'native_arity':A.native_arity(g)} + app(B,Bi,{'kind':kind,'bank':i,'operator':op,'label':label}) + add(5,3,Fraction(1),'raw c-basis inverse') + unary(1,A.n(0),'NATIVE','shared input N exposure') + add(2,1,Fraction(1),'shared input fanout b1+=N*t') + unary(1,A.inv(A.n(0)),'NATIVE','shared input N inverse') + for typ,d,src,z in ops: + if typ=='a': + if z[1]: + F.need(z[0]==0 and ((s==0 and d==2 and src==1)or(s==7 and d==2 and src==1)), + 'only the explicitly compiled shared input/output N-ADDs occur') + continue + add(d,src,z[0],'scalar nested response bridge') + elif typ=='s': + B=A.eye(banks);B[d],B[src]=B[src],B[d] + app(B,B,{'kind':'BANK_SWAP','banks':[d,src],'label':'nested response permutation'}) + else: + s+=1;u=choices[s-1][2][1];cont=s!=7 and any(v[1]for v in u) + for j,(a,b)in enumerate(u): + if j!=src:add(j,src,-a,f'query{s} scalar source-retraction entrance') + unary(src,A.n(0),'NATIVE',f'query{s} source common') + for j,(a,b)in enumerate(u): + if j!=src:add(j,src,-b,f'query{s} entrance fanout from existing source N') + add(d,src,Fraction(1),f'query{s} delivery') + unary(src,A.swap(0,s),'ADDRESS_OR_UNIT',f'query{s} source swap') + for j in range(banks): + if j!=src: + unary(j,A.n(s),'NATIVE',f'query{s} target fresh'if j==d else f'query{s} inactive fresh progress') + if cont: + for j,(a,b)in enumerate(u): + if j!=src: + coefficient=b if wrong_continuation_sign else -b + add(j,src,coefficient,f'query{s} pre-continuation fanout') + unary(src,A.n(0),'NATIVE',f'query{s} retained source N continuation') + for j,(a,b)in enumerate(u): + if j!=src:add(j,src,a,f'query{s} scalar source-retraction exit') + if not cont and any(v[1]for v in u): + F.need(s==7 and u[2][1]==1 and all(not v[1]for j,v in enumerate(u)if j!=2), + 'last post-N fanout cancels exactly the final shared output isolation') + add(5,3,Fraction(-1),'final c-basis change') + F.need(A.mm(M,Mi)==A.mm(Mi,M)==A.eye(banks),'all six physical columns, literal inverse in both orders') + return A,M,Mi,events + + +def prove(): + M,Mi,sources,H,L=formal_word() + A,physical,physical_inverse,events=physical_word() + fullfresh=A.prod(*(A.n(j)for j in range(1,8))) + expected=[[A.mul(fullfresh,evaluate(x,A))for x in row]for row in M] + F.need(physical==expected,'actual N-plane/ADDRESS event list binds every free-operator coefficient and its phase') + E=A.mul(fullfresh,A.n(0));public=[0,2,4,5] + for i in public: + F.need(physical[i]==[E if j==i else A.Z for j in range(6)],'physical full native public endpoints') + _,mutant,_,_=physical_word(True) + F.need(mutant!=physical,'wrong continuation sign is detected on the complete matrix') + Hhist=Counter(e['operator']['native_arity']for e in events if e['kind']=='NATIVE') + F.need(Hhist=={2:47},'complete prefix histogram') + touches={i:[]for i in range(6)} + for index,e in enumerate(events): + if e['kind']=='ADD':active=(e['dst'],e['src']) + elif e['kind']=='BANK_SWAP':active=e['banks'] + else:active=(e['bank'],) + # Every fresh progress is paid; its label lets an independent + # scheduler delay it only across an exact commutation contract. + if e['kind']=='NATIVE'and('target fresh'in e['label']or'inactive fresh progress'in e['label']):continue + for i in active:touches[i].append(index) + return { + 'status':'PASS_EXACT_NESTED_SIX_BANK_PREFIX_FOUR_PUBLIC_TWO_PIVOTS', + 'scientific_pin':'20ecf2891d80b5acf18d980b2164fb44ea7faa90', + 'domain':'Every f>=1 under exact Ni^2=-I, commuting distinct native planes and ADDRESS plane permutations; six arbitrary independent input fields. Free-operator proof allows arbitrary independent invertible Pi.', + 'changed_premise':'Repeated first-query response replacement with coupled source-retraction columns in a fixed two-dimensional E-plane; genuine common-N source continuations are retained at stages3,4,6.', + 'source_sequence':[e['src']for e in sources],'target_sequence':[e['dst']for e in sources], + 'source_retractions':sources,'events':events, + 'complete_matrix':F.sm(M),'complete_inverse':F.sm(Mi), + 'public_rows':public,'pivot_rows':[1,3], 'pivot_H':F.sm(H),'public_L':F.sm(L), + 'physical_matrix':[[A.serial(x)for x in row]for row in physical], + 'physical_inverse':[[A.serial(x)for x in row]for row in physical_inverse], + 'histogram':dict(Hhist),'native_rank_mass':94,'ambient_arity':16,'public_banks_including_pivots':6, + 'stock_if_pivots_finish':96,'D_before_pivot_tail':2, + 'query_count':7,'source_continuation_count':3,'shared_input_N_calls':2, + 'mandatory_nondeferred_touches':touches, + 'inverse':'Reverse every physical event; negate ADDs, invert each signed native/ADDRESS operator, reverse swaps. Checked both matrix orders without any initialized field.', + 'folds':['All pre-N retraction fanouts use the already-paid source N query.', + 'At a retained continuation, N(NP)=-P makes every N-valued exit a scalar fanout before the continuation.', + 'Final post-N b1 fanout cancels the shared output isolation after the final bank swap.'], + 'limits':['This is a six-bank PREFIX. H and L have not been cleared or given the five-factory tail schema.', + 'The complete invoice is not the optimistic two-continuation planning case: stages3,4,6 are all explicitly paid.', + 'No source exposure sharing or three-stage public touch window is assumed.', + 'The exact signed group algebra proves positive identities for every f; it is not a formal-kernel certificate.'], + 'source_pins':[{'path':str(HERE/p),'sha256':hashlib.sha256((HERE/p).read_bytes()).hexdigest()} + for p in('nested_prefix.py','free_ops.py','plane_group.py')], + 'negative_control':'Wrong pre-continuation fanout sign changes the actual all-column matrix.', + 'no_new_kappa':True} + + +def main(): + ap=argparse.ArgumentParser(description=__doc__);ap.add_argument('--write',action='store_true');args=ap.parse_args() + out=prove();out['producer_sha256']=hashlib.sha256(Path(__file__).read_bytes()).hexdigest() + out=json.loads(json.dumps(out));path=HERE/'NESTED-SIX.json' + if args.write:path.write_text(json.dumps(out,indent=2,sort_keys=True)+'\n') + else:F.need(json.loads(path.read_text())==out,'saved nested-six receipt differs') + print(out['status'],out['histogram'],'prefix only') + + +if __name__=='__main__':main() diff --git a/research/two-pivot-caller-readers/source/caller/pivot_plane_probe.py b/research/two-pivot-caller-readers/source/caller/pivot_plane_probe.py new file mode 100644 index 0000000000..fd793eba19 --- /dev/null +++ b/research/two-pivot-caller-readers/source/caller/pivot_plane_probe.py @@ -0,0 +1,92 @@ +#!/usr/bin/env python3 +"""Bounded n4 source-retraction screen; actual code/native closure not inferred.""" +from fractions import Fraction as F +from itertools import product +from pathlib import Path +import json, sys +sys.dont_write_bytecode=True +Z=(F(0),F(0));I=(F(1),F(0));N=(F(0),F(1)) +def add(a,b):return(a[0]+b[0],a[1]+b[1]) +def neg(a):return(-a[0],-a[1]) +def mul(a,b):return(a[0]*b[0]-a[1]*b[1],a[0]*b[1]+a[1]*b[0]) +def inv(a): + d=a[0]*a[0]+a[1]*a[1] + if not d:raise ValueError('nonunit') + return(a[0]/d,-a[1]/d) +def eye(n):return [[I if i==j else Z for j in range(n)] for i in range(n)] +def mm(A,B):return [[summ(mul(x,y) for x,y in zip(r,c)) for c in zip(*B)] for r in A] +def summ(xs): + a=Z + for b in xs:a=add(a,b) + return a +def es(n,d,s,c): + A=eye(n);A[d][s]=c;return A +def null(A): + A=[list(r) for r in A];m=len(A);n=len(A[0]);p=[];r=0 + for c in range(n): + k=next((k for k in range(r,m) if A[k][c]),None) + if k is None:continue + A[r],A[k]=A[k],A[r];v=A[r][c];A[r]=[x/v for x in A[r]] + for j in range(m): + if j!=r and A[j][c]: + v=A[j][c];A[j]=[x-v*y for x,y in zip(A[j],A[r])] + p.append(c);r+=1 + if r==m:break + out=[] + for c in range(n): + if c in p:continue + v=[F(0)]*n;v[c]=F(1) + for j,d in enumerate(p):v[d]=-A[j][c] + out.append(v) + return out + +def rank(A): + A=[list(r) for r in A];m=len(A);n=len(A[0]);r=0 + for c in range(n): + k=next((k for k in range(r,m) if A[k][c]!=Z),None) + if k is None:continue + A[r],A[k]=A[k],A[r];v=inv(A[r][c]);A[r]=[mul(x,v) for x in A[r]] + for j in range(m): + if j!=r and A[j][c]!=Z: + v=A[j][c];A[j]=[add(x,neg(mul(v,y))) for x,y in zip(A[j],A[r])] + r+=1 + if r==m:break + return r + +def prefixes(n=4): + ops=[('q',0,1,N),('a',0,2,I),('q',1,0,N),('a',0,2,neg(I)),('a',1,3,I),('q',2,1,N),('a',1,3,neg(I)),('q',3,2,N),('a',1,3,I),('a',2,0,I),('q',0,3,neg(N)),('a',2,0,neg(I))] + M=eye(n);Mi=eye(n);out=[] + for typ,d,s,c in ops: + M=mm(es(n,d,s,c),M);Mi=mm(Mi,es(n,d,s,neg(c))) + if typ=='q':out.append((M,Mi,s,d)) + return out + +def real_source(B,src): + ns=null([[z for x in r for z in (x[1],x[0])] for r in B]) + for v in ns: + u=[summ(mul(x,(v[2*j],v[2*j+1])) for j,x in enumerate(r)) for r in B] + if any(x[1] for x in u):raise ValueError('nonreal null witness') + if u[src][0]:return [x[0]/u[src][0] for x in u] + return None + +def serial(A):return [[[str(x),str(y)] for x,y in r] for r in A] +def run(): + pre=prefixes();found=[];count=0;dimension_fail=0 + for tail1 in product((-1,0,1),repeat=3): + u1=list(map(F,tail1));u1.insert(pre[0][2],F(1)) + v1=mm(pre[0][1],[[(x,F(0))] for x in u1]) + for tail2 in product((-1,0,1),repeat=3): + count+=1;u2=list(map(F,tail2));u2.insert(pre[1][2],F(1)) + v2=mm(pre[1][1],[[(x,F(0))] for x in u2]) + V=[[v1[i][0],v2[i][0]] for i in range(4)] + if rank(V)!=2:dimension_fail+=1;continue + choices=[] + for M,Mi,src,dst in pre: + u=real_source(mm(M,V),src) + if u is None:break + choices.append([str(x) for x in u]) + else:found.append({'first_source':list(map(str,u1)),'second_source':list(map(str,u2)),'input_plane':serial(V),'source_retractions':choices}) + return {'status':'BOUNDED_EXACT_SOURCE_RETRACTION_SCREEN','candidate_pairs':count,'source_tail_alphabet':[-1,0,1],'dimension_failures':dimension_fail,'solutions':found,'scope':'Old n4 five-shear ideal topology only; arbitrary real source-retraction columns allowed at later queries. Source-code algebra, native encoder and actual correction are not inferred.','native_invoice_if_admitted':'Same five raw carriers plus full global fresh progress; constant bank GL source changes only. Any N-dependent initial plane encoder and terminal correction remain paid/open.'} +if __name__=='__main__': + out=run();Path(__file__).with_name('PIVOT-PLANE-PROBE.json').write_text(json.dumps(out,indent=2,sort_keys=True)+'\n');print(out['status'],out['candidate_pairs'],'pairs',len(out['solutions']),'solutions') + if out['solutions']:print(json.dumps(out['solutions'][0])) diff --git a/research/two-pivot-caller-readers/source/caller/plane_group.py b/research/two-pivot-caller-readers/source/caller/plane_group.py new file mode 100644 index 0000000000..fddd6b0761 --- /dev/null +++ b/research/two-pivot-caller-readers/source/caller/plane_group.py @@ -0,0 +1,103 @@ +"""Exact all-chunk operator algebra for the minimal plane carrier. + +N_i^2=-I, N_i commute, and plane ADDRESS permutations permute the N_i. +All operations are literal Gaussian-unit identities, not binary tableaux. +Apache-2.0; substantial OpenAI Codex assistance. +""" +from fractions import Fraction + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +class Algebra: + def __init__(self, planes): + self.p = planes + self.idperm = tuple(range(planes)) + self.I = {(0, self.idperm): Fraction(1)} + self.Z = {} + + def mono(self, bits=0, perm=None, coefficient=1): + if not coefficient: + return {} + return {(bits, self.idperm if perm is None else tuple(perm)): Fraction(coefficient)} + + def n(self, i): + return self.mono(1 << i) + + def swap(self, i, j): + p = list(self.idperm) + p[i], p[j] = p[j], p[i] + return self.mono(perm=p) + + def add(self, a, b): + c = dict(a) + for g, v in b.items(): + c[g] = c.get(g, 0) + v + if not c[g]: + del c[g] + return c + + @staticmethod + def neg(a): + return {g: -v for g, v in a.items()} + + def mul(self, a, b): + c = {} + for (x, p), v in a.items(): + for (y, q), w in b.items(): + py = sum(1 << p[i] for i in range(self.p) if y >> i & 1) + sign = -1 if (x & py).bit_count() % 2 else 1 + r = tuple(p[q[i]] for i in range(self.p)) + c = self.add(c, self.mono(x ^ py, r, sign * v * w)) + return c + + def prod(self, *args): + c = self.I + for a in args: + c = self.mul(c, a) + return c + + def inv(self, a): + need(len(a) == 1, 'literal inverse requires one group word') + ((x, p), v), = a.items() + pi = [0] * self.p + for i, j in enumerate(p): + pi[j] = i + y = sum(1 << pi[i] for i in range(self.p) if x >> i & 1) + sign = -1 if x.bit_count() % 2 else 1 + b = self.mono(y, pi, sign / v) + need(self.mul(a, b) == self.mul(b, a) == self.I, 'exact phase inverse') + return b + + def ad(self, a, b): + return self.prod(a, b, self.inv(a)) + + def native_arity(self, a): + need(len(a) == 1, 'native arity only for a single actual operator') + ((bits, _), _), = a.items() + return 2 * bits.bit_count() + + def eye(self, n): + return [[self.I if i == j else self.Z for j in range(n)] for i in range(n)] + + def mm(self, a, b): + return [[self.sum(self.mul(x, y) for x, y in zip(r, c)) for c in zip(*b)] for r in a] + + def sum(self, terms): + a = self.Z + for b in terms: + a = self.add(a, b) + return a + + def es(self, n, dst, src, a): + m = self.eye(n) + m[dst][src] = self.add(m[dst][src], a) + return m + + def serial(self, a): + return [{'coefficient': str(c), 'N_planes': [i for i in range(self.p) if x >> i & 1], + 'ADDRESS_plane_permutation': list(p)} for (x, p), c in sorted(a.items())] + diff --git a/research/two-pivot-caller-readers/source/caller/quadratic_model_review.py b/research/two-pivot-caller-readers/source/caller/quadratic_model_review.py new file mode 100644 index 0000000000..27a44d0364 --- /dev/null +++ b/research/two-pivot-caller-readers/source/caller/quadratic_model_review.py @@ -0,0 +1,270 @@ +#!/usr/bin/env python3 +"""Independent finite controls for the parent's exact quadratic-chart model. + +This is a model audit, not selected-native admission or an optimization run. +Apache-2.0; substantial OpenAI Codex assistance. +""" +from pathlib import Path +from fractions import Fraction as F +from functools import lru_cache +import argparse, hashlib, importlib.util, json, sys +sys.dont_write_bytecode = True +HERE = Path(__file__).resolve().parent +ROOT = HERE.parent / 'root-chronology' +SOURCE = ROOT / 'quadratic_charts.py' +spec = importlib.util.spec_from_file_location('caller_quadratic_reviewed_model', SOURCE) +qc = importlib.util.module_from_spec(spec) +sys.modules[spec.name] = qc +spec.loader.exec_module(qc) + +def need(ok, message): + if not ok: + raise ValueError(message) + +def lin(rows, x): + return sum(((row & x).bit_count() & 1) << i for i, row in enumerate(rows)) + +@lru_cache(None) +def inverse_rows(rows): + # Deliberately use complete truth-table inversion, not the reviewed eliminator. + n = len(rows) + values = {lin(rows, x): x for x in range(1 << n)} + need(len(values) == 1 << n, 'independent address inverse exists') + return tuple(sum(((values[1 << j] >> i) & 1) << j for j in range(n)) for i in range(n)) + +def literal_x_action(circuit, n, x): + """Act on an X-character using literal P, C, even-linear D and unit events.""" + phase = 0 + for e in circuit: + kind = e[0] + if kind == 'P': + # Physical |x> -> |A x> gives character address A^{-T}. + inv = inverse_rows(tuple(e[1])) + rows = tuple(sum(((inv[j] >> i) & 1) << j for j in range(n)) for i in range(n)) + x = lin(rows, x) + elif kind == 'C': + phase += e[2] * ((e[1] & x).bit_count() & 1) + elif kind == 'D': + need(not any(e[1]) and all(a % 2 == 0 for a in e[2]), 'source D is an explicit Pauli Z') + x ^= sum(((a // 2) & 1) << i for i, a in enumerate(e[2])) + elif kind == 'phase': + phase += e[1] + else: + raise ValueError('uncovered source circuit event ' + kind) + return x, phase % 4 + +def check_source_families(): + path = ROOT / 'ENCODED-COMPLETE-Q3.json' + src = json.loads(path.read_text()) + n = src['ambient_arity'] + points = [0] + [1 << i for i in range(n)] + [(1 << i) | (1 << j) for i in range(n) for j in range(i + 1, n)] + # Also use high-weight points to detect a mistaken nonquadratic implementation. + points += [(1 << n) - 1, int('10' * (n // 2), 2), int('01' * (n // 2), 2)] + count = 0 + wrong_global_witness = None + for index, e in enumerate(src['events']): + if e['kind'] in ('ADD', 'BANK_SWAP', 'SCALE'): + continue + g = qc.decode(e, n) + op = e.get('exact_operator', e.get('operator')) + circuit = op.get('one_coordinate_literal_circuit', op.get('one_bit_circuit')) + need(circuit is not None, 'every source unary has a complete literal circuit') + if 'global_i_exponent_by_f_mod4' in op: + globals_ = tuple(op['global_i_exponent_by_f_mod4']) + else: + sign = 2 if op['global_sign'] == -1 else 0 + exponent = op['phase_exponent'] + globals_ = tuple((sign + exponent * (1 - r)) % 4 for r in range(4)) + base0, phase0 = literal_x_action(circuit, n, 0) + for x in points: + y, phase = literal_x_action(circuit, n, x) + need(y == g.act(x), 'source-family exact X-character address') + # One nonzero coordinate and f-1 zero coordinates suffice once the + # bitwise tensor construction and Gaussian phase polynomial are fixed. + for f in (1, 2, 3, 4): + expected = (globals_[f % 4] + phase + (f - 1) * phase0) % 4 + actual = (g.global_phase + g.q(x) + (f - 1) * g.q(0)) % 4 + need(actual == expected, 'source-family all-f phase normalization') + if wrong_global_witness is None and f == 2 and g.global_phase % 2: + wrong_global_witness = {'event_index': index, 'f': f, 'correct_phase': actual, + 'tensoring_the_global_i_phase': (f * g.global_phase + g.q(x) + (f - 1) * g.q(0)) % 4} + count += 1 + need(wrong_global_witness is not None and wrong_global_witness['correct_phase'] != wrong_global_witness['tensoring_the_global_i_phase'], + 'negative control detects tensoring a once-per-bank phase') + return {'unary_events': count, 'points_per_event': len(points), 'f_residues': [1, 2, 3, 4], + 'global_phase_negative_control': wrong_global_witness, + 'source_path': str(path), 'source_sha256': hashlib.sha256(path.read_bytes()).hexdigest()} + +def symmetric(n, bits): + rows = [0] * n + k = 0 + for i in range(n): + for j in range(i, n): + if bits >> k & 1: + rows[i] ^= 1 << j + if i != j: + rows[j] ^= 1 << i + k += 1 + return tuple(rows) + +def walsh_entry_numerator(g, row, column): + re = im = 0 + for x in range(1 << len(g.rows)): + p = (g.q(x) + 2 * (((row & g.act(x)).bit_count() + (column & x).bit_count()) & 1)) % 4 + a, b = ((1, 0), (0, 1), (-1, 0), (0, -1))[p] + re += a + im += b + return re, im + +def finite_core_controls(): + # Exhaust all 64 symmetric polar forms on three bits. Affine addresses and + # even linear phases are deliberately present, not just diagonal charts. + n = 3 + perm = (3, 2, 4) # invertible transvection + forms = [] + for bits in range(64): + A = symmetric(n, bits) + base = qc.chart(A) + g = qc.Mono(perm, bits % 8, tuple((a + 2 * ((bits >> i) & 1)) % 4 for i, a in enumerate(base.alpha)), base.quad, + bits % 4, (bits // 4) % 4) + r = qc.rank(g.polar()) + for row in range(1 << n): + values = [walsh_entry_numerator(g, row, col) for col in range(1 << n)] + support = [a * a + b * b for a, b in values if a or b] + need(len(support) == 1 << r, 'complete Walsh row support equals 2^polar_rank') + need(len(set(support)) == 1 and support[0] == 1 << (2 * n - r), 'complete Walsh magnitude matches native rank') + forms.append(g) + composition_checks = 0 + transport_checks = 0 + for j, g in enumerate(forms): + h = forms[(17 * j + 9) % len(forms)] + c = g @ h + inv = g.inv() + need(g @ inv == inv @ g == qc.identity(n), 'exact inverse preserves the once-only phase') + for x in range(1 << n): + need(c.act(x) == g.act(h.act(x)) and c.q(x) == (h.q(x) + g.q(h.act(x))) % 4, + 'complete phase/address composition') + need(c.global_phase == (g.global_phase + h.global_phase) % 4, 'once-only phase composition') + composition_checks += 1 + A = symmetric(n, (13 * j + 1) % 64) + B = qc.move(g, A) + need(all((B[i] >> k & 1) == (B[k] >> i & 1) for i in range(n) for k in range(n)), 'transport chart remains symmetric') + adapter = qc.chart(B).inv() @ g @ qc.chart(A) + need(not any(adapter.polar()), 'transport adapter has zero polar matrix') + for x in range(1 << n): + left, right = g @ qc.chart(A), qc.chart(B) @ adapter + need((left.act(x), left.q(x), left.global_phase) == (right.act(x), right.q(x), right.global_phase), + 'literal transport including linear, affine and global phase') + transport_checks += 1 + # A rank-zero affine/quadratic adapter must be a computational monomial. + # Conversely a nonzero polar fixture must not be mislabeled native-zero. + need(qc.rank(qc.chart((1, 0, 0)).polar()) == 1, 'negative control odd linear phase is paid') + return {'complete_polar_forms': 64, 'complete_Walsh_rows': 64 * 8, + 'complete_composition_points': composition_checks, 'complete_transport_points': transport_checks} + +UNITS = ((F(1), F(0)), (F(0), F(1)), (F(-1), F(0)), (F(0), F(-1))) +def plus(a, b): + return a[0] + b[0], a[1] + b[1] +def scale(c, a): + return c * a[0], c * a[1] +def unit(p, a): + return (a, (-a[1], a[0]), (-a[0], -a[1]), (a[1], -a[0]))[p % 4] + +def independently_act(events, banks, n, f, column): + # Direct sparse vector execution, not the parent's operator-entry dictionary. + state = {column: (F(1), F(0))} + mask = (1 << n) - 1 + for e in events: + if e['kind'] == 'ADD': + d, s, c = e['dst'], e['src'], F(e['coefficient']) + nxt = dict(state) + for (bank, x), value in state.items(): + if bank == s: + key = d, x + nxt[key] = plus(nxt.get(key, (F(0), F(0))), scale(c, value)) + state = {key: val for key, val in nxt.items() if val != (0, 0)} + elif e['kind'] == 'SCALE': + c = F(e['coefficient']) + need(c != 0, 'independent invertible bank scaling') + state = {key: scale(c, val) if key[0] == e['bank'] else val for key, val in state.items()} + elif e['kind'] == 'BANK_SWAP': + a, b = e['banks'] + state = {(b if bank == a else a if bank == b else bank, x): val for (bank, x), val in state.items()} + else: + g = qc.decode(e, n) + nxt = {} + for (bank, x), val in state.items(): + if bank != e['bank']: + nxt[bank, x] = val + continue + y = p = 0 + for t in range(f): + z = (x >> (n * t)) & mask + y |= g.act(z) << (n * t) + p += g.q(z) + nxt[bank, y] = unit(p + g.global_phase, val) + state = nxt + return state + +def compile_controls(): + n, banks = 3, 3 + fixtures = [qc.chart(symmetric(n, z)) for z in (13, 41, 55)] + g = qc.Mono((3, 2, 4), 5, (3, 1, 2), (6, 4, 0), 1, 3) + def unary(i, op): + return {'kind': 'NATIVE', 'bank': i, 'x_monomial': op.data()} + events = [unary(0, g), {'kind': 'SCALE', 'bank': 0, 'coefficient': '-2'}, + {'kind': 'ADD', 'dst': 1, 'src': 0, 'coefficient': '-2'}, unary(2, g.inv()), + {'kind': 'BANK_SWAP', 'banks': [1, 2]}, {'kind': 'ADD', 'dst': 0, 'src': 2, 'coefficient': '1/2'}, + unary(1, fixtures[0]), {'kind': 'SCALE', 'bank': 1, 'coefficient': '1/2'}, + {'kind': 'ADD', 'dst': 1, 'src': 0, 'coefficient': '-1'}, unary(0, fixtures[1])] + choices = [symmetric(n, z) for z in (7, 38, 63)] + compiled = qc.compile_word(events, banks, n, choices) + need(qc.replay(events, banks, n) == qc.replay(compiled, banks, n), 'parent all-f replay preserves all bank columns') + checks = 0 + for f in (1, 2): + for bank in range(banks): + for x in range(1 << (n * f)): + need(independently_act(events, banks, n, f, (bank, x)) == independently_act(compiled, banks, n, f, (bank, x)), + 'independent complete input-column vector replay') + checks += 1 + # A deliberately unaligned ADD is a defect, even though the source and + # destination use individually valid chart gauges. + mutant = list(compiled) + alignment = next(i for i, e in enumerate(mutant) if e.get('label') == 'paid quadratic chart alignment') + del mutant[alignment] + need(any(independently_act(events, banks, n, 1, (b, x)) != independently_act(mutant, banks, n, 1, (b, x)) + for b in range(banks) for x in range(1 << n)), 'negative control rejects missing ADD alignment') + return {'toy_banks': banks, 'one_coordinate_arity': n, 'complete_input_columns_f1_f2': checks, + 'compiled_native_rank_mass': sum(e.get('rank_per_f', 0) for e in compiled), + 'SCALE_scans_checked': 2, 'missing_alignment_negative_control': 'REJECTED'} + +def produce(): + initial = hashlib.sha256(SOURCE.read_bytes()).hexdigest() + out = {'status': 'PASS_SCOPED_INDEPENDENT_QUADRATIC_CHART_MODEL_REVIEW', + 'source_path': str(SOURCE), 'source_sha256': initial, + 'source_family_binding': check_source_families(), + 'finite_core_controls': finite_core_controls(), 'compile_controls': compile_controls(), + 'scope': ['Exact model and phase review; no bounded-search optimality claim.', + 'For these X-character monomial tensor families, polar rank is exactly the physical Clifford B rank per coordinate.', + 'The exact all-f closure is an algebraic tensor/phase argument; finite matrix tests are defect controls.', + 'Every nonzero rank child still needs selected-native lowering, all-f adapters and contraction-cap splitting before supplier admission.', + 'No source-read, precision, owner, COPY, finite-tape or joint BIT contract is supplied.'], + 'no_new_kappa': True} + need(initial == hashlib.sha256(SOURCE.read_bytes()).hexdigest(), 'reviewed source stable during controls') + out['producer_sha256'] = hashlib.sha256(Path(__file__).read_bytes()).hexdigest() + return out + +def main(): + ap = argparse.ArgumentParser(description=__doc__) + ap.add_argument('--write', action='store_true') + args = ap.parse_args() + out = produce() + path = HERE / 'QUADRATIC-MODEL-REVIEW.json' + if args.write: + path.write_text(json.dumps(out, indent=2, sort_keys=True) + '\n') + else: + need(json.loads(path.read_text()) == out, 'saved scoped model review differs') + print(out['status']) + +if __name__ == '__main__': + main() diff --git a/research/two-pivot-caller-readers/source/native-frames/ENCODED-STAGE-TAIL.json b/research/two-pivot-caller-readers/source/native-frames/ENCODED-STAGE-TAIL.json new file mode 100644 index 0000000000..9fbf65e1f3 --- /dev/null +++ b/research/two-pivot-caller-readers/source/native-frames/ENCODED-STAGE-TAIL.json @@ -0,0 +1,4403 @@ +{ + "all_parameter_changed_pair_identity": "With Q=Ad_N(R), after the changed nonfinal pair uprime=Q Po(h-A), hprime=-N Pe u-N(Q-I)Po(h-A)+A. Its inverse is u=Pe^-1[N(hprime-A)+(Q-I)uprime], h=Po^-1 Q uprime+A. The literal sequence saved here realizes those coefficients and every public reader before the original J-core fold.", + "ambient_arity_per_f": 16, + "banks": 8, + "complete_if_prefix_61H2_binds": { + "D": -10, + "H2": 67, + "H4": 1, + "native_rank_mass": 138, + "stock": 128 + }, + "events": [ + { + "bank": 1, + "kind": "NATIVE", + "label": "N", + "native_arity_per_f": 2, + "operator": { + "all_f_interpretation": "i^global_exponent times bitwise tensor of the complete one-bit literal operator, after regrouping chunks", + "global_i_exponent_by_f_mod4": [ + 1, + 0, + 3, + 2 + ], + "one_bit_circuit": [ + [ + "C", + 2, + 1 + ], + [ + "D", + [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 0, + 2, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ] + ], + [ + "C", + 1, + -1 + ], + [ + "D", + [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 2, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ] + ], + [ + "phase", + 1 + ] + ], + "one_bit_tableau": [ + [ + 1, + 0, + 2 + ], + [ + 2, + 0, + 2 + ], + [ + 4, + 0, + 0 + ], + [ + 8, + 0, + 0 + ], + [ + 16, + 0, + 0 + ], + [ + 32, + 0, + 0 + ], + [ + 64, + 0, + 0 + ], + [ + 128, + 0, + 0 + ], + [ + 256, + 0, + 0 + ], + [ + 512, + 0, + 0 + ], + [ + 1024, + 0, + 0 + ], + [ + 2048, + 0, + 0 + ], + [ + 4096, + 0, + 0 + ], + [ + 8192, + 0, + 0 + ], + [ + 16384, + 0, + 0 + ], + [ + 32768, + 0, + 0 + ], + [ + 1, + 1, + 3 + ], + [ + 2, + 2, + 1 + ], + [ + 0, + 4, + 0 + ], + [ + 0, + 8, + 0 + ], + [ + 0, + 16, + 0 + ], + [ + 0, + 32, + 0 + ], + [ + 0, + 64, + 0 + ], + [ + 0, + 128, + 0 + ], + [ + 0, + 256, + 0 + ], + [ + 0, + 512, + 0 + ], + [ + 0, + 1024, + 0 + ], + [ + 0, + 2048, + 0 + ], + [ + 0, + 4096, + 0 + ], + [ + 0, + 8192, + 0 + ], + [ + 0, + 16384, + 0 + ], + [ + 0, + 32768, + 0 + ] + ], + "selected_native_recipe": { + "left": { + "linear_Z4": [ + 2, + 2, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 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is a fully paid baseline for retiming, not a cheap-tail claim.", + "It is not merely the free inverse of the physical cut5 encoder; the changed pair is folded directly with its readers, and the Q resource is priced.", + "No supplier, exponent, owner, all-size, precision or tape conclusion is claimed." + ], + "literal_inverse": "Reverse saved events; negate scalar ADD coefficients; invert each full saved unary circuit and its actual global f phase; bank swaps are self inverse. Both matrix inverse orders are checked on all eight inputs.", + "no_new_kappa": true, + "physical_chart_proof": "The complete target E=N0 productfresh is central against every plane permutation, every Ni and this R, because R normalizes the full old three-plane product. Hence all event operators are actual physical operators on completed-E field coordinates. F=E N^-1 makes the all-input equality W diag(N^-1) M=I the exact physical endpoint, not a phase-free relabeling.", + "producer_sha256": "e46abc9524267fc761fec0ce3019b726831e7297a0b84a9acb762817fe571463", + "q": 3, + "scientific_pin": "20ecf2891d80b5acf18d980b2164fb44ea7faa90", + "source_pins": [ + { + "path": "/Users/ross/git/math/.research-automation/runs/kappa-four-coordinate-20261019T0717Z/caller/encoded_stage.py", + "sha256": "ef5aea9c207a88d677271035f27cf194237e9d269db4bd79ec3bad07fe0708ff" + }, + { + "path": "/Users/ross/git/math/.research-automation/runs/kappa-four-coordinate-20261019T0717Z/caller/ENCODED-STAGE.json", + "sha256": "466c57c3d14ec13089810129e550cddc0c873d1934531eb9d3a79196f1e4cb2a" + }, + { + "path": "/Users/ross/git/math/.research-automation/runs/kappa-four-coordinate-20261019T0717Z/native-frames/conjugated_reflection.py", + "sha256": "6b68a4a60b160fe28227c31909ed86bd7f80b1f3e07591032cd001dbeb242f6f" + }, + { + "path": "/Users/ross/git/math/.research-automation/runs/kappa-four-coordinate-20261019T0717Z/native-frames/native_model.py", + "sha256": "6397a86bd3d1461be182fcfa8602b0c70c489964a8c14f12436ba2506e11d9e3" + } + ], + "status": "PASS_COMPLETE_DEFAULT_ENCODED_STAGE_TAIL_ALL_COLUMNS_ALL_F", + "tail_invoice": { + "ADDRESS_scans": 6, + "ADD_scans": 25, + "BANK_SWAP_scans": 2, + "H2": 6, + "H4": 1, + "native_monomial_adapters_at_most": 14, + "native_rank_mass": 16, + "ordinary_helpers": 0, + "private_fields": 0 + } +} diff --git a/research/two-pivot-caller-readers/source/native-frames/HANDOFF-FAMILY-TAIL-PROOF.md b/research/two-pivot-caller-readers/source/native-frames/HANDOFF-FAMILY-TAIL-PROOF.md new file mode 100644 index 0000000000..5b74e10630 --- /dev/null +++ b/research/two-pivot-caller-readers/source/native-frames/HANDOFF-FAMILY-TAIL-PROOF.md @@ -0,0 +1,90 @@ +# Complete ordinary handoff tail for all q + +This is a written all-parameter proof of the tail in `handoff_family_tail.py`. +The exact serialized fixtures q=2,3,4 additionally replay all original +columns, actual signed-plane phases and both literal inverse orders. This +is not a formal-kernel proof or a claim that the stated bill is optimal. + +Assume q>=2, n=2q+2 banks and k=2q+1 fresh stages, each of two chunks of +length f>=1. The ambient dimension is m f, with m=4q+4=2n. Let N0 and +each fresh Nj be the actual operator `i Hp_f Hq_f`, so Nj^2=-I. The global +i is one i for the whole chunk pair, not i^f. Let Pj swap the common plane +and fresh plane j. Put F=product_(j=1..k) Nj and E=N0 F. E commutes with +every Pi and Nj, including all Gaussian phases. + +The prefix in `../caller/handoff_family.py` finishes every original public +bank with E applied to its own arbitrary input. Two carriers remain. Its +affine recurrence is written below, retaining all public readers; this is +the caller interface the present tail requires. + +Use completed-E coordinates `(u,h=Nv)` for the two carrier quantities. +A nonfinal handoff pair r, for 2<=r=2,f>=1 in the written affine induction. Finite complete literal event witnesses cover q2,q3,q4. Formal Pj are arbitrary independent invertible operators; the displayed native tariff requires actual ordinary plane swaps among completed identical native planes.", + "fixtures": [ + { + "actual_all_f_phase_binding": "PASS", + "all_original_columns": "PASS", + "banks": 6, + "complete_profile": { + "D": -8, + "H2": 38, + "H4": 1, + "rank_mass": 80, + "stock": 72 + }, + "defect_control_rejected": "omit final-pair public a restoration before reverse recurrence", + "factory_support": [ + { + "J_row": 0, + "actual_normal_form": [ + { + "ADDRESS_plane_permutation": [ + 5, + 1, + 2, + 3, + 4, + 0 + ], + "N_planes": [ + 5 + ], + "coefficient": "1" + } + ], + "direct_D_inverse_N_arity_per_f": 4, + "full_prefix_endpoint_arity_per_f": 8, + "native_arity_per_f": 2, + "native_planes": [ + 5 + ], + "word": [ + { + "coefficient": "1", + "word": [ + 5, + 0 + ] + } + ] + }, + { + "J_row": 1, + "actual_normal_form": [ + { + "ADDRESS_plane_permutation": [ + 3, + 1, + 2, + 4, + 0, + 5 + ], + "N_planes": [ + 3 + ], + "coefficient": "1" + } + ], + "direct_D_inverse_N_arity_per_f": 4, + "full_prefix_endpoint_arity_per_f": 8, + "native_arity_per_f": 2, + "native_planes": [ + 3 + ], + "word": [ + { + "coefficient": "1", + "word": [ + 4, + 3, + 0 + ] + } + ] + } + ], + "literal_inverse_both_orders": "PASS", + "q": 2, + "tail_counts": { + "ADDRESS_scans": 4, + "ADD_scans": 17, + "BANK_SWAP_scans": 1, + "H2": 4, + "H4": 1, + "native_adapter_scans_at_most": 10, + "ordinary_helpers": 0, + "private_fields": 0, + "rank_mass": 12 + }, + "tail_events": [ + { + "bank": 1, + "native_arity_per_f": 2, + "op": "NATIVE", + "sign": 1, + "word": [ + "N" + ] + }, + { + "bank": 1, + "native_arity_per_f": 0, + "op": "ADDRESS", + "sign": 1, + "word": [ + "P4^-1" + ] + }, + { + "bank": 3, + "native_arity_per_f": 2, + "op": "NATIVE", + "sign": 1, + "word": [ + "N" + ] + }, + { + "bank": 3, + "native_arity_per_f": 0, + "op": "ADDRESS", + "sign": 1, + "word": [ + "P5^-1" + ] + }, + { + "coefficient": 1, + "dst": 3, + "native_arity_per_f": 0, + "op": "ADD", + "src": 0 + }, + { + "bank": 1, + "native_arity_per_f": 0, + "op": "ADDRESS", + "sign": 1, + "word": [ + "P3^-1" + ] + }, + { + "banks": [ + 1, + 3 + ], + "native_arity_per_f": 0, + "op": "BANK_SWAP" + }, + { + "coefficient": -1, + "dst": 1, + "native_arity_per_f": 0, + "op": "ADD", + "src": 3 + }, + { + "coefficient": 1, + "dst": 1, + "native_arity_per_f": 0, + "op": "ADD", + "src": 2 + }, + { + "bank": 1, + "native_arity_per_f": 4, + "op": "NATIVE", + "sign": 1, + "word": [ + "N^-1", + "P2^-1", + "N" + ] + }, + { + "coefficient": -1, + "dst": 1, + "native_arity_per_f": 0, + "op": "ADD", + "src": 0 + }, + { + "coefficient": -1, + "dst": 1, + "native_arity_per_f": 0, + "op": "ADD", + "src": 2 + }, + { + "coefficient": -1, + "dst": 1, + "native_arity_per_f": 0, + "op": "ADD", + "src": 4 + }, + { + "coefficient": 1, + "dst": 3, + "native_arity_per_f": 0, + "op": "ADD", + "src": 1 + }, + { + "coefficient": 1, + "dst": 3, + 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"src": 3 + }, + { + "bank": 1, + "native_arity_per_f": 2, + "op": "NATIVE", + "sign": 1, + "word": [ + "N^-1" + ] + }, + { + "bank": 3, + "native_arity_per_f": 2, + "op": "NATIVE", + "sign": 1, + "word": [ + "N^-1" + ] + } + ] + }, + { + "actual_all_f_phase_binding": "PASS", + "all_original_columns": "PASS", + "banks": 8, + "complete_profile": { + "D": -8, + "H2": 66, + "H4": 1, + "rank_mass": 136, + "stock": 128 + }, + "defect_control_rejected": "omit final-pair public a restoration before reverse recurrence", + "factory_support": [ + { + "J_row": 0, + "actual_normal_form": [ + { + "ADDRESS_plane_permutation": [ + 5, + 1, + 2, + 3, + 4, + 6, + 0, + 7 + ], + "N_planes": [ + 5 + ], + "coefficient": "1" + } + ], + "direct_D_inverse_N_arity_per_f": 4, + "full_prefix_endpoint_arity_per_f": 12, + "native_arity_per_f": 2, + "native_planes": [ + 5 + ], + "word": [ + { + "coefficient": "1", + "word": [ + 6, + 5, + 0 + ] + } + ] + }, + { + "J_row": 1, + "actual_normal_form": [ + { + "ADDRESS_plane_permutation": [ + 3, + 1, + 2, + 4, + 7, + 5, + 6, + 0 + ], + "N_planes": [ + 3, + 7 + ], + "coefficient": "-1" + } + ], + "direct_D_inverse_N_arity_per_f": 6, + "full_prefix_endpoint_arity_per_f": 10, + "native_arity_per_f": 4, + "native_planes": [ + 3, + 7 + ], + "word": [ + { + "coefficient": "-1", + "word": [ + 7, + 0, + 4, + 3, + 0 + ] + } + ] + } + ], + "literal_inverse_both_orders": "PASS", + "q": 3, + "tail_counts": { + "ADDRESS_scans": 6, + "ADD_scans": 25, + "BANK_SWAP_scans": 2, + "H2": 5, + "H4": 1, + "native_adapter_scans_at_most": 12, + "ordinary_helpers": 0, + "private_fields": 0, + "rank_mass": 14 + }, + "tail_events": [ + { + "bank": 1, + "native_arity_per_f": 2, + "op": "NATIVE", + "sign": 1, + "word": [ + "N" + ] + }, + { + "bank": 1, + "native_arity_per_f": 0, + "op": "ADDRESS", + "sign": 1, + "word": [ + "P6^-1" + ] + }, + { + "bank": 3, + "native_arity_per_f": 2, + "op": "NATIVE", + "sign": 1, + "word": [ + "N" + ] + }, + { + "bank": 3, + 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], + "direct_D_inverse_N_arity_per_f": 6, + "full_prefix_endpoint_arity_per_f": 14, + "native_arity_per_f": 4, + "native_planes": [ + 5, + 9 + ], + "word": [ + { + "coefficient": "-1", + "word": [ + 9, + 0, + 6, + 5, + 0 + ] + } + ] + }, + { + "J_row": 1, + "actual_normal_form": [ + { + "ADDRESS_plane_permutation": [ + 3, + 1, + 2, + 4, + 7, + 5, + 6, + 8, + 0, + 9 + ], + "N_planes": [ + 3, + 7 + ], + "coefficient": "-1" + } + ], + "direct_D_inverse_N_arity_per_f": 6, + "full_prefix_endpoint_arity_per_f": 14, + "native_arity_per_f": 4, + "native_planes": [ + 3, + 7 + ], + "word": [ + { + "coefficient": "-1", + "word": [ + 8, + 7, + 0, + 4, + 3, + 0 + ] + } + ] + } + ], + "literal_inverse_both_orders": "PASS", + "q": 4, + "tail_counts": { + "ADDRESS_scans": 8, + "ADD_scans": 35, + "BANK_SWAP_scans": 3, + "H2": 6, + "H4": 1, + "native_adapter_scans_at_most": 14, + "ordinary_helpers": 0, + "private_fields": 0, + "rank_mass": 16 + }, + "tail_events": [ + { + "bank": 1, + 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+ "native_arity_per_f": 0, + "op": "ADD", + "src": 8 + }, + { + "coefficient": 1, + "dst": 3, + "native_arity_per_f": 0, + "op": "ADD", + "src": 8 + }, + { + "bank": 3, + "native_arity_per_f": 0, + "op": "ADDRESS", + "sign": 1, + "word": [ + "P1^-1" + ] + }, + { + "coefficient": -1, + "dst": 3, + "native_arity_per_f": 0, + "op": "ADD", + "src": 0 + }, + { + "coefficient": -1, + "dst": 3, + "native_arity_per_f": 0, + "op": "ADD", + "src": 2 + }, + { + "coefficient": -1, + "dst": 3, + "native_arity_per_f": 0, + "op": "ADD", + "src": 4 + }, + { + "coefficient": -1, + "dst": 3, + "native_arity_per_f": 0, + "op": "ADD", + "src": 6 + }, + { + "coefficient": -1, + "dst": 3, + "native_arity_per_f": 0, + "op": "ADD", + "src": 8 + }, + { + "coefficient": -1, + "dst": 3, + "native_arity_per_f": 0, + "op": "ADD", + "src": 1 + }, + { + "coefficient": 1, + "dst": 1, + "native_arity_per_f": 0, + "op": "ADD", + "src": 3 + }, + { + "bank": 1, + "native_arity_per_f": 2, + "op": "NATIVE", + "sign": 1, + "word": [ + "N^-1" + ] + }, + { + "bank": 3, + "native_arity_per_f": 2, + "op": "NATIVE", + "sign": 1, + "word": [ + "N^-1" + ] + } + ] + } + ], + "limits": [ + "All native adapters, public ADDRESS/ADD scans and physical bank accesses are paid; their finite constants depend on q.", + "The written induction, finite all-column witnesses and actual all-f operator lift are separate from a formal-kernel certificate.", + "Native retiming may fuse calls and must be validated as a changed complete event word; no source code or idle is silently omitted.", + "No new exponent, all-size dispatcher, stock-owner, numerical precision or tape implementation is claimed." + ], + "no_new_kappa": true, + "ordinary_factory_support_proof": "After aligning terminal rows with J, D0 has N-plane support{5,9,13,...<=2q+1} ofsize floor(q/2), D1 support{3,7,11,...<=2q+1} ofsize ceil(q/2). Induction on the displayed homogeneous anti-diagonal update adds the next odd native plane to the alternating factory. All planes are distinct; no N^2 cancellation occurs. Their sum isq, not one charge per unexamined word symbol. D_i^-1 N has exactarity2(|support_i|+1)f.", + "producer_sha256": "66b656426f974fcd64540b0ab75e53d4cffcbdb35c4e15b495a7b8beeb180b46", + "scientific_pin": "20ecf2891d80b5acf18d980b2164fb44ea7faa90", + "scope_of_mass_gate": "This is a fully priced constructive tail and its exact profile. The growing factory arities explain why the displayed direct inversion loses the prefix2q slack. It is not a lower bound against all joint H/L words, new bank encoders, native charts or operator-valued bridges.", + "source_ADDRESS_geometry": "In the odd handoff the homogeneous old-v coefficient before postADDRESS is literally -Fprev*v: no new native query acts on it. A physical postADDRESS preserves its native arity while the ambient acquires one fresh native plane. This scoped deficit explains why merely replacing that final ADDRESS does not supply its missing progress; a changed held/delivery map could be outside it.", + "source_pins": [ + { + "path": "/Users/ross/git/math/.research-automation/runs/kappa-four-coordinate-20261019T0717Z/native-frames/parametric_factory_tail.py", + "sha256": "4addbe1695a69a7520e6401a0c6878b00846adade11cc498d1770049c9ce8f59" + }, + { + "path": "/Users/ross/git/math/.research-automation/runs/kappa-four-coordinate-20261019T0717Z/caller/plane_group.py", + "sha256": "0c54c2e2462390bd0e9a8d47fc765b70e168ced1e0ef5de49e0afed653e26feb" + }, + { + "path": "/Users/ross/git/math/.research-automation/runs/kappa-four-coordinate-20261019T0717Z/caller/handoff_family.py", + "sha256": "337c5c061f283673fd00057ba16d1cc0b65257cd29b02a3e071eb6c569294fe4" + } + ], + "source_receipt_sha256": "75a32dd9f41998b63ac8913ee16a2333242b82508f5bba405fda9eb13c1ae955", + "status": "PASS_COMPLETE_GENERIC_HANDOFF_TAIL_WITH_READERS" +} diff --git a/research/two-pivot-caller-readers/source/native-frames/lifted_algebra.py b/research/two-pivot-caller-readers/source/native-frames/lifted_algebra.py new file mode 100644 index 0000000000..a63509e504 --- /dev/null +++ b/research/two-pivot-caller-readers/source/native-frames/lifted_algebra.py @@ -0,0 +1,123 @@ +"""Exact all-f tensor algebra with one distinguished Pauli-controlled coordinate. +Apache-2.0; substantial OpenAI Codex assistance. No finite-f extrapolation. +""" +from dataclasses import dataclass +from fractions import Fraction as F +from native_model import * +@dataclass(frozen=True) +class G: + a:F=F(0);b:F=F(0) + def __add__(s,t): + if not isinstance(t,G):t=G(F(t)) + return G(s.a+t.a,s.b+t.b) + def __neg__(s):return G(-s.a,-s.b) + def __sub__(s,t):return s+-t + def __mul__(s,t): + if not isinstance(t,G):t=G(F(t)) + return G(s.a*t.a-s.b*t.b,s.a*t.b+s.b*t.a) + def conj(s):return G(s.a,-s.b) + def __truediv__(s,t): + if not isinstance(t,G):t=G(F(t)) + d=t.a*t.a+t.b*t.b;need(bool(d),'nonzero Gaussian divisor');return s*t.conj()*G(1/d) + def __bool__(s):return bool(s.a or s.b) + def encode(s):return[str(s.a),str(s.b)] +ZERO=G();ONE=G(F(1));I=G(F(0),F(1));UNITS=(ONE,I,-ONE,-I) +def phasevec(q):return tuple(UNITS[(q if isinstance(q,int)else q(r))%4]for r in range(4)) +def cadd(a,c):return tuple(x+y for x,y in zip(a,c)) +def cmul(a,c):return tuple(x*y for x,y in zip(a,c)) +def cconj(a):return tuple(x.conj()for x in a) +def czero(a):return not any(a) +class Algebra: + def __init__(self,stages=4): + self.stages=stages;self.m=2+2*stages;self.rep={};self.products={};self.inverses={};self.phase_cache={};self.model=Model(1,stages);self.idkey=self.canonical(ce.ident(self.m))[0] + self.one={(self.idkey,self.idkey):(ONE,)*4};self.N=self.lift(self.model.N,exponent=1);self.U=self.lift(self.model.U);self.V=self.product(self.N,self.adjoint(self.U));self.P=[self.lift(x)for x in self.model.P];self.T=[self.lift(x,exponent=1)for x in self.model.T];self.Q=[] + for s in range(stages+1):self.Q.append(self.lift(ce.xgate(self.m,1<<(2*s)),ce.ident(self.m))) + def canonical(self,op): + key=op.tab + # Same signed tableau means the representative differs by exactly a Gaussian unit. + state,depth=b.sparse_column(op);first=state[min(state)];q=None + for j in range(4): + a,c=b.gaussian_unit(first,-j) + if a>0 and c>=0:q=j;break + need(q is not None,'canonical Gaussian amplitude phase') + if key not in self.rep:self.rep[key]=op.then(phase(op.n,-q)) + return key,q + def multiply_keys(self,a,c): + if(a,c)not in self.products:self.products[(a,c)]=self.canonical(mul(self.rep[a],self.rep[c])) + return self.products[(a,c)] + def adjoint_key(self,a): + if a not in self.inverses:self.inverses[a]=self.canonical(self.rep[a].adjoint()) + return self.inverses[a] + def lift(self,dist,bulk=None,exponent=0): + if bulk is None:bulk=dist + kd,qd=self.canonical(dist);kb,qb=self.canonical(bulk) + need(b.binary_tableau(dist)==b.binary_tableau(bulk),'distinguished difference must be Pauli only') + return{(kd,kb):phasevec(lambda r:exponent*(1-r)+qd+qb*(r-1))} + def add(self,a,c): + out=dict(a) + for k,v in c.items(): + w=cadd(out.get(k,(ZERO,)*4),v) + if czero(w):out.pop(k,None) + else:out[k]=w + return out + def scale(self,a,c): + if not isinstance(c,G):c=G(F(c)) + return{k:tuple(c*x for x in v)for k,v in a.items()if c} + def product(self,a,c): + out={} + for(ad,ab),av in a.items(): + for(cd,cb),cv in c.items(): + kd,qd=self.multiply_keys(ad,cd);kb,qb=self.multiply_keys(ab,cb);phase=phasevec(lambda r:qd+qb*(r-1));value=cmul(cmul(av,cv),phase);key=(kd,kb);value=cadd(out.get(key,(ZERO,)*4),value) + if czero(value):out.pop(key,None) + else:out[key]=value + return out + def adjoint(self,a): + out={} + for(ad,ab),av in a.items(): + kd,qd=self.adjoint_key(ad);kb,qb=self.adjoint_key(ab);value=cmul(cconj(av),phasevec(lambda r:qd+qb*(r-1)));out=self.add(out,{(kd,kb):value}) + return out + def mat_identity(self,n):return[[dict(self.one)if i==j else{}for j in range(n)]for i in range(n)] + def mat_product(self,a,c): + n=len(a);out=[[{}for j in range(n)]for i in range(n)] + for i in range(n): + for k in range(n): + if not a[i][k]:continue + for j in range(n): + if c[k][j]:out[i][j]=self.add(out[i][j],self.product(a[i][k],c[k][j])) + return out + def router(self,n,a,c,selector=0,sign=1): + out=self.mat_identity(n);Q=self.scale(self.Q[selector],sign);ep=self.scale(self.add(self.one,Q),F(1,2));em=self.scale(self.add(self.one,self.scale(Q,-1)),F(1,2));out[a][a]=out[c][c]=ep;out[a][c]=out[c][a]=em;return out + def diagonal(self,n,bank,op):out=self.mat_identity(n);out[bank][bank]=op;return out + def continuation(self,choice): + if choice=='U':return self.U + if choice=='V':return self.V + # alpha_f=(-i)^(f+1), selected completed fresh1 p-bit. Conditional + # continuation is directly admitted by the R diag(U,I) R word. + need(choice in('C+','C-'),'known role') + Q=self.Q[1];ep=self.scale(self.add(self.one,Q),F(1,2));em=self.scale(self.add(self.one,self.scale(Q,-1)),F(1,2));alpha=phasevec(lambda r:-r-1);av={k:cmul(v,alpha)for k,v in self.V.items()} + return self.add(self.product(ep if choice=='C+'else em,self.U),self.product(em if choice=='C+'else ep,av)) + def box(self,n,stage,kind,target,source,role='U',c=1,target_P=False): + out=self.mat_identity(n);W=self.continuation(role);P=self.P[stage] + if kind=='F':out[source][source]=self.product(W,P);out[target][source]=self.scale(self.N,c) + elif kind=='G': + Wi=self.adjoint(W);out[source][source]=Wi;out[target][target]=P;out[target][source]=self.scale(self.product(self.product(P,self.N),Wi),c) + else:raise ValueError(kind) + if target_P: + need(kind=='F','only forward postdelivery/pre-T target P admitted') + out=self.mat_product(self.diagonal(n,target,P),out) + return out + def allf_target_residual(self,a): + # Right-normalize the desired full native common N. A positive result + # has entries in the fixed distinguished Pauli algebra, bulk identity. + Ni=self.adjoint(self.N);res=[] + for row in a: + rr=[] + for entry in row: + v=self.product(entry,Ni) + if any(kb!=self.idkey for kd,kb in v):return None + if any(b.binary_tableau(self.rep[kd])!=b.binary_tableau(ce.ident(self.m))for kd,kb in v):return None + rr.append(v) + res.append(rr) + return res + def fingerprint(self,a): + return tuple(tuple(tuple(sorted((str(k),tuple((v.a,v.b)for v in vec))for k,vec in entry.items()))for entry in row)for row in a) diff --git a/research/two-pivot-caller-readers/source/native-frames/native_model.py b/research/two-pivot-caller-readers/source/native-frames/native_model.py new file mode 100644 index 0000000000..0ab770f491 --- /dev/null +++ b/research/two-pivot-caller-readers/source/native-frames/native_model.py @@ -0,0 +1,67 @@ +"""Pinned Gaussian Clifford model for common2/fresh2 native bridges. +Apache-2.0; substantial OpenAI Codex assistance. Frozen imports are read only. +""" +from pathlib import Path +import hashlib,importlib.util,sys +sys.dont_write_bytecode=True +BASE=Path(__file__).resolve().parents[1] +PIN='20ecf2891d80b5acf18d980b2164fb44ea7faa90' +CE_PATH=BASE/'vendor/clifford_exact.py' +CE_SHA='2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962' +BOUND_PATH=BASE/'vendor/full_stabilizer_bound.py' +BOUND_SHA='f073a00ad4831616e873eb110fd33ad7226010a7c2f6cfa6a6b63167bf58ef75' +def need(ok,why): + if not ok:raise ValueError(why) +def load(name,path,sha): + need(hashlib.sha256(path.read_bytes()).hexdigest()==sha,'source pin '+str(path)) + spec=importlib.util.spec_from_file_location(name,path);mod=importlib.util.module_from_spec(spec);sys.modules[name]=mod;spec.loader.exec_module(mod);return mod +ce=load('native_frames_pinned_clifford',CE_PATH,CE_SHA) +b=load('native_frames_frozen_independent',BOUND_PATH,BOUND_SHA) +def mul(*ops):return b.standard_product(ce,*ops) +def same(a,c,why,phase=True): + need(a.tab==c.tab,why+' signed tableau') + if phase:need(b.sparse_column(a)==b.sparse_column(c),why+' actual Gaussian phase') +def phase(n,p):return ce.Op(n,ce.identity(n),[('phase',p%4)]) +def symplectic_defect_rank(op): + return b.binary_rank(x^y for x,y in zip(b.binary_tableau(op),b.binary_tableau(ce.ident(op.n)))) +def pauli(n,x=0,z=0,p=0): + out=ce.diag(n,[0]*n,[2*((z>>j)&1)for j in range(n)]) + return mul(phase(n,p),ce.xgate(n,x),out) +def conjugated_pauli(op,x=0,z=0,p=0): + triple=ce.apply(op.tab,(x,z,p));return pauli(op.n,*triple),triple +class Model: + def __init__(self,f=1,stages=4): + need(f>=1 and stages>=1,'positive chunk/stages');self.f=f;self.stages=stages;self.n=(2+2*stages)*f;self.I=ce.ident(self.n) + self.N=self.Npair(0,1);self.U=self.Hp(0);self.V=mul(self.N,self.U.adjoint()) + self.P=[self.swap_pair(s+1)for s in range(stages)];self.T=[self.Npair(2+2*s,3+2*s)for s in range(stages)] + self.Q=ce.xgate(self.n,1) + def Hp(self,chunk): + out=self.I + for j in range(self.f): + bit=chunk*self.f+j;alpha=[0]*self.n;alpha[bit]=2 + out=mul(ce.diag(self.n,[0]*self.n,alpha),ce.cgate(self.n,1<=4,'pqqp uses4 stages');gs=[self.I,self.I];controls=[];F=self.I + for s,(kind,W) in enumerate(zip('FGFG',[self.U,self.V,self.V,self.U])): + required=self.phi(gs[1])if kind=='F'else mul(W,self.N.adjoint(),gs[1],self.N,W.adjoint()) + L=mul(required,gs[0].adjoint());controls.append(L);gs[0]=required + if kind=='F':gs=[gs[0],mul(W,self.P[s],gs[1],W.adjoint())] + else:gs=[mul(W.adjoint(),gs[0],W),mul(self.P[s],gs[1])] + F=mul(self.T[s],F) + return gs,controls diff --git a/research/two-pivot-caller-readers/source/root-chronology/CHART-CYCLE-PACK-HANDOFF-SIX.json b/research/two-pivot-caller-readers/source/root-chronology/CHART-CYCLE-PACK-HANDOFF-SIX.json new file mode 100644 index 0000000000..f5b003bda5 --- /dev/null +++ b/research/two-pivot-caller-readers/source/root-chronology/CHART-CYCLE-PACK-HANDOFF-SIX.json @@ -0,0 +1,595 @@ +{ + "candidate_count": 7609, + "cycle_count": 36, + "cycles": [ + [ + 0, + 7, + 48, + 49, + 84, + 103, + 115, + 127, + 133, + 157, + 169, + 175 + ], + [ + 1, + 25, + 145, + 181, + 193, + 259, + 265, + 289, + 301, + 337, + 619 + ], + [ + 2, + 13, + 26, + 31, + 55, + 56, + 85, + 102, + 114, + 128, + 134, + 156, + 170, + 176 + ], + [ + 4, + 52, + 130, + 136, + 172, + 202, + 262, + 274, + 364, + 388, + 460, + 574, + 580, + 610 + ], + [ + 5, + 53, + 131, + 137, + 173, + 191, + 209, + 233, + 299, + 305, + 353, + 455, + 515, + 527, + 533, + 593 + ], + [ + 6, + 24, + 36, + 54, + 126, + 132, + 168, + 198, + 258, + 264, + 282, + 318, + 360, + 372, + 378 + ], + [ + 8, + 50, + 86, + 104, + 110, + 158, + 212, + 224, + 254, + 266, + 362, + 386, + 458, + 572, + 578, + 596 + ], + [ + 9, + 51, + 129, + 135, + 153, + 165, + 213, + 225, + 243, + 255, + 273, + 279, + 291, + 297, + 321, + 381, + 417, + 441, + 501, + 549, + 603 + ], + [ + 10, + 28, + 148, + 184, + 208, + 232, + 298, + 310, + 340, + 622 + ], + [ + 11, + 29, + 149, + 185, 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Odd sum of edge parity labels therefore forces at least one violation. Edge disjointness adds rank2 per selected subgraph; the certificate checks are exact integers.", + "rank_mass_lower_bound": 72, + "scope": "Fixed native-chart compiler and exact handoff-six ADD/ADDRESS skeleton only.", + "solver_status": 0, + "source_path": "/Users/ross/git/math/.research-automation/runs/kappa-four-coordinate-20261019T0717Z/root-chronology/INDEPENDENT-HANDOFF-SIX.json", + "source_sha256": "594bd4cabfcbbfff4de18e49381f46480118f8f1e41412431fa9ffc4b1ee9eaa", + "status": "PASS_EXACT_PACKED_CHART_CYCLE_CERTIFICATE" +} diff --git a/research/two-pivot-caller-readers/source/root-chronology/CHRONOLOGY.json b/research/two-pivot-caller-readers/source/root-chronology/CHRONOLOGY.json new file mode 100644 index 0000000000..5e6c22c5b3 --- /dev/null +++ b/research/two-pivot-caller-readers/source/root-chronology/CHRONOLOGY.json @@ -0,0 +1,836 @@ +{ + "algebra": "N_a commute; N_a^2=-I; P N_a P^-1=N_P(a). Exact phases and block permutations retained.", + "all_f": "Algebra holds for the independently pinned phase-normalized N_f. Native arity 2 per occupied block is 2f at chunk size f. 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A coupled word can combine several responses.", + "No actual whole supplier, improved BIT, joint transfer or new kappa." + ], + "no_new_kappa": true, + "orders": [ + { + "events": [ + "S_before", + "N", + "S_after", + "T", + "ADD" + ], + "kernel": { + "block_permutation": [ + 0, + 1, + 2, + 3 + ], + "native_arity": 0, + "native_blocks": [], + "sign": 1 + } + }, + { + "events": [ + "S_before", + "N", + "S_after", + "ADD", + "T" + ], + "kernel": { + "block_permutation": [ + 0, + 1, + 2, + 3 + ], + "native_arity": 2, + "native_blocks": [ + 1 + ], + "sign": 1 + } + }, + { + "events": [ + "S_before", + "N", + "T", + "S_after", + "ADD" + ], + "kernel": { + "block_permutation": [ + 0, + 1, + 2, + 3 + ], + "native_arity": 0, + "native_blocks": [], + "sign": 1 + } + }, + { + "events": [ + "S_before", + "N", + "T", + "ADD", + "S_after" + ], + "kernel": { + "block_permutation": [ + 1, + 0, + 2, + 3 + ], + "native_arity": 4, + "native_blocks": [ + 0, + 1 + ], + "sign": -1 + } + }, + { + "events": [ + "S_before", + "N", + "ADD", + "S_after", + "T" + ], + "kernel": { + "block_permutation": [ + 1, + 0, + 2, + 3 + ], + "native_arity": 2, + "native_blocks": [ + 0 + ], + "sign": 1 + } + }, + { + "events": [ + "S_before", + "N", + "ADD", + "T", + "S_after" + ], + "kernel": { + "block_permutation": [ + 1, + 0, + 2, + 3 + ], + "native_arity": 2, + "native_blocks": [ + 0 + ], + "sign": 1 + } + }, + { + "events": [ + "S_before", + "T", + "N", + "S_after", + "ADD" + ], + "kernel": { + "block_permutation": [ + 0, + 1, + 2, + 3 + ], + "native_arity": 0, + "native_blocks": [], + "sign": 1 + } + }, + { + "events": [ + "S_before", + "T", + "N", + "ADD", + "S_after" + ], + "kernel": { + "block_permutation": [ + 1, + 0, + 2, + 3 + ], + "native_arity": 4, + "native_blocks": [ + 0, + 1 + ], + "sign": -1 + } + }, + { + "events": [ + "S_before", + "T", + "ADD", + "N", + "S_after" + ], + "kernel": { + "block_permutation": [ + 1, + 0, + 2, + 3 + ], + "native_arity": 2, + "native_blocks": [ + 1 + ], + "sign": -1 + } + }, + { + "events": [ + "S_before", + "ADD", + "N", + "S_after", + "T" + ], + "kernel": { + "block_permutation": [ + 1, + 0, + 2, + 3 + ], + "native_arity": 0, + "native_blocks": [], + "sign": 1 + } + }, + { + "events": [ + "S_before", + "ADD", + "N", + "T", + "S_after" + ], + "kernel": { + "block_permutation": [ + 1, + 0, + 2, + 3 + ], + "native_arity": 0, + "native_blocks": [], + "sign": 1 + } + }, + { + "events": [ + "S_before", + "ADD", + "T", + "N", + "S_after" + ], + "kernel": { + "block_permutation": [ + 1, + 0, + 2, + 3 + ], + "native_arity": 0, + "native_blocks": [], + "sign": 1 + } + }, + { + "events": [ + "T", + "S_before", + "N", + "S_after", + "ADD" + ], + "kernel": { + "block_permutation": [ + 0, + 1, + 2, + 3 + ], + "native_arity": 0, + "native_blocks": [], + "sign": 1 + } + }, + { + "events": [ + "T", + "S_before", + "N", + "ADD", + "S_after" + ], + "kernel": { + "block_permutation": [ + 1, + 0, + 2, + 3 + ], + "native_arity": 4, + "native_blocks": [ + 0, + 1 + ], + "sign": -1 + } + }, + { + "events": [ + "T", + "S_before", + "ADD", + "N", + "S_after" + ], + "kernel": { + "block_permutation": [ + 1, + 0, + 2, + 3 + ], + "native_arity": 2, + "native_blocks": [ + 1 + ], + "sign": -1 + } + }, + { + "events": [ + "T", + "ADD", + "S_before", + "N", + "S_after" + ], + "kernel": { + "block_permutation": [ + 0, + 1, + 2, + 3 + ], + "native_arity": 2, + "native_blocks": [ + 1 + ], + "sign": -1 + } + }, + { + "events": [ + "ADD", + "S_before", + "N", + "S_after", + "T" + ], + "kernel": { + "block_permutation": [ + 0, + 1, + 2, + 3 + ], + "native_arity": 0, + "native_blocks": [], + "sign": 1 + } + }, + { + "events": [ + "ADD", + "S_before", + "N", + "T", + "S_after" + ], + "kernel": { + "block_permutation": [ + 0, + 1, + 2, + 3 + ], + "native_arity": 0, + "native_blocks": [], + "sign": 1 + } + }, + { + "events": [ + "ADD", + "S_before", + "T", + "N", + "S_after" + ], + "kernel": { + "block_permutation": [ + 0, + 1, + 2, + 3 + ], + "native_arity": 0, + "native_blocks": [], + "sign": 1 + } + }, + { + "events": [ + "ADD", + "T", + "S_before", + "N", + "S_after" + ], + "kernel": { + "block_permutation": [ + 0, + 1, + 2, + 3 + ], + "native_arity": 0, + "native_blocks": [], + "sign": 1 + } + } + ], + "scope": "S,N,S source chronology and one fresh target T, one delivery ADD; no common U, extra bank bridge or general local synthesis. 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".research-automation/runs/kappa-four-coordinate-20261019T0717Z/native-frames/ENCODED-STAGE-TAIL.json": "ae81532cb0d3be9e4e384f4f97e10281d1fe81b39c6c447c06cf00dd555cf1b8" + }, + "status": "SERIALIZED_COMPLETED_ENCODED_CALLER_PENDING_INDEPENDENT_REPLAY", + "width": 8 +} diff --git a/research/two-pivot-caller-readers/source/root-chronology/EXACT-CHART-RESULTS.json b/research/two-pivot-caller-readers/source/root-chronology/EXACT-CHART-RESULTS.json new file mode 100644 index 0000000000..a6d3cf7573 --- /dev/null +++ b/research/two-pivot-caller-readers/source/root-chronology/EXACT-CHART-RESULTS.json @@ -0,0 +1,59 @@ +{ + "limits": [ + "The exact lower-bound certificate concerns n6 only; n8 has a matching break-even candidate but no general lower-bound claim here.", + "This is a finite exact certificate plus an all-f chart-compiler argument, not a formal-kernel theorem." + ], + "lower_bound": { + "ambient_arity": 12, + "banks": 6, + "cycles": 36, + "matching_word_mass": 72, + "native_mass_at_least": 72 + }, + "moment_consequence": "Within this fixed compiler, every full-output width6 caller has rankmass>=6*12. If every recursive rankr<12 and b>0, sum r^(1-b)>12^(-b)*sum r >=6*12^(1-b). Thus no favorable positive-b moment in this compiler; added costs cannot help.", + "no_new_kappa": true, + "positive_words": [ + { + "D": 0, + "ambient_arity": 12, + "banks": 6, + "candidate": "SIGNED-CHART-HANDOFF-SIX.json", + "histogram": { + "2": 21, + "4": 4, + "6": 1, + "8": 1 + }, + "mass": 72, + "stock": 72 + }, + { + "D": 0, + "ambient_arity": 16, + "banks": 8, + "candidate": "SIGNED-CHART-HANDOFF-Q3.json", + "histogram": { + "2": 48, + "4": 2, + "8": 3 + }, + "mass": 128, + "stock": 128 + } + ], + "producer_sha256": "feffe91b94f1b41c250580c727656d85d808a32c481f3dabff967bd51dc593b4", + "proof": "For any bit assignment to the chart graph, XOR of variable endpoint labels around every selected Eulerian subgraph is zero. Its odd signed edge sum forces at least one charged violation. Selected edge sets are disjoint; each violation has native rank2f. The bound72f matches the independently replayed word.", + "scope": "All native-product chart retimings with the fixed literal ADD/ADDRESS/bank-SWAP skeleton of INDEPENDENT-HANDOFF-SIX.json. It does not cover altered joint bridges, changed ADD skeletons, new source deliveries, projective splitting or different endpoint contracts.", + "sources": { + "/Users/ross/git/math/.research-automation/runs/kappa-four-coordinate-20261019T0717Z/root-chronology/CHART-CYCLE-PACK-HANDOFF-SIX.json": "41b31ffd411ec8de46f218039ed1efa4f2d9edd9f5ebeac9fd21aae2880e09ab", + "/Users/ross/git/math/.research-automation/runs/kappa-four-coordinate-20261019T0717Z/root-chronology/HANDOFF-COMPLETE-Q3.json": "540b372de474495125620b481952b66f9b8766ffb03e3c49d8dc23b7a5b1e84b", + "/Users/ross/git/math/.research-automation/runs/kappa-four-coordinate-20261019T0717Z/root-chronology/INDEPENDENT-HANDOFF-SIX.json": "594bd4cabfcbbfff4de18e49381f46480118f8f1e41412431fa9ffc4b1ee9eaa", + "/Users/ross/git/math/.research-automation/runs/kappa-four-coordinate-20261019T0717Z/root-chronology/SIGNED-CHART-HANDOFF-Q3.json": "a55def49f15798c0c00c501f363a3889b54d92adc93e27bebf657de9f82b3970", + 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"PASS_EXACT_RETIMED_WORDS_AND_FIXED_N6_MASS_FLOOR" +} diff --git a/research/two-pivot-caller-readers/source/root-chronology/HANDOFF-COMPLETE-Q3.json b/research/two-pivot-caller-readers/source/root-chronology/HANDOFF-COMPLETE-Q3.json new file mode 100644 index 0000000000..3f0d09a31c --- /dev/null +++ b/research/two-pivot-caller-readers/source/root-chronology/HANDOFF-COMPLETE-Q3.json @@ -0,0 +1,5458 @@ +{ + "all_original_columns": 8, + "ambient_arity": 16, + "both_literal_inverse_orders": true, + "deficit": -8, + "events": [ + { + "coefficient": "1", + "dst": 5, + "kind": "ADD", + "label": "raw c-basis", + "src": 3 + }, + { + "coefficient": "1", + "dst": 7, + "kind": "ADD", + "label": "raw c-basis", + "src": 3 + }, + { + "bank": 1, + "kind": "NATIVE", + "label": "shared input N exposure", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7 + ], + "native_arity": 2, + "native_blocks": [ + 0 + ], + "sign": 1 + } + }, + { + "coefficient": "1", + "dst": 2, + 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"proof": "In the simultaneous X-character basis every source literal is affine monomial with a Z4 quadratic phase. The saved C,P,D,X,phase circuits are interpreted independently. Composing phase polynomials exactly and collecting Gaussian coefficients for all four f classes proves the uniform tensor-family matrix equality. No finite-f relation is promoted.", + "sources": { + "/Users/ross/git/math/.research-automation/runs/kappa-four-coordinate-20261019T0717Z/caller/ENCODED-PHYSICAL-PREFIX.json": "c86df96803014f17ecda80f3cba88b15b72bf91f2254e6fc9362a87e6e0c6093", + "/Users/ross/git/math/.research-automation/runs/kappa-four-coordinate-20261019T0717Z/native-frames/ENCODED-STAGE-TAIL.json": "ae81532cb0d3be9e4e384f4f97e10281d1fe81b39c6c447c06cf00dd555cf1b8", + "/Users/ross/git/math/.research-automation/runs/kappa-four-coordinate-20261019T0717Z/root-chronology/quadratic_charts.py": "de2a36f6a6b567360c90477b58da44e2f1b618fd006d058ab1ea04e983952c3f" + }, + "status": "PASS_INDEPENDENT_ACTUAL_COMPLETE_ENCODED_CALLER_ALL_F", + "stock": 128, + "width": 8 +} diff --git a/research/two-pivot-caller-readers/source/root-chronology/INDEPENDENT-HANDOFF-FAMILY.json b/research/two-pivot-caller-readers/source/root-chronology/INDEPENDENT-HANDOFF-FAMILY.json new file mode 100644 index 0000000000..2726c75a53 --- /dev/null +++ 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"coefficient": "1", + "dst": 1, + "kind": "ADD", + "src": 3 + }, + { + "bank": 1, + "kind": "NATIVE", + "label": "N^-1", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 0 + ], + "sign": -1 + } + }, + { + "bank": 3, + "kind": "NATIVE", + "label": "N^-1", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 0 + ], + "sign": -1 + } + } + ], + "limits": [ + "The n4 complete caller still has mass60 against stock48.", + "No unobserved bank interval or future scalable caller is assumed.", + "Native adapters, tape/controller realization, precision and compatible BIT are separate obligations." + ], + "no_new_kappa": true, + "original_histogram": { + "2": 28, + "4": 1 + }, + "plane_algebra_sha256": "eed0590640dadcd48c683d142899396b563e843a6c15c9df3cc5d1ecdc107a2c", + "producer_sha256": "8773bb4bd31d76e45e3644e88069e48fab6f98aa9d0a2a879643835b96b98f33", + "proof": "Inductively old bank i equals pending[i] times new bank i. Equal pending products commute through ADD, commuting unary events preserve the invariant, BANK_SWAP exchanges pending products, and a flush realizes the exact pending product in strictly contracting pieces. Final pending products are identity.", + "rank_mass": 60, + "source_path": "/Users/ross/git/math/.research-automation/runs/kappa-four-coordinate-20261019T0717Z/root-chronology/INDEPENDENT-SHARED-CALLER.json", + "source_sha256": "68c4e9b19b396bc3e45cf6ef32c3034e536059c8cc36d8a4be8fdc4ad2cb9c23", + "status": "PASS_EXACT_PAID_PROGRESS_BATCHING" +} diff --git a/research/two-pivot-caller-readers/source/root-chronology/SAVED-QUADRATIC-WORDS-VALIDATION.json b/research/two-pivot-caller-readers/source/root-chronology/SAVED-QUADRATIC-WORDS-VALIDATION.json new file mode 100644 index 0000000000..08640d2498 --- /dev/null +++ b/research/two-pivot-caller-readers/source/root-chronology/SAVED-QUADRATIC-WORDS-VALIDATION.json @@ -0,0 +1,60 @@ +{ + "cases": [ + { + "ambient_arity": 16, + "both_literal_inverse_orders": true, + "histogram": { + "1": 16, + "2": 21, + "3": 1, + "6": 4, + "7": 4, + "8": 1, + "9": 1 + }, + "native_rank_mass": 130, + "omitted_query_rejected": true, + "source": "/Users/ross/git/math/.research-automation/runs/kappa-four-coordinate-20261019T0717Z/root-chronology/INDEPENDENT-ENCODED-COMPLETE.json", + "source_sha256": "8a813a7350e2c98c1ec8a61bf772dab98aa4b224a24bb876026c2c07b39bf0b2", + "stock": 128, + "width": 8, + "witness": "/Users/ross/git/math/.research-automation/runs/kappa-four-coordinate-20261019T0717Z/root-chronology/CLUSTER-INDEPENDENT-ENCODED-COMPLETE-ALLPAIRS.json", + "witness_sha256": "b8208943ed1347df432c3263c7ef666bc86140d717df281703600f0a1bb12e2b" + }, + { + "ambient_arity": 16, + "both_literal_inverse_orders": true, + "histogram": { + "1": 14, + "2": 23, + "3": 2, + "5": 2, + "6": 3, + "7": 4, + "8": 1 + }, + "native_rank_mass": 130, + "omitted_query_rejected": true, + "source": "/Users/ross/git/math/.research-automation/runs/kappa-four-coordinate-20261019T0717Z/caller/BALANCED-PHYSICAL-REPLAY-Q3.json", + "source_sha256": "ee3033e7cf709885ad65c2c5e956930b177642f87920070d54d9b6d28ca27dc1", + "stock": 128, + "width": 8, + "witness": "/Users/ross/git/math/.research-automation/runs/kappa-four-coordinate-20261019T0717Z/root-chronology/CLUSTER-BALANCED-PHYSICAL-REPLAY-Q3-ALLPAIRS.json", + "witness_sha256": "cf590c93cd3c780e751c80aaf543f3e9256b293293f8459e19ffc9e5c59f70eb" + } + ], + "domain": "Every integer f>=1; exact Gaussian coefficient tuples for all four residue classes; every original independent bank column.", + "limits": [ + "No optimizer is run and no numerical optimizer bound is used.", + "Rank130 exceeds stock128 before precision, ownership, COPY and tape costs.", + "Every rank invoice still needs native lowering and contracting splits for recursive admission.", + "Older search receipts are historical; this receipt binds only these saved choices to the current exact compiler." + ], + "no_new_kappa": true, + "sources": { + "/Users/ross/git/math/.research-automation/runs/kappa-four-coordinate-20261019T0717Z/root-chronology/audit_encoded_complete.py": "b42056d820b94d503f61fbee137d1da1225074a2fed620e8dab83f3919492ff6", + "/Users/ross/git/math/.research-automation/runs/kappa-four-coordinate-20261019T0717Z/root-chronology/quadratic_charts.py": "de2a36f6a6b567360c90477b58da44e2f1b618fd006d058ab1ea04e983952c3f", + "/Users/ross/git/math/.research-automation/runs/kappa-four-coordinate-20261019T0717Z/root-chronology/verify_saved_quadratic_words.py": "033fc6d73ab0429a5cbd75842f72d443a86f66c1bb14b9b3feaa7e959ff404e5" + }, + "status": "PASS_SAVED_QUADRATIC_WORDS_ALL_F" +} diff --git a/research/two-pivot-caller-readers/source/root-chronology/SIGNED-CHART-HANDOFF-Q3.json b/research/two-pivot-caller-readers/source/root-chronology/SIGNED-CHART-HANDOFF-Q3.json new file mode 100644 index 0000000000..f8cda66da5 --- /dev/null +++ b/research/two-pivot-caller-readers/source/root-chronology/SIGNED-CHART-HANDOFF-Q3.json @@ -0,0 +1,2526 @@ +{ + "ambient_arity": 16, + "choices": [ + 0, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 1, + 1, + 0, + 1, + 1, + 2, + 2, + 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impossibility theorem is claimed.", + "The serialized word is independently checked exactly on all original columns and both inverse orders.", + "Complete native/precision/ownership/source/tape and compatible BIT obligations remain." + ], + "native_mass": 128, + "no_new_kappa": true, + "nodes": 601, + "producer_sha256": "b1ed5ee5ddfaac1e2d0242b499ad69d7adde8e6d636d095be58315b9739176e8", + "scipy_version": "1.18.1", + "solver_float_gap": 0.0, + "solver_float_lower_bound": 128.0, + "solver_message": "Optimization terminated successfully. 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35, + 35, + 3, + 3, + 3, + 3, + 3, + 1, + 1 + ], + "deficit": 0, + "edges": 624, + "events": [ + { + "coefficient": "1", + "dst": 5, + "kind": "ADD", + "label": "input c-basis inverse", + "src": 3 + }, + { + "bank": 1, + "kind": "NATIVE", + "label": "paid chart alignment before ADD", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 0 + ], + "sign": 1 + } + }, + { + "coefficient": "1", + "dst": 2, + "kind": "ADD", + "label": "shared entrance b1 += N t", + "src": 1 + }, + { + "bank": 1, + "kind": "ADDRESS_OR_UNIT", + "label": "exact chart phase", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 0, + "native_blocks": [], + "sign": -1 + } + }, + { + "bank": 5, + "kind": "NATIVE", + "label": "paid chart alignment before ADD", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 0 + ], + "sign": -1 + } + }, + { + "coefficient": "-1", + "dst": 5, + "kind": "ADD", + "label": "scalar nested response bridge", + "src": 1 + }, + { + "coefficient": "1", + "dst": 0, + "kind": "ADD", + "label": "scalar nested response bridge", + "src": 4 + }, + { + "bank": 3, + "kind": "NATIVE", + "label": "paid chart alignment before ADD", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 0 + ], + "sign": -1 + } + }, + { + "coefficient": "-1", + "dst": 3, + "kind": "ADD", + "label": "scalar nested response bridge", + "src": 1 + }, + { + "coefficient": "1", + "dst": 0, + "kind": "ADD", + "label": "scalar nested response bridge", + "src": 2 + }, + { + "coefficient": "-1", + "dst": 2, + "kind": "ADD", + "label": "query1 scalar entrance", + "src": 0 + }, + { + "coefficient": "1", + "dst": 1, + "kind": "ADD", + "label": "query1 raw delivery", + "src": 0 + }, + { + "bank": 0, + "kind": "ADDRESS_OR_UNIT", + "label": "retimed original ADDRESS", + "operator": { + "block_permutation": [ + 1, + 0, + 2, + 3, + 4, + 5 + ], + "native_arity": 0, + "native_blocks": [], + "sign": 1 + } + }, + { + "coefficient": "1", + "dst": 2, + "kind": "ADD", + "label": "query1 scalar exit", + "src": 0 + }, + { + "coefficient": "-1", + "dst": 0, + "kind": "ADD", + "label": "scalar nested response bridge", + "src": 2 + }, + { + "coefficient": "1", + "dst": 1, + "kind": "ADD", + "label": "scalar nested response bridge", + "src": 3 + }, + { + "coefficient": "-1", + "dst": 3, + "kind": "ADD", + "label": "query2 scalar entrance", + "src": 1 + }, + { + "coefficient": "-1", + "dst": 5, + "kind": "ADD", + "label": "query2 scalar entrance", + "src": 1 + }, + { + "bank": 1, + "kind": "ADDRESS_OR_UNIT", + "label": "exact chart phase", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 0, + "native_blocks": [], + "sign": -1 + } + }, + { + "coefficient": "1", + "dst": 2, + "kind": "ADD", + "label": "query2 raw delivery", + "src": 1 + }, + { + "bank": 1, + "kind": "ADDRESS_OR_UNIT", + "label": "retimed original ADDRESS", + "operator": { + "block_permutation": [ + 2, + 1, + 0, + 3, + 4, + 5 + ], + "native_arity": 0, + "native_blocks": [], + "sign": 1 + } + }, + { + "bank": 3, + "kind": "NATIVE", + "label": "paid chart alignment before ADD", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 2 + ], + "sign": 1 + } + }, + { + "bank": 1, + "kind": "NATIVE", + "label": "paid chart alignment before ADD", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 0 + ], + "sign": -1 + } + }, + { + "coefficient": "1", + "dst": 3, + "kind": "ADD", + "label": "query2 scalar exit", + "src": 1 + }, + { + "bank": 5, + "kind": "NATIVE", + "label": "paid chart alignment before ADD", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 2 + ], + "sign": 1 + } + }, + { + "coefficient": "1", + "dst": 5, + "kind": "ADD", + "label": "query2 scalar exit", + "src": 1 + }, + { + "coefficient": "-1", + "dst": 1, + "kind": "ADD", + "label": "scalar nested response bridge", + "src": 3 + }, + { + "bank": 2, + "kind": "NATIVE", + "label": "paid chart alignment before ADD", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 2 + ], + "sign": 1 + } + }, + { + "coefficient": "1", + "dst": 5, + "kind": "ADD", + "label": "query3 entrance from source N exposure", + "src": 2 + }, + { + "coefficient": "1", + "dst": 3, + "kind": "ADD", + "label": "query3 raw delivery", + "src": 2 + }, + { + "bank": 2, + "kind": "ADDRESS_OR_UNIT", + "label": "retimed original ADDRESS", + "operator": { + "block_permutation": [ + 3, + 1, + 2, + 0, + 4, + 5 + ], + "native_arity": 0, + "native_blocks": [], + "sign": 1 + } + }, + { + "bank": 2, + "kind": "NATIVE", + "label": "paid chart alignment 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"kind": "ADD", + "label": "scalar nested response bridge", + "src": 3 + }, + { + "banks": [ + 2, + 3 + ], + "kind": "BANK_SWAP", + "label": "nested response bank permutation" + }, + { + "bank": 4, + "kind": "NATIVE", + "label": "paid chart alignment before ADD", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 2 + ], + "sign": 1 + } + }, + { + "coefficient": "-1", + "dst": 0, + "kind": "ADD", + "label": "scalar nested response bridge", + "src": 4 + }, + { + "coefficient": "1", + "dst": 1, + "kind": "ADD", + "label": "scalar nested response bridge", + "src": 5 + }, + { + "coefficient": "-1", + "dst": 5, + "kind": "ADD", + "label": "query4 scalar entrance before changed source identity", + "src": 1 + }, + { + "coefficient": "-1", + "dst": 3, + "kind": "ADD", + "label": "query4 current encoder c1 -= a", + "src": 0 + }, + { + "coefficient": "-1", + "dst": 3, + "kind": "ADD", + "label": "query4 current encoder c1 -= b2", + "src": 4 + }, + { + "bank": 1, + "kind": "ADDRESS_OR_UNIT", + "label": "exact chart phase", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 0, + "native_blocks": [], + "sign": -1 + } + }, + { + "coefficient": "-1", + "dst": 1, + "kind": "ADD", + "label": "query4 isolate N c2 from held N u", + "src": 3 + }, + { + "banks": [ + 1, + 3 + ], + "kind": "BANK_SWAP", + "label": "query4 source handoff BEFORE source ADDRESS" + }, + { + "bank": 1, + "kind": "ADDRESS_OR_UNIT", + "label": "retimed original ADDRESS", + "operator": { + "block_permutation": [ + 4, + 1, + 2, + 3, + 0, + 5 + ], + "native_arity": 0, + "native_blocks": [], + "sign": 1 + } + }, + { + "banks": [ + 3, + 5 + ], + "kind": "BANK_SWAP", + "label": "query4 put completed public c2 into slot5" + }, + { + "bank": 3, + "kind": "NATIVE", + "label": "paid chart alignment before ADD", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 3 + ], + "sign": 1 + } + }, + { + "bank": 4, + "kind": "NATIVE", + "label": "paid chart alignment before ADD", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 3 + ], + "sign": 1 + } + }, + { + "coefficient": "1", + "dst": 3, + "kind": "ADD", + "label": "query5 cancel b2 from the dirty first-pivot field", + "src": 4 + }, + { + "banks": [ + 4, + 3 + ], + "kind": "BANK_SWAP", + "label": "query5 source handoff BEFORE source ADDRESS" + }, + { + "bank": 2, + "kind": "NATIVE", + "label": "paid chart alignment before ADD", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 3 + ], + "sign": 1 + } + }, + { + "coefficient": "-1", + "dst": 2, + "kind": "ADD", + "label": "query5 current-source fanout b1 -= (-v-N a) BEFORE source ADDRESS", + "src": 4 + }, + { + "bank": 4, + "kind": "ADDRESS_OR_UNIT", + "label": "retimed original ADDRESS", + "operator": { + "block_permutation": [ + 5, + 1, + 2, + 3, + 4, + 0 + ], + "native_arity": 0, + "native_blocks": [], + "sign": 1 + } + }, + { + "banks": [ + 4, + 3 + ], + "kind": "BANK_SWAP", + "label": "query5 restore pivot3 and completed public b2 slot4" + }, + { + "bank": 0, + "kind": "NATIVE", + "label": "paid chart alignment before ADD", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 3 + ], + "sign": 1 + } + }, + { + "coefficient": "-1", + "dst": 2, + "kind": "ADD", + "label": "finish b1 using the current completed public a", + "src": 0 + }, + { + "banks": [ + 1, + 3 + ], + "kind": "BANK_SWAP", + "label": "handoff tail pivot swap" + }, + { + "bank": 1, + "kind": "ADDRESS_OR_UNIT", + "label": "retimed original ADDRESS", + "operator": { + "block_permutation": [ + 5, + 1, + 2, + 3, + 4, + 0 + ], + "native_arity": 0, + "native_blocks": [], + "sign": 1 + } + }, + { + "bank": 3, + "kind": "ADDRESS_OR_UNIT", + "label": "retimed original ADDRESS", + "operator": { + "block_permutation": [ + 4, + 1, + 2, + 0, + 3, + 5 + ], + "native_arity": 0, + "native_blocks": [], + "sign": 1 + } + }, + { + "coefficient": "-1", + "dst": 1, + "kind": "ADD", + "label": "handoff tail ADD", + "src": 3 + }, + { + "coefficient": "1", + "dst": 1, + "kind": "ADD", + "label": "handoff tail ADD", + "src": 0 + }, + { + "coefficient": "1", + "dst": 1, + "kind": "ADD", + "label": "handoff tail ADD", + "src": 2 + }, + { + "bank": 1, + "kind": "ADDRESS_OR_UNIT", + "label": "retimed original ADDRESS", + "operator": { + "block_permutation": [ + 2, + 1, + 0, + 3, + 4, + 5 + ], + "native_arity": 0, + "native_blocks": [], + "sign": 1 + } + }, + { + "coefficient": "-1", + "dst": 1, + "kind": "ADD", + "label": "handoff tail ADD", + "src": 0 + }, + { + "coefficient": "-1", + "dst": 1, + "kind": "ADD", + "label": "handoff tail ADD", + "src": 2 + }, + { + "coefficient": "-1", + "dst": 1, + "kind": "ADD", + "label": "handoff tail 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"sign": 1 + } + }, + { + "coefficient": "1", + "dst": 3, + "kind": "ADD", + "label": "handoff tail ADD", + "src": 2 + }, + { + "bank": 3, + "kind": "NATIVE", + "label": "paid chart alignment before ADD", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 5 + ], + "sign": 1 + } + }, + { + "bank": 4, + "kind": "NATIVE", + "label": "paid chart alignment before ADD", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 4, + "native_blocks": [ + 4, + 5 + ], + "sign": 1 + } + }, + { + "coefficient": "1", + "dst": 3, + "kind": "ADD", + "label": "handoff tail ADD", + "src": 4 + }, + { + "coefficient": "1", + "dst": 3, + "kind": "ADD", + "label": "handoff tail ADD", + "src": 4 + }, + { + "bank": 3, + "kind": "ADDRESS_OR_UNIT", + "label": "retimed original ADDRESS", + "operator": { + "block_permutation": [ + 1, + 0, + 2, + 3, + 4, + 5 + ], + "native_arity": 0, + "native_blocks": [], + "sign": 1 + } + }, + { + "bank": 0, + "kind": "NATIVE", + "label": "paid chart alignment before ADD", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 5 + ], + "sign": 1 + } + }, + { + "coefficient": "-1", + "dst": 3, + "kind": "ADD", + "label": "handoff tail ADD", + "src": 0 + }, + { + "bank": 2, + "kind": "NATIVE", + "label": "paid chart alignment before ADD", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 5 + ], + "sign": 1 + } + }, + { + "coefficient": "-1", + "dst": 3, + "kind": "ADD", + "label": "handoff tail ADD", + "src": 2 + }, + { + "coefficient": "-1", + "dst": 3, + "kind": "ADD", + "label": "handoff tail ADD", + "src": 4 + }, + { + "bank": 3, + "kind": "NATIVE", + "label": "paid chart alignment before ADD", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 2, + "native_blocks": [ + 1 + ], + "sign": 1 + } + }, + { + "bank": 1, + "kind": "NATIVE", + "label": "paid chart alignment before ADD", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 6, + "native_blocks": [ + 1, + 4, + 5 + ], + "sign": 1 + } + }, + { + "coefficient": "-1", + "dst": 3, + "kind": "ADD", + "label": "handoff tail ADD", + "src": 1 + }, + { + "coefficient": "1", + "dst": 1, + "kind": "ADD", + "label": "handoff tail ADD", + "src": 3 + }, + { + "bank": 0, + "kind": "NATIVE", + "label": "paid final chart restoration", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 4, + "native_blocks": [ + 0, + 1 + ], + "sign": 1 + } + }, + { + "bank": 2, + "kind": "NATIVE", + "label": "paid final chart restoration", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 4, + "native_blocks": [ + 0, + 1 + ], + "sign": 1 + } + }, + { + "bank": 4, + "kind": "NATIVE", + "label": "paid final chart restoration", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 4, + "native_blocks": [ + 0, + 1 + ], + "sign": 1 + } + }, + { + "bank": 5, + "kind": "NATIVE", + "label": "paid final chart restoration", + "operator": { + "block_permutation": [ + 0, + 1, + 2, + 3, + 4, + 5 + ], + "native_arity": 8, + "native_blocks": [ + 1, + 3, + 4, + 5 + ], + "sign": 1 + } + } + ], + "histogram": { + "2": 21, + "4": 4, + "6": 1, + "8": 1 + }, + "limits": [ + "A numerical optimizer produced the candidate; no optimum or impossibility theorem is claimed.", + "The serialized word is independently checked exactly on all original columns and both inverse orders.", + "Complete native/precision/ownership/source/tape and compatible BIT obligations remain." + ], + "native_mass": 72, + "no_new_kappa": true, + "nodes": 295, + "producer_sha256": "b1ed5ee5ddfaac1e2d0242b499ad69d7adde8e6d636d095be58315b9739176e8", + "scipy_version": "1.18.1", + "solver_float_gap": 0.0, + "solver_float_lower_bound": 72.0, + "solver_message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "solver_status": 0, + "source_path": "/Users/ross/git/math/.research-automation/runs/kappa-four-coordinate-20261019T0717Z/root-chronology/INDEPENDENT-HANDOFF-SIX.json", + "source_sha256": "594bd4cabfcbbfff4de18e49381f46480118f8f1e41412431fa9ffc4b1ee9eaa", + "status": "PASS_EXACT_SIGNED_GRAPH_RETIMING_CANDIDATE", + "stock": 72, + "width": 6 +} diff --git a/research/two-pivot-caller-readers/source/root-chronology/audit_encoded_complete.py b/research/two-pivot-caller-readers/source/root-chronology/audit_encoded_complete.py new file mode 100644 index 0000000000..061512583a --- /dev/null +++ b/research/two-pivot-caller-readers/source/root-chronology/audit_encoded_complete.py @@ -0,0 +1,69 @@ +#!/usr/bin/env python3 +"""Independent actual-circuit binding and all-column audit of encoded caller. +Apache-2.0; substantial OpenAI Codex assistance. +""" +from pathlib import Path +import argparse,hashlib,json +import quadratic_charts as q +HERE=Path(__file__).resolve().parent + +def circuit(events,n): + I=q.identity(n);out=I + for e in events: + kind=e[0] + if kind=='P': + ri=q.inverse(tuple(e[1]));rows=tuple(sum(((ri[j]>>i)&1)<>i)&1)for i in range(n)),(0,)*n) + elif kind=='phase':g=q.Mono(I.rows,0,(0,)*n,(0,)*n,e[1]%4) + else:raise ValueError('unsupported source literal '+kind) + out=g@out + return out + +def actual(e,n): + if 'exact_operator'in e: + d=e['exact_operator'];g=circuit(d['one_coordinate_literal_circuit'],n);p=d['phase_exponent'];return q.Mono(g.rows,g.offset,g.alpha,g.quad,(g.constant-p)%4,(p+(2 if d['global_sign']==-1 else 0))%4) + d=e['operator'];g=circuit(d['one_bit_circuit'],n);v=d['global_i_exponent_by_f_mod4'];s=(v[1]-v[0])%4 + q.need(all(v[r]==(v[0]+s*r)%4 for r in range(4)),'literal all-f global phase is affine in f') + return q.Mono(g.rows,g.offset,g.alpha,g.quad,(g.constant+s)%4,v[0]) + +def inverse_events(events,n): + out=[] + for e in reversed(events): + if e['kind']=='ADD':e=dict(e,coefficient=str(-q.Fraction(e['coefficient']))) + elif e['kind']=='SCALE':e=dict(e,coefficient=str(1/q.Fraction(e['coefficient']))) + elif e['kind']!='BANK_SWAP':e=dict(kind='INVERSE',bank=e['bank'],x_monomial=q.decode(e,n).inv().data()) + out.append(e) + return out + +def run(): + pp=HERE.parent/'caller/ENCODED-PHYSICAL-PREFIX.json';tp=HERE.parent/'native-frames/ENCODED-STAGE-TAIL.json' + p=json.loads(pp.read_bytes());t=json.loads(tp.read_bytes());n=16;b=8;events=p['events']+t['events'];assembled=[] + for e in events: + e=dict(e) + if e['kind']not in('ADD','BANK_SWAP'): + g=actual(e,n) + if 'exact_operator'in e:q.need(g==q.decode(e,n),'independent literal circuit binds every prefix unary including global phase') + else:e['x_monomial']=g.data() + want=e.get('native_arity_per_f',e['operator'].get('native_arity')) + q.need(q.rank(g.polar())==want,'literal X-quadratic native rank independently matches invoice') + assembled.append(e) + I=q.identity(n);E=q.Mono(I.rows,(1< 0, 'a strictly contracting native plane fits') + + def flush(i, reason): + g = pending[i] + need(g.perm == I.perm, 'pending progress remains a native-plane product') + indices = [j for j in range(planes) if g.mask >> j & 1] + pieces = [indices[j:j + cap_planes] for j in range(0, len(indices), cap_planes)] + if not pieces and g.sign != 1: + pieces = [[]] + product = I + for j, piece in enumerate(pieces): + h = Op(g.sign if j == 0 else 1, sum(1 << t for t in piece), I.perm) + product = h @ product + out.append(dict(kind='NATIVE' if piece else 'ADDRESS_OR_UNIT', bank=i, + operator=h.data(), label='paid grouped pending progress', + flush_reason=reason)) + need(not piece or 2 * (2 * len(piece)) ** 2 < ambient ** 2, + 'every emitted grouped child strictly contracts') + need(product == g, 'exact grouped phase and all pending planes') + decisions.append(dict(bank=i, reason=reason, pending=g.data(), + emitted_arities=[2 * len(x) for x in pieces])) + pending[i] = I + + for index, e in enumerate(events): + kind = e['kind'] + is_progress = (kind == 'NATIVE' and + re.fullmatch(r'query\d+ (?:target fresh|inactive fresh progress)', + e.get('label', '')) is not None) + if is_progress: + g = operator(e['operator']) + need(g.perm == I.perm and g.mask.bit_count() == 1, + 'only explicitly labelled single fresh progress can be delayed') + pending[e['bank']] = g @ pending[e['bank']] + continue + if kind == 'ADD': + i, j = e['dst'], e['src'] + if pending[i] != pending[j]: + flush(i, f'ADD at input event {index}') + flush(j, f'ADD at input event {index}') + elif kind == 'BANK_SWAP': + i, j = e['banks'] + pending[i], pending[j] = pending[j], pending[i] + else: + i = e['bank'] + g = operator(e['operator']) + if g @ pending[i] != pending[i] @ g: + flush(i, f'noncommuting unary at input event {index}') + out.append(e) + for i in range(banks): + flush(i, 'complete endpoint') + return out, decisions + + +def plus(a, b, coefficient=1): + out = dict(a) + for k, v in b.items(): + out[k] = out.get(k, 0) + coefficient * v + if not out[k]: + del out[k] + return out + + +def left(g, a): + out = {} + for h, v in a.items(): + product = g @ h + unsigned = Op(1, product.mask, product.perm) + out = plus(out, {unsigned: product.sign * v}) + return out + + +def identity(banks, planes): + return [[{ident(planes): Fraction(1)} if i == j else {} + for j in range(banks)] for i in range(banks)] + + +def apply(rows, e, inverse=False): + out = [[dict(x) for x in row] for row in rows] + if e['kind'] == 'ADD': + i, j = e['dst'], e['src'] + c = Fraction(e['coefficient']) * (-1 if inverse else 1) + out[i] = [plus(a, b, c) for a, b in zip(out[i], out[j])] + elif e['kind'] == 'BANK_SWAP': + i, j = e['banks'] + out[i], out[j] = out[j], out[i] + else: + g = operator(e['operator']) + if inverse: + g = g.inverse() + i = e['bank'] + out[i] = [left(g, x) for x in out[i]] + return out + + +def replay(events, banks, planes): + start = identity(banks, planes) + out = start + for e in events: + out = apply(out, e) + recovered = out + for e in reversed(events): + recovered = apply(recovered, e, True) + need(recovered == start, 'literal inverse all arbitrary columns') + recovered = start + for e in reversed(events): + recovered = apply(recovered, e, True) + for e in events: + recovered = apply(recovered, e) + need(recovered == start, 'literal inverse opposite order') + return out + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument('--write', action='store_true') + args = parser.parse_args() + source = HERE / 'INDEPENDENT-SHARED-CALLER.json' + data = source.read_bytes() + original = json.loads(data) + events = original['events'] + new, decisions = schedule(events, 4, 6, 12) + need(replay(events, 4, 6) == replay(new, 4, 6), + 'all four physical output columns preserved including native phases') + H = Counter(e['operator']['native_arity'] for e in new if e['kind'] == 'NATIVE') + old_H = Counter(e['operator']['native_arity'] for e in events if e['kind'] == 'NATIVE') + need(sum(r * c for r, c in H.items()) == sum(r * c for r, c in old_H.items()), + 'batching does not claim any removed native rank mass') + # A legal batch is not permission to drop its paid transform. + mutant = [e for e in new if e.get('label') != 'paid grouped pending progress'] + need(replay(mutant, 4, 6) != replay(events, 4, 6), 'omitted grouped progress rejected') + out = dict(status='PASS_EXACT_PAID_PROGRESS_BATCHING', no_new_kappa=True, + producer_sha256=hashlib.sha256(Path(__file__).read_bytes()).hexdigest(), + source_path=str(source), source_sha256=hashlib.sha256(data).hexdigest(), + plane_algebra_sha256=hashlib.sha256((HERE / 'chronology.py').read_bytes()).hexdigest(), + original_histogram=dict(sorted(old_H.items())), + batched_histogram=dict(sorted(H.items())), rank_mass=sum(r*c for r,c in H.items()), + events=new, decisions=decisions, + proof='Inductively old bank i equals pending[i] times new bank i. Equal pending products commute through ADD, commuting unary events preserve the invariant, BANK_SWAP exchanges pending products, and a flush realizes the exact pending product in strictly contracting pieces. Final pending products are identity.', + domain='Every f>=1 in the exact signed native-plane and ADDRESS algebra; all four arbitrary dirty fields. All grouped queries remain explicitly paid.', + controls=['Both literal inverse orders', 'All physical input columns', 'Dropped grouped progress rejected'], + limits=['The n4 complete caller still has mass60 against stock48.', + 'No unobserved bank interval or future scalable caller is assumed.', + 'Native adapters, tape/controller realization, precision and compatible BIT are separate obligations.']) + out = json.loads(json.dumps(out)) + target = HERE / 'PAID-PROGRESS-BATCHING.json' + if args.write: + target.write_text(json.dumps(out, indent=2, sort_keys=True) + '\n') + else: + need(json.loads(target.read_bytes()) == out, 'saved batching receipt differs') + print(out['status'], out['original_histogram'], '->', out['batched_histogram']) + + +if __name__ == '__main__': + main() diff --git a/research/two-pivot-caller-readers/source/root-chronology/chronology.py b/research/two-pivot-caller-readers/source/root-chronology/chronology.py new file mode 100644 index 0000000000..d71cf34957 --- /dev/null +++ b/research/two-pivot-caller-readers/source/root-chronology/chronology.py @@ -0,0 +1,114 @@ +#!/usr/bin/env python3 +"""Exact signed native-block permutation algebra. Apache-2.0; Codex assistance. + +This small census covers only one source N, one target T, source S wrappers, +one delivery ADD. It neither enumerates general monomial circuits nor callers. +""" +from dataclasses import dataclass +from itertools import permutations +from pathlib import Path +import argparse, hashlib, json + +def need(p, m): + if not p: + raise ValueError(m) + +@dataclass(frozen=True) +class Op: + sign: int + mask: int + perm: tuple + + def __matmul__(self, b): + moved = sum(1 << self.perm[i] for i in range(len(self.perm)) if b.mask >> i & 1) + phase = -1 if (self.mask & moved).bit_count() % 2 else 1 + return Op(self.sign * b.sign * phase, self.mask ^ moved, + tuple(self.perm[b.perm[i]] for i in range(len(self.perm)))) + + def inverse(self): + ip = tuple(self.perm.index(i) for i in range(len(self.perm))) + mask = sum(1 << ip[i] for i in range(len(ip)) if self.mask >> i & 1) + return Op(self.sign * (-1 if self.mask.bit_count() % 2 else 1), mask, ip) + + def data(self): + return dict(sign=self.sign, native_blocks=[i for i in range(len(self.perm)) if self.mask >> i & 1], + block_permutation=list(self.perm), native_arity=2*self.mask.bit_count()) + +def ident(b): + return Op(1, 0, tuple(range(b))) + +def native(b, i): + return Op(1, 1 << i, tuple(range(b))) + +def swap(b, i): + p = list(range(b)); p[0], p[i] = p[i], p[0] + return Op(1, 0, tuple(p)) + +def conj(a, b): + return a @ b @ a.inverse() + +def run(): + b=4; I=ident(b); N=native(b,0); T=native(b,1); S=swap(b,1) + need(S @ N == T @ S, 'native/address covariance') + for a in [I,N,T,S,N@S,T@N@S]: + need(a @ a.inverse() == I == a.inverse() @ a, 'literal two-sided inverse') + # All interleavings of S_before,N,S_after on source and T on target, + # with one ADD. Source S,N,S order is fixed. The source remains T. + orders=[]; kernels={} + for order in permutations(('S_before','N','S_after','T','ADD')): + if not (order.index('S_before') < order.index('N') < order.index('S_after')): + continue + src=I; target=I; cross=None + for event in order: + if event.startswith('S_'): + src=S@src + elif event=='N': + src=N@src + elif event=='T': + target=T@target + if cross is not None: + cross=T@cross + else: + cross=src + need(src==T and target==T and cross is not None, 'clean global fresh diagonal') + kernel=T.inverse()@cross + kernels[kernel]=kernels.get(kernel,0)+1 + orders.append(dict(events=order,kernel=kernel.data())) + F=native(b,1)@native(b,2)@native(b,3) + cases=[] + for K,multiplicity in sorted(kernels.items(),key=lambda z:(z[0].mask,z[0].perm,z[0].sign)): + # Re-label the one fresh block to make chronological pair i1,j2. + relabel=Op(1,0,(0,2,1,3)); Ki=K; Kj=conj(relabel,K) + D=native(b,1) + cases.append(dict(kernel=K.data(),multiplicity=multiplicity, + final_single_response=(F@K).data(), + old_first_at_between_cut=conj(D,Ki@Kj).data(), + new_first_at_between_cut=conj(D,Kj@Ki).data())) + full=[z for z in cases if z['final_single_response']['native_arity']==2*b] + need(len(full)==1, 'one full-width single-response type in restricted chronology') + need(full[0]['kernel']['native_blocks']==[0], 'full response is common N times swap') + need(full[0]['old_first_at_between_cut']['native_arity']==0, 'old-first is monomial') + need(full[0]['new_first_at_between_cut']['native_arity']==4, 'new-first costs rank4') + # Deliberately reversing the cut product cannot inherit monomial price. + need(full[0]['new_first_at_between_cut']['native_arity'] != 0, 'wrong product order rejected') + return dict(status='PASS_RESTRICTED_ONE_ADD_LOCAL_CHRONOLOGY',no_new_kappa=True, + source_sha256=hashlib.sha256(Path(__file__).read_bytes()).hexdigest(), + block_count=b, complete_orders=len(orders), distinct_kernels=len(kernels), + orders=orders,cases=cases, + algebra='N_a commute; N_a^2=-I; P N_a P^-1=N_P(a). Exact phases and block permutations retained.', + scope='S,N,S source chronology and one fresh target T, one delivery ADD; no common U, extra bank bridge or general local synthesis. Endpoint test is a single isolated response F_all K only.', + all_f='Algebra holds for the independently pinned phase-normalized N_f. Native arity 2 per occupied block is 2f at chunk size f. Permutation adapters preserve native rank.', + limits=['No general caller obstruction. A coupled word can combine several responses.', + 'No actual whole supplier, improved BIT, joint transfer or new kappa.']) + +def main(): + p=argparse.ArgumentParser();p.add_argument('--write',action='store_true');args=p.parse_args() + out=json.loads(json.dumps(run()));dest=Path(__file__).with_name('CHRONOLOGY.json') + if args.write: + dest.write_text(json.dumps(out,indent=2,sort_keys=True)+'\n') + else: + need(json.loads(dest.read_text())==out,'saved chronology differs') + print(out['status'],out['complete_orders'],'orders',out['distinct_kernels'],'kernels') + +if __name__=='__main__': + main() diff --git a/research/two-pivot-caller-readers/source/root-chronology/native_chart_search.py b/research/two-pivot-caller-readers/source/root-chronology/native_chart_search.py new file mode 100644 index 0000000000..cf80b5cfc7 --- /dev/null +++ b/research/two-pivot-caller-readers/source/root-chronology/native_chart_search.py @@ -0,0 +1,171 @@ +#!/usr/bin/env python3 +"""Bounded native-chart retiming of a fixed exact physical event word. + +Apache-2.0; substantial OpenAI Codex assistance. Positive outputs are exact +replayed words; a failed beam search establishes no optimization lower bound. +""" +from pathlib import Path +from collections import Counter +from math import isqrt +from heapq import nsmallest +import argparse, hashlib, json +from chronology import Op, ident, need +from batch_paid_progress import operator, replay + +HERE = Path(__file__).resolve().parent + + +def search(events, banks, planes, ambient, beam, exponent, all_masks): + cap = isqrt((ambient * ambient - 1) // 8) + # Ordering heuristic only. Mathematical admission never uses these floats. + costs = [0.0] + for k in range(1, planes + 1): + costs.append(min(costs[k - j] + 2*j * (ambient/(2*j))**exponent + for j in range(1, min(k, cap) + 1))) + states = {(0,) * banks: (0.0, ())} + counts = [] + full = (1 << planes) - 1 + for index, e in enumerate(events): + kind = e['kind'] + if kind == 'ADD': + dst, src = e['dst'], e['src'] + candidates = {} + for state, (cost, path) in states.items(): + a, b = state[dst], state[src] + masks = range(full + 1) if all_masks else sorted({0, full, a, b, a & b, a | b}) + for mask in masks: + s = list(state) + s[dst] = s[src] = mask + s = tuple(s) + c = cost + costs[(a ^ mask).bit_count()] + costs[(b ^ mask).bit_count()] + old = candidates.get(s) + if old is None or c < old[0]: + candidates[s] = (c, path + (mask,)) + kept = nsmallest(beam, candidates.items(), key=lambda kv: (kv[1][0], kv[0])) + states = dict(kept) + counts.append(dict(event=index, expanded=len(candidates), retained=len(states))) + elif kind == 'BANK_SWAP': + i, j = e['banks'] + converted = {} + for state, value in states.items(): + s = list(state) + s[i], s[j] = s[j], s[i] + converted[tuple(s)] = value + states = converted + else: + g = operator(e['operator']) + i = e['bank'] + converted = {} + for state, value in states.items(): + moved = sum(1 << g.perm[j] for j in range(planes) if state[i] >> j & 1) + s = list(state) + s[i] = g.mask ^ moved + converted[tuple(s)] = value + states = converted + best_state, (cost, path) = min(states.items(), key=lambda kv: + (kv[1][0] + sum(costs[m.bit_count()] for m in kv[0]), kv[0])) + return path, counts, cost + sum(costs[m.bit_count()] for m in best_state) + + +def compile_word(events, banks, planes, ambient, choices): + I = ident(planes) + pending = [I] * banks + out = [] + choice = iter(choices) + cap = isqrt((ambient * ambient - 1) // 8) + + def emit(i, g, label): + need(g.perm == I.perm, 'alignment is a native tensor product') + bits = [j for j in range(planes) if g.mask >> j & 1] + pieces = [bits[j:j+cap] for j in range(0, len(bits), cap)] + if not pieces and g.sign != 1: + pieces = [[]] + product = I + for j, piece in enumerate(pieces): + h = Op(g.sign if j == 0 else 1, sum(1 << t for t in piece), I.perm) + product = h @ product + need(not piece or 2*(2*len(piece))**2 < ambient**2, 'strictly contracting child') + out.append(dict(kind='NATIVE' if piece else 'ADDRESS_OR_UNIT', bank=i, + operator=h.data(), label=label)) + need(product == g, 'literal alignment phase and support') + + for e in events: + if e['kind'] == 'ADD': + r = Op(1, next(choice), I.perm) + for i in (e['dst'], e['src']): + emit(i, r.inverse() @ pending[i], 'paid chart alignment before ADD') + pending[i] = r + out.append(e) + elif e['kind'] == 'BANK_SWAP': + i, j = e['banks'] + pending[i], pending[j] = pending[j], pending[i] + out.append(e) + else: + i = e['bank'] + g = operator(e['operator']) + address = Op(1, 0, g.perm) + q = g @ pending[i] @ address.inverse() + need(q.perm == I.perm, 'native pending chart after actual ADDRESS conjugation') + if address != I: + out.append(dict(kind='ADDRESS_OR_UNIT', bank=i, operator=address.data(), + label='retimed original ADDRESS')) + if q.sign != 1: + emit(i, Op(q.sign, 0, I.perm), 'exact chart phase') + pending[i] = Op(1, q.mask, I.perm) + need(next(choice, None) is None, 'one prescribed alignment per ADD') + for i in range(banks): + emit(i, pending[i], 'paid final chart restoration') + return out + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument('--source', choices=('four', 'six', 'six_complete'), default='four') + parser.add_argument('--beam', type=int, default=256) + parser.add_argument('--all-masks', action='store_true') + parser.add_argument('--exponent', type=float, default=.005) + parser.add_argument('--write', action='store_true') + args = parser.parse_args() + if args.source == 'four': + source = HERE / 'INDEPENDENT-SHARED-CALLER.json' + banks, planes, ambient = 4, 6, 12 + elif args.source == 'six': + source = HERE.parent / 'caller/NESTED-SIX.json' + banks, planes, ambient = 6, 8, 16 + else: + source = HERE / 'INDEPENDENT-COMPLETE-SIX.json' + banks, planes, ambient = 6, 8, 16 + raw = source.read_bytes() + events = json.loads(raw)['events'] + choices, widths, screen = search(events, banks, planes, ambient, args.beam, + args.exponent, args.all_masks) + compiled = compile_word(events, banks, planes, ambient, choices) + need(replay(compiled, banks, planes) == replay(events, banks, planes), + 'all physical columns and both literal inverse orders preserved') + H = Counter(e['operator']['native_arity'] for e in compiled if e['kind'] == 'NATIVE') + out = dict(status='PASS_EXACT_RETIMED_NATIVE_CHART_WORD', no_new_kappa=True, + producer_sha256=hashlib.sha256(Path(__file__).read_bytes()).hexdigest(), + source_path=str(source), source_sha256=hashlib.sha256(raw).hexdigest(), + mode=args.source, beam=args.beam, all_alignment_masks=args.all_masks, + heuristic_exponent=args.exponent, heuristic_float_cost=screen, + choices=list(choices), beam_widths=widths, events=compiled, + histogram=dict(sorted(H.items())), rank_mass=sum(r*c for r,c in H.items()), + total_input_stock=ambient*banks, scalar_and_address_event_count=sum(e['kind']!='NATIVE' for e in compiled), + invariant='Old logical bank i equals the current native-plane product times the retimed physical bank. An ADD aligns both banks to a common paid chart; ADDRESS conjugates the chart exactly; final charts are paid and restored.', + limits=['Beam search is bounded and not an optimality or impossibility proof.', + 'Search floats only order candidates. Exact replay verifies the saved positive identity, not a strict moment.', + 'The six-bank source is a prefix with two unfinished pivots; retiming does not close them.', + 'All native monomial adapters, physical scans, precision and joint BIT obligations remain paid.']) + out = json.loads(json.dumps(out)) + suffix = f'{args.source.upper()}-{args.beam}' + ('-ALL' if args.all_masks else '-CHOSEN') + path = HERE / f'NATIVE-CHART-{suffix}.json' + if args.write: + path.write_text(json.dumps(out, indent=2, sort_keys=True) + '\n') + else: + need(json.loads(path.read_bytes()) == out, 'saved chart search differs') + print(out['status'], args.source, out['histogram'], 'mass', out['rank_mass'], + 'stock', out['total_input_stock'], 'no completed supplier claim') + + +if __name__ == '__main__': + main() diff --git a/research/two-pivot-caller-readers/source/root-chronology/quadratic_charts.py b/research/two-pivot-caller-readers/source/root-chronology/quadratic_charts.py new file mode 100644 index 0000000000..80f2d4d055 --- /dev/null +++ b/research/two-pivot-caller-readers/source/root-chronology/quadratic_charts.py @@ -0,0 +1,221 @@ +#!/usr/bin/env python3 +"""Exact X-character monomial algebra and bounded quadratic-chart retiming. + +Apache-2.0; substantial OpenAI Codex assistance. Rank screens do not admit a +physical supplier. A saved positive word must separately lower every child. +""" +from dataclasses import dataclass +from functools import lru_cache +from fractions import Fraction +from heapq import nsmallest +from math import isqrt +import argparse, hashlib, json +from pathlib import Path + +HERE=Path(__file__).resolve().parent +def need(c,m): + if not c: raise ValueError(m) +def parity(x): return x.bit_count()&1 +def linear(rows,x): return sum(parity(r&x)<>i&1),None) + need(j is not None,'invertible binary address');a[i],a[j]=a[j],a[i] + for j in range(n): + if j!=i and a[j]>>i&1:a[j]^=a[i] + return tuple(r>>n for r in a) +@lru_cache(None) +def rank(rows): + basis={} + for r in rows: + while r: + p=r.bit_length()-1 + if p in basis:r^=basis[p] + else:basis[p]=r;break + return len(basis) + +@dataclass(frozen=True) +class Mono: + rows:tuple + offset:int + alpha:tuple + quad:tuple + constant:int=0 + global_phase:int=0 + # Actual all-f family: i^global_phase times the f-fold tensor power. + def q(self,x): + return (self.constant+sum(a for i,a in enumerate(self.alpha) if x>>i&1) + +2*sum(parity(r&x) for i,r in enumerate(self.quad) if x>>i&1))%4 + def act(self,x):return linear(self.rows,x)^self.offset + def __matmul__(self,b):return compose(self,b) + def inv(self):return adjoint(self) + def data(self):return dict(rows=list(self.rows),offset=self.offset,alpha=list(self.alpha),quad=list(self.quad),constant=self.constant,global_phase=self.global_phase) + def polar(self): + r=[(self.alpha[i]&1)<>j&1:r[i]^=1<>j)&1)<>i)&1 for i,r in enumerate(rows)),tuple(r&~((1<<(i+1))-1) for i,r in enumerate(rows))) +def old_operator(e,n): + d=e['operator'];p=d['block_permutation'];rows=[0]*n + for i,j in enumerate(p):rows[2*j]=1<<(2*i);rows[2*j+1]=1<<(2*i+1) + out=Mono(tuple(rows),0,(0,)*n,(0,)*n) + alpha=[0]*n;offset=0 + for i in d['native_blocks']:alpha[2*i]=3;alpha[2*i+1]=1;offset^=3<<(2*i) + N=Mono(identity(n).rows,offset,tuple(alpha),(0,)*n,0,(len(d['native_blocks'])+(2 if d['sign']==-1 else 0))%4) + return N@out +def decode(e,n): + if 'x_monomial' in e: + d=e['x_monomial'];return Mono(tuple(d['rows']),d['offset'],tuple(d['alpha']),tuple(d['quad']),d.get('constant',0),d.get('global_phase',0)) + if e['kind']=='ADDRESS_LINEAR': + # Physical P_A acts on X characters by A^-T. + ri=inverse(tuple(e['operator']['address_rows'])) + rows=tuple(sum(((ri[j]>>i)&1)<>j)&1)<>i&1 else 0)for i in range(n)),0,(0,)*n,(0,)*n) + alpha=(3,1,0,0,0,0);N=Mono(I.rows,3,alpha,(0,)*n,0,1) + need(R@R==I and N@N==Mono(I.rows,0,(0,)*n,(0,)*n,0,2),'literal reflection and native square') + A=N@R@N.inv();need(rank(A.polar())==2,'independent conjugated reflection rank') + for a in (R,N,A,N@R): + need(a@a.inv()==I==a.inv()@a,'both literal inverses') + for b in (R,N,A): + c=a@b + for x in range(1<=1 for each explicitly serialized q fixture, actual signed native planes, all arbitrary independent input fields and both literal inverse orders.',limits=['Written all-q induction is separate from finite fixture replay.','Complete native rankmass exceedsstock by8; no positive moment or kappa.','Different joint cleanup or changed source/held map remains outside this computation.']) + + +def main(): + ap=argparse.ArgumentParser();ap.add_argument('--write',action='store_true');args=ap.parse_args();out=json.loads(json.dumps(run())) + p=HERE/'INDEPENDENT-HANDOFF-FAMILY.json' + if args.write: + p.write_text(json.dumps(out,indent=2,sort_keys=True)+'\n') + for f in out['fixtures']: + f=dict(f,sources=out['sources'],producer_sha256=out['producer_sha256']);(HERE/f"HANDOFF-COMPLETE-Q{f['q']}.json").write_text(json.dumps(f,indent=2,sort_keys=True)+'\n') + else:need(json.loads(p.read_bytes())==out,'saved family audit differs') + print(out['status'],[(f['q'],f['native_mass'],f['stock'],f['grouped_histogram'])for f in out['fixtures']]) +if __name__=='__main__':main() diff --git a/research/two-pivot-caller-readers/source/root-chronology/signed_chart_optimization.py b/research/two-pivot-caller-readers/source/root-chronology/signed_chart_optimization.py new file mode 100644 index 0000000000..8e77075106 --- /dev/null +++ b/research/two-pivot-caller-readers/source/root-chronology/signed_chart_optimization.py @@ -0,0 +1,70 @@ +#!/usr/bin/env python3 +"""Paid native-chart retiming as a signed binary graph optimization. + +The optimization is only a search. Every output is checked by independent +exact all-column replay; a solver bound is not called a mathematical proof. +Apache-2.0; substantial OpenAI Codex assistance. +""" +from pathlib import Path +from collections import Counter +import argparse, hashlib, json, sys +from chronology import need +from batch_paid_progress import operator, replay +from native_chart_search import compile_word +HERE=Path(__file__).resolve().parent + + +def graph(events,banks,planes): + state=[[(0,0)]*planes for unused in range(banks)] + edges=[];choices=[];nodes=1 + for e in events: + if e['kind']=='ADD': + chosen=list(range(nodes,nodes+planes));nodes+=planes;choices.append(chosen) + for bank in(e['dst'],e['src']): + for j,(v,c)in enumerate(state[bank]):edges.append((v,chosen[j],c)) + state[bank]=[(v,0)for v in chosen] + elif e['kind']=='BANK_SWAP': + i,j=e['banks'];state[i],state[j]=state[j],state[i] + else: + g=operator(e['operator']);old=state[e['bank']];new=[None]*planes + for j,(v,c)in enumerate(old): + dest=g.perm[j];new[dest]=(v,c^((g.mask>>dest)&1)) + state[e['bank']]=new + for row in state: + for v,c in row:edges.append((v,0,c)) + return nodes,edges,choices + + +def main(): + import numpy as np + import scipy + from scipy.optimize import milp,Bounds,LinearConstraint + from scipy.sparse import coo_array + ap=argparse.ArgumentParser();ap.add_argument('--source',default='INDEPENDENT-HANDOFF-SIX.json');ap.add_argument('--seconds',type=float,default=60);ap.add_argument('--output',default='SIGNED-CHART-HANDOFF-SIX.json');args=ap.parse_args() + source=Path(args.source);source=source if source.is_absolute()else HERE/source + raw=source.read_bytes();data=json.loads(raw);events=data['events'] + banks=data.get('width',6);ambient=data.get('ambient_arity',12);planes=ambient//2 + nodes,edges,choices=graph(events,banks,planes);m=len(edges);nv=nodes+2*m + rows=[];cols=[];values=[];rhs=[] + for k,(a,b,c)in enumerate(edges): + for col,value in((a,1),(b,1),(nodes+k,-1),(nodes+m+k,-2)): + rows.append(k);cols.append(col);values.append(value) + rhs.append(-c) + A=coo_array((values,(rows,cols)),shape=(m,nv)).tocsc() + objective=np.zeros(nv);objective[nodes:nodes+m]=2 + lower=np.zeros(nv);upper=np.ones(nv);upper[0]=0 + result=milp(objective,integrality=np.ones(nv),bounds=Bounds(lower,upper),constraints=LinearConstraint(A,rhs,rhs),options={'time_limit':args.seconds,'mip_rel_gap':0}) + need(result.x is not None,'optimizer returned no candidate') + assignment=[int(round(x))for x in result.x] + need(all(abs(x-z)<1e-6 for x,z in zip(result.x,assignment)),'candidate exactly roundable to binary') + need(assignment[0]==0 and all(v in(0,1)for v in assignment),'all variables binary') + for k,(a,b,c)in enumerate(edges):need(assignment[a]+assignment[b]+c-assignment[nodes+k]-2*assignment[nodes+m+k]==0,'exact integer edge equation') + masks=[sum(assignment[v]<>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<> i & 1) + for i in range(operator.n): + if x >> i & 1: + phase += 2 * ((rows[i] >> (i + 1)) & (x >> (i + 1))).bit_count() + result[x] = gaussian_unit(value, phase) + state = result + elif kind == 'C': + direction, sign = event[1:] + result = {} + for x, (a, b) in state.items(): + for y, value in ((x, (a-sign*b, b+sign*a)), + (x ^ direction, (a+sign*b, b-sign*a))): + u, v = result.get(y, (0, 0)) + result[y] = u + value[0], v + value[1] + state = {x: value for x, value in result.items() if value != (0, 0)} + denominator += 1 + else: + raise ValueError(event) + while denominator and all(not ((a | b) & 1) for a, b in state.values()): + state = {x: (a // 2, b // 2) for x, (a, b) in state.items()} + denominator -= 1 + return state, denominator + + +def standard_product(ce, *operators): + """Return operators[0] ... operators[-1] in conventional product order.""" + result = ce.ident(operators[0].n) + for operator in reversed(operators): + result = result.then(operator) + return result + + +def canonical_predecessor(): + for name, expected in PINS.items(): + need(hashlib.sha256((OLD / name).read_bytes()).hexdigest() == expected, 'frozen source pin: ' + name) + spec = importlib.util.spec_from_file_location('stabilizer_frozen_endpoint', OLD / 'canonical_endpoints.py') + module = importlib.util.module_from_spec(spec) + sys.modules[spec.name] = module + spec.loader.exec_module(module) + need(hashlib.sha256(module.CP.read_bytes()).hexdigest() == '2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962', 'native compiler pin') + return module + + +def deliberate_monomial(ce, n, cut, variant): + """Dense pair stabilizer: nonorthogonal GL2, fresh GL, and cross chirps. + + This is one prescribed construction, not a seed or search. The common + address matrix is A=[[0,1],[1,1]], and Q_CC=I+A^-T A^-1=[[1,1],[1,0]]. + """ + rows = [1 << i for i in range(n)] + rows[:2] = [2, 3] + fresh = list(range(2, n)) + # Swap completed and future directions, then mix every fresh direction. + past = 2 + 5 * (cut + 1) - 1 + future = 2 + 5 * (cut + 1) + if future < n: + rows[past], rows[future] = rows[future], rows[past] + for index in range(len(fresh) - 1): + a, b = fresh[index], fresh[index + 1] + rows[a] ^= rows[b] + rows[0] ^= sum(1 << i for i in fresh if (i + variant) % 2 == 0) + rows[1] ^= sum(1 << i for i in fresh if (i + variant) % 3 == 0) + quadratic = [3, 1] + [0] * (n - 2) + for i in fresh: + j = (i + variant) % 2 + quadratic[i] ^= 1 << j + quadratic[j] ^= 1 << i + if (i + variant) % 3 == 1: + quadratic[i] ^= 1 << i + for a, b in zip(fresh[::2], fresh[1::2]): + quadratic[a] ^= 1 << b + quadratic[b] ^= 1 << a + operator = ce.perm(n, rows).then(ce.diag(n, quadratic)).then(ce.xgate(n, (1 << (2 + variant % (n - 2))) | 1)) + common = ce.cgate(n, 1).adjoint().then(ce.cgate(n, 2)) + other = standard_product(ce, common, operator, common.adjoint()) + need(native_rank(operator) == native_rank(other) == 0, 'prescribed full pair stabilizer admission') + # Sparse complete-column phase witness for the actual rank-zero conjugate. + state, den = sparse_column(other) + need(den == 0 and len(state) == 1 and next(iter(state.values())) in ((1, 0), (0, 1), (-1, 0), (0, -1)), 'actual second-cut monomial phase') + return operator, {'address_rows': rows, 'quadratic_rows': quadratic, 'second_front_zero_column': [list(state.items()), den]} + + +def verify_free_word(): + """Independent group-ring replay of the frozen arbitrary-input B1 word.""" + data = json.loads((OLD / 'NONCOMMON-B1.json').read_text()) + + def reduce(word): + result = [] + for symbol in word: + if result and result[-1] == -symbol: + result.pop() + else: + result.append(symbol) + return tuple(result) + + rows = [{((), 0): 1}, {((), 1): 1}] + for gate in data['word']: + if gate['op'] == 'LEFT': + rows[gate['dst']] = {(reduce(tuple(gate['word']) + word), column): coefficient for (word, column), coefficient in rows[gate['dst']].items()} + elif gate['op'] == 'ADD': + destination = dict(rows[gate['dst']]) + for key, coefficient in rows[gate['src']].items(): + destination[key] = destination.get(key, 0) + gate['q'] * coefficient + if destination[key] == 0: + del destination[key] + rows[gate['dst']] = destination + elif gate['op'] == 'EXCHANGE': + rows = [rows[1], {key: -coefficient for key, coefficient in rows[0].items()}] + else: + raise ValueError(gate) + endpoint = (-3, 5, -2, 4, -1) + need(rows == [{(endpoint, 0): 1}, {(endpoint, 1): 1}], 'independent arbitrary-column group-ring identity') + return {'input_columns': 2, 'free_invertible_operators': 5, 'endpoint': list(endpoint)} + + +def run(): + old = canonical_predecessor() + ce = old.ce + records, phase_cases, controls = [], [], [] + for group in range(3): + for coordinate, p in enumerate(old.bus['groups7'][group]): + q = old.bus['groups7'][(group + 1) % 3][coordinate] + r = old.bus['groups7'][(group + 2) % 3][coordinate] + chart = ce.perm(7, ce.transpose(old.completion(p, q), 7)) + if group == 2: + pre = old.build(7, old.winner[p]['pre_events']) + else: + direction = q ^ r + pre = ce.perm(7, [(1 << i) ^ (direction if direction >> i & 1 else 0) for i in range(7)]) + canonical_pre, _ = ce.monomial(chart.then(pre).then(chart.adjoint())) + local_p = canonical_pre.adjoint() + local_fresh = ce.fourier(7, range(2, 7)) + local_common = ce.cgate(7, 1).then(ce.cgate(7, 2).adjoint()) + first = standard_product(ce, local_fresh, local_p, local_common) + rank_first = native_rank(first) + need(rank_first == (3 if group == 2 else 5), 'actual fixed first-factor native rank') + # Complete phase check against the pinned compiler's literal lowering. + recipe, lowered = ce.lower_child(first) + need(recipe['rank'] == rank_first and first.tab == lowered.tab, 'native lowering signed tableau') + need(sparse_column(first) == sparse_column(lowered), 'independent local global phase') + cases = [] + for length in (1, 3, 5, 9): + n = 2 + 5 * length + cp, cq = ce.cgate(n, 1), ce.cgate(n, 2) + common = cp.then(cq.adjoint()) + fresh = [ce.fourier(n, range(2 + 5 * stage, 7 + 5 * stage)) for stage in range(length)] + ps = [old.embed(n, canonical_pre.circuit, [0, 1] + list(range(2 + 5 * stage, 7 + 5 * stage))).adjoint() for stage in range(length)] + qtotal, baseline, fpast, factored = ps[0], ps[0], fresh[0], standard_product(ce, fresh[0], ps[0], common) + monomials = [] + for stage in range(1, length): + monomial, _ = deliberate_monomial(ce, n, stage - 1, stage) + monomials.append(monomial) + insertion = standard_product(ce, fpast.adjoint(), monomial, fpast) + qtotal = standard_product(ce, ps[stage], insertion, qtotal) + baseline = standard_product(ce, ps[stage], baseline) + fpast = standard_product(ce, fresh[stage], fpast) + factor = standard_product(ce, fresh[stage], ps[stage]) + need(native_rank(factor) == 5, 'later factor native rank') + factored = standard_product(ce, factor, monomial, factored) + original = standard_product(ce, fpast, qtotal, common) + need(original.tab == factored.tab, 'exact signed tableau of telescoping factorization') + # Independent columns/multiplication agree with exact compiler. + independent = binary_product(binary_tableau(fpast), binary_product(binary_tableau(qtotal), binary_tableau(common))) + need(independent == binary_tableau(original), 'independent symplectic endpoint multiplication') + rank_y = native_rank(original) + bound = 5 * (length - 1) + rank_first + need(rank_y <= bound < n, 'universal theorem bound on deliberate insertion') + baseline_y = standard_product(ce, fpast, baseline, common) + need(native_rank(baseline_y) == bound, 'identity insertion attains universal Y bound') + fx = standard_product(ce, ce.fourier(n), ce.xgate(n, 1), qtotal) + rank_x = native_rank(fx) + # At genuine B1 size17, independently compare full columns for + # a representative A port and C port; this fixes global phase. + if length == 3 and coordinate == 0 and group in (0, 2): + original_state = sparse_column(original) + need(original_state == sparse_column(factored), 'global B1 exact Gaussian column') + phase_wrong = factored.then(ce.Op(n, ce.identity(n), [('phase', 1)])) + need(phase_wrong.tab == original.tab and sparse_column(phase_wrong) != original_state, 'global-phase omission control') + phase_cases.append({'group': group, 'p': p, 'n': n, 'output_support': len(original_state[0]), 'denominator_depth': original_state[1]}) + cases.append({'L': length, 'm': n, 'X_native_rank': rank_x, 'Y_native_rank': rank_y, 'Y_rank_upper_bound': bound, 'identity_insertion_Y_native_rank': native_rank(baseline_y), 'Y_deficit_lower_bound': n - bound}) + records.append({'group': group, 'coordinate': coordinate, 'p': p, 'q': q, 'first_factor_rank': rank_first, 'cases': cases}) + # An undressed logical ADDRESS swap has a real hidden native query. + n = 4 + cp, cq, past = ce.cgate(n, 1), ce.cgate(n, 2), ce.cgate(n, 4) + dx = standard_product(ce, cp, past) + swap = ce.perm(n, [1, 2, 8, 4]) + dressed = standard_product(ce, dx.adjoint(), swap, dx) + need(native_rank(standard_product(ce, dx, dressed, dx.adjoint())) == 0, 'dressed swap admitted') + hidden = native_rank(standard_product(ce, dx, swap, dx.adjoint())) + need(hidden == 2, 'undressed swap admission control') + common = standard_product(ce, cq, cp.adjoint()) + no_chirp = ce.perm(n, [2, 3, 4, 8]) + need(native_rank(standard_product(ce, common, no_chirp, common.adjoint())) > 0, 'common chirp omission control') + wrong_inverse = standard_product(ce, past, swap, past) + right_inverse = standard_product(ce, past.adjoint(), swap, past) + need(wrong_inverse.tab != right_inverse.tab, 'positive/adjoint past-frame control') + controls.extend(['undressed_swap_costs_rank2', 'common_chirp_omission_breaks_second_front', 'past_frame_inverse_sign_is_essential', 'global_phase_i_rejected_on_two_B1_ports']) + return { + 'status': 'PASS_FULL_MONOMIAL_INSERTION_Y_RANK_OBSTRUCTION_NO_NEW_KAPPA', + 'scientific_pin': PIN, + 'sources_sha256': PINS, + 'source_sha256': hashlib.sha256(Path(__file__).read_bytes()).hexdigest(), + 'free_word': verify_free_word(), + 'theorem': {'C_Y_rank_upper': '5L-2 = m-4', 'AB_Y_rank_upper': '5L = m-2', 'm': '2+5L', 'quantifiers': 'Every L>=1; every locally admitted monomial pre_s on common2 plus own fresh5 with fixed first-factor ranks3/5; every insertion whose physical X-cut pullback is any invertible monomial. Second-front admission is unnecessary for the upper bound. Arbitrary permutations and diagonal nonzero phases, including non-Clifford monomials, are covered by the row-support proof.'}, + 'factorization': 'F_all P_last (F_past^-1 M_last-1 F_past) ... P_1 (F_0^-1 M_0 F_0) P_0 R = (F_last P_last) M_last-1 ... (F_1 P_1) M_0 (F_0 P_0 R)', + 'records': records, + 'independent_global_phase_cases': phase_cases, + 'defect_controls': controls, + 'all_size': 'Tensor columnwise over f>=1: each later factor has row support2^(5f), first factor2^(3f) C or2^(5f) A/B; monomials preserve support. Thus terminal Y has row support <=2^((m-4)f) C or2^((m-2)f) A/B and cannot be a rank-mf native child, even with arbitrary input values.', + 'cost_boundary': {'OPEN_local_histogram': {'1': 8, '2': 40, '3': 16}, 'OPEN_local_rank_mass': 136, 'ordinary_helpers': 0, 'private_fields': 0, 'isolated_unary_completion_rank_lower_bound_per_twelve_port_Y_bank': 32, 'insertion_scans': 'All actual monomial address/phase scans remain paid; zero native rank does not mean zero work.'}, + 'limits': ['No arbitrary multibank insertion, changed scalar word, changed entrance code, overlapping local fresh supports, or different raw local boundary is excluded.', 'The proof does not calculate an optimal paid completion word, owner allocation, all-size rounded precision, physical tape controller, or positive conditional kappa.', 'This is a written all-parameter proof with finite exact operator checks, not formal-kernel verification.'], + 'attribution': 'Uses frozen source-carrier/common-F normalizers and canonical endpoint charts from the2026-10-18 run; predecessor complex and algebra lanes plus root own those constructions. This lane supplies the exact telescoping argument, full arbitrary-monomial support bound, independent symplectic arithmetic and Gaussian phase evaluator.' + } + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--write', action='store_true') + args = parser.parse_args() + output = json.loads(json.dumps(run())) + target = HERE / 'FULL-STABILIZER-BOUND.json' + if args.write: + target.write_text(json.dumps(output, indent=2, sort_keys=True) + '\n') + else: + need(json.loads(target.read_bytes()) == output, 'stored exact receipt mismatch') + print(output['status']) + print('12 ports x L1/3/5/9; arbitrary-monomial proof;2 exact n17 phase checks;4 defect controls') + + +if __name__ == '__main__': + main() diff --git a/research/two-pivot-caller-readers/verify.py b/research/two-pivot-caller-readers/verify.py new file mode 100644 index 0000000000..6927d9a958 --- /dev/null +++ b/research/two-pivot-caller-readers/verify.py @@ -0,0 +1,178 @@ +#!/usr/bin/env python3 +"""Exact caller replay. Ross Richardson; substantial OpenAI Codex assistance. + +Apache-2.0. Immutable predecessor implementations are compiled from the same +bytes authenticated below, with optimize=0 to preserve historical assertions. +This direct verifier needs Python's standard library, no Git and no network. +""" +from pathlib import Path +from fractions import Fraction +from collections import Counter +import copy +import hashlib +import importlib +import importlib.abc +import importlib.util +import json +import sys + +sys.dont_write_bytecode=True +ROOT=Path(__file__).resolve().parent +META=json.loads((ROOT/'BINDINGS.json').read_bytes()) +PINS={row['path']:row for row in META['files']} +def need(condition,message): + if not condition:raise ValueError(message) +need(len(PINS)==len(META['files']),'duplicate retained-source path') +def checked(relative,raw=None): + row=PINS[relative];path=ROOT/relative + need(path.resolve()==path,'retained source must not be a symlink') + if raw is None:raw=path.read_bytes() + need(hashlib.sha256(raw).hexdigest()==row['sha256'],'retained source hash: '+relative) + return raw +for relative in PINS:checked(relative) + +def rejection(action,needle): + try:action() + except ValueError as error: + need(needle in str(error),'wrong rejecting predicate: '+str(error)) + else:raise ValueError('negative control unexpectedly accepted: '+needle) + +# Positive and negative source-binding controls use real source bytes. The +# loader below has no bytecode-cache path, including for dynamic source loads. +first=next(p for p in PINS if p.endswith('.py')) +need(checked(first,checked(first))==checked(first),'identical source positive control') +rejection(lambda:checked(first,checked(first)+b'\n# altered source\n'),'retained source hash') +MODULES={} +for relative in PINS: + if relative.startswith('source/') and relative.endswith('.py'): + stem=Path(relative).stem + need(stem not in MODULES,'ambiguous retained module '+stem) + MODULES[stem]=relative +class ByteLoader(importlib.abc.Loader): + def __init__(self,relative):self.relative=relative + def create_module(self,spec):return None + def exec_module(self,module): + raw=checked(self.relative) + exec(compile(raw,str(ROOT/self.relative),'exec',dont_inherit=True,optimize=0),module.__dict__) +class ByteFinder(importlib.abc.MetaPathFinder): + def find_spec(self,fullname,path=None,target=None): + if fullname in MODULES: + relative=MODULES[fullname] + return ORIGINAL_SPEC(fullname,str(ROOT/relative),loader=ByteLoader(relative)) +ORIGINAL_SPEC=importlib.util.spec_from_file_location +def bound_spec(name,location,*args,**kwargs): + path=Path(location).resolve() + if path.is_relative_to(ROOT): + relative=str(path.relative_to(ROOT)) + need(relative in PINS,'undeclared dynamic source '+relative) + return ORIGINAL_SPEC(name,str(path),loader=ByteLoader(relative)) + return ORIGINAL_SPEC(name,location,*args,**kwargs) +importlib.util.spec_from_file_location=bound_spec +sys.meta_path.insert(0,ByteFinder()) +def module(name):return importlib.import_module(name) +def data(relative):return json.loads(checked('source/'+relative)) +def source_path(original): + candidates=[p for p,row in PINS.items() if p.startswith('source/') and (row['origin']==original or row['origin'].endswith('/'+original))] + need(len(candidates)==1,'one retained original source for '+original) + return ROOT/candidates[0] + +# Receipts contain original absolute provenance paths. All retained bytes are +# separately checked above. These explicitly enumerated metadata fields are +# omitted ONLY when comparing replay's mathematical body to its frozen receipt. +PROVENANCE={'sources','source_pins','producer_sha256','helper_sha256', + 'native_model_sha256','reflection_source_sha256','source_path','source_sha256', + 'path','witness','witness_sha256'} +def body(value): + if isinstance(value,dict):return {str(k):body(v) for k,v in value.items() if k not in PROVENANCE} + if isinstance(value,(list,tuple)):return [body(v) for v in value] + return value +def difference(a,b,path='root'): + if type(a)!=type(b):return path+': type mismatch' + if isinstance(a,dict): + if a.keys()!=b.keys():return path+': keys '+str(set(a)^set(b)) + for k in a: + if a[k]!=b[k]:return difference(a[k],b[k],path+'.'+k) + elif isinstance(a,list): + if len(a)!=len(b):return path+': lengths '+str((len(a),len(b))) + for i,(x,y) in enumerate(zip(a,b)): + if x!=y:return difference(x,y,path+'['+str(i)+']') + elif a!=b:return path+': '+repr(a)[:150]+' != '+repr(b)[:150] + return path +RESULTS=[] +def replay(name,function,receipt): + actual=json.loads(json.dumps(getattr(module(name),function)())) + expected=data(receipt) + aa,bb=body(actual),body(expected) + need(aa==bb,'mathematical receipt mismatch '+receipt+' '+difference(aa,bb)) + RESULTS.append({'entry':name+'.'+function,'status':actual['status'],'mathematical_receipt':receipt}) + print('PASS_REPLAY',name,function,flush=True) + return actual + +def charts(): + c=module('chronology');b=module('batch_paid_progress');nc=module('native_chart_search');sg=module('signed_chart_optimization') + cases=[] + for name in ['SIGNED-CHART-HANDOFF-SIX.json','SIGNED-CHART-HANDOFF-Q3.json']: + d=data('root-chronology/'+name);sp=source_path(d['source_path']);raw=sp.read_bytes();original=json.loads(raw) + need(hashlib.sha256(raw).hexdigest()==d['source_sha256'],'fixed-chart original bytes') + n,m=d['width'],d['ambient_arity'];events=nc.compile_word(original['events'],n,m//2,m,d['choices']) + need(events==d['events'],'fixed-chart serialized choices') + need(b.replay(events,n,m//2)==b.replay(original['events'],n,m//2),'fixed-chart every original column and both inverse orders') + h=Counter(e['operator']['native_arity'] for e in events if e['kind']=='NATIVE') + need(sum(r*v for r,v in h.items())==d['native_mass']==n*m,'fixed-chart break-even bill') + need(all(2*r*r1: + need(len(sys.argv)==2 and sys.argv[1]=='--json','only --json is supported') + print(json.dumps(report,indent=2,sort_keys=True)) +else:print(report['status'],','.join(report['claims']),'no_new_kappa=true',flush=True)