From dfb50f3dbcc386ec44856b65b055568d8b52b9df Mon Sep 17 00:00:00 2001 From: Ali Romman <226877337+aliromman@users.noreply.github.com> Date: Sat, 24 Oct 2026 15:04:24 -0500 Subject: [PATCH 1/2] Prove the forward BIT early-helper query interface --- research/bit-early-helper-queries/PROOF.md | 207 + research/bit-early-helper-queries/README.md | 120 + research/bit-early-helper-queries/RESULT.json | 17276 ++++++++++++++++ .../bit-early-helper-queries/SOURCES.json | 42 + research/bit-early-helper-queries/TASK.json | 67 + research/bit-early-helper-queries/VERIFY.json | 23 + research/bit-early-helper-queries/model.py | 354 + research/bit-early-helper-queries/verify.py | 78 + 8 files changed, 18167 insertions(+) create mode 100644 research/bit-early-helper-queries/PROOF.md create mode 100644 research/bit-early-helper-queries/README.md create mode 100644 research/bit-early-helper-queries/RESULT.json create mode 100644 research/bit-early-helper-queries/SOURCES.json create mode 100644 research/bit-early-helper-queries/TASK.json create mode 100644 research/bit-early-helper-queries/VERIFY.json create mode 100644 research/bit-early-helper-queries/model.py create mode 100644 research/bit-early-helper-queries/verify.py diff --git a/research/bit-early-helper-queries/PROOF.md b/research/bit-early-helper-queries/PROOF.md new file mode 100644 index 0000000000..868e21b274 --- /dev/null +++ b/research/bit-early-helper-queries/PROOF.md @@ -0,0 +1,207 @@ +# Forward BIT helper queries at the source entrance + +This file gives a source interface. It does not give a new kappa value. + +Use the retained PR589/PR555 word at repository commit +`1ec1119972c9aefe42525172d07b332fcff81cb4`. The source is +[WORD.json.gz](https://github.com/CrocSwap/integer-mult-bounds/blob/1ec1119972c9aefe42525172d07b332fcff81cb4/research/kappa-rebuild/bit/sources/pr589-regenerated/WORD.json.gz). +Its compressed SHA256 is +`e3e301e62bc2b41dbf1ceac0acf3d35824ebeab1848c5a2142d4577b109da52f`. +The source has 111 X fields, 111 Y fields, and 439 independent helper fields. +Its nine owned center queries remain paid. + +The rescheduling uses the entrance prologue from +[PR5388](https://github.com/CrocSwap/integer-mult-bounds/pull/5388), with its +[proof at commit 568717635d8d11175a80024c9c596e16f54b1ea4](https://github.com/CrocSwap/integer-mult-bounds/blob/568717635d8d11175a80024c9c596e16f54b1ea4/research/native-helper-query-bank/PROOF.md). +This BIT source needs no scalar first-departure basis change or helper +completion child. + +## Exact source cuts + +Every helper starts in frame zero. Before its first MOVE, it is never the +destination of an ADD. Earlier source instructions can read it. Thus every +first-departure row is exactly its original helper input. The scalar matrix +of all 439 such rows is the identity. + +Of these first MOVEs, 286 have rank one. Each of the 111 port lines has between +two and five of them. The receipt gives all owners, event indices, frames, +and prior read counts. All helpers finish at the same full rank-eight frame. + +Let P be the projector on one port line. Write Q=D_P, D=D_(I-P), and R=D_I. +The two earliest first-query helpers on that line give two independent Q +observations. Their final job is R=DQ. Select these two helpers at every port. +This gives 222 local observations with no input, output, or observation +normalizer. All other helpers keep their original jobs. A later global stage +requires the separate port-route extension below. + +## Optional common-axis maps + +The larger 286-query interface can use one common rank-one axis. For a source +root r, put u=r/2, so u has squared norm one. Let e be the first coordinate +vector. If u=e, set K=I. Otherwise set v=u-e and + + K = I - 2 v v^T / (v^T v). + +Then K is symmetric, K squared is I, and K e=u. For the head and tail address +coordinates, use the block map diag(K,K). This is in coordinates where the +fixed tail reversal has already been removed. Conjugation by that fixed +reversal gives the native convention. + +For a projector A, the address matrix in these coordinates is + + D_A = [[I-A, A], [A, I-A]]. + +Direct rational matrix products give + + D_(u u^T) diag(K,K) = diag(K,K) D_(e e^T), + D_I diag(K,K) = diag(K,K) D_I. + +Thus input map K, observation map K, and output map K give the common Q +observation and preserve the full R target. The checker verifies these exact +16-by-16 identities for all 111 source lines. It also compares every line with +the actual source first-frame basis. The maps are fixed address maps in the +retained common-cover contract. This check does not claim direct execution of +a dense address map on a smaller cover. + +The direct two-per-port interface does not need these maps. + +## Matching the actual global stage chart + +The local identity R=Q D_(I-P) does not identify R with the fresh-stage helper +job Q D_B automatically. The retained global controller moves main data through +port-specific routes. A helper must also have an explicit route. + +Use the actual 15-by-15 matrix rho from +[BIT-P3-NATIVE-BINDING.json](https://github.com/CrocSwap/integer-mult-bounds/blob/1ec1119972c9aefe42525172d07b332fcff81cb4/research/kappa-rebuild/bit/BIT-P3-NATIVE-BINDING.json). +For each port, its old local projector L has rank eight and the fresh plane B +has rank seven. The source matrix satisfies + + rho^2 = I, + rho P rho = P, + rho L rho = P+B. + +Give a selected helper the input rho xi. Apply rho to its held observation +and to its final output. The resulting observation is Q xi, since rho fixes +P. The output is D_(P+B) xi = Q D_B xi. Thus it has the same Q and fresh D as +the main controller port. The source accepts these separately routed inputs +because its helper-to-main block is zero on all source columns. + +The checker loads and hashes the actual binding. It checks all 111 matrices, +the three head identities, and the corresponding 30-by-30 native address +identities. The same matrices embed at every stage by placing B on that +stage's seven axes and fixing all other axes. This uses the retained fixed +right-route contract on one common future cover. No smaller cover is assumed. + +For 222 selected helpers, a fresh-stage call adds 666 fixed cover-route maps: +one at each input, observation, and output. It adds no native child. The +222-cut source replay and all helper target ranks remain unchanged. The local +stage can omit these routes. A complete caller must pay ordinary movement for +the added maps. + +## Rescheduling the existing child + +For each selected helper, copy its entrance value into a fresh owned raw field. +Run its actual first rank-one MOVE on that raw field. Copy the result into a +fresh owned observation field. Apply the observation map only in the optional +common-axis variant. Keep the raw field for the source cut. + +Then run the original source. Omit only the selected first MOVEs. At each +omitted event, the original helper still has its unchanged entrance value. +The raw field has exactly the value and frame that the child would produce. +Swap these whole fields and their frame tags. Clear the owned raw field. The +persistent source state is now exactly the original state after that child. +The source can continue with every later instruction unchanged. + +Induction over the replacement cuts proves the whole source identity. In +particular, all reads in the initial Y prefix receive the correct original +helper values. No dirty persistent field is cleared. The old value left in +an owned raw field is a duplicate. The transformed persistent field retains +all its input information. Clear each owned observation after its last use. + +For 222 selected queries, the extra work is 444 owned COPYs, 888 owned CLEARs, +222 whole-field SWAPs, and at most 444 extra owned fields. There is no new +paid child. The 286-query common-axis version uses 572 COPYs, 1144 CLEARs, +286 SWAPs, at most 572 owned fields, and 843 nonidentity head chart maps. +Ordinary field movement and storage still need a complete caller tariff. + +## Forward source for both shear directions + +At each port the original main entrance frames are P and zero. The exit +frames are I and I-P. Its scalar main map is (x,y) to (x,y+x). Therefore its +physical main block is + + F = [[D, 0], [DQ, D]]. + +Let S swap the two external main fields. Then + + S F S = [[D, DQ], [0, D]]. + +Since Q squared is I for BIT, this is the opposite shear direction with the +same Q. The swaps act only on the main fields. The helper prologue and every +helper output remain unchanged. This uses the forward physical source twice +with different main assignments. It does not use a reverse first-departure +claim. + +The reverse-source census is different: it has 253 first rank-one helper +MOVEs, but every one of its 439 first-departure rows contains a main input. +The forward raw-helper argument does not establish a reverse helper bank. + +## Changes to helper arguments before the source + +At the end of the prologue, let a helper pair hold normalized inputs xi_h and +xi_k, observations Q xi_h and Q xi_k, and raw fields with the corresponding +native frames. To make the invertible change + + xi_k += Q xi_h, + +update its stored input, its observation, and its raw field. The observation +update is + + Q xi_k += xi_h, + +because Q squared is I. For two helpers on the same port and stage, the raw-field update adds the +stored input rho xi_h. No new native child is required. In the common-axis variant the raw update uses K_k xi_h. +All source inputs must be fixed before the original source begins. + +The checker verifies this update on all 439 arbitrary helper columns for 111 +disjoint pairs. It also runs the complete source and all 222 replacement cuts +on those changed inputs, keeping both I and Q coefficient columns. The source +then returns R times the changed helper vector. +This is a coupled output block. It is not the original independent helper +job list until a complete controller proves the required decoding. No helper +target may be credited twice or removed from the invoice. + +## Checks and limits + +Run from the repository root: + + python3 -B research/bit-early-helper-queries/verify.py + python3 -O -B research/bit-early-helper-queries/verify.py + +Both runs give `PASS_BIT_EARLY_HELPER_QUERIES` and the same exact report. They check all 661 persistent input columns, all owned input columns, +the complete source frames, all actual global port routes, both the 222- and +286-cut variants, the nine +original COPY lifetimes, and the full original paid profile: + + 1323 H1 + 1342 H2 + 79 H3 + 44 H4 + 102 H5 + 11 H6 + 19 H7. + +The helper target profile stays 439 H8 in the interface without feedback. +The verifier rejects changed bytes in each of the four declared source inputs. +It also rejects a wrong held input, a wrong frame-tag swap, a dirty owned input, +an uncleared raw field, and an uncleared observation. + +The exact rational address identities extend to each column multiplicity by +using K tensor I_f and P tensor I_f. The scalar owner program is unchanged. +Its sums are not tensor powered. The all-column source identity permits +arbitrary operator-valued helper inputs, so the stated pre-source feedback is +a valid substitution when every stored copy is updated. + +No profitable caller, outer multiplication assembly, precision allocation, +full GL cover materialization, or native payload execution was run here. This +interface alone does not improve kappa. + +The retained source and its +[attribution](https://github.com/CrocSwap/integer-mult-bounds/blob/1ec1119972c9aefe42525172d07b332fcff81cb4/research/kappa-rebuild/bit/README.md) +remain unchanged. The source credits eumemic, Anthropic Claude assistance, and +its cited predecessors. This BIT adaptation and checker have substantial +OpenAI Codex assistance. diff --git a/research/bit-early-helper-queries/README.md b/research/bit-early-helper-queries/README.md new file mode 100644 index 0000000000..d54323c7de --- /dev/null +++ b/research/bit-early-helper-queries/README.md @@ -0,0 +1,120 @@ +# Early helper queries for the retained forward BIT source + +This package proves a finite source interface. It exposes two original helper +queries at each of 111 ports before the retained forward word starts. It adds +no native child and binds the responses and outputs to all 111 actual port +routes. The complete kappa calculation does not improve: no profitable caller +or full ordinary-work tariff is supplied. + +Read [the proof](PROOF.md) and [the exact result](RESULT.json). The source pins +are in [SOURCES.json](SOURCES.json). The publication base is +`32890bc5de034ab8fc93ac88ead7279a6a416d04`. The source was studied at +`1ec1119972c9aefe42525172d07b332fcff81cb4`; all four live inputs have the same +bytes at both commits. The selected record in the package metadata is only +historical provenance. No selected record or frozen predecessor is changed. + +## What the interface gives + +All 439 helper first-query rows equal their independent entrance inputs. +Of these first queries, 286 have rank one. Each port has at least two. Select +the two earliest at every port to obtain the direct 222-query interface. + +For each selected helper, keep an owned copy of the raw first query and an +owned observation. Run the original source. At its original first-query cut, +swap the whole helper and raw fields, including their frame tags. Clear the +owned duplicate. Every original source column and subsequent scalar event +then has the original value and frame. + +The actual port route rho fixes the port projector P and sends the local +rank-eight projector to P plus the fresh seven-plane B. Input, observation, +and output routes therefore give the response Q xi and final job Q D_B xi. +The proof checks the 15-by-15 head matrices and their 30-by-30 native address +matrices. It uses the retained fixed common-cover route contract. + +| Interface | Early queries | Owned COPY | Owned CLEAR | Whole-field SWAP | Extra owned fields | Additional maps | +| --- | ---: | ---: | ---: | ---: | ---: | --- | +| Direct local ports | 222 | 444 | 888 | 222 | 444 | None | +| Direct ports at a fresh global stage | 222 | 444 | 888 | 222 | 444 | 666 fixed cover routes | +| Optional common-axis local variant | 286 | 572 | 1,144 | 286 | 572 | 843 nonidentity head chart maps | + +These are different variants. The 286-query counts must not replace the +222-query counts. The optional common-axis row is a local interface; its 843 +maps do not pay the 222-query fresh-stage routes. + +The unchanged paid profile is + + 1323 H1 + 1342 H2 + 79 H3 + 44 H4 + 102 H5 + 11 H6 + 19 H7. + +Without feedback, all 439 helper targets remain H8. The package also checks +111 disjoint pre-source feedback pairs. In BIT, Q squared is I, so the held +input, response, and raw field can all receive the exact paired update. The +source then returns a coupled helper block. A caller must decode that full +block before it can claim the original independent target list. + +The reverse source has main-input contamination in all 439 first helper rows. +This package does not expose a reverse cold-helper bank. Swapping the two main +roles gives the opposite main shear with the same forward source. + +## Reproduce + +Use Python 3.12. The verifier uses only the standard library. + +```sh +python3 -B research/bit-early-helper-queries/verify.py +python3 -O -B research/bit-early-helper-queries/verify.py +python3 -B scripts/research_package.py --package research/bit-early-helper-queries --check-only +python3 -B scripts/research_package.py --package research/bit-early-helper-queries +``` + +Expected verifier output: + +```text +PASS_BIT_EARLY_HELPER_QUERIES queries=222 routes=111 source_controls=4 owned_controls=5 new_kappa=false +``` + +The complete replay checks 661 persistent input columns and 445 owned input +columns for the direct interface. It also checks the 286-cut variant, all +nine original COPY lifetimes, all 111 native routes, and the changed helper +arguments. Normal and optimized runs must give the same exact result. + +The verifier rejects a byte mutation in each declared source, a wrong held +input, a wrong frame-tag swap, a dirty owned input, an uncleared raw field, +and an uncleared observation. It does not rerun a discovery search. + +The direct verifier also works in the committed package export without Git. +The registered metadata checks use Git to resolve provenance. No native +payload, full GL cover, uniform compiler, ordinary precision or outer +multiplication assembly is executed by this package. + +## Open next questions + +[TASK.json](TASK.json) records the next questions. First give a literal caller +that uses the observations and closes every coupled helper output. This is +needed before any complete paid-versus-target claim. Then bind its common +cover and charge all route, movement, storage, and precision costs. A +profitable complete caller is the present blocker. + +## Credit and related work + +The retained forward word comes from +[PR #589](https://github.com/CrocSwap/integer-mult-bounds/pull/589) and +[PR #555](https://github.com/CrocSwap/integer-mult-bounds/pull/555). Their +[pinned source notice](https://github.com/CrocSwap/integer-mult-bounds/blob/32890bc5de034ab8fc93ac88ead7279a6a416d04/research/e8-bit-p111-tuned/NOTICE.md) +credits eumemic with substantial Anthropic Claude assistance and preserves +its earlier contributors. The +[tuned-source credit](https://github.com/CrocSwap/integer-mult-bounds/blob/32890bc5de034ab8fc93ac88ead7279a6a416d04/research/e8-bit-p111-tuned/tune/README.md) +records the transport changes. The +[retained BIT reconstruction](https://github.com/CrocSwap/integer-mult-bounds/blob/32890bc5de034ab8fc93ac88ead7279a6a416d04/research/kappa-rebuild/bit/README.md) +supplies the regenerated word and actual route binding used here. + +The entrance prologue follows +[PR #5388](https://github.com/CrocSwap/integer-mult-bounds/pull/5388) and its +[pinned proof](https://github.com/CrocSwap/integer-mult-bounds/blob/568717635d8d11175a80024c9c596e16f54b1ea4/research/native-helper-query-bank/PROOF.md). +That pending proof is conceptual credit, not an executable dependency. +[PR #5421](https://github.com/CrocSwap/integer-mult-bounds/pull/5421) instead +uses nine owned BIT relations in the reverse word. This package preserves +arbitrary forward helper inputs and does not delete their target credits. + +This BIT adaptation, route proof, checker, and package have substantial +OpenAI Codex assistance. New files are Apache-2.0. No predecessor file is +copied or changed by this package. diff --git a/research/bit-early-helper-queries/RESULT.json b/research/bit-early-helper-queries/RESULT.json new file mode 100644 index 0000000000..e5660f7517 --- /dev/null +++ b/research/bit-early-helper-queries/RESULT.json @@ -0,0 +1,17276 @@ +{ + "evidence": { + "added_ordinary_work": { + "nonidentity_head_chart_maps": 843, + "owned_CLEAR": 1144, + "owned_COPY": 572, + "owned_fields": 572, + "whole_field_SWAP": 286 + }, + "added_paid_children": {}, + "base": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "common_query_normalizers": [ + { + "K": [ + [ + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ 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+ "schema_version": 1, + "task_id": "bit-helper-contract", + "priority_revision": 7, + "base_commit": "32890bc5de034ab8fc93ac88ead7279a6a416d04", + "original_card": { + "id": "bit-helper-contract", + "question": "Can one precisely specified helper-mixing word satisfy a replacement for the inherited H2/K interface?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/r439-bsection-stars-seed01/README.md", + "research/r439-copy-path-sharing-barrier/README.md" + ], + "methods": [ + "Derive a replacement interface lemma and price its implementation.", + "Seek an exact dirty-input or chronological-cut counterexample to the proposed replacement." + ], + "acceptance_gate": "A full boundary contract and paid profile; unchanged scalar counts alone are insufficient. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "research/r439-bsection-stars-seed01/verify.py" + ], + "expected": "PASS_R439_BSECTION_STARS", + "inspect": "Compare the two false H2/K flags with the unchanged paid profile in its README.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Write one replacement H2/K implication for a single helper-star operation, then try to falsify it on dirty inputs.", + "bottleneck_link": "A legitimate replacement could admit a cheaper bit circuit; scalar savings alone do not alter the selected moment.", + "allowed_variations": [ + "Choose one helper-star or quartet instance; narrow to one boundary implication." + ], + "scope_change_triggers": [ + "Changing only source count or scalar addition count without an interface argument." + ], + "overlap_terms": [ + "H2_D_frame0_targets_from_helpers", + "K_equals_D", + "helper-star" + ] + }, + "scope_status": "changed", + "actual_scope": "Expose 222 original forward BIT helper queries before the source starts, bind all 111 actual port routes, and verify the complete source endpoint and owned return.", + "scope_change_reason": "The user assigned publication of the saved source interface. It changes the entrance observation contract and does not replace the source H2/K word or claim a complete supplier.", + "bottleneck_link": "A controller can use two independent early Q observations per port without a new native child. Its complete target decoding and ordinary tariff remain open.", + "budget_minutes": 60, + "stop_rule": "Verify the pinned finite source, its route matrices, all input columns and rejection controls. Do not search for a new caller or claim a kappa gain.", + "outcome": "partial", + "evidence": "PROOF.md and RESULT.json; exact 222-cut and 286-cut replays, 111 rational port routes, source-pin mutations, and owned-return controls.", + "author": "OpenAI Codex research assistance", + "ai_assistance": "This BIT adaptation, proof, code and packaging have substantial OpenAI Codex assistance. The retained source and the PR5388 entrance method keep their own credits.", + "open_questions": [ + { + "question": "Can a complete controller use the early responses and close every coupled helper output?", + "why_it_matters": "Early observations alone do not change the recursive paid-minus-target invoice or the multiplication exponent.", + "first_step": "Write one literal caller with all active helper inputs and final targets, then check its full operator endpoint before pricing it.", + "blocked_by": "No profitable complete caller has been constructed." + }, + { + "question": "Can that caller fund the fixed cover routes and ordinary work?", + "why_it_matters": "The finite interface adds movement and owned storage even though it adds no native child.", + "first_step": "Bind the caller to one common cover and derive its movement, storage and precision terms from the reported operations.", + "blocked_by": "A concrete caller and its full output contract are required first." + } + ] +} diff --git a/research/bit-early-helper-queries/VERIFY.json b/research/bit-early-helper-queries/VERIFY.json new file mode 100644 index 0000000000..0a080f079e --- /dev/null +++ b/research/bit-early-helper-queries/VERIFY.json @@ -0,0 +1,23 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/kappa-rebuild/bit/BIT-P3-NATIVE-BINDING.json", + "research/kappa-rebuild/bit/sources/pr589-regenerated/WORD.json.gz", + "research/kappa-rebuild/bit/sources/pr589-regenerated/records/249-records.bin", + "research/kappa-rebuild/bit/sources/pr589-regenerated/records/frames.json" + ], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 120, + "checks": "Exact source pins; all-column source and feedback replays; 111 native route identities; source mutations and five held-state/owned-return controls." + } + ] +} diff --git a/research/bit-early-helper-queries/model.py b/research/bit-early-helper-queries/model.py new file mode 100644 index 0000000000..2502c563b7 --- /dev/null +++ b/research/bit-early-helper-queries/model.py @@ -0,0 +1,354 @@ +#!/usr/bin/env python3 +"""Check the forward BIT helper-query interface on the retained source.""" +from collections import Counter, defaultdict +from fractions import Fraction as F +from hashlib import sha256 +from pathlib import Path +import gzip +import json +import struct + +ROOT = Path(__file__).resolve().parents[2] +SOURCE = ROOT / 'research/kappa-rebuild/bit/sources/pr589-regenerated' +WORD_HASH = 'e3e301e62bc2b41dbf1ceac0acf3d35824ebeab1848c5a2142d4577b109da52f' +LOCAL = {1: 1323, 2: 1342, 3: 79, 4: 44, 5: 102, 6: 11, 7: 19} + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def eye(n): + return [[F(i == j) for j in range(n)] for i in range(n)] + + +def mul(a, b): + result = [[F(0)] * len(b[0]) for _ in a] + for i, row in enumerate(a): + for k, x in enumerate(row): + if x: + for j, y in enumerate(b[k]): + if y: + result[i][j] += x * y + return result + + +def rank(a): + rows = [list(map(F, row)) for row in a] + pivot = 0 + for column in range(len(rows[0])): + index = next((i for i in range(pivot, len(rows)) if rows[i][column]), None) + if index is None: + continue + rows[pivot], rows[index] = rows[index], rows[pivot] + value = rows[pivot][column] + rows[pivot] = [x/value for x in rows[pivot]] + for i in range(pivot+1, len(rows)): + value = rows[i][column] + rows[i] = [x-value*y for x, y in zip(rows[i], rows[pivot])] + pivot += 1 + if pivot == len(rows): + break + return pivot + + +def block(a): + n = len(a) + return [[a[i % n][j % n] if i // n == j // n else F(0) + for j in range(2*n)] for i in range(2*n)] + + +def partial(p): + n = len(p) + return [[(F(i % n == j % n) - p[i % n][j % n] + if i // n == j // n else p[i % n][j % n]) + for j in range(2*n)] for i in range(2*n)] + + +def census(word, records): + writes = Counter() + reads = Counter() + first = {} + for index, (op, a, b, c, d, tag) in enumerate(records): + if op == 0 and 222 <= a < 661 and a not in first: + first[a] = dict(owner=a, source_event=index, old_frame=b, + new_frame=c, rank=d, prior_writes=writes[a], + prior_reads=reads[a], roots=word['frames'][c]) + elif op == 1: + writes[a] += 1 + reads[b] += 1 + need(len(first) == 439, 'Every helper has a first MOVE') + need(all(row['prior_writes'] == 0 and row['old_frame'] == 0 + for row in first.values()), 'Every first helper argument is its original input') + selected = sorted((row for row in first.values() if row['rank'] == 1), + key=lambda row: row['source_event']) + need(len(selected) == 286, 'The source has 286 first rank-one queries') + for row in selected: + need(len(row['roots']) == 1, 'Each selected frame is one source line') + row['port'] = row['roots'][0] + groups = defaultdict(list) + for row in selected: + groups[row['port']].append(row['owner']) + need(len(groups) == 111 and min(map(len, groups.values())) == 2, + 'Every port has at least two distinct raw helper queries') + return first, selected, dict(sorted(groups.items())) + + +def normalizers(word, frames): + identity = eye(8) + central = [[F(i == j == 0) for j in range(8)] for i in range(8)] + query, full = partial(central), partial(identity) + rows = [] + for port, source_root in enumerate(word['lines']): + u = [F(x, 2) for x in source_root] + need(sum(x*x for x in u) == 1, 'The root has unit norm') + v = [u[i] - F(i == 0) for i in range(8)] + norm = sum(x*x for x in v) + k = identity if not norm else [[F(i == j) - 2*v[i]*v[j]/norm + for j in range(8)] for i in range(8)] + p = [[x*y for y in u] for x in u] + complement = [[F(i == j)-p[i][j] for j in range(8)] for i in range(8)] + final_y = frames[str(word['final'][111+port])] + need(word['start'][port] == port+2 and word['start'][111+port] == 0 + and word['final'][port] == 1, 'The actual main entrance and X exit frames match') + need(final_y['dim'] == 7 and rank(final_y['B']) == 7 + and all(sum(F(x)*y for x, y in zip(row, u)) == 0 for row in final_y['B']), + 'The actual Y exit is the exact complementary frame') + need(mul(full, partial(p)) == partial(complement), 'The actual main diagonal is D_(I-P)') + need(mul(partial(complement), partial(p)) == full, 'The actual main shear is D_(I-P) Q') + frame = frames[str(port + 2)] + basis = frame['B'] + need(frame['dim'] == 1 and len(basis) == 1, 'The actual first frame has rank one') + z = list(map(F, basis[0])); scale = sum(x*x for x in z) + need([[x*y/scale for y in z] for x in z] == p, 'The native frame uses the same projector') + need(mul(k, k) == identity and [row[0] for row in k] == u, + 'The rational Householder map is its own inverse') + need(mul(mul(k, central), k) == p, 'The head normalizer gives the source projector') + big_k, event = block(k), partial(p) + need(mul(event, big_k) == mul(big_k, query), 'E K = K Q exactly') + need(mul(full, big_k) == mul(big_k, full), 'K commutes with the full helper endpoint') + need(mul(query, query) == eye(16), 'The BIT common query is an involution') + rows.append(dict(port=port, K=[[str(x) for x in row] for row in k], + nonidentity=k != identity)) + return rows + + +def stage_routes(word): + path = ROOT / 'research/kappa-rebuild/bit/BIT-P3-NATIVE-BINDING.json' + raw = path.read_bytes() + binding = json.loads(raw) + local = [[F(i == j and i < 8) for j in range(15)] for i in range(15)] + result = [] + for row in binding['ports']: + port = row['port'] + rho = [[F(x) for x in line] for line in row['chart_15']] + root = list(map(F, word['lines'][port])) + p = [[root[i]*root[j]/4 if i < 8 and j < 8 else F(0) + for j in range(15)] for i in range(15)] + target = [[p[i][j]+F(i == j and i >= 8) for j in range(15)] for i in range(15)] + need(mul(rho, rho) == eye(15), 'The actual port route is an involution') + need(mul(mul(rho, p), rho) == p, 'The actual port route fixes the query projector') + need(mul(mul(rho, local), rho) == target, + 'The actual port route sends the helper target to P plus the fresh seven-plane') + need(mul(block(rho), partial(p)) == mul(partial(p), block(rho)), + 'The held helper query commutes with the actual address route') + need(mul(mul(block(rho), partial(local)), block(rho)) == partial(target), + 'The helper output is the exact routed native rank-eight job') + result.append(dict(port=port, local_head_axes=list(range(8)), + fresh_stage_axes=list(range(8, 15)), + rho_sha256=sha256(json.dumps(row['chart_15']).encode()).hexdigest())) + need(sorted(row['port'] for row in result) == list(range(111)), + 'Every actual native port route is checked exactly once') + return dict(binding_sha256=sha256(raw).hexdigest(), ports=result, + selected_helpers=222, added_native_children={}, + added_cover_route_maps_per_fresh_stage=666, + input='rho_(port,stage) xi', observation='Q_port xi', + output='D_(P_port+B_stage) xi = Q_port D_Bstage xi', + proof='rho is used at the helper input, held observation, and helper output. It fixes P_port and conjugates the source local rank-eight projector to P_port+B_stage. The source scalar identity accepts the separately routed inputs. The same15-coordinate identities embed at each fresh stage with all other coordinates fixed.') + + +def replay(word, frames, records, selected, hoist, fault=None, input_rows=None): + slots = {row['source_event']: (index, row) for index, row in enumerate(selected)} + count = len(selected) + total = 662 + 2*count + initial = input_rows or [1 << i for i in range(661)] + first_owned_column = max(row.bit_length() for row in initial) + values = list(initial) + [1 << (first_owned_column+i) for i in range(total-661)] + current = list(word['start']) + [-1]*(total-661) + values[661] = 0 + paid = Counter() + if hoist: + for index, row in enumerate(selected): + raw, observation = 662+index, 662+count+index + if fault != 'dirty_owned_input' or index: + values[raw] = 0 + values[observation] = 0 + values[raw] ^= values[row['owner']] + current[raw] = row['new_frame'] + paid[1] += 1 + values[observation] ^= values[raw] + current[observation] = 'Q' + if fault == 'wrong_held_input': + values[662] ^= 1 + owned = None + cuts = 0 + for event_index, (op, a, b, c, f, tag) in enumerate(records): + if op == 0: + need(current[a] == b, 'The MOVE entrance frame matches') + if hoist and event_index in slots: + index, row = slots[event_index] + raw = 662+index + need(values[a] == values[raw] == initial[a], + 'The source cut equals the held original helper input') + need(current[a] == 0 and current[raw] == c, + 'The held raw field has the child exit frame') + values[a], values[raw] = values[raw], values[a] + if fault != 'wrong_swap_tags' or cuts: + current[a], current[raw] = current[raw], current[a] + if fault != 'uncleared_raw' or cuts: + values[raw] = 0 + current[raw] = -1 + cuts += 1 + else: + current[a] = c + paid[f] += 1 + elif op == 1: + need(current[a] == current[b] == f, 'Every source ADD has its original common frame') + need(a != b and a != owned, 'The scalar destination is legal') + if c & 1: + values[a] ^= values[b] + elif op == 2: + need(owned is None and b == 661 and values[b] == 0 and current[a] == c, + 'The original owned COPY entrance is unchanged') + owned = a + values[b], current[b] = values[a], f + paid[abs(frames[str(c)]['dim']-frames[str(f)]['dim'])] += 1 + elif op == 3: + need(owned == a and b == 661 and values[b] == values[a], + 'The original center value stays unchanged until its ERASE') + values[b], current[b], owned = 0, -1, None + else: + raise ValueError('Unknown source opcode') + expected = [initial[i] ^ (initial[i-111] if 111 <= i < 222 else 0) + for i in range(661)] + need(values[:661] == expected, 'All 661 independent source columns have the exact endpoint') + need(current[:661] == word['final'] and owned is None, 'All source exit frames are unchanged') + need(dict(paid) == LOCAL, 'The complete paid profile is unchanged') + if hoist: + for index, row in enumerate(selected): + observation = 662+count+index + need(values[observation] == initial[row['owner']], 'The normalized observation has its original input') + if fault != 'uncleared_observation' or index: + values[observation] = 0 + current[observation] = -1 + need(cuts == count and not any(values[661:]), 'Every owned field is cleared after use') + return dict(all_persistent_inputs=661, owned_input_columns=total-661 if hoist else 1, + replacement_cuts=cuts, paid=dict(sorted(paid.items())), + original_ADDs=sum(event[0] == 1 for event in records), + original_COPYs=sum(event[0] == 2 for event in records), + endpoint_row_sha256=sha256(json.dumps(expected).encode()).hexdigest()) + + +def feedback(groups): + width = 439 + low = (1 << width)-1 + def q(row): + return ((row & low) << width) | (row >> width) + inputs = [1 << i for i in range(width)] + observations = [q(row) for row in inputs] + pairs = [] + for port, owners in groups.items(): + a, b = owners[0]-222, owners[1]-222 + old_a = inputs[a] + inputs[b] ^= observations[a] + observations[b] ^= old_a + need(observations[b] == q(inputs[b]), 'The response update uses Q squared equal to identity') + pairs.append([port, a+222, b+222]) + need(all(observations[i] == q(inputs[i]) for i in range(width)), 'All stored input/response pairs agree') + for _, aa, bb in reversed(pairs): + a, b = aa-222, bb-222 + inputs[b] ^= q(inputs[a]) + need(inputs == [1 << i for i in range(width)], 'The helper input change is invertible') + return dict(disjoint_pairs=pairs, arbitrary_helper_columns=439, + ring='F2[Q]/(Q^2-1)', response_update='xi_k += Q xi_h; observation_k += xi_h', + endpoint='The source returns R times the changed helper input vector. A controller must retain or decode this full operator block; this check does not restore the original helper jobs for free.') + + +def reverse_census(records): + values = [1 << i for i in range(661)]+[0] + first = {} + for index, (op, a, b, c, f, tag) in enumerate(reversed(records)): + if op == 0 and 222 <= a < 661 and a not in first: + first[a] = (f, (values[a] & ((1 << 222)-1)).bit_count()) + elif op == 1 and c & 1: + values[a] ^= values[b] + elif op == 3: + values[b] = values[a] + elif op == 2: + values[b] = 0 + return dict(helpers=len(first), first_rank_one=sum(r == 1 for r, m in first.values()), + helper_only_rows=sum(m == 0 for r, m in first.values())) + + +def run(): + raw = (SOURCE/'WORD.json.gz').read_bytes() + need(sha256(raw).hexdigest() == WORD_HASH, 'The source gzip hash matches') + word = json.loads(gzip.decompress(raw)) + frame_bytes = (SOURCE/'records/frames.json').read_bytes() + frames = json.loads(frame_bytes)['frames'] + record_bytes = (SOURCE/'records/249-records.bin').read_bytes() + records = list(struct.iter_unpack('<6i', record_bytes)) + first, selected, groups = census(word, records) + maps = normalizers(word, frames) + routes = stage_routes(word) + need(all(word['start'][i] == 0 and word['final'][i] == 1 for i in range(222, 661)), + 'All 439 helpers have the same full-rank endpoint') + original = replay(word, frames, records, selected, False) + hoisted = replay(word, frames, records, selected, True) + paired_owners = {owner for owners in groups.values() for owner in owners[:2]} + paired = [row for row in selected if row['owner'] in paired_owners] + need(len(paired) == 222, 'The direct port interface has two helpers per port') + paired_replay = replay(word, frames, records, paired, True) + feedback_inputs = [1 << i for i in range(661)] + for owners in groups.values(): + a, b = owners[:2] + feedback_inputs[b] ^= 1 << (661+a) + feedback_replay = replay(word, frames, records, paired, True, input_rows=feedback_inputs) + controls = {} + for fault in ('wrong_held_input', 'wrong_swap_tags', 'dirty_owned_input', + 'uncleared_raw', 'uncleared_observation'): + try: + replay(word, frames, records, selected, True, fault) + except ValueError as error: + controls[fault] = str(error) + else: + raise ValueError('A bad hoist was accepted') + count = len(selected) + return dict(status='PASS_FORWARD_BIT_EARLY_HELPER_QUERY_INTERFACE', + base='1ec1119972c9aefe42525172d07b332fcff81cb4', + source_sha256={'WORD.json.gz': sha256(raw).hexdigest(), + 'records/frames.json': sha256(frame_bytes).hexdigest(), + 'records/249-records.bin': sha256(record_bytes).hexdigest()}, + independent_cold_helpers=439, scalar_first_departure_basis='I_439', + selected_first_queries=selected, per_port_helpers=groups, + common_query_normalizers=maps, routed_stage_interface=routes, + original_replay=original, hoisted_replay=hoisted, + added_paid_children={}, target_profile={8: 439}, + direct_port_interface=dict(selected_owners=sorted(paired_owners), + selected_queries=222, normalizer_maps=0, source_replay=paired_replay, + contract='At each port use its own Q=D_P. Both chosen helpers start with that exact Q. Their endpoint is D_I8=Q D_(I8-P).', + extra_ordinary_work=dict(owned_COPY=444, owned_CLEAR=888, + whole_field_SWAP=222, owned_fields=444)), + added_ordinary_work=dict(owned_COPY=2*count, owned_CLEAR=4*count, + whole_field_SWAP=count, owned_fields=2*count, + nonidentity_head_chart_maps=3*sum(maps[row['port']]['nonidentity'] for row in selected)), + feedback=feedback(groups), feedback_source_replay=feedback_replay, + reverse_first_departures=reverse_census(records), + negative_controls=controls, new_kappa=False, + limits='This is the forward native finite interface. Original scalar endpoint and chart replacement checks are exact on all source columns. The rational address identities bind the response and return maps. It does not prove a profitable controller, full cover hosting, ordinary-work precision, uniform compilation, or multiplication kappa.', + credit='The BIT source is the retained PR589/PR555 construction. The held-query rescheduling follows PR5388 at commit568717635d8d11175a80024c9c596e16f54b1ea4. This BIT adaptation and its checker have substantial OpenAI Codex assistance.') + + +if __name__ == '__main__': + print(json.dumps(run(), indent=2, sort_keys=True)) diff --git a/research/bit-early-helper-queries/verify.py b/research/bit-early-helper-queries/verify.py new file mode 100644 index 0000000000..5e44e456af --- /dev/null +++ b/research/bit-early-helper-queries/verify.py @@ -0,0 +1,78 @@ +#!/usr/bin/env python3 +"""Verify the pinned forward BIT helper-query interface and its controls.""" +import argparse +from hashlib import sha256 +import json +from pathlib import Path + +import model + +PACKAGE = Path(__file__).resolve().parent +ROOT = PACKAGE.parents[1] +SOURCE_PATHS = { + 'research/kappa-rebuild/bit/sources/pr589-regenerated/WORD.json.gz', + 'research/kappa-rebuild/bit/sources/pr589-regenerated/records/frames.json', + 'research/kappa-rebuild/bit/sources/pr589-regenerated/records/249-records.bin', + 'research/kappa-rebuild/bit/BIT-P3-NATIVE-BINDING.json', +} + + +def check_sources(pins, changed=None): + result = {} + for row in pins: + path = row['path'] + data = changed[path] if changed and path in changed else (ROOT / path).read_bytes() + digest = sha256(data).hexdigest() + if digest != row['sha256']: + raise ValueError('Source bytes differ: ' + path) + result[path] = digest + return result + + +def run(): + sources = json.loads((PACKAGE / 'SOURCES.json').read_text()) + pins = [row for row in sources['files'] if row['usage'] == 'input'] + paths = [row['path'] for row in pins] + declared = json.loads((PACKAGE / 'VERIFY.json').read_text())['inputs'] + if len(paths) != 4 or set(paths) != SOURCE_PATHS or set(declared) != SOURCE_PATHS: + raise ValueError('The four live source inputs must be pinned and declared') + checked = check_sources(pins) + controls = [] + for path in sorted(SOURCE_PATHS): + data = (ROOT / path).read_bytes() + changed = bytes([data[0] ^ 1]) + data[1:] + try: + check_sources(pins, {path: changed}) + except ValueError as error: + if str(error) != 'Source bytes differ: ' + path: + raise + controls.append({'source': path, 'result': 'REJECT_CHANGED_BYTES'}) + else: + raise ValueError('A source mutation passed: ' + path) + evidence = model.run() + return { + 'schema_version': 1, + 'status': 'PASS_BIT_EARLY_HELPER_QUERIES', + 'publication_base': sources['base_commit'], + 'source_sha256': checked, + 'source_mutation_controls': controls, + 'evidence': evidence, + 'new_kappa': False, + } + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--output', type=Path) + args = parser.parse_args() + result = json.loads(json.dumps(run())) + retained = PACKAGE / 'RESULT.json' + if retained.exists() and json.loads(retained.read_text()) != result: + raise ValueError('The retained result differs from the exact replay') + if args.output: + args.output.write_text(json.dumps(result, indent=2, sort_keys=True) + '\n') + print('PASS_BIT_EARLY_HELPER_QUERIES queries=222 routes=111 source_controls=4 owned_controls=5 new_kappa=false') + + +if __name__ == '__main__': + main() From e81d99a86dcaab33ac8e1133d158df6100c376f5 Mon Sep 17 00:00:00 2001 From: Ali Romman <226877337+aliromman@users.noreply.github.com> Date: Sat, 24 Oct 2026 15:28:11 -0500 Subject: [PATCH 2/2] Remove stale predecessor status from BIT query note --- research/bit-early-helper-queries/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/research/bit-early-helper-queries/README.md b/research/bit-early-helper-queries/README.md index d54323c7de..4707189c94 100644 --- a/research/bit-early-helper-queries/README.md +++ b/research/bit-early-helper-queries/README.md @@ -110,7 +110,7 @@ supplies the regenerated word and actual route binding used here. The entrance prologue follows [PR #5388](https://github.com/CrocSwap/integer-mult-bounds/pull/5388) and its [pinned proof](https://github.com/CrocSwap/integer-mult-bounds/blob/568717635d8d11175a80024c9c596e16f54b1ea4/research/native-helper-query-bank/PROOF.md). -That pending proof is conceptual credit, not an executable dependency. +That proof is conceptual credit, not an executable dependency. [PR #5421](https://github.com/CrocSwap/integer-mult-bounds/pull/5421) instead uses nine owned BIT relations in the reverse word. This package preserves arbitrary forward helper inputs and does not delete their target credits.