From 3a7920cb39340913027042a65cb79ea9043779ad Mon Sep 17 00:00:00 2001 From: Aaron Wang Date: Wed, 14 Oct 2026 12:00:59 -0400 Subject: [PATCH 1/2] research: independent enclosure of the pivot-566+554 T74 complex root (no new kappa) Independent-verification card independent-moment, scope changed to the pending supplier endpoint behind PR1800-PR1928. Aaron Wang, with help from opencode. --- research/t74-k554-root-enclosure/INPUTS.json | 110 ++++++ research/t74-k554-root-enclosure/README.md | 78 +++++ research/t74-k554-root-enclosure/RESULT.json | 84 +++++ research/t74-k554-root-enclosure/SOURCES.json | 30 ++ research/t74-k554-root-enclosure/TASK.json | 65 ++++ research/t74-k554-root-enclosure/VERIFY.json | 27 ++ .../crosscheck_decimal.py | 36 ++ .../t74-k554-root-enclosure/extract_inputs.py | 67 ++++ .../t74-k554-root-enclosure/test_package.py | 73 ++++ research/t74-k554-root-enclosure/verify.py | 320 ++++++++++++++++++ 10 files changed, 890 insertions(+) create mode 100644 research/t74-k554-root-enclosure/INPUTS.json create mode 100644 research/t74-k554-root-enclosure/README.md create mode 100644 research/t74-k554-root-enclosure/RESULT.json create mode 100644 research/t74-k554-root-enclosure/SOURCES.json create mode 100644 research/t74-k554-root-enclosure/TASK.json create mode 100644 research/t74-k554-root-enclosure/VERIFY.json create mode 100644 research/t74-k554-root-enclosure/crosscheck_decimal.py create mode 100644 research/t74-k554-root-enclosure/extract_inputs.py create mode 100644 research/t74-k554-root-enclosure/test_package.py create mode 100644 research/t74-k554-root-enclosure/verify.py diff --git a/research/t74-k554-root-enclosure/INPUTS.json b/research/t74-k554-root-enclosure/INPUTS.json new file mode 100644 index 0000000000..51fd7b007c --- /dev/null +++ b/research/t74-k554-root-enclosure/INPUTS.json @@ -0,0 +1,110 @@ +{ + "m": 73, + "schema_version": 1, + "sources": { + "pr1672": { + "complex_lower": "4199387390313861303339177484801756442495778596256450738650818800407/2500000000000000000000000000000000000000000000000000000000000000000000", + "conservative_complex_lower": "8398774766397181318443389806932001359929734105781555583223880640081/5000000000000000000000000000000000000000000000000000000000000000000000", + "git_blob": "bcff1fe102ce25b852011497a00949461d14e6d7", + "global_profile": { + "1": 1560432, + "2": 336336, + "3": 278724, + "4": 84912, + "48": 22748, + "5": 54612, + "8": 5328 + }, + "grid_digits": 70, + "head": "b8ab040dbb7638e79249e763c60e877765d9d3b7", + "headline_kappa": "1676938111022438771190100017020725032555691674761792047536039179/1000000000000000000000000000000000000000000000000000000000000000000", + "headline_kappa_field": "expected/kappa", + "headline_kappa_file_sha256": "41d7bd51c18eb354c6a785780ddefd35b3a8e2513daa2c4f585b236b7173e943", + "headline_kappa_git_blob": "bcff1fe102ce25b852011497a00949461d14e6d7", + "headline_kappa_path": "research/gmx-t74-k554-signed-001/new/SPEC.json", + "idle_remainder_profile": { + "48": 22748 + }, + "live": 66304, + "path": "research/gmx-t74-k554-signed-001/new/SPEC.json", + "pr": 1672, + "provider_counts": { + "extra": 417, + "gauge44": 249 + }, + "provider_profiles": { + "extra": { + "1": 2340, + "2": 508, + "3": 420, + "4": 126, + "5": 82, + "8": 8 + }, + "gauge44": { + "1": 2348, + "2": 500, + "3": 416, + "4": 130, + "5": 82, + "8": 8 + } + }, + "rank_mass": 4816512, + "sha256": "41d7bd51c18eb354c6a785780ddefd35b3a8e2513daa2c4f585b236b7173e943", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1672" + }, + "pr1928": { + "complex_lower": 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+ "headline_kappa_field": "kappa_rational", + "headline_kappa_file_sha256": "d72b5053ceea907bfb23befc0b73024c8b03d5128ac95f9a50462827ff8d6c09", + "headline_kappa_git_blob": "881309466b325073e16e110a2e74a2fc117f82cb", + "headline_kappa_path": "research/capped-fusion-t74-k554/outer/OUTER-CLAIM.json", + "idle_remainder_profile": { + "48": 22748 + }, + "live": 66304, + "path": "research/capped-fusion-t74-k554/new/SPEC.json", + "pr": 1928, + "provider_counts": { + "extra": 417, + "gauge44": 249 + }, + "provider_profiles": { + "extra": { + "1": 2340, + "2": 508, + "3": 420, + "4": 126, + "5": 82, + "8": 8 + }, + "gauge44": { + "1": 2348, + "2": 500, + "3": 416, + "4": 130, + "5": 82, + "8": 8 + } + }, + "rank_mass": 4816512, + "sha256": "75510fe5113baa42468c5835ebc9728bdc204acd6e07b898b3bc300e453d3443", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1928" + } + } +} diff --git a/research/t74-k554-root-enclosure/README.md b/research/t74-k554-root-enclosure/README.md new file mode 100644 index 0000000000..2b300b081b --- /dev/null +++ b/research/t74-k554-root-enclosure/README.md @@ -0,0 +1,78 @@ +# Independent enclosure of the pivot-566+554 T74 complex root + +**Independent verification of a pending supplier number. No new κ, no change to the selected record, and no check of the outer reduction.** + +The open claims from https://github.com/CrocSwap/integer-mult-bounds/pull/1800 to https://github.com/CrocSwap/integer-mult-bounds/pull/1928 all price the same pending complex supplier: the pivot-566 stack with the pivot-554 helper-donor kernel (lineage https://github.com/CrocSwap/integer-mult-bounds/pull/1625 and https://github.com/CrocSwap/integer-mult-bounds/pull/1672). At their "free ε → 1" point, κ approaches this supplier's complex moment root b. https://github.com/CrocSwap/integer-mult-bounds/pull/1928 takes b as its certified native endpoint minus 10^-10010. Up to now, the only certificates of that endpoint came from the authors' own engines. + +This package checks the endpoint with code that shares no algorithm with those engines. + +## Object + +Both pinned PR heads record the same data in `new/SPEC.json`: + +- global profile `{1:1560432, 2:336336, 3:278724, 4:84912, 5:54612, 8:5328, 48:22748}`, m = 73, live W = 66304; +- native and conservative endpoints on a 10^-70 grid (https://github.com/CrocSwap/integer-mult-bounds/pull/1672, head `b8ab040d`) and on a 10^-10000 grid (https://github.com/CrocSwap/integer-mult-bounds/pull/1928, head `07e4e423`). + +`extract_inputs.py` copies these fields, the two provider profiles, the provider counts, the idle remainder and each PR's headline κ into [INPUTS.json](INPUTS.json), with the Git blob and SHA-256 of each source file. With the pull refs fetched, `extract_inputs.py --check` rebuilds the file byte for byte. + +The moment definitions come from the repository's written review, not from code. The native moment is `sum_r H[r] (r/m)^(1-x) / W` ([native-complex-moment552/PROOF.md](../native-complex-moment552/PROOF.md)). The conservative model adds the inherited fallback of `32 m^2 N` rank-one children on a 10^-16 fraction, N = number of children ([three-stage-cover-assembly.tex](../../notes/three-stage-cover-assembly.tex), line 24). An endpoint e on a 10^-d grid is certified when M(e) < 1 < M(e + 10^-d). + +## Method + +`verify.py` uses only the standard library and imports nothing from the repository or from either PR. + +- **Logs.** Write A = ln(16/15), B = ln(25/24), C = ln(81/80); each is 2 atanh(1/31), 2 atanh(1/49) or 2 atanh(1/161). Then ln 2 = 7A + 5B + 3C, ln 3 = 11A + 8B + 5C and ln 5 = 16A + 12B + 7C. The verifier checks these identities exactly from the prime factorizations. ln 73 = 3 ln 2 + 2 ln 3 + 2 atanh(1/145). Every rank here is 5-smooth, so each ln(73/r) is a nonnegative integer combination of four atanh series. +- **Exp.** Halve the argument s times, sum a Taylor polynomial with an explicit tail bound, then square s times. +- **Rounding.** Every quantity is an integer multiple of 2^-bits rounded outward. The final test compares two exact integers. A sign that the enclosure cannot decide counts as failure; precision is raised at most twice and never turns an undecided sign into a pass. + +The authors' engines use a Mercator series and binary range reduction with atanh((x-1)/(x+1)) (`code/fine_mercator.py`, `code/fine_moment.py`). Earlier independent audits used a prime-by-prime log chain (pending-claims-independent-pricing) or binary reduction (pr1407-complex-moment-audit-seed39). This package uses neither. + +## Result + +`PASS_T74_K554_ROOT_ENCLOSURE_INDEPENDENT`, about 15 s on Python 3.12. + +- **Brackets.** All four pass: native and conservative, at both grids. The 10^-70 cases decide at 360 bits and the 10^-10000 cases at 33,347 bits, without precision refinement. +- **Nesting.** For both models, the 10^-70 endpoint of https://github.com/CrocSwap/integer-mult-bounds/pull/1672 equals the 10^-70 floor of the 10^-10000 endpoint of https://github.com/CrocSwap/integer-mult-bounds/pull/1928. +- **Profile composition.** At both heads, 249 gauge44 calls and 417 extra calls with their recorded per-call profiles, plus 22,748 idle rank-48 children, sum to the global profile. Rank mass is 4,816,512 and the deficit is 73 × 66,304 − 4,816,512 = 23,680. +- **Headline κ.** The κ of https://github.com/CrocSwap/integer-mult-bounds/pull/1928 (`outer/OUTER-CLAIM.json`) lies 2.003 × 10^-10010 below the native endpoint, as its stated choice of b implies. The κ of https://github.com/CrocSwap/integer-mult-bounds/pull/1672 (`new/SPEC.json`, 47-inequality outer) lies 2.817 × 10^-6 below. +- **Controls.** All ten are rejected. At 10^-70: next grid point as endpoint, previous grid point as endpoint, one child moved from rank 1 to rank 2, m = 72, W − 1, conservative endpoint without the surcharge, native endpoint with the surcharge. At 10^-10000: the first two and the surcharge-omission control again. + +The optional `crosscheck_decimal.py` (about 4 to 5 minutes) repeats the 10^-10000 case with Python's `decimal` ln and exp at 10,060 digits. It finds all seven log values inside the enclosures and the same four signs. `decimal` rounds to nearest, so this corroborates the result but does not certify it. + +## Reproduce + +From the repository root: + +```sh +python3 scripts/research_package.py --package research/t74-k554-root-enclosure --check-only +python3.12 scripts/research_package.py --package research/t74-k554-root-enclosure +python3.12 -B research/t74-k554-root-enclosure/crosscheck_decimal.py # optional, slow +git fetch origin pull/1672/head pull/1928/head +python3 research/t74-k554-root-enclosure/extract_inputs.py --check # optional, needs the pull refs +``` + +`verify.py --write` regenerates [RESULT.json](RESULT.json); without it the run must reproduce the file byte for byte. + +## Scope + +This checks one number per model and grid, plus the arithmetic that composes the profile. The following are taken as given: + +- the global profile and the per-call provider profiles (no replay of words, owners or hosting); +- the moment model and the native, surcharge-free complex recurrence, from the PR552/PR559 review; +- the outer reduction from b to κ, the fine source-prime padding and the ε → 1 transfer (see https://github.com/CrocSwap/integer-mult-bounds/pull/1797 for an audit of the PR1786 lemmas on a different supplier); +- all inherited all-size/compiler, realization, hosting, precision/tape, exact-recovery, analytic and bit H1-H5 assumptions. + +It is a finite check of recorded endpoints, not a proof of any multiplication theorem. + +## Open next questions + +The structured list is in [TASK.json](TASK.json). + +1. **Outer ledger of https://github.com/CrocSwap/integer-mult-bounds/pull/1928.** Does `outer/LEDGER.json` follow from the endpoint certified here, checked by code that does not import `outer/*.py`? This package certifies b only. A first step is to re-derive the slack list from `outer/RETUNED-SLACKS.md` and the PR1673 note and compare each slack exactly. Nothing blocks it. +2. **Profile against the emitted program.** Does the global profile equal the one emitted by the T74 hosted template and owner map? The seed78 emitted-ledger rebuild could be adapted to the two-provider layout (249 + 417 calls). The PR's template and owner archives are reproduced externally, so a maintainer replay capsule would make this cheap. + +## Credit + +Supplier construction: mdumitrean (https://github.com/CrocSwap/integer-mult-bounds/pull/1625, pivot-566 kernel), Jeremy Kothe (https://github.com/CrocSwap/integer-mult-bounds/pull/1672 and the refinement chain to https://github.com/CrocSwap/integer-mult-bounds/pull/1928), Rohan Arun (https://github.com/CrocSwap/integer-mult-bounds/pull/1319, T74 fill) and the lineage credited in those PRs. Outer: Vlado Vojdanovski (https://github.com/CrocSwap/integer-mult-bounds/pull/1673) and chafreaky (https://github.com/CrocSwap/integer-mult-bounds/pull/1786). The moment definitions are from the PR552/PR559 review and `notes/three-stage-cover-assembly.tex`. The audit pattern follows Sagar Thakrar's frontier1094-emitted-ledger-seed78 and the selected-suppliers-de-diagnostic and pr1407-complex-moment-audit-seed39 packages. + +Prepared by Aaron Wang, with help from opencode. New material is Apache-2.0. diff --git a/research/t74-k554-root-enclosure/RESULT.json b/research/t74-k554-root-enclosure/RESULT.json new file mode 100644 index 0000000000..4df6b640db --- /dev/null +++ b/research/t74-k554-root-enclosure/RESULT.json @@ -0,0 +1,84 @@ +{ + "brackets": { + "pr1672/conservative": { + "bits": 360, + "endpoint_side": -1, + "next_side": 1, + "on_grid": true, + "pass": true + }, + "pr1672/native": { + "bits": 360, + "endpoint_side": -1, + "next_side": 1, + "on_grid": true, + "pass": true + }, + "pr1928/conservative": { + "bits": 33347, + "endpoint_side": -1, + "next_side": 1, + "on_grid": true, + "pass": true + }, + "pr1928/native": { + "bits": 33347, + "endpoint_side": -1, + "next_side": 1, + "on_grid": true, + "pass": true + } + }, + "controls": { + "pr1672": { + "conservative_endpoint_without_surcharge": true, + "dimension_72": true, + "live_minus_one": true, + "native_endpoint_with_surcharge": true, + "next_grid_as_endpoint": true, + "one_child_rank1_to_rank2": true, + "previous_grid_as_endpoint": true + }, + "pr1928": { + "conservative_endpoint_without_surcharge": true, + "next_grid_as_endpoint": true, + "previous_grid_as_endpoint": true + } + }, + "headline_kappa_below_native_endpoint": { + "pr1672": { + "below": true, + "endpoint_minus_kappa": "2.816845103e-6" + }, + "pr1928": { + "below": true, + "endpoint_minus_kappa": "2.003359509e-10010" + } + }, + "inputs_sha256": "609c486efb1fe1e03ff2c84ba11085b231b9372e81fb2650bda821ce84e6e1ae", + "ledgers": { + "pr1672": { + "calls": 666, + "children": 2343092, + "deficit": 23680, + "rank_mass": 4816512 + }, + "pr1928": { + "calls": 666, + "children": 2343092, + "deficit": 23680, + "rank_mass": 4816512 + } + }, + "m": 73, + "nesting": { + "conservative": { + "coarse_equals_floor_of_fine": true + }, + "native": { + "coarse_equals_floor_of_fine": true + } + }, + "scope": "Native and conservative complex moment brackets and the profile composition only. The outer reduction that turns the endpoint into each headline kappa is not checked here.", + "status": "PASS_T74_K554_ROOT_ENCLOSURE_INDEPENDENT" +} diff --git a/research/t74-k554-root-enclosure/SOURCES.json b/research/t74-k554-root-enclosure/SOURCES.json new file mode 100644 index 0000000000..a9a8b3ccd7 --- /dev/null +++ b/research/t74-k554-root-enclosure/SOURCES.json @@ -0,0 +1,30 @@ +{ + "schema_version": 1, + "base_commit": "ae95f60feec79897b153dba6459bb3f9fd4d7b8e", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11", + "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "06c96f5579bb67ed1b86d334e78fbed7da6945f1", + "sha256": "6686ad58f1fbdbc87134a78901b60fd53a20d3984355e91defbbebc9e9fa8075" + }, + { + "path": "research/native-complex-moment552/PROOF.md", + "usage": "provenance", + "git_blob": "9adf304048b62c6db9250a611a8d4b0b60ed8276", + "sha256": "d5d498edc56fdef8c5798af7f5ec66948bd2f66c553b9efe366cdaab01bd3453" + }, + { + "path": "notes/three-stage-cover-assembly.tex", + "usage": "provenance", + "git_blob": "983ffb6ac8fb9117360cd0797c00c05dfa071c9d", + "sha256": "ccf34a6d37c4af14bebeab15be50ab204eb1caebe546385520050ec30089441d" + } + ] +} diff --git a/research/t74-k554-root-enclosure/TASK.json b/research/t74-k554-root-enclosure/TASK.json new file mode 100644 index 0000000000..4025aeef75 --- /dev/null +++ b/research/t74-k554-root-enclosure/TASK.json @@ -0,0 +1,65 @@ +{ + "schema_version": 1, + "task_id": "independent-moment", + "priority_revision": 3, + "base_commit": "ae95f60feec79897b153dba6459bb3f9fd4d7b8e", + "original_card": { + "id": "independent-moment", + "question": "Can one selected pricing or assembly claim be checked by a genuinely independent exact implementation?", + "starting_points": [ + "certificates/selected-result.json" + ], + "methods": [ + "Reconstruct the rank ledger from original operations rather than trusting its aggregate.", + "Implement certified moment inequalities through a different exact enclosure method." + ], + "acceptance_gate": "Demonstrate independence, source binding, positive cases and semantic failure controls.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Record the selected certificate and complex_profile rather than taking a PR headline as input.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Recompute one small part of the ledger or one certified enclosure using an independent implementation.", + "bottleneck_link": "Independent pricing prevents unsupported frontier claims and can reveal genuine accounting slack.", + "allowed_variations": [ + "Reconstruct either a source ledger or a numeric enclosure with a different method." + ], + "scope_change_triggers": [ + "Importing the primary function and calling its output independent verification." + ], + "overlap_terms": [ + "independent moment", + "rank histogram", + "exact enclosure" + ] + }, + "scope_status": "changed", + "actual_scope": "Independent exact enclosure of the complex moment root of the pending pivot-566+554 T74 supplier (profile {1:1560432, 2:336336, 3:278724, 4:84912, 5:54612, 8:5328, 48:22748}, m=73, W=66304): native and conservative brackets at the 1e-70 endpoints of PR1672 (head b8ab040d) and the 1e-10000 endpoints of PR1928 (head 07e4e423), their nesting, the provider/idle profile composition, and the position of each PR's headline kappa below the native endpoint.", + "scope_change_reason": "The selected #1094 ledger, both moment endpoints, invoice and outer slacks already have independent checks (frontier1094-emitted-ledger-seed78, selected-suppliers-de-diagnostic, pr1407-complex-moment-audit-seed39, PR1735). The card's enclosure method is applied instead to the supplier root behind the highest open claims (PR1800 through PR1928), where kappa tends to this root at the free epsilon -> 1 point and no independent enclosure was found.", + "bottleneck_link": "Every pending claim from PR1800 to PR1928 takes this certified native endpoint as b; an error in it would propagate to all of them. This package checks that number by a code-disjoint method. It does not check the outer reduction, the construction or admission, and it does not change kappa.", + "budget_minutes": 120, + "stop_rule": "Stop when both models' brackets pass at both grids with all semantic controls rejected, or report the first bracket that fails or stays undecided at four times the default precision.", + "outcome": "completed", + "evidence": "RESULT.json: four brackets pass (1e-70 at 360 bits; 1e-10000 at 33347 bits, no refinement needed); the 1e-70 endpoints equal the 1e-70 floors of the 1e-10000 endpoints for both models; both PR heads' provider profiles (249 gauge44 + 417 extra calls) plus 22748 idle rank-48 children sum to the global profile, rank mass 4816512, deficit 23680; PR1928's headline kappa is 2.003e-10010 below its native endpoint, PR1672's is 2.817e-6 below. 10 semantic controls rejected. Optional crosscheck_decimal.py (decimal at 10060 digits) agrees on all 7 log enclosures and 4 signs.", + "author": "Aaron Wang", + "ai_assistance": "Substantial: prepared with help from opencode (agent harness) for analysis, code and packaging.", + "open_questions": [ + { + "question": "Does the capped/fine-padding outer ledger of PR1928 (outer/LEDGER.json) follow from the endpoint certified here, checked by code that does not import outer/*.py?", + "why_it_matters": "This package certifies b only; the headline kappa also depends on the outer slacks and the epsilon -> 1 transfer.", + "first_step": "Re-derive the slack list from outer/RETUNED-SLACKS.md and the PR1673 note, and compare each slack exactly with outer/LEDGER.json.", + "blocked_by": "None; PR1797 covers the PR1786 transfer lemmas on a different supplier, not this ledger." + }, + { + "question": "Does the global profile used here equal the profile emitted by the PR1928 hosted template and owner map?", + "why_it_matters": "This package takes the SPEC.json global profile and provider profiles as data; frontier1094-emitted-ledger-seed78 shows how to rebuild such a profile from emitted programs.", + "first_step": "Adapt the seed78 emitted-ledger rebuild to the T74 two-provider layout (249 gauge44, 417 extra calls) on PR1928's committed template.", + "blocked_by": "PR1928's GLOBAL-TEMPLATE and OWNERS archives are reproduced externally; a maintainer replay capsule would make this cheap." + } + ] +} diff --git a/research/t74-k554-root-enclosure/VERIFY.json b/research/t74-k554-root-enclosure/VERIFY.json new file mode 100644 index 0000000000..feaba86d3d --- /dev/null +++ b/research/t74-k554-root-enclosure/VERIFY.json @@ -0,0 +1,27 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 300, + "checks": "INPUTS.json pin; exact log-identity check; profile composition for both PR heads; native and conservative brackets at 1e-70 (PR1672) and 1e-10000 (PR1928); nesting of the two grids; headline kappa below the native endpoint; 10 semantic controls rejected; RESULT.json byte-equal" + }, + { + "argv": [ + "{python}", + "-B", + "{package}/test_package.py" + ], + "timeout_seconds": 120, + "checks": "log and exp enclosures against float, fail-closed low precision, 1e-70 brackets, 7 controls, ledger control, input pin" + } + ] +} diff --git a/research/t74-k554-root-enclosure/crosscheck_decimal.py b/research/t74-k554-root-enclosure/crosscheck_decimal.py new file mode 100644 index 0000000000..e033e6a2f7 --- /dev/null +++ b/research/t74-k554-root-enclosure/crosscheck_decimal.py @@ -0,0 +1,36 @@ +#!/usr/bin/env python3 +"""Optional third implementation (about 4-5 minutes): Python's decimal ln/exp at 10,060 digits. + +Checks that decimal's ln(73/r) lies inside each verify.py log enclosure at the +PR1928 precision, and that decimal gives the same four moment signs. decimal +rounds to nearest, so this is corroboration, not a certificate; verify.py is +the certificate. Aaron Wang, with help from opencode. Apache-2.0. +""" +from decimal import Decimal, getcontext +from fractions import Fraction as Q +import verify as V + +getcontext().prec = 10060 +src = V.load_inputs()['sources']['pr1928'] +bits = V.default_bits(10000) +scale = Decimal(2) ** bits +for r, (lo, hi) in V.log_table(73, (1, 2, 3, 4, 5, 8, 48), bits).items(): + ln = (Decimal(73) / Decimal(r)).ln() + assert Decimal(lo) / scale <= ln <= Decimal(hi) / scale, r +prof = {int(r): int(n) for r, n in src['global_profile'].items()} +W, N = int(src['live']), sum(prof.values()) + + +def moment_minus_one(x, surcharge): + x = Decimal(x.numerator) / Decimal(x.denominator) + s = sum(Decimal(r * n) / Decimal(73 * W) * (x * (Decimal(73) / Decimal(r)).ln()).exp() for r, n in prof.items()) + if surcharge: + s += Decimal(32 * 73 * N) / (Decimal(10) ** 16 * W) * (x * Decimal(73).ln()).exp() + return s - 1 + + +g = Q(1, 10 ** 10000) +for field, surcharge in (('complex_lower', False), ('conservative_complex_lower', True)): + e = Q(src[field]) + assert moment_minus_one(e, surcharge) < 0 < moment_minus_one(e + g, surcharge), field +print('PASS_DECIMAL_CROSSCHECK | 7 log enclosures | 4 moment signs agree') diff --git a/research/t74-k554-root-enclosure/extract_inputs.py b/research/t74-k554-root-enclosure/extract_inputs.py new file mode 100644 index 0000000000..bb01edd488 --- /dev/null +++ b/research/t74-k554-root-enclosure/extract_inputs.py @@ -0,0 +1,67 @@ +#!/usr/bin/env python3 +"""Rebuild INPUTS.json from the two pinned PR heads (needs a fetched pull ref). + + git fetch origin pull/1672/head pull/1928/head + python3 research/t74-k554-root-enclosure/extract_inputs.py [--check] + +Reads only data fields of each package's new/SPEC.json. Imports nothing from +either package. Aaron Wang, with help from opencode. Apache-2.0. +""" +import argparse +import hashlib +import json +import subprocess +from pathlib import Path + +HERE = Path(__file__).resolve().parent +SOURCES = { + 'pr1672': dict(pr=1672, head='b8ab040dbb7638e79249e763c60e877765d9d3b7', + path='research/gmx-t74-k554-signed-001/new/SPEC.json', grid_digits=70, + kappa=('research/gmx-t74-k554-signed-001/new/SPEC.json', ('expected', 'kappa'))), + 'pr1928': dict(pr=1928, head='07e4e4231459e36b1055396306dcbd950248df62', + path='research/capped-fusion-t74-k554/new/SPEC.json', grid_digits=10000, + kappa=('research/capped-fusion-t74-k554/outer/OUTER-CLAIM.json', ('kappa_rational',))), +} + + +def git(*args): + return subprocess.run(['git', *args], check=True, capture_output=True, cwd=HERE).stdout + + +def build(): + out = dict(schema_version=1, m=73, sources={}) + for key, src in SOURCES.items(): + raw = git('show', src['head'] + ':' + src['path']) + spec = json.loads(raw) + exp = spec['expected'] + kpath, kkeys = src['kappa'] + kraw = git('show', src['head'] + ':' + kpath) + kappa = json.loads(kraw) + for k in kkeys: + kappa = kappa[k] + out['sources'][key] = dict( + headline_kappa=kappa, headline_kappa_path=kpath, headline_kappa_field='/'.join(kkeys), + headline_kappa_git_blob=git('rev-parse', src['head'] + ':' + kpath).decode().strip(), + headline_kappa_file_sha256=hashlib.sha256(kraw).hexdigest(), + pr=src['pr'], url='https://github.com/CrocSwap/integer-mult-bounds/pull/%d' % src['pr'], + head=src['head'], path=src['path'], + git_blob=git('rev-parse', src['head'] + ':' + src['path']).decode().strip(), + sha256=hashlib.sha256(raw).hexdigest(), grid_digits=src['grid_digits'], + live=exp['live'], rank_mass=exp['rank_mass'], global_profile=exp['global_profile'], + idle_remainder_profile=exp['idle_remainder_profile'], provider_counts=exp['provider_counts'], + provider_profiles={p: v['expected_profile'] for p, v in spec['providers'].items()}, + complex_lower=exp['complex_lower'], conservative_complex_lower=exp['conservative_complex_lower']) + return json.dumps(out, indent=1, sort_keys=True) + '\n' + + +if __name__ == '__main__': + ap = argparse.ArgumentParser(description=__doc__, formatter_class=argparse.RawDescriptionHelpFormatter) + ap.add_argument('--check', action='store_true', help='compare with the committed INPUTS.json instead of writing') + a = ap.parse_args() + text = build() + if a.check: + assert (HERE / 'INPUTS.json').read_text(encoding='utf-8') == text, 'INPUTS.json differs from the pinned PR heads' + print('PASS_INPUTS_MATCH_PINNED_PR_HEADS') + else: + (HERE / 'INPUTS.json').write_text(text, encoding='utf-8', newline='\n') + print('wrote INPUTS.json') diff --git a/research/t74-k554-root-enclosure/test_package.py b/research/t74-k554-root-enclosure/test_package.py new file mode 100644 index 0000000000..e1695830a8 --- /dev/null +++ b/research/t74-k554-root-enclosure/test_package.py @@ -0,0 +1,73 @@ +"""Unit tests and semantic controls for the T74 k554 root enclosure. + +Aaron Wang, with help from opencode. Apache-2.0. +""" +from fractions import Fraction as Q +import math +import sys +import unittest +from pathlib import Path + +sys.path.insert(0, str(Path(__file__).resolve().parent)) +import verify as V # noqa: E402 + +BITS = 400 + + +class Arithmetic(unittest.TestCase): + def test_log_identities(self): + V.check_log_identities() + + def test_logs_enclose_float(self): + logs = V.log_table(73, (1, 2, 3, 4, 5, 8, 48), BITS) + for r, (lo, hi) in logs.items(): + self.assertLess(lo, hi) + self.assertLess(hi - lo, 2 ** 16) # well inside the verifier's 128 guard bits + self.assertAlmostEqual(lo / 2 ** BITS, math.log(73 / r), places=14) + + def test_exp_encloses_float(self): + y = (Q(1, 137) * 2 ** BITS).__floor__() + lo, hi = V.exp_interval(y, y + 1, BITS) + self.assertLess(hi - lo, 2 ** 12) + self.assertAlmostEqual(lo / 2 ** BITS, math.exp(1 / 137), places=14) + + def test_fail_closed_on_low_precision(self): + src = V.load_inputs()['sources']['pr1672'] + self.assertEqual(V.side(src, Q(src['complex_lower']), False, 64), 0) + + +class Brackets(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.src = V.load_inputs()['sources']['pr1672'] + + def test_native_bracket(self): + self.assertTrue(V.bracket(self.src, False)['pass']) + + def test_conservative_bracket(self): + self.assertTrue(V.bracket(self.src, True)['pass']) + + def test_controls_rejected(self): + controls = V.controls(self.src) + self.assertEqual(len(controls), 7) + for name, rejected in controls.items(): + self.assertTrue(rejected, name) + + +class Ledger(unittest.TestCase): + def test_composition(self): + for src in V.load_inputs()['sources'].values(): + self.assertEqual(V.ledger(src)['deficit'], 23680) + + def test_composition_control(self): + src = dict(V.load_inputs()['sources']['pr1672']) + src['provider_counts'] = dict(src['provider_counts'], extra=416) + with self.assertRaises(ValueError): + V.ledger(src) + + def test_inputs_pinned(self): + V.check_inputs_pin() + + +if __name__ == '__main__': + unittest.main() diff --git a/research/t74-k554-root-enclosure/verify.py b/research/t74-k554-root-enclosure/verify.py new file mode 100644 index 0000000000..55481742f6 --- /dev/null +++ b/research/t74-k554-root-enclosure/verify.py @@ -0,0 +1,320 @@ +#!/usr/bin/env python3 +"""Independent exact enclosure of the pivot-566+554 T74 complex moment root. + +For a profile H, dimension m and live stock W, the native complex moment is + M(x) = sum_r H[r] (r/m)^(1-x) / W = sum_r (r H[r] / (m W)) * exp(x ln(m/r)) +(research/native-complex-moment552/PROOF.md). The conservative model adds the +inherited fallback 32 m^2 N / 10^16 children of rank one, N = sum_r H[r] +(notes/three-stage-cover-assembly.tex), i.e. 32 m N exp(x ln m) / (10^16 W). +An endpoint e on a 10^-d grid is certified when M(e) < 1 < M(e + 10^-d). + +Method, chosen to share no algorithm with the authors' engines (Mercator series +and binary range reduction with atanh((x-1)/(x+1))) or with earlier audits: + ln 2, ln 3, ln 5 are fixed integer combinations of A = ln(16/15), + B = ln(25/24), C = ln(81/80); ln 73 = ln 72 + ln(73/72); each ln(p/q) with + p - q = 1 is 2 atanh(1/(p+q)). exp uses argument halving, a Taylor + polynomial and repeated squaring. Every quantity is an integer multiple of + 2^-bits rounded outward, and the final comparisons are exact integer + comparisons. Inconclusive signs fail closed. + +Standard library only; imports and executes nothing from the repository or +from either source package. Aaron Wang, with help from opencode. Apache-2.0. +""" +import argparse +import hashlib +import json +import math +import sys +import time +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +sys.set_int_max_str_digits(0) # the PR1928 endpoints have about 10,000 digits +INPUTS_SHA256 = '609c486efb1fe1e03ff2c84ba11085b231b9372e81fb2650bda821ce84e6e1ae' + +# ln(p/q) = 2 atanh(1/(p+q)) for these unit-gap ratios; exponent vectors over (2, 3, 5). +RATIOS = {'A': ((16, 15), (4, -1, -1)), 'B': ((25, 24), (-3, -1, 2)), 'C': ((81, 80), (-4, 4, -1))} +# ln p = sum coefficient * ratio log, for p = 2, 3, 5. +PRIME_LOGS = {2: (7, 5, 3), 3: (11, 8, 5), 5: (16, 12, 7)} + + +def require(ok, message): + if not ok: + raise ValueError(message) + + +def cdiv(a, b): + return -((-a) // b) + + +def check_log_identities(): + """Exact check that PRIME_LOGS inverts the exponent vectors of RATIOS.""" + for i, (p, coeff) in enumerate(PRIME_LOGS.items()): + vec = [sum(c * RATIOS[k][1][j] for c, k in zip(coeff, 'ABC')) for j in range(3)] + require(vec == [int(i == j) for j in range(3)], 'log identity for %d' % p) + for (num, den), vec in RATIOS.values(): + require(num - den == 1 and num * 2 ** max(0, -vec[0]) * 3 ** max(0, -vec[1]) * 5 ** max(0, -vec[2]) + == den * 2 ** max(0, vec[0]) * 3 ** max(0, vec[1]) * 5 ** max(0, vec[2]), 'ratio factorization') + + +def atanh_inv(k, bits): + """Integer interval [lo, hi] containing 2^bits * atanh(1/k), k >= 2.""" + one, k2 = 1 << bits, k * k + terms = int(bits / (2 * math.log2(k))) + 2 + plo, phi = one // k, cdiv(one, k) + lo = hi = 0 + for j in range(terms): + lo += plo // (2 * j + 1) + hi += cdiv(phi, 2 * j + 1) + plo, phi = plo // k2, cdiv(phi, k2) + # remaining terms: sum_{j>=terms} k^-(2j+1)/(2j+1) <= k^-(2 terms+1) * k^2/((2 terms+1)(k^2-1)); phi bounds 2^bits k^-(2 terms+1) + hi += cdiv(phi * k2, (2 * terms + 1) * (k2 - 1)) + return lo, hi + + +def combine(parts, coeffs): + lo = sum(c * (p[0] if c > 0 else p[1]) for p, c in zip(parts, coeffs)) + hi = sum(c * (p[1] if c > 0 else p[0]) for p, c in zip(parts, coeffs)) + return lo, hi + + +def factor235(n): + e = [] + for p in (2, 3, 5): + k = 0 + while n % p == 0: + n //= p + k += 1 + e.append(k) + require(n == 1, 'rank is not 5-smooth') + return e + + +def log_table(m, ranks, bits): + """Integer intervals for 2^bits ln(m/r); requires m = 73 (so m - 1 = 72 is 5-smooth).""" + require(m == 73, 'this enclosure is written for m = 73') + base = [tuple(2 * v for v in atanh_inv(num + den, bits)) for (num, den), _ in RATIOS.values()] + d73 = tuple(2 * v for v in atanh_inv(73 + 72, bits)) + out = {} + for r in ranks: + require(0 < r < m, 'child rank range') + e = [a - b for a, b in zip(factor235(72), factor235(r))] # 72/r over (2, 3, 5) + coeff = [sum(e[i] * PRIME_LOGS[p][j] for i, p in enumerate((2, 3, 5))) for j in range(3)] + lo, hi = combine(base, coeff) + out[r] = (lo + d73[0], hi + d73[1]) + return out + + +def exp_interval(ylo, yhi, bits): + """Integer interval containing 2^bits exp(y) for 2^bits y in [ylo, yhi], 0 <= y < 1/2.""" + one = 1 << bits + require(0 <= ylo <= yhi < one // 2, 'exp range') + s = int(math.isqrt(bits)) + 1 + guard = s + 32 + w = bits + guard + xlo, xhi = (ylo << guard) >> s, cdiv(yhi << guard, 1 << s) + W1 = 1 << w + slo = shi = tlo = thi = W1 + n = 0 + while True: + n += 1 + tlo = ((tlo * xlo) >> w) // n + thi = cdiv(cdiv(thi * xhi, W1), n) + slo += tlo + shi += thi + if thi <= 1: + break + shi += thi + 1 # tail after term n is at most term n since x/(n+1) <= 1/2 + for _ in range(s): + slo = (slo * slo) >> w + shi = cdiv(shi * shi, W1) + return slo >> guard, cdiv(shi, 1 << guard) + + +def scaled_product(x, lohi): + """Interval of 2^bits * x * L for exact x > 0 and L given by an integer interval.""" + return (x.numerator * lohi[0]) // x.denominator, cdiv(x.numerator * lohi[1], x.denominator) + + +def side(src, x, surcharge, bits, m=None, profile=None, live=None): + """-1 if M(x) < 1, +1 if M(x) > 1, 0 if the enclosure at this precision cannot decide.""" + m = m or 73 + profile = profile or {int(r): int(n) for r, n in src['global_profile'].items()} + live = live or int(src['live']) + logs = log_table(m, tuple(sorted(set(profile) | {1})), bits) + lo_sum = hi_sum = 0 + for r, n in profile.items(): + if r == m: + elo = ehi = 1 << bits + else: + elo, ehi = exp_interval(*scaled_product(x, logs[r]), bits) + lo_sum += r * n * elo + hi_sum += r * n * ehi + target = m * live << bits + if surcharge: + N = sum(profile.values()) + elo, ehi = exp_interval(*scaled_product(x, logs[1]), bits) + lo_sum, hi_sum, target = (10 ** 16 * lo_sum + 32 * m * m * N * elo, + 10 ** 16 * hi_sum + 32 * m * m * N * ehi, 10 ** 16 * target) + if hi_sum < target: + return -1 + if lo_sum > target: + return 1 + return 0 + + +def default_bits(digits): + return int(digits * math.log2(10)) + 128 + + +def bracket(src, surcharge, endpoint=None, bits=None, **model): + d = int(src['grid_digits']) + grid = Q(1, 10 ** d) + e = Q(endpoint if endpoint is not None else src['conservative_complex_lower' if surcharge else 'complex_lower']) + bits = bits or default_bits(d) + at, nxt = side(src, e, surcharge, bits, **model), side(src, e + grid, surcharge, bits, **model) + for _ in range(2): # refine only an undecided sign; never accept an undecided one + if at and nxt: + break + bits *= 2 + at, nxt = side(src, e, surcharge, bits, **model), side(src, e + grid, surcharge, bits, **model) + on_grid = (e * 10 ** d).denominator == 1 + return {'on_grid': on_grid, 'endpoint_side': at, 'next_side': nxt, 'bits': bits, + 'pass': on_grid and at == -1 and nxt == 1} + + +def ledger(src): + m, live = 73, int(src['live']) + total = {} + for p, cnt in src['provider_counts'].items(): + for r, n in src['provider_profiles'][p].items(): + total[int(r)] = total.get(int(r), 0) + int(cnt) * int(n) + for r, n in src['idle_remainder_profile'].items(): + total[int(r)] = total.get(int(r), 0) + int(n) + glob = {int(r): int(n) for r, n in src['global_profile'].items()} + require(total == glob, 'provider profiles and idle remainder do not sum to the global profile') + mass = sum(r * n for r, n in glob.items()) + require(mass == int(src['rank_mass']), 'rank mass') + require(max(glob) < m, 'child rank range') + return dict(calls=sum(int(c) for c in src['provider_counts'].values()), children=sum(glob.values()), + rank_mass=mass, deficit=m * live - mass) + + +def controls(src, names=None): + """Each semantic mutation must make the bracket fail; True means rejected.""" + d = int(src['grid_digits']) + g = Q(1, 10 ** d) + nat, con = Q(src['complex_lower']), Q(src['conservative_complex_lower']) + prof = {int(r): int(n) for r, n in src['global_profile'].items()} + moved = {**prof, 1: prof[1] - 1, 2: prof[2] + 1} + cases = { + 'next_grid_as_endpoint': lambda: bracket(src, False, endpoint=nat + g), + 'previous_grid_as_endpoint': lambda: bracket(src, False, endpoint=nat - g), + 'one_child_rank1_to_rank2': lambda: bracket(src, False, profile=moved), + 'dimension_72': lambda: _m72(src), + 'live_minus_one': lambda: bracket(src, False, live=int(src['live']) - 1), + 'conservative_endpoint_without_surcharge': lambda: bracket(src, False, endpoint=con), + 'native_endpoint_with_surcharge': lambda: bracket(src, True, endpoint=nat), + } + out = {} + for name, run in cases.items(): + if names is None or name in names: + out[name] = not run()['pass'] + return out + + +def _m72(src): + """m = 72 cannot use the m = 73 log table; evaluate it with ln(72/r) = ln(73/r) - ln(73/72).""" + d = int(src['grid_digits']) + bits = default_bits(d) + e, g = Q(src['complex_lower']), Q(1, 10 ** d) + prof = {int(r): int(n) for r, n in src['global_profile'].items()} + logs = log_table(73, tuple(sorted(set(prof) | {1})), bits) + d73 = tuple(2 * v for v in atanh_inv(145, bits)) + + def sgn(x): + lo_sum = hi_sum = 0 + for r, n in prof.items(): + l = (logs[r][0] - d73[1], logs[r][1] - d73[0]) + elo, ehi = exp_interval(*scaled_product(x, l), bits) + lo_sum += r * n * elo + hi_sum += r * n * ehi + t = 72 * int(src['live']) << bits + return -1 if hi_sum < t else (1 if lo_sum > t else 0) + return {'pass': sgn(e) == -1 and sgn(e + g) == 1} + + +def load_inputs(): + return json.loads((HERE / 'INPUTS.json').read_text(encoding='utf-8')) + + +def check_inputs_pin(): + require(hashlib.sha256((HERE / 'INPUTS.json').read_bytes()).hexdigest() == INPUTS_SHA256, 'INPUTS.json pin') + + +def run(): + check_inputs_pin() + check_log_identities() + inputs = load_inputs() + coarse, fine = inputs['sources']['pr1672'], inputs['sources']['pr1928'] + result = dict(status=None, inputs_sha256=INPUTS_SHA256, m=inputs['m'], ledgers={}, brackets={}, nesting={}, controls={}) + for key, src in inputs['sources'].items(): + result['ledgers'][key] = ledger(src) + for model, surcharge in (('native', False), ('conservative', True)): + b = bracket(src, surcharge) + result['brackets']['%s/%s' % (key, model)] = b + for model, field in (('native', 'complex_lower'), ('conservative', 'conservative_complex_lower')): + e70, e10k = Q(coarse[field]), Q(fine[field]) + floor70 = Q((e10k * 10 ** 70).__floor__(), 10 ** 70) + result['nesting'][model] = dict(coarse_equals_floor_of_fine=(floor70 == e70)) + result['controls']['pr1672'] = controls(coarse) + result['controls']['pr1928'] = controls(fine, ('next_grid_as_endpoint', 'previous_grid_as_endpoint', + 'conservative_endpoint_without_surcharge')) + result['headline_kappa_below_native_endpoint'] = { + key: dict(below=Q(src['headline_kappa']) < Q(src['complex_lower']), + endpoint_minus_kappa=_sci(Q(src['complex_lower']) - Q(src['headline_kappa']))) + for key, src in inputs['sources'].items()} + result['scope'] = ('Native and conservative complex moment brackets and the profile composition only. The outer ' + 'reduction that turns the endpoint into each headline kappa is not checked here.') + ok = (all(b['pass'] for b in result['brackets'].values()) and all(n['coarse_equals_floor_of_fine'] for n in result['nesting'].values()) + and all(all(c.values()) for c in result['controls'].values()) + and all(h['below'] for h in result['headline_kappa_below_native_endpoint'].values())) + require(ok, 'enclosure failed: ' + json.dumps(result, default=str)[:2000]) + result['status'] = 'PASS_T74_K554_ROOT_ENCLOSURE_INDEPENDENT' + return result + + +def _sci(x): + sign = '-' if x < 0 else '' + x = abs(x) + if x == 0: + return '0' + e = math.floor(math.log10(x.numerator) - math.log10(x.denominator)) + mant = x / Q(10) ** e + while mant >= 10: + mant, e = mant / 10, e + 1 + while mant < 1: + mant, e = mant * 10, e - 1 + return '%s%se%d' % (sign, str(Q((mant * 10 ** 9).__floor__(), 10 ** 9).__float__()), e) + + +def main(): + ap = argparse.ArgumentParser(description=__doc__, formatter_class=argparse.RawDescriptionHelpFormatter) + ap.add_argument('--write', action='store_true', help='rewrite RESULT.json instead of comparing with it') + a = ap.parse_args() + t0 = time.perf_counter() + result = run() + text = json.dumps(result, indent=1, sort_keys=True) + '\n' + path = HERE / 'RESULT.json' + if a.write: + path.write_text(text, encoding='utf-8', newline='\n') + else: + require(path.read_text(encoding='utf-8') == text, 'RESULT.json differs from this run') + n_ctl = sum(len(c) for c in result['controls'].values()) + print('%s | brackets %d | nesting %d | controls %d rejected | %.1f s' % ( + result['status'], len(result['brackets']), len(result['nesting']), n_ctl, time.perf_counter() - t0)) + + +if __name__ == '__main__': + main() From b10c1a196cf5fbbdedc43c9fd26ff2e834849600 Mon Sep 17 00:00:00 2001 From: Aaron Wang Date: Wed, 14 Oct 2026 12:03:50 -0400 Subject: [PATCH 2/2] research: full autolinks for PR references in t74-k554-root-enclosure notes --- research/t74-k554-root-enclosure/README.md | 8 ++++---- research/t74-k554-root-enclosure/TASK.json | 20 ++++++++++---------- 2 files changed, 14 insertions(+), 14 deletions(-) diff --git a/research/t74-k554-root-enclosure/README.md b/research/t74-k554-root-enclosure/README.md index 2b300b081b..dccf9230ba 100644 --- a/research/t74-k554-root-enclosure/README.md +++ b/research/t74-k554-root-enclosure/README.md @@ -58,8 +58,8 @@ python3 research/t74-k554-root-enclosure/extract_inputs.py --check # optiona This checks one number per model and grid, plus the arithmetic that composes the profile. The following are taken as given: - the global profile and the per-call provider profiles (no replay of words, owners or hosting); -- the moment model and the native, surcharge-free complex recurrence, from the PR552/PR559 review; -- the outer reduction from b to κ, the fine source-prime padding and the ε → 1 transfer (see https://github.com/CrocSwap/integer-mult-bounds/pull/1797 for an audit of the PR1786 lemmas on a different supplier); +- the moment model and the native, surcharge-free complex recurrence, from the review of CrocSwap/integer-mult-bounds#552 and CrocSwap/integer-mult-bounds#559; +- the outer reduction from b to κ, the fine source-prime padding and the ε → 1 transfer (see https://github.com/CrocSwap/integer-mult-bounds/pull/1797 for an audit of the CrocSwap/integer-mult-bounds#1786 lemmas on a different supplier); - all inherited all-size/compiler, realization, hosting, precision/tape, exact-recovery, analytic and bit H1-H5 assumptions. It is a finite check of recorded endpoints, not a proof of any multiplication theorem. @@ -68,11 +68,11 @@ It is a finite check of recorded endpoints, not a proof of any multiplication th The structured list is in [TASK.json](TASK.json). -1. **Outer ledger of https://github.com/CrocSwap/integer-mult-bounds/pull/1928.** Does `outer/LEDGER.json` follow from the endpoint certified here, checked by code that does not import `outer/*.py`? This package certifies b only. A first step is to re-derive the slack list from `outer/RETUNED-SLACKS.md` and the PR1673 note and compare each slack exactly. Nothing blocks it. +1. **Outer ledger of https://github.com/CrocSwap/integer-mult-bounds/pull/1928.** Does `outer/LEDGER.json` follow from the endpoint certified here, checked by code that does not import `outer/*.py`? This package certifies b only. A first step is to re-derive the slack list from `outer/RETUNED-SLACKS.md` and the CrocSwap/integer-mult-bounds#1673 note and compare each slack exactly. Nothing blocks it. 2. **Profile against the emitted program.** Does the global profile equal the one emitted by the T74 hosted template and owner map? The seed78 emitted-ledger rebuild could be adapted to the two-provider layout (249 + 417 calls). The PR's template and owner archives are reproduced externally, so a maintainer replay capsule would make this cheap. ## Credit -Supplier construction: mdumitrean (https://github.com/CrocSwap/integer-mult-bounds/pull/1625, pivot-566 kernel), Jeremy Kothe (https://github.com/CrocSwap/integer-mult-bounds/pull/1672 and the refinement chain to https://github.com/CrocSwap/integer-mult-bounds/pull/1928), Rohan Arun (https://github.com/CrocSwap/integer-mult-bounds/pull/1319, T74 fill) and the lineage credited in those PRs. Outer: Vlado Vojdanovski (https://github.com/CrocSwap/integer-mult-bounds/pull/1673) and chafreaky (https://github.com/CrocSwap/integer-mult-bounds/pull/1786). The moment definitions are from the PR552/PR559 review and `notes/three-stage-cover-assembly.tex`. The audit pattern follows Sagar Thakrar's frontier1094-emitted-ledger-seed78 and the selected-suppliers-de-diagnostic and pr1407-complex-moment-audit-seed39 packages. +Supplier construction: mdumitrean (https://github.com/CrocSwap/integer-mult-bounds/pull/1625, pivot-566 kernel), Jeremy Kothe (https://github.com/CrocSwap/integer-mult-bounds/pull/1672 and the refinement chain to https://github.com/CrocSwap/integer-mult-bounds/pull/1928), Rohan Arun (https://github.com/CrocSwap/integer-mult-bounds/pull/1319, T74 fill) and the lineage credited in those PRs. Outer: Vlado Vojdanovski (https://github.com/CrocSwap/integer-mult-bounds/pull/1673) and chafreaky (https://github.com/CrocSwap/integer-mult-bounds/pull/1786). The moment definitions are from the review of CrocSwap/integer-mult-bounds#552 and CrocSwap/integer-mult-bounds#559 and `notes/three-stage-cover-assembly.tex`. The audit pattern follows Sagar Thakrar's frontier1094-emitted-ledger-seed78 and the selected-suppliers-de-diagnostic and pr1407-complex-moment-audit-seed39 packages. Prepared by Aaron Wang, with help from opencode. New material is Apache-2.0. diff --git a/research/t74-k554-root-enclosure/TASK.json b/research/t74-k554-root-enclosure/TASK.json index 4025aeef75..66eccb0f9a 100644 --- a/research/t74-k554-root-enclosure/TASK.json +++ b/research/t74-k554-root-enclosure/TASK.json @@ -39,27 +39,27 @@ ] }, "scope_status": "changed", - "actual_scope": "Independent exact enclosure of the complex moment root of the pending pivot-566+554 T74 supplier (profile {1:1560432, 2:336336, 3:278724, 4:84912, 5:54612, 8:5328, 48:22748}, m=73, W=66304): native and conservative brackets at the 1e-70 endpoints of PR1672 (head b8ab040d) and the 1e-10000 endpoints of PR1928 (head 07e4e423), their nesting, the provider/idle profile composition, and the position of each PR's headline kappa below the native endpoint.", - "scope_change_reason": "The selected #1094 ledger, both moment endpoints, invoice and outer slacks already have independent checks (frontier1094-emitted-ledger-seed78, selected-suppliers-de-diagnostic, pr1407-complex-moment-audit-seed39, PR1735). The card's enclosure method is applied instead to the supplier root behind the highest open claims (PR1800 through PR1928), where kappa tends to this root at the free epsilon -> 1 point and no independent enclosure was found.", - "bottleneck_link": "Every pending claim from PR1800 to PR1928 takes this certified native endpoint as b; an error in it would propagate to all of them. This package checks that number by a code-disjoint method. It does not check the outer reduction, the construction or admission, and it does not change kappa.", + "actual_scope": "Independent exact enclosure of the complex moment root of the pending pivot-566+554 T74 supplier (profile {1:1560432, 2:336336, 3:278724, 4:84912, 5:54612, 8:5328, 48:22748}, m=73, W=66304): native and conservative brackets at the 1e-70 endpoints of CrocSwap/integer-mult-bounds#1672 (head b8ab040d) and the 1e-10000 endpoints of CrocSwap/integer-mult-bounds#1928 (head 07e4e423), their nesting, the provider/idle profile composition, and the position of each PR's headline kappa below the native endpoint.", + "scope_change_reason": "The selected CrocSwap/integer-mult-bounds#1094 ledger, both moment endpoints, invoice and outer slacks already have independent checks (frontier1094-emitted-ledger-seed78, selected-suppliers-de-diagnostic, pr1407-complex-moment-audit-seed39, CrocSwap/integer-mult-bounds#1735). The card's enclosure method is applied instead to the supplier root behind the highest open claims (CrocSwap/integer-mult-bounds#1800 through CrocSwap/integer-mult-bounds#1928), where kappa tends to this root at the free epsilon -> 1 point and no independent enclosure was found.", + "bottleneck_link": "Every pending claim from CrocSwap/integer-mult-bounds#1800 to CrocSwap/integer-mult-bounds#1928 takes this certified native endpoint as b; an error in it would propagate to all of them. This package checks that number by a code-disjoint method. It does not check the outer reduction, the construction or admission, and it does not change kappa.", "budget_minutes": 120, "stop_rule": "Stop when both models' brackets pass at both grids with all semantic controls rejected, or report the first bracket that fails or stays undecided at four times the default precision.", "outcome": "completed", - "evidence": "RESULT.json: four brackets pass (1e-70 at 360 bits; 1e-10000 at 33347 bits, no refinement needed); the 1e-70 endpoints equal the 1e-70 floors of the 1e-10000 endpoints for both models; both PR heads' provider profiles (249 gauge44 + 417 extra calls) plus 22748 idle rank-48 children sum to the global profile, rank mass 4816512, deficit 23680; PR1928's headline kappa is 2.003e-10010 below its native endpoint, PR1672's is 2.817e-6 below. 10 semantic controls rejected. Optional crosscheck_decimal.py (decimal at 10060 digits) agrees on all 7 log enclosures and 4 signs.", + "evidence": "RESULT.json: four brackets pass (1e-70 at 360 bits; 1e-10000 at 33347 bits, no refinement needed); the 1e-70 endpoints equal the 1e-70 floors of the 1e-10000 endpoints for both models; both PR heads' provider profiles (249 gauge44 + 417 extra calls) plus 22748 idle rank-48 children sum to the global profile, rank mass 4816512, deficit 23680; CrocSwap/integer-mult-bounds#1928's headline kappa is 2.003e-10010 below its native endpoint, CrocSwap/integer-mult-bounds#1672's is 2.817e-6 below. 10 semantic controls rejected. Optional crosscheck_decimal.py (decimal at 10060 digits) agrees on all 7 log enclosures and 4 signs.", "author": "Aaron Wang", "ai_assistance": "Substantial: prepared with help from opencode (agent harness) for analysis, code and packaging.", "open_questions": [ { - "question": "Does the capped/fine-padding outer ledger of PR1928 (outer/LEDGER.json) follow from the endpoint certified here, checked by code that does not import outer/*.py?", + "question": "Does the capped/fine-padding outer ledger of CrocSwap/integer-mult-bounds#1928 (outer/LEDGER.json) follow from the endpoint certified here, checked by code that does not import outer/*.py?", "why_it_matters": "This package certifies b only; the headline kappa also depends on the outer slacks and the epsilon -> 1 transfer.", - "first_step": "Re-derive the slack list from outer/RETUNED-SLACKS.md and the PR1673 note, and compare each slack exactly with outer/LEDGER.json.", - "blocked_by": "None; PR1797 covers the PR1786 transfer lemmas on a different supplier, not this ledger." + "first_step": "Re-derive the slack list from outer/RETUNED-SLACKS.md and the CrocSwap/integer-mult-bounds#1673 note, and compare each slack exactly with outer/LEDGER.json.", + "blocked_by": "None; CrocSwap/integer-mult-bounds#1797 covers the CrocSwap/integer-mult-bounds#1786 transfer lemmas on a different supplier, not this ledger." }, { - "question": "Does the global profile used here equal the profile emitted by the PR1928 hosted template and owner map?", + "question": "Does the global profile used here equal the profile emitted by the CrocSwap/integer-mult-bounds#1928 hosted template and owner map?", "why_it_matters": "This package takes the SPEC.json global profile and provider profiles as data; frontier1094-emitted-ledger-seed78 shows how to rebuild such a profile from emitted programs.", - "first_step": "Adapt the seed78 emitted-ledger rebuild to the T74 two-provider layout (249 gauge44, 417 extra calls) on PR1928's committed template.", - "blocked_by": "PR1928's GLOBAL-TEMPLATE and OWNERS archives are reproduced externally; a maintainer replay capsule would make this cheap." + "first_step": "Adapt the seed78 emitted-ledger rebuild to the T74 two-provider layout (249 gauge44, 417 extra calls) on CrocSwap/integer-mult-bounds#1928's committed template.", + "blocked_by": "CrocSwap/integer-mult-bounds#1928's GLOBAL-TEMPLATE and OWNERS archives are reproduced externally; a maintainer replay capsule would make this cheap." } ] }