diff --git a/.github/workflows/tensor-e8-rate-audit.yml b/.github/workflows/tensor-e8-rate-audit.yml new file mode 100644 index 0000000000..0b8b57a73e --- /dev/null +++ b/.github/workflows/tensor-e8-rate-audit.yml @@ -0,0 +1,31 @@ +name: Tensor E8 paid-rate audit +on: + pull_request: + paths: + - 'research/tensor-e8-rate-audit/**' + - '.github/workflows/tensor-e8-rate-audit.yml' + push: + paths: + - 'research/tensor-e8-rate-audit/**' + - '.github/workflows/tensor-e8-rate-audit.yml' + workflow_dispatch: +permissions: + contents: read +jobs: + verify: + runs-on: ubuntu-24.04 + timeout-minutes: 5 + strategy: + fail-fast: false + matrix: + python: ['3.11', '3.13'] + steps: + - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 + with: + persist-credentials: false + - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 + with: + python-version: ${{ matrix.python }} + - run: python -B -I -O research/tensor-e8-rate-audit/verify.py --check research/tensor-e8-rate-audit/RESULTS.json + - run: python -B -I -O research/tensor-e8-rate-audit/test_verify.py + - run: git diff --exit-code diff --git a/research/tensor-e8-rate-audit/CLAIM.json b/research/tensor-e8-rate-audit/CLAIM.json new file mode 100644 index 0000000000..e53c5c8405 --- /dev/null +++ b/research/tensor-e8-rate-audit/CLAIM.json @@ -0,0 +1,29 @@ +{ + "track": "Adversarial mathematical audit", + "seed": 66, + "seed_source": "OS randomness via Python secrets.randbelow(100)", + "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60", + "started_at": "2026-10-13T03:44:57Z", + "claimed_at": "2026-10-13T03:48:14.740784+00:00", + "expected_finish": "2026-10-13T04:30:00Z", + "object": "PR647 PROVIDER-PROOF.md sections 8\u20139: full tensor-depth paid histogram and limit 9^n*kappa_n^* = 28/(2739 log 3)", + "source_head": "956bb581e7f97328e1b53baa5aca3d2490f2f607", + "method": "Independently aggregate helper lifetimes and solve histogram recurrences; exact rational log/moment bounds and a quantitative analytic error bound. Depths 1\u201366, seed selects the maximum audited depth; no random search.", + "deliverable": "Scoped audit proof, exact reproducible receipt, negative controls, source pins and attribution; no new multiplication kappa.", + "candidates": [ + "Tensor E8 paid-profile asymptotic coefficient (#647), chosen because existing packaged verifier covers depth one only", + "Square-root assembly wall pass/accounting assumptions (#657), not selected", + "Dirty echo complete recurrence (#673), not selected because neighbouring #663 already audits the underlying binary interface" + ], + "overlap": "497 open PR titles inspected; relevant #647/#657/#673 bodies, files and comments read; latest #677 checked immediately before claim. No pinned issues and no sprint coordination issue; local claim only.", + "stopping_rule": "One bounded audit; stop expansion by 04:18 UTC and reserve the final quarter for independent checks, overlap refresh and handoff.", + "finish_target_revised": "2026-10-13T04:04:00Z after user requested faster turnaround", + "verification_started": "2026-10-13T03:56:54Z", + "result": { + "updated_at": "2026-10-13T03:58:51.513691+00:00", + "status": "Completed analytic profile audit; packaging PR", + "finding": "Corroborated leading coefficient; derived center-copy correction plus O(n/9^n) error with explicit finite-depth bounds. All depths 1\u201366 and nine negative controls pass.", + "link": "https://github.com/swbiggart/integer-mult-bounds/tree/research/seed66-mathematical-audit/research/tensor-e8-rate-audit", + "overlap_refresh": "501 open PRs through #681; PR647 unchanged; no pinned issues. No overlapping tensor-rate audit identified." + } +} diff --git a/research/tensor-e8-rate-audit/NOTICE.md b/research/tensor-e8-rate-audit/NOTICE.md new file mode 100644 index 0000000000..7cd48fc03d --- /dev/null +++ b/research/tensor-e8-rate-audit/NOTICE.md @@ -0,0 +1,25 @@ +# Attribution and license + +Prepared by Scott Woolsey Biggart (@swbiggart), with substantial OpenAI Codex +assistance in the mathematics, implementation, review and writing. No independent +human referee or formal proof is claimed. New material is under the repository's +Apache-2.0 license; see ../../LICENSE. + +This audit depends on the paid tensor profile in Artus / @artuskg's PR647, +head 956bb581e7f97328e1b53baa5aca3d2490f2f607. That contribution credits OpenAI +Pro for the retained provider proof, Codex for its recovery and scrutiny, +and a separate Codex referee for its depth-one checker. The limit +28/(2739 log 3), the construction and all original count formulas belong to +that predecessor. Our additions are the independent general-depth accounting, +explicit finite-depth bounds and the center-copy correction expansion. +No predecessor implementation is imported by our checker. + +Retain the precursor credits recorded in PR647: Jacob Sussman's E8 unit and +phase-frame/cover work; Chafik Boukhalfa's explicit programs; eumemic's batched +recursion; Ryan Shea's transfer work; and the P390/P401 and paired-cube lineage. +OpenAI's exact-Fourier source is part of PR647's transfer, which this audit +does not use or revalidate. See the immutable PR647 NOTICE.md and source hashes +in SOURCE.json for its complete provenance and retained notices. + +The elementary atanh/logarithm and exponential bounds are classical. No +literature-priority claim is made for them, tensorization or moment methods. diff --git a/research/tensor-e8-rate-audit/PROOF.md b/research/tensor-e8-rate-audit/PROOF.md new file mode 100644 index 0000000000..aeee978dd2 --- /dev/null +++ b/research/tensor-e8-rate-audit/PROOF.md @@ -0,0 +1,156 @@ +# Quantitative audit of the tensor E8 paid moment + +This audits sections 4.2, 8 and 9 of PR647's `PROVIDER-PROOF.md` at +`956bb581e7f97328e1b53baa5aca3d2490f2f607`. It corroborates the stated leading +constant and adds explicit finite-depth bounds and a first correction term. +It assumes the provider's listed register paths and three-stage assembly. +It does not independently prove their scalar, frame, RAM or Fourier realization. + +Let architecture depth n >= 1, h=9^n, v=120^n, r=8^n, +R=(885v-1081r)/14, W=R+2v, m=3h and D=2v-3hr. Let H(s) be the complete +global paid histogram. Define + + Phi(k) = sum_s H(s) (s/m)^(1-k). + +The root k_n of Phi(k_n)=W is a supremum for this profile's strict moment +condition, not an admitted equality witness or a multiplication exponent. + +## Independent accounting + +`lifetime_profile` aggregates chronological dimension changes for outputs, +pair routes, consumed inputs, gathers, decoders and returned child outputs. +It counts eight equal recursive subtrees by multiplicity. Root input loads, +root output finishes, both data endpoints, every copied-center descent and +the final two pivot lines are separately paid. These are dimension invoices; +checking a dimension path does not establish the actual frame inclusions. + +An independent expression unrolls the recursion by level. At an internal level +j=0,...,n-2, put d=9^j and c=v/15^j. The **local** contributions are: + +| Rank | Count | +| --- | ---: | +| h-d | c | +| d | 113c | +| h-2d | 56c | +| 8d | 2c | +| h-9d | 2c | +| 9d | 2c/15 | + +At the terminal level d=h/9, c=v/15^(n-1), they are +(d,112c), (7d,56c), (8d,2c), (h,c/15). +Finally add (1,2v), (h-1,2v), (h,r). Multiply the local histogram by three, +then add (2,2v) for the global endpoints. Equal ranks are combined. +The terminal level must be treated separately: it has no decoder subtree. + +The helper allocations obey R_1=6968 and R_n=59*120^n+8R_(n-1). +Summing the displayed counts and their ranks, or summing the register paths, +gives the source identities + + S = (1334v-1726r)/7, + sum H = 3S+2v = (4016v-5178r)/7, + sum sH(s) = mW-D. + +These follow for every n by geometric sums/induction. The executable comparison +covers every integer n from 1 through 66. Finite agreement is additional evidence, +not a proof by enumeration of the universal identities. + +Since D/v=2-3(3/5)^n >= 1/5, Phi(0)W. +There is exactly one k_n in (0,1). + +## A root enclosure without root finding + +Write + + M = Phi'(0)/v = sum_s [sH(s)/(mv)] log(m/s), + delta = (W-Phi(0))/v = D/(mv), + A = h*delta = D/(3v), U = log(m). + +For 0<=z<1, z <= exp(z)-1 <= z/(1-z). Therefore + + delta/(M+delta*U) <= k_n <= delta/M. (1) + +For the upper endpoint, Phi(k)-Phi(0) >= v*k*M holds for every k>=0. +For the lower endpoint k=delta/(M+delta*U), kU<1, and + + (Phi(k)-Phi(0))/v <= k*M/(1-kU) = delta. + +Thus there is no numerical root-search stopping condition hidden in (1). +With rational bounds M_lo<=M<=M_hi and U<=U_hi, the reported interval is + + A/(M_hi+(A/h)*U_hi) <= h*k_n <= A/M_lo. (2) + +Logarithms use the atanh series after reducing the argument to [1,2), with a +geometric remainder. Specifically, for u=(x-1)/(x+1), + + 2 sum_(j=0..63) u^(2j+1)/(2j+1) <= log x + <= that sum + 2u^129/[129(1-u^2)]. + +Binary reduction also needs the same formula for log 2. Endpoints are rounded +outwards to multiples of 2^-180. All subsequent arithmetic is rational. The +36-place decimal strings in the receipt are floors for display; the fraction +fields, not those strings, are the certified endpoints. + +## An explicit error bound for the asymptotic derivative + +Let t=3/5, L=(913/14)log 3 and B_n=sum_(j=0..n-2)t^j, with B_1=0. +The following bounds hold for every n>=1: + + L-E_high <= M <= L+E_low, + + E_high = [131 B_n + 113 t^(n-1) + 2]/h + + (87/14) log(3) / 15^(n-1), + + E_low = [(651/5) B_n + (603/5)t^(n-1) + 10/3] log(3h)/h + + log(3)/15^n. (3) + +Here is a direct derivation. Put f(x)=x log(1/x). Assign the output rank h-d, +pair rank h-2d, internal input/decoder ranks h-9d, and root data rank h-1 to +the high-rank group. At the terminal level assign one of the two 8d entries +to that group (the output); assign the other (input growth) to the low group. +Every high-rank x=s/(3h) lies in [7/27,1/3]. On this interval +0=0)15^-j+6=2739/14. Their f(1/3) contribution is L. +The high-rank distance losses are at most +[131 B_n+113t^(n-1)+2]/h. At the terminal level the two h-9d entries +are absent; adding these plus the infinite tail costs +[2+59/14]log(3)/15^(n-1). This gives E_high. + +All remaining terms are nonnegative. Bounding every log(3h/s) by log(3h), +their internal rank coefficients are 113+2*8+(2/15)*9=651/5 and their +terminal coefficients are 112+8+9/15=603/5. Root rank-one loading and the +global rank-two endpoints contribute 2+4/3=10/3. The copied-center term +is exactly log(3)/15^n. This gives E_low. Thus (3) does not rely on an +unquantified dominated-convergence argument. It also handles n=1. + +Combining (2) and (3), M=L+O(n/9^n). The gap between the two exact-log +bounds in (2) is O(n/9^n), because A is bounded, M is bounded away from +zero eventually, and U=O(n). Consequently the refined expansion is + + 9^n k_n = [28/(2739 log 3)] [1 - (3/2)(3/5)^n] + + O(n/9^n). (4) + +In particular the leading coefficient asserted in PR647 is correct under +its paid profile. The copied-center correction decays as (3/5)^n, much +more slowly than n/9^n. The ordinary exponent itself still tends to zero. +No search for an improved provider or new multiplication kappa is implied. + +## Scope and failure detection + +The executable checks all 66 profiles, their counts, masses, analytic +bounds (3), and rational root brackets. At depth 66 it certifies + + 0 < (C-9^66 k_66)/C < 4*10^-15, + C = 28/(2739 log 3). + +Omitting the centers or rank-two endpoints fails at depths 1,2,6,66. +A separate mutation replaces one rank-1 and one rank-9 child by one rank-2 +and one rank-8 child at depth two. It preserves both child count and rank +mass, but changes the logarithmic derivative and fails the histogram +comparison. Thus mass-only validation would be insufficient. + +This is a mathematical profile audit and analytic consequence. The pinned +source's all-size RAM theorem, physical program and supplied-root cyclic +transfer remain outside this audit; it is not a proof-assistant result. diff --git a/research/tensor-e8-rate-audit/README.md b/research/tensor-e8-rate-audit/README.md new file mode 100644 index 0000000000..cfc5ba6230 --- /dev/null +++ b/research/tensor-e8-rate-audit/README.md @@ -0,0 +1,39 @@ +# Tensor E8 rate audit: the center-copy correction controls convergence + +The paid profile in PR647's retained tensor-provider proof passes an +independent count and moment audit at every depth 1–66. Its asserted limit +is corroborated, and [PROOF.md](PROOF.md) derives the sharper expansion + + 9^n k_n = 28/(2739 log 3) * (1 - (3/2)(3/5)^n) + O(n/9^n). + +Here k_n is the root of that profile's moment equation. It is not a new +multiplication saving or a claim to realize a different physical supplier. +The copied-center correction dominates the other asymptotic profile effects. +At depth 66, the scaled root is below its limit by less than 4e-15 relatively. + +Reproduce from the repository root, Python 3.9+ with no dependencies: + +```sh +python3 -B research/tensor-e8-rate-audit/verify.py --check research/tensor-e8-rate-audit/RESULTS.json +``` + +Expected: `PASS_TENSOR_E8_RATE_AUDIT: 66 depths; 9 negative controls; exact rational bounds`. +Additional independent checks: `python3 -B research/tensor-e8-rate-audit/test_verify.py`. +Assertions are not used for acceptance, and isolated optimized execution is supported. + +Two implementations reconstruct the profile: aggregated chronological register +lifetimes and a closed level sum. Exact rational log bounds give a rigorous +root enclosure without numerical root finding. The receipt records all 66 +profiles' hashes, counts, masses and rational bounds. Decimal fields are +truncated display values; use the fraction fields as bounds. This finite +replay supports the accompanying algebraic proof and does not formalize it. + +The new evidence concerns the general-depth profile retained in #647; +#647's packaged verifier primarily realizes depth one. Its broader scalar, +frame, ownership, exact-RAM and Fourier claims are not certified by this audit. +No earlier closed search is reopened. No selected certificate changes. + +Base: `66849e1475c930fd7732b1a0067ffee7e1e95f60`. +Audited PR647: `956bb581e7f97328e1b53baa5aca3d2490f2f607`. +[Source pins](SOURCE.json), [assignment and local claim](CLAIM.json), +[validation](VALIDATION.md), [attribution](NOTICE.md). diff --git a/research/tensor-e8-rate-audit/RESULTS.json b/research/tensor-e8-rate-audit/RESULTS.json new file mode 100644 index 0000000000..2c26392aa4 --- /dev/null +++ b/research/tensor-e8-rate-audit/RESULTS.json @@ -0,0 +1,1614 @@ +{ + "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60", + "depth_66_relative_shortfall_less_than": "4/1000000000000000", + "depths": [ + { + "W": 7208, + "center_factor": "1/10", + "children": 62928, + "deficit": 24, + "depth": 1, + "h": 9, + "helpers": 6968, + "histogram_sha256": "523fb42e98fccdf6dbde7ff16a43023cdd1bd58122e14694f8ff8634b456159f", + "m": 27, + "normalized_derivative": [ + 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no search", + "limit_bounds": [ + "42909875144244888034033716760208657141324695421140860928/4611430889423185837835212508433085806325396005243230452299", + "766247770432944429179173513575154591809369561091801088/82346980168271175675628794793447960827239214379343400885" + ], + "limit_decimal_floor": [ + "0.009305110750475154078568355107926614", + "0.009305110750475154078568355107926614" + ], + "negative_controls": [ + "omit_center_copies_depth_1", + "omit_rank_two_endpoints_depth_1", + "omit_center_copies_depth_2", + "omit_rank_two_endpoints_depth_2", + "omit_center_copies_depth_6", + "omit_rank_two_endpoints_depth_6", + "omit_center_copies_depth_66", + "omit_rank_two_endpoints_depth_66", + "same_mass_same_count_wrong_moment" + ], + "schema": 1, + "seed": 66, + "source_head": "956bb581e7f97328e1b53baa5aca3d2490f2f607", + "source_pr": 647 +} diff --git a/research/tensor-e8-rate-audit/SOURCE.json b/research/tensor-e8-rate-audit/SOURCE.json new file mode 100644 index 0000000000..ed941a8c15 --- /dev/null +++ b/research/tensor-e8-rate-audit/SOURCE.json @@ -0,0 +1,28 @@ +{ + "repository": "https://github.com/CrocSwap/integer-mult-bounds", + "pr": 647, + "head": "956bb581e7f97328e1b53baa5aca3d2490f2f607", + "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60", + "files": { + "research/e8-paid-copy-ram-20261013/PROVIDER-PROOF.md": { + "sha256": "cdc496acb844de3b3bcf03f811d1bd345e476b40f0b1cb7c866066612770e834", + "git_blob": "5ab62f906f47a38b258a1e327b5a2c1efc633b89" + }, + "research/e8-paid-copy-ram-20261013/README.md": { + "sha256": "8169f11a39b5d33733c96b96f099d970b24c5f2c82610af234fb62801ae58fe0", + "git_blob": "240915e3d130b485421b73ae7e619ff9cd5c9fe7" + }, + "research/e8-paid-copy-ram-20261013/NOTICE.md": { + "sha256": "a2151fd291023846f7629f5cc2e7c20b467923552628a76a663a067c115edf90", + "git_blob": "736cb5724159ddada07845fb39ed5d7d650a4d3c" + }, + "research/e8-paid-copy-ram-20261013/verify.py": { + "sha256": "324566e5fa7591ce2e9c4c673f7482c17698f63d9b9d26a0af2f5eb9d4bdae45", + "git_blob": "147026e9f997713acc2a321f15263c80812205d0" + }, + "research/e8-paid-copy-ram-20261013/RESULTS.json": { + "sha256": "094ce1afb700ba6cf4854f482fdb7110347d2ebbead8328cc044c25e40ceddaa", + "git_blob": "90ac6f426b1007646fb4e45167c2c544c6d0aeff" + } + } +} diff --git a/research/tensor-e8-rate-audit/VALIDATION.md b/research/tensor-e8-rate-audit/VALIDATION.md new file mode 100644 index 0000000000..28a37f80e0 --- /dev/null +++ b/research/tensor-e8-rate-audit/VALIDATION.md @@ -0,0 +1,51 @@ +# Validation and limits + +Base: `66849e1475c930fd7732b1a0067ffee7e1e95f60`. +Audited source: PR647 at `956bb581e7f97328e1b53baa5aca3d2490f2f607`. +Execution date: 2026-10-13 UTC, macOS arm64. + +The deterministic exact receipt covers all integer architecture depths 1–66; +there is no randomized search, unfinished search region or inferred impossibility. +Assignment seed 66 selects the last depth. The written proof covers the stated +profile algebraically for all positive depths, subject to the scope in PROOF.md. + +Completed local checks: + +- Exact receipt on Python 3.9.6, 3.11.16 and 3.13.16; isolated optimized + acceptance checked on 3.11 and 3.13. +- Five tests: published depth-one/two histograms; independently implemented + Decimal log checks at 120 digits; direct nonlinear moments at 250 digits + for depths 1,2,3,6,16,66; nine cost/geometry controls; malformed depth and + corrupted-receipt rejection, including optimized Python. Decimal checks + are diagnostics, not the basis of the rational mathematical certificate. +- All five source-file SHA256 and Git blob IDs in SOURCE.json match the + fetched immutable PR647 head. +- PR647's complete original `verify.py --check` was freshly replayed in an + isolated archive checkout and returned `ALL_EXACT_CHECKS_PASSED`. + This reuses the predecessor's implementation and does not count as an + independent general-depth proof. +- The selected-record integrity check passed. The selected certificate and + all `upstream/` content are unchanged. Whitespace and patch-scope checks pass. + +Receipt SHA256: +`8114160ebe85b5d09520eb1e1c340d56e5cc874c2949e923cb86d30b75d6dcff`. + +The source replay can be repeated without checking out another branch: + +```sh +git fetch https://github.com/CrocSwap/integer-mult-bounds.git 956bb581e7f97328e1b53baa5aca3d2490f2f607 +mkdir -p /tmp/tensor-e8-pr647-replay +git archive 956bb581e7f97328e1b53baa5aca3d2490f2f607 research/e8-paid-copy-ram-20261013 | tar -x -C /tmp/tensor-e8-pr647-replay +python3 -B /tmp/tensor-e8-pr647-replay/research/e8-paid-copy-ram-20261013/verify.py --check +``` + +No full repository suite pass is claimed. The earlier contribution's full +`make verify` attempt stopped at the unchanged selected bit supplier because +this machine lacks `boost/multiprecision/cpp_int.hpp`. That expensive suite +was not repeated for this isolated research package. A new path-scoped CI +workflow checks only this package; remote status is reported separately. + +Before submission, 501 open PRs through #681 were inspected for overlap; +PR647's source head was unchanged and had no comments. No pinned coordination +issue existed. The local claim has one result update with the published branch +link. Credit and substantial AI assistance are disclosed in NOTICE.md. diff --git a/research/tensor-e8-rate-audit/test_verify.py b/research/tensor-e8-rate-audit/test_verify.py new file mode 100644 index 0000000000..b06f20cebf --- /dev/null +++ b/research/tensor-e8-rate-audit/test_verify.py @@ -0,0 +1,81 @@ +#!/usr/bin/env python3 +"""Independent Decimal diagnostics and failure controls (not interval proofs).""" +import importlib.util +import json +from decimal import Decimal as D, localcontext +from fractions import Fraction as Q +from pathlib import Path +import subprocess +import sys +import tempfile +import unittest + +HERE = Path(__file__).resolve().parent +spec = importlib.util.spec_from_file_location('tensor_rate_audit', HERE/'verify.py') +audit = importlib.util.module_from_spec(spec) +spec.loader.exec_module(audit) + + +def dec(x): + x = Q(x) + return D(x.numerator)/D(x.denominator) + + +class AuditTests(unittest.TestCase): + def test_source_depth_one_and_two_histograms(self): + # Literal independently published histograms in PR647 sections 8/README. + self.assertEqual(dict(audit.lifetime_profile(1)[0]), + {1:41040,2:240,7:20160,8:1440,9:48}) + self.assertEqual(dict(audit.lifetime_profile(2)[0]), + {1:4968000,2:28800,8:86400,9:328320,63:161280, + 72:92160,79:2419200,80:129600,81:384}) + + def test_log_bounds_with_separate_decimal_implementation(self): + values = [Q(1),Q(3,2),Q(2),Q(3),Q(27,7),Q(243,242),Q(3*9**66)] + values += [Q(3*9**6,s) for s in audit.closed_profile(6)] + with localcontext() as ctx: + ctx.prec = 120 + for x in values: + lo,hi = audit.log_bounds(x) + expected = dec(x).ln() + self.assertLessEqual(dec(lo),expected) + self.assertLessEqual(expected,dec(hi)) + self.assertLess(hi-lo,Q(1,10**50)) + + def test_root_brackets_by_direct_high_precision_moments(self): + # A different implementation evaluates the nonlinear moment directly. + # This is a diagnostic; the proof of the rational enclosure is analytic. + with localcontext() as ctx: + ctx.prec = 250 + for n in (1,2,3,6,16,66): + h,v,_,_,_,m,deficit = audit.parameters(n) + hist = audit.closed_profile(n) + lo,hi = map(Q,audit.audit(n)['scaled_root_bounds']) + logs = {s:(D(m)/D(s)).ln() for s in hist} + def increase(scaled): + k = dec(scaled)/D(h) + return sum(D(s*c)*((k*logs[s]).exp()-1) for s,c in hist.items()) + self.assertLess(increase(lo),D(deficit)) + self.assertGreater(increase(hi),D(deficit)) + + def test_cost_and_same_mass_mutants(self): + self.assertEqual(len(audit.negative_controls()),9) + + def test_invalid_domain_and_optimized_failure(self): + for depth in (0,-1,True,Q(3,2)): + with self.assertRaises(ValueError): + audit.parameters(depth) + # A corrupted receipt must fail even when Python disables assertions. + result = json.loads((HERE/'RESULTS.json').read_text()) + result['depths'][0]['helpers'] += 1 + with tempfile.TemporaryDirectory() as directory: + bad = Path(directory)/'bad.json' + bad.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + proc = subprocess.run([sys.executable,'-B','-I','-O',str(HERE/'verify.py'), + '--check',str(bad)],capture_output=True,text=True) + self.assertNotEqual(proc.returncode,0) + self.assertIn('receipt mismatch',proc.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/research/tensor-e8-rate-audit/verify.py b/research/tensor-e8-rate-audit/verify.py new file mode 100644 index 0000000000..cf9cae0eb1 --- /dev/null +++ b/research/tensor-e8-rate-audit/verify.py @@ -0,0 +1,242 @@ +#!/usr/bin/env python3 +"""Exact audit of PR647's tensor paid profile. Standard library; Python 3.9+.""" +import argparse +from collections import Counter +from fractions import Fraction as Q +from functools import lru_cache +import hashlib +import json +from pathlib import Path + +HERE = Path(__file__).resolve().parent +MAX_DEPTH = 66 +BITS = 180 +DEN = 1 << BITS + + +def require(ok, message): + if not ok: + raise ValueError(message) + + +def parameters(n): + require(type(n) is int and n >= 1, 'positive integer depth required') + h, v, r = 9**n, 120**n, 8**n + R = (885*v-1081*r)//14 + return h, v, r, R, R+2*v, 3*h, 2*v-3*h*r + + +def lifetime_profile(n, *, centers=True, endpoints=True): + """Aggregate chronological moves; multiplicity replaces identical siblings. + + A register move is charged abs(end-start). No source histogram is imported. + This checks dimension accounting, not the frame inclusions or scalar word. + """ + h, v, r, _, _, _, _ = parameters(n) + local, allocations = Counter(), 0 + + def path(count, *dimensions): + for start, end in zip(dimensions, dimensions[1:]): + rank = abs(end-start) + if rank: + local[rank] += count + + def core(k, d, copies): + nonlocal allocations + ports, tails = 120**k, 120**(k-1) + # Output helpers, pair helpers, and gather helpers are distinct roles. + allocations += copies*(ports + 6720*tails + 8*tails) + path(copies*ports, 0, h-d) # outputs, held at cap + path(copies*6720*tails, 0, d, h-d, h) # pair route + path(copies*ports, d, 9*d, h) # consumed inputs + path(copies*8*tails, 0, 9*d) # new gathers + if k > 1: + allocations += copies*ports # decoder helpers + core(k-1, 9*d, 8*copies) + path(copies*ports, 0, h-9*d, h-d, h) + path(copies*8*tails, h-9*d, h) # child outputs after use + + allocations += v # root input helpers + core(n, 1, 1) + path(v, 0, 1) # root input load + path(v, h-1, h) # root output finish + path(v, 1, h) # data source + path(v, 0, h-1) # data target + if centers: + path(r, h, 0) # private copied centers + global_hist = Counter({s: 3*c for s, c in local.items()}) + if endpoints: + global_hist[2] += 2*v # final two pivot lines + return global_hist, allocations + + +def closed_profile(n): + """Independent level-sum formula, with the terminal level separate.""" + h, v, r, _, _, _, _ = parameters(n) + out = Counter() + def add(rank, count): + if rank: + out[rank] += count + for j in range(n-1): + d, c = 9**j, v//15**j + for s, a, b in [(h-d,1,1),(d,113,1),(h-2*d,56,1), + (8*d,2,1),(h-9*d,2,1),(9*d,2,15)]: + add(s, 3*c*a//b) + d, c = 9**(n-1), v//15**(n-1) + for s, a, b in [(d,112,1),(7*d,56,1),(8*d,2,1),(h,1,15)]: + add(s, 3*c*a//b) + for s, c in [(1,6*v),(h-1,6*v),(h,3*r),(2,2*v)]: + add(s,c) + return out + + +@lru_cache(None) +def log_bounds(x): + """atanh series after binary reduction, with a rational geometric tail.""" + x = Q(x) + require(x >= 1, 'log argument below one') + exponent = x.numerator.bit_length()-x.denominator.bit_length() + if x < 2**exponent: + exponent -= 1 + y = x / 2**exponent + require(1 <= y < 2, 'log reduction failed') + + def unit(a): + u = (a-1)/(a+1) + term, total = u, Q(0) + for j in range(64): + total += term/(2*j+1) + term *= u*u + lower = 2*total + upper = lower + 2*term/(129*(1-u*u)) + return lower, upper + a,b = unit(y) + c,d = unit(Q(2)) + lo,hi = a+exponent*c, b+exponent*d + # Common dyadic endpoints keep later exact arithmetic small. + return (Q((lo.numerator*DEN)//lo.denominator,DEN), + Q(-((-hi.numerator*DEN)//hi.denominator),DEN)) + + +def derivative_bounds(n, hist): + h,v,_,_,_,m,_ = parameters(n) + lo = hi = Q(0) + for s,c in hist.items(): + a,b = log_bounds(Q(m,s)) + lo += s*c*a + hi += s*c*b + return lo/(m*v), hi/(m*v) + + +def quantitative_bounds(n): + """Universal error envelopes around L=(913/14) log(3); see PROOF.md.""" + h,_,_,_,_,_,_ = parameters(n) + t = Q(3,5) + series = (1-t**(n-1))/(1-t) + ell_lo,ell_hi = log_bounds(Q(3)) + _,U = log_bounds(Q(3*h)) + high = (131*series+113*t**(n-1)+2)/h + Q(87,14)*ell_hi/15**(n-1) + low = (Q(651,5)*series+Q(603,5)*t**(n-1)+Q(10,3))*U/h + ell_hi/15**n + return Q(913,14)*ell_lo-high, Q(913,14)*ell_hi+low + + +def rational(x): + return str(x.numerator)+'/'+str(x.denominator) + + +def decimal(x, digits=36): + scale = 10**digits + z = x.numerator*scale//x.denominator + return str(z//scale)+'.'+str(z%scale).zfill(digits) + + +def audit(n): + h,v,r,R,W,m,D = parameters(n) + H,helpers = lifetime_profile(n) + require(H == closed_profile(n), f'depth {n}: profile constructions differ') + require(helpers == R, f'depth {n}: helper count') + S = (1334*v-1726*r)//7 + require(sum(H.values()) == 3*S+2*v == (4016*v-5178*r)//7, + f'depth {n}: child count') + require(sum(s*c for s,c in H.items()) == m*W-D, + f'depth {n}: paid rank mass') + require(0 < D < m*W and 0 < min(H) <= max(H) <= h, + f'depth {n}: moment domain') + require(sum(H.values()) > W, f'depth {n}: unique root endpoint') + Mlo,Mhi = derivative_bounds(n,H) + Jlo,Jhi = quantitative_bounds(n) + require(Jlo <= Mlo <= Mhi <= Jhi, f'depth {n}: analytic derivative envelope') + _,U = log_bounds(Q(m)) + A = Q(D,3*v) # h*(W-Phi(0))/v + lower = A/(Mhi+(A/h)*U) + upper = A/Mlo + require(0 < lower < upper < Q(h,2), f'depth {n}: root bracket') + # The proof bounds the actual root, not just a finite numerical search. + data = {'depth':n,'h':h,'v':v,'helpers':R,'W':W,'m':m,'deficit':D, + 'children':sum(H.values()),'histogram_sha256':hashlib.sha256( + json.dumps(sorted(H.items()),separators=(',',':')).encode()).hexdigest(), + 'normalized_derivative':[rational(Mlo),rational(Mhi)], + 'scaled_root_bounds':[rational(lower),rational(upper)], + 'scaled_root_decimal_floor':[decimal(lower),decimal(upper)], + 'center_factor':rational(1-Q(3,2)*Q(3,5)**n)} + return data + + +def negative_controls(): + names = [] + for n in (1,2,6,66): + h,v,_,_,W,m,D = parameters(n) + for kwargs,name in [({'centers':False},'omit_center_copies'), + ({'endpoints':False},'omit_rank_two_endpoints')]: + H,_ = lifetime_profile(n,**kwargs) + require(sum(s*c for s,c in H.items()) != m*W-D, + 'negative control escaped: '+name) + names.append(f'{name}_depth_{n}') + # Same number of calls and identical mass, but changed moment geometry. + H,_ = lifetime_profile(2) + mutated = H.copy() + mutated[1] -= 1; mutated[9] -= 1 + mutated[2] += 1; mutated[8] += 1 + require(sum(mutated.values()) == sum(H.values()), 'control call count changed') + require(sum(s*c for s,c in mutated.items()) == sum(s*c for s,c in H.items()), + 'control mass changed') + a,b = derivative_bounds(2,H) + c,d = derivative_bounds(2,mutated) + require(b < c or d < a, 'same-mass mutant escaped derivative check') + require(mutated != closed_profile(2), 'same-mass mutant escaped histogram') + names.append('same_mass_same_count_wrong_moment') + return names + + +def receipt(): + results = [audit(n) for n in range(1,MAX_DEPTH+1)] + l,u = log_bounds(Q(3)) + constant = [Q(28,2739)/u,Q(28,2739)/l] + # At seed-selected endpoint, certify relative error below 4e-15. + lo,hi = map(Q,results[-1]['scaled_root_bounds']) + require(lo > constant[1]*(1-Q(4,10**15)) and hi < constant[0], + 'depth 66 convergence target failed') + return {'schema':1,'base_commit':'66849e1475c930fd7732b1a0067ffee7e1e95f60', + 'source_pr':647,'source_head':'956bb581e7f97328e1b53baa5aca3d2490f2f607', + 'seed':66,'domain':'all integer depths 1 through 66; no search', + 'limit_bounds':[rational(x) for x in constant], + 'limit_decimal_floor':[decimal(x) for x in constant], + 'depth_66_relative_shortfall_less_than':'4/1000000000000000', + 'depths':results,'negative_controls':negative_controls()} + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--output',type=Path) + parser.add_argument('--check',type=Path) + args = parser.parse_args() + result = receipt() + payload = json.dumps(result,indent=2,sort_keys=True)+'\n' + if args.check: + require(args.check.read_bytes() == payload.encode(), 'receipt mismatch') + if args.output: + args.output.write_text(payload) + print('PASS_TENSOR_E8_RATE_AUDIT: 66 depths; 9 negative controls; exact rational bounds') + +if __name__ == '__main__': + main()