From 85a361233431befe4b11cf878f7b1b77a244d473 Mon Sep 17 00:00:00 2001 From: Aaron Wang Date: Tue, 13 Oct 2026 17:50:24 -0400 Subject: [PATCH] Independent verification: prove and certify the a < D/E diagnostic for the selected complex and bit ledgers (no new kappa) Navinor (with help from opencode). Apache-2.0. Code-disjoint recheck of the two recorded moment acceptances in research/community-frontier1094-audit/ASSEMBLY.json (complex m=73 W=14336; bit m=64 W=28416 with the bad-residue surcharge) at their certified endpoints and next 1e-24 grid points, with ln enclosed by rational square-root bisection (exp-inversion bisection cross-check) and exact rational arithmetic. Proves the autoresearch.md section-2 diagnostic a < D/E for the priced bill (strictly, surcharge included) and certifies the ceilings 0.0016805907097543 (complex) and 0.0017385572484014 (bit), with the screening extremum over rank-mass-preserving repackings. 12 positive/negative controls. Selected record unchanged. --- .../README.md | 169 ++++++ .../RESULT.json | 136 +++++ .../SOURCES.json | 36 ++ .../TASK-CARD.md | 88 ++++ .../TASK.json | 65 +++ .../VERIFY.json | 22 + .../verify.py | 480 ++++++++++++++++++ 7 files changed, 996 insertions(+) create mode 100644 research/selected-suppliers-de-diagnostic/README.md create mode 100644 research/selected-suppliers-de-diagnostic/RESULT.json create mode 100644 research/selected-suppliers-de-diagnostic/SOURCES.json create mode 100644 research/selected-suppliers-de-diagnostic/TASK-CARD.md create mode 100644 research/selected-suppliers-de-diagnostic/TASK.json create mode 100644 research/selected-suppliers-de-diagnostic/VERIFY.json create mode 100644 research/selected-suppliers-de-diagnostic/verify.py diff --git a/research/selected-suppliers-de-diagnostic/README.md b/research/selected-suppliers-de-diagnostic/README.md new file mode 100644 index 0000000000..150189ed95 --- /dev/null +++ b/research/selected-suppliers-de-diagnostic/README.md @@ -0,0 +1,169 @@ +# selected-suppliers-de-diagnostic + +**Independent verification and diagnostic only. No new kappa; the selected +record is unchanged.** + +Contributor: Navinor (with help from opencode). Apache-2.0. Task card: +[TASK-CARD.md](TASK-CARD.md); structured metadata: [TASK.json](TASK.json). + +## What is checked + +One selected pricing claim and one prescribed diagnostic, for both supplier +ledgers of the selected record +([`certificates/selected-result.json`](../../certificates/selected-result.json)): + +1. **Moment acceptance of the whole completed construction.** The priced bill + of a ledger with width `m`, live stock `W`, histogram `n_r` and bad-residue + surcharge coefficient `c_s` is + + `f(a) = (1/(mW)) · Σ_r n_r r (m/r)^a + c_s m^a`. + + The exact moment is the acceptance test: the recorded endpoints must give + `f(a) < 1` strictly, and the next `10^-24` grid point must give `f(a) > 1`. + This package recomputes both signs for the complex k8/T16 gauge44 ledger + (`m = 73`, `W = 14,336`, `N = 144`, no surcharge) and the bit PR589 + p111-tuned nine-stage ledger (`m = 64`, `W = 28,416`, surcharge + `c_s = 32·m·Σn_r / (10^16 W)`) with an implementation disjoint from the + retained engines. + +2. **The `a < D/E` small-saving diagnostic** of + [autoresearch.md](../../autoresearch.md) section 2, which the repository + states without an in-repo proof. With `D = mW − Σ n_r r` and + `E = Σ n_r r ln(m/r)` (and `D_eff = D − c_s mW`, `E_eff = E + c_s mW ln m` + when the surcharge is present) the diagnostic is rigorous: + + **Lemma.** `f` is convex on `ℝ`, `f(0) = 1 − D_eff/(mW) < 1` and + `f'(0) = E_eff/(mW) > 0`. The tangent at `a = 0` reaches 1 at + `a = D_eff/E_eff`, and convexity gives `f(a) > f(0) + a f'(0)` for `a > 0`. + Hence the exact root `a*` satisfies **`a* < D_eff/E_eff` strictly** whenever + `D_eff > 0`. For `c_s = 0` this is exactly `a* < D/E`. + + The lemma turns the diagnostic into a valid *screen*: a proposed histogram + whose `D/E` is below a target saving cannot reach it. The exact moment + remains the acceptance test. + +## Results + +| Ledger | recorded endpoint `a` | moment residual at `a` | at `a + 10^-24` | certified `D/E` ceiling | `D/E ÷ a` | screening extremum | +|---|---|---|---|---|---|---| +| complex (m=73, W=14336) | 0.001675462676808103522925 | −1.304215e-24 | +1.624723e-24 | **0.001680590709754321699421** | 1.003061 | 0.013708749 (cap 51) | +| bit (m=64, W=28416) | 0.001733427039589844234749 | −1.598690e-24 | +1.669360e-24 | **0.001738557248401367986042** | 1.002960 | 0.016127138 (cap 45) | + +- The residual intervals agree with both recorded engines' residuals in + `research/community-frontier1094-audit/ASSEMBLY.json` (`mercator` and + `base_two`), and reproduce the accept/reject sharpness at the next grid + point. The complex values match the independently recorded + `moment_minus_one` of + `research/community-frontier1094-audit/INDEPENDENT1094.json` digit for digit. +- The diagnostic overestimates the exact root by about **0.30%** on the + complex ledger and **0.29%** on the bit ledger at the current small savings: + it is nearly sharp here, and safe as a screen in this regime. +- The ledger aggregates are reconstructed from the published histograms and + checked against the coverage identities: complex `D = 73W − Σ n_r r = + W − 64N = 5,120` (which also re-derives `W = 14,336` from the histogram and + `N = 144`), and bit `D = 64W − Σ n_r r = T(2Kv − L·cst) = 32(2·4·111 − 9·63) + = 10,272`. +- **Screening extremum.** If a repacking kept `m`, `W` and the rank mass and + moved fractional rank mass up to the halving-guard cap (`m² > 2r²`, i.e. + `r ≤ 51` for `m = 73` and `r ≤ 45` for `m = 64`), `D/E` could rise to about + 0.0137 (complex) and 0.0161 (bit). Both exceed the `1/99 ≈ 0.010101` + planning target, so the `D/E` screen alone does **not** exclude target-scale + gain from repacking; that needs the exact moment plus a coverage/realizability + argument. For the complex local word that argument exists: the packing + ceiling of + [PR #1240](https://github.com/CrocSwap/integer-mult-bounds/pull/1240) + (0.001690054109089 for the fixed local word, with idle-mass optimization) + supersedes the per-histogram ceiling above and already rules out the target + there. The bit word has no such realizability analysis; its question is open. + +## Method and independence + +`verify.py` imports nothing from the repository's retained engines +(`moment.py`, `base_two_moment.py`, the atanh prime chain of +`research/pending-claims-independent-pricing`, or the Mercator/base-two +transcriptions in `research/community-batch970-audit/submitted/957/`). Exact +rational arithmetic throughout; every enclosure comes from an explicit +inequality, and no floating point is used. + +- `ln` is enclosed by **rational square-root bisection**: `x^(1/2^k)` is + bracketed by repeated integer square roots on a `2^-320` dyadic grid + (`k = 112`), then `ln(1+u)` is bracketed by `u − u²/2 ≤ ln(1+u) ≤ u`. + This shares no series with the three retained log engines. +- Independent cross-check: `ln` by **bisection inverting a certified Taylor + exponential**. Both methods must agree on every `ln(m/r)` used. +- `exp` is a Taylor partial sum with an explicit rational geometric tail bound + (order 48; the largest exponent used in the bill is `a·ln 73 < 0.0073`, tail + below `10^-150`). This matches the standard approach of the retained engines + and is disclosed as such. +- Positive fixtures: the exactly solvable single-rank ledger `H={1:1}, + m=2, W=1`, whose root is exactly `a* = 1 < 1/ln 2 = D/E`; agreement with the + recorded residual intervals; and the reconstructed ledger identities. +- Semantic failure controls, each required to be rejected: tampered assembly + pin; bit ledger priced at the wrong width `m = 73`; a one-count histogram + mutation that breaks the complex coverage identity; a child rank outside + `(0, m)`; a zero-deficit ledger; claiming the endpoint two grid steps up as + accepting; doubling the bit surcharge (breaks acceptance); negative surcharge + in the diagnostic. + +## Limits + +- The paid profiles are taken from the published ledgers + (`ASSEMBLY.json` `complex_profile`; `EXPECTED.json` `nine.profile`, pinned by + the git blob recorded in the assembly's `bit_supplier` block). This package + does not rebuild either word from its original operations; that reconstruction + exists for the complex owner map through the audits composed in + `research/community-batch1099-audit/check_frontier1094.py`, but not in this + package. +- The conservative (surcharge-on-complex) endpoints of `ASSEMBLY.json` are not + rechecked here. +- `D/E` bounds the root of one fixed histogram. It is not a repacking bound and + not a realizability statement (see the screening extremum above). +- Nothing here verifies the inherited all-size/compiler, common-label/ + mutable-source realization, whole-call hosting, precision/tape, analytic + transfer or bit H1–H5 obligations. This is not a multiplication theorem. + +## Reproduce + +From the repository root (Python 3.10+, standard library only, seconds): + +```sh +python3 -B research/selected-suppliers-de-diagnostic/verify.py +python3 scripts/research_package.py --package research/selected-suppliers-de-diagnostic --check-only +``` + +Observed: `PASS_INDEPENDENT_DE_DIAGNOSTIC`, 12 controls. Machine-readable +output: [RESULT.json](RESULT.json). + +## Open next questions + +- **Bit-word realizability ceiling.** Question: does any repacking of the + PR589 bit word's rank mass under its own coverage law stay below `1/99`? + Why it matters: the bit side is currently non-binding, but the screening + extremum (0.0161) shows the `D/E` screen alone cannot settle it. First step: + adapt the idle-mass/coverage-law argument of + [PR #1240](https://github.com/CrocSwap/integer-mult-bounds/pull/1240) + to the bit coverage identity `D = T(2Kv − L·cst)` and the 32-replica + template. Blocker: the bit word's admissible idle inventory and hosting + constraints are not yet written as a local profile law. +- **Ledger reconstruction for the bit supplier.** Question: can `nine.profile` + be rebuilt from the original gate operations of the pinned + `tune/bitE8mut-p111-tuned.json.gz` word rather than taken from EXPECTED.json? + Why it matters: it would close the last aggregate the selected assembly + trusts without a from-operations audit. First step: compute the per-frame + transition ranks of the word file and compare against `word.local_histogram` + and `nine.profile`. Blocker: the paid-rank charging convention lives in the + supplier's own checker, so a code-disjoint restatement is a substantial + piece of work. + +## Credit + +Prepared by Navinor (with help from opencode). Predecessor credit: the pricing +model and the `a < D/E` diagnostic are Douglas Colkitt's (autoresearch.md, +`research/pending-claims-independent-pricing`); the complex ledger is Rohan +Arun's #1094 construction on Jeremy Kothe's packing chain, audited by Josie +Elliston and Sagar Thakrar; the bit supplier is the PR589/PR555 lineage +(eumemic and predecessors, retained unchanged by the selected record); the +fixed-word packing-ceiling lineage (including +[PR #1240](https://github.com/CrocSwap/integer-mult-bounds/pull/1240)) is +static44, PR525, PR643 and the author of that PR. Substantial AI assistance +is disclosed: with help from opencode. diff --git a/research/selected-suppliers-de-diagnostic/RESULT.json b/research/selected-suppliers-de-diagnostic/RESULT.json new file mode 100644 index 0000000000..af8875af8a --- /dev/null +++ b/research/selected-suppliers-de-diagnostic/RESULT.json @@ -0,0 +1,136 @@ +{ + "controls": [ + "single-rank-root-exact", + "complex:endpoint+2grid-rejects", + "bit:endpoint+2grid-rejects", + "ln-methods-agree-all-ranks", + "tampered-assembly-pin", + "bit-wrong-width", + "complex-mutated-histogram", + "child-rank-out-of-range", + "zero-deficit", + "complex-endpoint-shifted-two-grids", + "bit-doubled-surcharge-breaks-acceptance", + "negative-surcharge-rejected" + ], + "de": { + "bit": { + "bound_over_endpoint": "1.002959575854278607764228189688", + "de_bound": [ + "6716498849108485438649450606155833307836727395592882794067658104038005669888/3863260099881333624513858835593294900673007092465174223719840631455296171269925", + "28692708936946875427960156383369779483549542073485092893083213533621042190420530346442382353055862782744734411288490692864870842474314787936079517569430696615910129298046976/16503746979474097674732558770199530816783711799921927373131777740944174035254029485862815723123613835007464494069899435512614203045855558480100011879308830689604452235601849259" + ], + "de_decimal": [ + "0.001738557248401367986041737064", + "0.001738557248401367986041737064" + ], + "endpoint": "1733427039589844234749/1000000000000000000000000", + "endpoint_strictly_below": true, + "screening_extremum_decimal": "0.016127137741294849878735081990", + "screening_note": "D/E ceiling over rank-mass-preserving repackings with fractional counts at ranks up to the halving guard; screening only, not a realizability bound", + "screening_rank_cap": 45 + }, + "complex": { + "bound_over_endpoint": "1.003060666774139969497930899145", + "de_bound": [ + "526561458342785933489590138418352161594475477002745556271554887680/313319272376414409589114114548757778435191907651477925967778534543091", + "449891379454319638281053850768598185886969711830191663310075557261183758067148787031904068610389085714992091063352089512320826605549429968900851518086516385513472/267698361560077478243855787264911104037839339471018448471487781183426965230512792496298832690400711209963783457126350066134939696540440020116568844246112092146253943" + ], + "de_decimal": [ + "0.001680590709754321699421243685", + "0.001680590709754321699421243685" + ], + "endpoint": "67018507072324140917/40000000000000000000000", + "endpoint_strictly_below": true, + "screening_extremum_decimal": "0.013708748952667005455954855724", + "screening_note": "D/E ceiling over rank-mass-preserving repackings with fractional counts at ranks up to the halving guard; screening only, not a realizability bound", + "screening_rank_cap": 51 + } + }, + "ledger": { + "bit": { + "K": 4, + "L": 9, + "T": 32, + "W": 28416, + "deficit": 10272, + "m": 64 + }, + "complex": { + "N": 144, + "W": 14336, + "deficit": 5120, + "m": 73 + } + }, + "lemma": "For f(a) = (1/(mW)) sum_r n_r r (m/r)^a + c_s m^a with 0 < r < m, W >= 1 and c_s >= 0, f is convex and f(0) = 1 - D_eff/(mW) with D_eff > 0. The tangent at a = 0 meets 1 at D_eff/E_eff, so the exact root satisfies a* < D_eff/E_eff strictly. For c_s = 0 this is the autoresearch.md section-2 diagnostic a < D/E.", + "limitations": [ + "The paid profiles are taken from the published ledgers (ASSEMBLY.json complex_profile; EXPECTED.json nine.profile); this package does not rebuild either word from its original operations.", + "The conservative (surcharge-on-complex) endpoints of ASSEMBLY.json are not rechecked here.", + "D/E is a per-histogram ceiling; an upper bound over all repackings needs the coverage-law argument, see https://github.com/CrocSwap/integer-mult-bounds/pull/1240 for the complex local word." + ], + "method": { + "arithmetic": "exact fractions throughout; enclosures from explicit inequalities only; no floating point", + "exp": "Taylor partial sums, order 48, rational geometric tail bound", + "imports": "no repository engine imported", + "ln": "rational square-root bisection (x^(1/2^k), k=112, 2^-320 grid), ln(1+u) bracketed by u-u^2/2 <= ln(1+u) <= u", + "ln_cross": "bisection inverting a Taylor exponential (order 48)" + }, + "moment": { + "bit": { + "accept": true, + "endpoint": "1733427039589844234749/1000000000000000000000000", + "next_grid_decimal": [ + "0.000000000000000000000001669360", + "0.000000000000000000000001669360" + ], + "next_grid_residual": [ + 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+ ], + "residual_decimal": [ + "-0.000000000000000000000001304215", + "-0.000000000000000000000001304215" + ], + "sharp_next_grid": true + } + }, + "scope": "Independent verification and diagnostic only. The moment sign is the acceptance test; D/E is a diagnostic upper bound on the root of one fixed ledger histogram and is not a realizability or repacking bound. No kappa change; the selected record is unchanged.", + "single_rank_falsification": { + "de_bound": [ + "411376139330301510538742295639337626245683966408394965837152256/285144211126433720203841574680972129454022440738251316999678699", + "1757388200993436087035366604564836663620975436836686184804982645551499054949799949343375268009332366074187855716219099657503228927927460816018951242525454630912/1218128676667914702210261406273120648250082381656893638715114745536083312233871830850575512044985540889710828271815433200112047942452501392139125178344799025135" + ], + "ln2": [ + "0.693147180559945309417232121458", + "0.693147180559945309417232121458" + ], + "root": "1" + }, + "status": "PASS_INDEPENDENT_DE_DIAGNOSTIC" +} diff --git a/research/selected-suppliers-de-diagnostic/SOURCES.json b/research/selected-suppliers-de-diagnostic/SOURCES.json new file mode 100644 index 0000000000..d7714609a5 --- /dev/null +++ b/research/selected-suppliers-de-diagnostic/SOURCES.json @@ -0,0 +1,36 @@ +{ + "schema_version": 1, + "base_commit": "dadfea6e8a78ff6ba901705f87532a71c6f5bbb8", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11", + "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "c05fafaa25ba95b2d5af86b1800427198e3d20eb", + "sha256": "89b5928bc92c81e2647b6d702a7ad85a6795b8f44e2eb267b2ff3145d8f2b2ce" + }, + { + "path": "research/community-frontier1094-audit/ASSEMBLY.json", + "usage": "input", + "git_blob": "5fd676df060f3b450782fdf5ff5f6beb63a5eeb0", + "sha256": "1122cb3a575f8c788345fc1bf4c108ac7c3250fb81a5988671f5eb04b3ab3045" + }, + { + "path": "research/community-frontier1094-audit/INDEPENDENT1094.json", + "usage": "input", + "git_blob": "009a385e26858058a18188364078d162aa6f9519", + "sha256": "301fb8a0e4ab7e3c383ff974c54c08178283b2a3453c5282757f692a3c7a4bfd" + }, + { + "path": "research/e8-bit-p111-tuned/tune/EXPECTED.json", + "usage": "input", + "git_blob": "e293ddc557742637f9f679f083a1a282d87b1b13", + "sha256": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4" + } + ] +} diff --git a/research/selected-suppliers-de-diagnostic/TASK-CARD.md b/research/selected-suppliers-de-diagnostic/TASK-CARD.md new file mode 100644 index 0000000000..72bf428fdc --- /dev/null +++ b/research/selected-suppliers-de-diagnostic/TASK-CARD.md @@ -0,0 +1,88 @@ +# Local task card (autoresearch.md section 3) + +Task ID / proposed scope key: `independent-moment` / `c6f2494b197df3bc3591` +(draw: track `independent-verification`, chooser seed +`9246ead964f301161b3d7eec63704082`, OS-random assignment; refined below to the +card's "certified enclosure with a different method" variation). + +Base commit; exact predecessor and dependency heads: +`dadfea6e8a78ff6ba901705f87532a71c6f5bbb8` (origin/main at entry). +Selected record `certificates/selected-result.json` +(sha256 `10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32`); +selected assembly `research/community-frontier1094-audit/ASSEMBLY.json` +(sha256 `1122cb3a575f8c788345fc1bf4c108ac7c3250fb81a5988671f5eb04b3ab3045`); +bit supplier pin `research/e8-bit-p111-tuned/tune/EXPECTED.json` +(git blob `e293ddc557742637f9f679f083a1a282d87b1b13`, as recorded inside the +selected assembly's `bit_supplier` block). + +Concrete object and question: +The two supplier ledgers of the selected record: the complex k8/T16 gauge44 +hosted profile (`complex_profile` in ASSEMBLY.json, width m = 73, live stock +W = 14,336, calls N = 144) and the bit PR589 p111-tuned nine-stage profile +(`nine.profile` / `nine.bit.live` in EXPECTED.json, width m = 64, W = 28,416, +bad-residue surcharge). Question: (1) can the recorded moment acceptance at the +two certified endpoints be reproduced by a genuinely independent exact +implementation; (2) what does the prescribed small-saving diagnostic +`a < D/E` give exactly for each ledger, and is the inequality actually implied +by the priced moment? + +Scope status: refined. The card's question and method are unchanged +("certified moment inequalities through a different exact enclosure method"); +the refinement names the two ledgers, the endpoints, the widths/stocks and the +diagnostic. The earlier note that the endpoint-moment card was already covered +by three code-disjoint engines (Mercator, base-two, atanh prime chain) is why +this session does not add a fourth series engine: the log enclosure here is by +rational square-root bisection, the new content is the `a < D/E` lemma and its +application, and the bit ledger is included (the packing ceiling of +https://github.com/CrocSwap/integer-mult-bounds/pull/1240 covers the complex +local word only). + +Existing restriction being changed (or exact claim being audited): +None changed. Audited claims: the ASSEMBLY `moments` accept/reject decisions at +the complex and bit endpoints (and their next 1e-24 grid points), the ledger +aggregates `rank_mass`/deficit and their coverage identities, and the +`a < D/E` diagnostic asserted in autoresearch.md section 2 without an in-repo +proof. + +Method; explicit parameter ranges/candidate alphabet: +Stdlib-only exact rationals plus outward-rounded dyadic interval arithmetic at +2^-320. ln by rational square-root bisection (x^(1/2^k) by squaring bisection, +ln(1+u) bracketed by u - u^2/2 <= ln(1+u) <= u); cross-checked against an +independent alternating Leibniz enclosure. exp by Taylor partial sums with an +explicit rational tail bound. Parameters are the fixed ledgers above; the only +free integer is the bisection depth (k = 32) and Taylor order (48), both +checked to move intervals by far less than 2^-200. No search domain. + +Nearest overlapping PRs and why this adds something: +https://github.com/CrocSwap/integer-mult-bounds/pull/1240 (complex local-word +packing ceiling via idle-mass optimization; no bit side, no D/E lemma), +research/pending-claims-independent-pricing (atanh prime-chain endpoint +certification for pending claims) and +research/community-batch970-audit/submitted/957/.../audit_endpoint_reduction.py +(Mercator/base-two endpoint audit, PR957 lineage). None of them proves or +computes the `a < D/E` diagnostic or covers the bit ledger's D/E. + +Optimistic full cost budget; required observable improvement: +Budget ~60 minutes total with the last quarter for verification and handoff; +no kappa change is possible or claimed (this is verification/diagnostic work). +Required observable: independent residual intervals agreeing with the recorded +ASSEMBLY residuals and the same accept/reject signs, certified D/E bounds on +both ledgers, and every semantic failure control rejected. + +Success evidence; falsification test; time/compute cap: +Success = verify.py prints PASS with (i) both moment residuals negative at the +recorded endpoints and positive at the next grid point, (ii) exact ledger +identities reproduced, (iii) certified a* < D/E intervals containing decimal +cross-checks. Falsification = the smallest failing instance: the sign flip of +the residual at the next grid point, or any mutated ledger that is not +rejected. Compute cap: seconds per run, stdlib only. + +Predecessor authors; intended artifact and reproduction command: +Predecessors: Douglas Colkitt (repository pricing model, autoresearch +diagnostic), Rohan Arun (#1094 complex ledger), the PR589 bit supplier lineage +(eumemic/PR555/PR543 lineage per the selected record), Sagar Thakrar and +Josie Elliston (independent audits), Jeremy Kothe (packing chain), +static44/PR525/PR643 and the author of +https://github.com/CrocSwap/integer-mult-bounds/pull/1240 (packing-ceiling +lineage). Artifact: `research/selected-suppliers-de-diagnostic/`. +Command: `python3 -B research/selected-suppliers-de-diagnostic/verify.py`. diff --git a/research/selected-suppliers-de-diagnostic/TASK.json b/research/selected-suppliers-de-diagnostic/TASK.json new file mode 100644 index 0000000000..900f40886b --- /dev/null +++ b/research/selected-suppliers-de-diagnostic/TASK.json @@ -0,0 +1,65 @@ +{ + "schema_version": 1, + "task_id": "independent-moment", + "priority_revision": 2, + "base_commit": "dadfea6e8a78ff6ba901705f87532a71c6f5bbb8", + "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": "refined", + "actual_scope": "Independent exact recheck of the two recorded moment acceptances (complex m=73 W=14336 no surcharge; bit m=64 W=28416 with the bad-residue surcharge) at their certified endpoints and next 1e-24 grid points, plus a proved and certified a < D/E diagnostic ceiling for each ledger, with code-disjoint square-root-bisection and exp-inversion log enclosures.", + "scope_change_reason": "The card's question and method are unchanged; refinement names the two ledgers, endpoints and widths. The endpoint-moment card is already covered for the selected record by three code-disjoint series engines (Mercator, base-two, atanh prime chain), so this session does not add a fourth series engine: the new content is the proof and application of the a < D/E diagnostic stated in autoresearch.md section 2, and the bit ledger, which the complex local-word packing ceiling of https://github.com/CrocSwap/integer-mult-bounds/pull/1240 does not cover.", + "bottleneck_link": "The priced moment is the acceptance test for any supplier change; the a < D/E diagnostic is the repository's own fast screen for it. Proving the screen valid (a* < D_eff/E_eff strictly, surcharge included) and measuring its slack (0.30% complex, 0.29% bit at the current ledgers) tells improvers when the screen is decisive and when the exact moment is required. The screening extremum shows the screen alone cannot decide the 1/99 planning target, redirecting effort to coverage/realizability arguments.", + "budget_minutes": 60, + "stop_rule": "Stop after one priced endpoint pair per ledger and one diagnostic; kill any route needing a word rebuild from original operations (out of this session's budget; handed off). One bounded pivot only: from moment re-verification to the D/E lemma after the moment coverage saturation was confirmed.", + "outcome": "completed", + "evidence": "research/selected-suppliers-de-diagnostic/RESULT.json from verify.py: PASS_INDEPENDENT_DE_DIAGNOSTIC; moment residuals match the recorded mercator/base_two intervals and INDEPENDENT1094's moment_minus_one digits; certified D/E ceilings 0.0016805907097543 (complex) and 0.0017385572484014 (bit); 12 positive/negative controls including the exactly solvable single-rank root a*=1<1/ln2.", + "author": "Navinor (with help from opencode)", + "ai_assistance": "Substantial AI assistance: with help from opencode. No model is cited per donor instruction.", + "open_questions": [ + { + "question": "Does any repacking of the PR589 bit word's rank mass under its own coverage law D = T(2Kv - L*cst) stay below 1/99?", + "why_it_matters": "The screening extremum 0.0161 exceeds the 1/99 planning target, so the D/E screen cannot settle it; the bit side is currently non-binding but supplies the required budget multiplier 5.83.", + "first_step": "Adapt the idle-mass/coverage-law ceiling argument of https://github.com/CrocSwap/integer-mult-bounds/pull/1240 to the bit coverage identity and the 32-replica template.", + "blocked_by": "The bit word's admissible idle inventory and hosting constraints are not yet written as a local profile law." + }, + { + "question": "Can nine.profile be rebuilt from the original gate operations of the pinned tune/bitE8mut-p111-tuned.json.gz word instead of taken from EXPECTED.json?", + "why_it_matters": "It would close the last aggregate the selected assembly trusts without a from-operations audit.", + "first_step": "Compute the per-frame transition ranks of the pinned word and compare with word.local_histogram and nine.profile.", + "blocked_by": "The paid-rank charging convention lives in the supplier's own checker, so a code-disjoint restatement is substantial work." + } + ] +} diff --git a/research/selected-suppliers-de-diagnostic/VERIFY.json b/research/selected-suppliers-de-diagnostic/VERIFY.json new file mode 100644 index 0000000000..135eef98c1 --- /dev/null +++ b/research/selected-suppliers-de-diagnostic/VERIFY.json @@ -0,0 +1,22 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/community-frontier1094-audit/ASSEMBLY.json", + "research/community-frontier1094-audit/INDEPENDENT1094.json", + "research/e8-bit-p111-tuned/tune/EXPECTED.json" + ], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 120, + "checks": "Source pins (ASSEMBLY sha256, EXPECTED git blob as recorded in the assembly's bit_supplier block), reconstructed ledger aggregates and both coverage identities, moment residual signs at the two certified endpoints and their next 1e-24 grid points with agreement against the recorded mercator/base_two intervals, two disjoint ln enclosures agreeing on every used log, the certified a < D/E ceilings, the exactly solvable single-rank root a*=1<1/ln2, and 12 positive/negative controls (tampered pin, wrong width, mutated histogram, out-of-range rank, zero deficit, shifted endpoint, doubled surcharge, negative surcharge)." + } + ] +} diff --git a/research/selected-suppliers-de-diagnostic/verify.py b/research/selected-suppliers-de-diagnostic/verify.py new file mode 100644 index 0000000000..f9a9d5e510 --- /dev/null +++ b/research/selected-suppliers-de-diagnostic/verify.py @@ -0,0 +1,480 @@ +#!/usr/bin/env python3 +# SPDX-License-Identifier: Apache-2.0 +"""Independent exact check of the selected suppliers' moment acceptance and +the a < D/E small-saving diagnostic. + +Navinor (with help from opencode). Apache-2.0. + +Code-disjoint by construction: this file imports nothing from the repository's +retained moment engines (moment.py, base_two_moment.py, the atanh prime chain of +research/pending-claims-independent-pricing, or +research/community-batch970-audit/submitted/957/.../audit_endpoint_reduction.py). +It restates the priced bill from the published ledgers and computes: + + 1. ledger aggregates (rank mass, deficit) and their coverage identities, + reconstructed from the published histograms rather than taken from the + recorded aggregates; + 2. the moment residual f(a) - 1 at the two certified endpoints of + research/community-frontier1094-audit/ASSEMBLY.json and at their next + 1e-24 grid points, with ln enclosed by rational square-root bisection + (independent cross-check: bisection inverting a Taylor exp) and exp by + Taylor partial sums with an explicit rational tail bound; + 3. the certified D/E diagnostic: for the priced bill + f(a) = (1/(mW)) * sum_r n_r r (m/r)^a + c_s m^a, + convexity gives a* < D_eff / E_eff strictly, where + D_eff = mW - sum n_r r - c_s mW, E_eff = sum n_r r ln(m/r) + c_s mW ln m. + For c_s = 0 this is exactly the autoresearch.md section-2 diagnostic + "a < D/E" with D = mW - sum n_r r, E = sum n_r r log(m/r). + +Acceptance is the exact moment sign; D/E is a diagnostic upper bound only. +No kappa change is claimed or possible here. +""" +import hashlib +import json +import sys +from fractions import Fraction as Q +from math import isqrt +from pathlib import Path + +try: + sys.set_int_max_str_digits(1000000) +except AttributeError: # Python 3.10 has no digit cap + pass + +ROOT = Path(__file__).resolve().parents[2] +ASSEMBLY = ROOT / 'research/community-frontier1094-audit/ASSEMBLY.json' +INDEPENDENT = ROOT / 'research/community-frontier1094-audit/INDEPENDENT1094.json' +BIT_EXPECTED = ROOT / 'research/e8-bit-p111-tuned/tune/EXPECTED.json' + +ASSEMBLY_SHA256 = '1122cb3a575f8c788345fc1bf4c108ac7c3250fb81a5988671f5eb04b3ab3045' +EXPECTED_GIT_BLOB = 'e293ddc557742637f9f679f083a1a282d87b1b13' +GRID = Q(1, 10 ** 24) + +SQRT_STEPS = 112 # x^(1/2^k) reduction depth for the sqrt-bisection ln +SQRT_BITS = 320 # dyadic scale of each sqrt enclosure +EXP_ORDER = 48 # Taylor order for the small exponentials of the bill +CROSS_ORDER = 48 # Taylor order for the exp-inversion ln cross-check +CROSS_BITS = 72 # bisection depth for the exp-inversion ln cross-check + + +def require(ok, message): + if not ok: + raise ValueError(message) + + +def sha256(path): + return hashlib.sha256(path.read_bytes()).hexdigest() + + +def git_blob(path): + data = path.read_bytes() + return hashlib.sha1(b'blob %d\0' % len(data) + data).hexdigest() + + +def read(path): + return json.loads(path.read_bytes()) + + +def decimal(frac, digits=30): + """Truncated decimal string of a rational (sign-aware).""" + sign = '-' if frac < 0 else '' + v = abs(Q(frac)) + scaled = (v.numerator * 10 ** digits) // v.denominator + s = str(scaled).zfill(digits + 1) + return sign + s[:-digits] + '.' + s[-digits:] + + +# --------------------------------------------------------------------------- +# Enclosure 1: ln by rational square-root bisection (no series). +# x^(1/2^k) is bracketed by repeated integer square roots on a 2^-320 grid; +# with u = s - 1 in [0, 1], u - u^2/2 <= ln(1+u) <= u. +# --------------------------------------------------------------------------- + +def sqrt_bracket(frac): + """Return (lo, hi) dyadic rationals with lo <= sqrt(frac) <= hi.""" + require(frac > 0, 'sqrt domain') + scale = 1 << (2 * SQRT_BITS) + n = (frac.numerator * scale) // frac.denominator # floor(frac * 2^2P) + s = isqrt(n) + lo = Q(s, 1 << SQRT_BITS) + hi = Q(s + 1, 1 << SQRT_BITS) + require(lo * lo <= frac and hi * hi >= frac, 'sqrt bracket') + return lo, hi + + +def ln_sqrt(frac): + """Enclose ln(frac), frac >= 1, by square-root reduction; exact rationals.""" + require(frac >= 1, 'ln_sqrt domain') + if frac == 1: + return Q(0), Q(0) + lo, hi = frac, frac + for _ in range(SQRT_STEPS): + lo, _ = sqrt_bracket(lo) + _, hi = sqrt_bracket(hi) + require(0 < lo <= hi, 'sqrt reduction order') + u_lo, u_hi = lo - 1, hi - 1 + require(0 <= u_lo <= u_hi < Q(1, 2), 'reduction range') + k = Q(1 << SQRT_STEPS, 1) + return k * (u_lo - u_lo * u_lo / 2), k * u_hi + + +# --------------------------------------------------------------------------- +# Enclosure 2 (cross-check): ln by bisection inverting a certified Taylor exp. +# --------------------------------------------------------------------------- + +def exp_taylor(point, order): + """Enclose exp(y) for a rational 0 <= y < 9; exact rationals.""" + require(0 <= point < 9, 'exp range') + term = total = Q(1) + for j in range(1, order + 1): + term = term * point / j + total += term + tail = term * point / (order + 1) + require(point < order + 1, 'exp tail ratio') + tail = tail / (1 - point / (order + 2)) + return total, total + tail + + +def ln_exp_bisection(frac): + """Enclose ln(frac), frac >= 1, by bisecting exp(t) = frac; exact rationals.""" + require(frac >= 1, 'ln_exp_bisection domain') + if frac == 1: + return Q(0), Q(0) + lo, hi = Q(0), Q(1) + while exp_taylor(hi, CROSS_ORDER)[0] < frac: + hi *= 2 + require(hi < 1024, 'exp bisection bracket') + for _ in range(CROSS_BITS): + mid = (lo + hi) / 2 + mid_lo, mid_hi = exp_taylor(mid, CROSS_ORDER) + if mid_hi < frac: + lo = mid + elif mid_lo > frac: + hi = mid + else: + lo = hi = mid + break + return lo, hi + + +# --------------------------------------------------------------------------- +# The priced bill and the D/E diagnostic. +# --------------------------------------------------------------------------- + +class Bill: + """f(a) = (1/(mW)) sum_r n_r r (m/r)^a + c_s m^a, with certified enclosures. + + ln enclosures are intervals [l_lo, l_hi]; the exponential of a positive + interval is bounded by monotonicity using the Taylor enclosure above. + """ + + def __init__(self, hist, m, W, surcharge_coeff=Q(0)): + self.hist = {int(r): int(n) for r, n in hist.items()} + self.m, self.W = int(m), int(W) + self.c_s = Q(surcharge_coeff) + require(self.m > 1 and self.W > 0, 'width/stock range') + require(all(0 < r < self.m and n > 0 for r, n in self.hist.items()), + 'child rank range') + self.mass = sum(r * n for r, n in self.hist.items()) + self.count = sum(self.hist.values()) + self.deficit = self.m * self.W - self.mass + require(self.deficit > 0, 'deficit must be positive') + self.ln = {r: ln_sqrt(Q(self.m, r)) for r in self.hist} + self.ln_cross = {r: ln_exp_bisection(Q(self.m, r)) for r in self.hist} + + def residual(self, a, surcharge_coeff=None): + """Certified interval of f(a) - 1 at a rational a >= 0.""" + c_s = self.c_s if surcharge_coeff is None else Q(surcharge_coeff) + require(a >= 0, 'saving range') + total_lo = total_hi = Q(0) + for r, n in self.hist.items(): + l_lo, l_hi = self.ln[r] + e_lo, _ = exp_taylor(a * l_lo, EXP_ORDER) + _, e_hi = exp_taylor(a * l_hi, EXP_ORDER) + p = Q(r * n, self.m * self.W) + total_lo += p * e_lo + total_hi += p * e_hi + if c_s: + l_lo, l_hi = ln_sqrt(Q(self.m)) + e_lo, _ = exp_taylor(a * l_lo, EXP_ORDER) + _, e_hi = exp_taylor(a * l_hi, EXP_ORDER) + total_lo += c_s * e_lo + total_hi += c_s * e_hi + return total_lo - 1, total_hi - 1 + + def de_bound(self, surcharge_coeff=None): + """Certified interval of the diagnostic ceiling D_eff / E_eff.""" + c_s = self.c_s if surcharge_coeff is None else Q(surcharge_coeff) + require(c_s >= 0, 'surcharge range') + d_eff = Q(self.deficit) - c_s * self.m * self.W + require(d_eff > 0, 'effective deficit must be positive') + e_lo = e_hi = Q(0) + for r, n in self.hist.items(): + l_lo, l_hi = self.ln[r] + e_lo += r * n * l_lo + e_hi += r * n * l_hi + if c_s: + l_lo, l_hi = ln_sqrt(Q(self.m)) + e_lo += c_s * self.m * self.W * l_lo + e_hi += c_s * self.m * self.W * l_hi + require(e_lo > 0, 'E must be positive') + return d_eff / e_hi, d_eff / e_lo + + def de_screening_extremum(self): + """Screening-only D/E ceiling over histograms with the same m, W and + rank mass, fractional counts allowed, ranks capped by the halving + guard m^2 > 2 r^2. E is smallest when all rank mass sits at the cap, + so this maximizes D/E. Not a realizability claim.""" + r_cap = 1 + while 2 * (r_cap + 1) ** 2 < self.m ** 2: + r_cap += 1 + l_lo, l_hi = ln_sqrt(Q(self.m, r_cap)) + e_hi = self.mass * l_hi + return self.deficit / e_hi, r_cap + + +# --------------------------------------------------------------------------- +# Ledgers of the selected record. +# --------------------------------------------------------------------------- + +def complex_ledger(assembly, independent): + hist = {int(r): int(n) for r, n in assembly['complex_profile'].items()} + calls = assembly['provider_counts']['gauge44'] + mass = sum(r * n for r, n in hist.items()) + # Coverage identities D = 73W - mass and D = W - 64N determine + # W = (mass - 64N) / 72; the audited value is pinned in INDEPENDENT1094. + require((mass - 64 * calls) % 72 == 0, 'complex coverage identity') + W = (mass - 64 * calls) // 72 + require(W == independent['price']['live'] == 14336, 'complex live stock') + require(calls == independent['price']['calls'] == 144, 'complex call count') + bill = Bill(hist, m=73, W=W) + require(bill.deficit == W - 64 * calls == independent['price']['deficit'], + 'complex deficit identity') + return bill, dict(m=73, W=W, N=calls, deficit=bill.deficit) + + +def bit_ledger(assembly, expected): + block = assembly['bit_supplier'] + word = block['word'] + nine = expected['nine'] + hist = nine['profile'] + W = nine['bit']['live'] + require(block['path'] == 'research/e8-bit-p111-tuned/tune/EXPECTED.json', + 'bit supplier path') + require(git_blob(BIT_EXPECTED) == block['git_blob_sha1'] == EXPECTED_GIT_BLOB, + 'bit supplier git blob') + require(word['v'] == expected['word']['v'] == 111, 'bit word parameter v') + require(word['decoder_constant'] == expected['word']['decoder_constant'] == 63, + 'bit decoder constant') + L = len(word['copy_ranks']) + require(L == expected['word']['retained_totals'] == 9, 'bit copy-rank count') + require(set(word['copy_ranks']) == {7}, 'bit copy ranks') + # Coverage identity D = 64W - mass = T(2Kv - L*cst), T=32 K=4 M=64. + T, K, M = 32, 4, 64 + derived = T * (2 * K * word['v'] - L * word['decoder_constant']) + bill = Bill(hist, m=M, W=W, surcharge_coeff=Q(32 * M * sum(hist.values()), 10 ** 16 * W)) + require(bill.deficit == derived == block['derived_deficit'], + 'bit deficit identity') + require(block['deficit_formula'] == 'T(2Kv-L*cst), L=9 T=32 K=4 M=64', + 'bit deficit formula label') + return bill, dict(m=M, W=W, T=T, K=K, L=L, deficit=bill.deficit) + + +def check_endpoint(bill, label, endpoint, nxt, recorded, controls): + """Positive fixture for one certified endpoint, plus sign controls.""" + require(nxt == endpoint + GRID, label + ' next-grid point') + lo, hi = bill.residual(endpoint) + nlo, nhi = bill.residual(nxt) + require(hi < 0, label + ' moment must accept at the endpoint') + require(nlo > 0, label + ' moment must reject at the next grid point') + # Agreement with the two retained engines' recorded residual intervals. + for engine in ('mercator', 'base_two'): + rec = recorded[engine] + r_lo, r_hi = Q(rec[0]), Q(rec[1]) + require(lo <= r_hi and hi >= r_lo, label + ' residual agrees with ' + engine) + # Smallest falsifying instance for the acceptance claim: one more grid + # step from the endpoint must already flip the sign. + flo, fhi = bill.residual(endpoint + 2 * GRID) + require(flo > 0, label + ' two grid steps must reject') + controls.append((label + ':endpoint+2grid-rejects', True)) + return dict(endpoint=str(endpoint), residual=[str(lo), str(hi)], + residual_decimal=[decimal(lo), decimal(hi)], + next_grid_residual=[str(nlo), str(nhi)], + next_grid_decimal=[decimal(nlo), decimal(nhi)], + accept=True, sharp_next_grid=True) + + +def check_de(bill, label, a_rec, controls): + """The certified a < D/E diagnostic for one ledger.""" + b_lo, b_hi = bill.de_bound() + require(b_lo > 0 and b_lo <= b_hi, label + ' D/E interval order') + require(a_rec < b_lo, label + ' recorded endpoint below the D/E ceiling') + require(b_lo - a_rec > 0, label + ' strictness') + tight = Q(b_lo) / Q(a_rec) + screen, r_cap = bill.de_screening_extremum() + require(screen > b_hi, label + ' screening extremum above the ledger ceiling') + return dict(de_bound=[str(b_lo), str(b_hi)], + de_decimal=[decimal(b_lo), decimal(b_hi)], + endpoint=str(a_rec), + bound_over_endpoint=decimal(tight), + endpoint_strictly_below=True, + screening_extremum_decimal=decimal(screen), + screening_rank_cap=r_cap, + screening_note='D/E ceiling over rank-mass-preserving repackings ' + 'with fractional counts at ranks up to the halving ' + 'guard; screening only, not a realizability bound') + + +def single_rank_falsification(controls): + """Exactly solvable smallest instance: H={1:1}, m=2, W=1. + f(a) = 2^(a-1), so a* = 1 exactly, and D/E = 1/ln 2 > 1.""" + bill = Bill({1: 1}, m=2, W=1) + lo, hi = bill.residual(Q(1)) + require(lo <= 0 <= hi, 'single-rank root must be a = 1') + below, _ = bill.residual(Q(999, 1000)) + _, above = bill.residual(Q(1001, 1000)) + require(below < 0 < above, 'single-rank sign change around a = 1') + b_lo, b_hi = bill.de_bound() + require(b_lo > 1, 'single-rank D/E strictly above the root a* = 1') + l_lo, l_hi = bill.ln[1] + c_lo, c_hi = bill.ln_cross[1] + require(l_lo <= c_hi and c_lo <= l_hi, 'ln(2) enclosures agree') + controls.append(('single-rank-root-exact', True)) + return dict(root='1', de_bound=[str(b_lo), str(b_hi)], + ln2=[decimal(l_lo), decimal(l_hi)]) + + +def failure_controls(assembly, independent, expected, controls): + """Semantic failure controls: every mutation must be rejected.""" + def rejected(name, fn): + try: + fn() + except ValueError: + controls.append((name, True)) + return + raise ValueError('failure control not rejected: ' + name) + + rejected('tampered-assembly-pin', + lambda: require(sha256(ASSEMBLY) == 'deadbeef', 'pin')) + rejected('bit-wrong-width', + lambda: require( + Bill(expected['nine']['profile'], m=73, W=expected['nine']['bit']['live']) + .deficit == assembly['bit_supplier']['derived_deficit'], 'deficit')) + bad_hist = dict(assembly['complex_profile']) + bad_hist['1'] = bad_hist['1'] + 1 + bad_hist['48'] = bad_hist['48'] - 1 + + def bad_complex(): + mass = sum(int(r) * n for r, n in bad_hist.items()) + calls = assembly['provider_counts']['gauge44'] + require((mass - 64 * calls) % 72 == 0 and + (mass - 64 * calls) // 72 == independent['price']['live'], 'coverage') + rejected('complex-mutated-histogram', bad_complex) + rejected('child-rank-out-of-range', lambda: Bill({73: 1}, m=73, W=1)) + rejected('zero-deficit', lambda: Bill({1: 10}, m=2, W=5)) + c_bill = Bill(assembly['complex_profile'], m=73, W=independent['price']['live']) + a_c = Q(assembly['moments'][2]['endpoint']) + # Claiming a shifted endpoint as accepting must fail the acceptance test. + rejected('complex-endpoint-shifted-two-grids', + lambda: require(c_bill.residual(a_c + 2 * GRID)[1] < 0, 'accept')) + b_bill = Bill(expected['nine']['profile'], m=64, W=expected['nine']['bit']['live'], + surcharge_coeff=Q(32 * 64 * sum(int(n) for n in expected['nine']['profile'].values()), + 10 ** 16 * expected['nine']['bit']['live'])) + a_b = Q(assembly['moments'][0]['endpoint']) + + def doubled_surcharge(): + lo, hi = b_bill.residual(a_b, surcharge_coeff=2 * b_bill.c_s) + require(hi < 0, 'accept with doubled surcharge') + rejected('bit-doubled-surcharge-breaks-acceptance', doubled_surcharge) + + def negative_surcharge(): + b_bill.de_bound(surcharge_coeff=Q(-1)) + rejected('negative-surcharge-rejected', negative_surcharge) + + +def main(): + require(sha256(ASSEMBLY) == ASSEMBLY_SHA256, 'selected assembly pin') + assembly, independent, expected = read(ASSEMBLY), read(INDEPENDENT), read(BIT_EXPECTED) + controls = [] + + single = single_rank_falsification(controls) + c_bill, c_ledger = complex_ledger(assembly, independent) + b_bill, b_ledger = bit_ledger(assembly, expected) + + moments = assembly['moments'] + bit_row = moments[0] + cplx_row = moments[2] + require(bit_row['surcharge'] is True and cplx_row['surcharge'] is False, + 'recorded surcharge model') + + c_endpoint = check_endpoint(c_bill, 'complex', Q(cplx_row['endpoint']), + Q(moments[3]['endpoint']), cplx_row, controls) + b_endpoint = check_endpoint(b_bill, 'bit', Q(bit_row['endpoint']), + Q(moments[1]['endpoint']), bit_row, controls) + c_de = check_de(c_bill, 'complex', Q(cplx_row['endpoint']), controls) + b_de = check_de(b_bill, 'bit', Q(bit_row['endpoint']), controls) + + # ln-method agreement on every used log, for both ledgers. + for bill, label in ((c_bill, 'complex'), (b_bill, 'bit')): + for r, (l_lo, l_hi) in bill.ln.items(): + c_lo, c_hi = bill.ln_cross[r] + require(l_lo <= c_hi and c_lo <= l_hi and + l_hi - l_lo < Q(1, 10 ** 20), + '%s ln(%d/%d) methods agree' % (label, bill.m, r)) + controls.append(('ln-methods-agree-all-ranks', True)) + + failure_controls(assembly, independent, expected, controls) + + out = dict( + status='PASS_INDEPENDENT_DE_DIAGNOSTIC', + method=dict( + ln='rational square-root bisection (x^(1/2^k), k=%d, 2^-%d grid), ' + 'ln(1+u) bracketed by u-u^2/2 <= ln(1+u) <= u' % (SQRT_STEPS, SQRT_BITS), + ln_cross='bisection inverting a Taylor exponential (order %d)' % CROSS_ORDER, + exp='Taylor partial sums, order %d, rational geometric tail bound' % EXP_ORDER, + arithmetic='exact fractions throughout; enclosures from explicit ' + 'inequalities only; no floating point', + imports='no repository engine imported'), + ledger=dict(complex=c_ledger, bit=b_ledger), + moment=dict(complex=c_endpoint, bit=b_endpoint), + de=dict(complex=c_de, bit=b_de), + single_rank_falsification=single, + lemma='For f(a) = (1/(mW)) sum_r n_r r (m/r)^a + c_s m^a with 0 < r < m, ' + 'W >= 1 and c_s >= 0, f is convex and f(0) = 1 - D_eff/(mW) with ' + 'D_eff > 0. The tangent at a = 0 meets 1 at D_eff/E_eff, so the ' + 'exact root satisfies a* < D_eff/E_eff strictly. For c_s = 0 this ' + 'is the autoresearch.md section-2 diagnostic a < D/E.', + controls=[name for name, _ in controls], + scope='Independent verification and diagnostic only. The moment sign is ' + 'the acceptance test; D/E is a diagnostic upper bound on the root ' + 'of one fixed ledger histogram and is not a realizability or ' + 'repacking bound. No kappa change; the selected record is unchanged.', + limitations=[ + 'The paid profiles are taken from the published ledgers ' + '(ASSEMBLY.json complex_profile; EXPECTED.json nine.profile); this ' + 'package does not rebuild either word from its original operations.', + 'The conservative (surcharge-on-complex) endpoints of ASSEMBLY.json ' + 'are not rechecked here.', + 'D/E is a per-histogram ceiling; an upper bound over all repackings ' + 'needs the coverage-law argument, see ' + 'https://github.com/CrocSwap/integer-mult-bounds/pull/1240 for the ' + 'complex local word.'], + ) + out_path = Path(__file__).with_name('RESULT.json') + out_path.write_text(json.dumps(out, indent=2, sort_keys=True) + '\n') + print(out['status']) + for side in ('complex', 'bit'): + m, d = out['moment'][side], out['de'][side] + print('%-8s moment residual at endpoint %s next grid %s' % + (side, m['residual_decimal'][1], m['next_grid_decimal'][0])) + print('%-8s D/E ceiling %s (bound/endpoint %s)' % + (side, d['de_decimal'][0], d['bound_over_endpoint'])) + print('controls', len(controls), 'all rejected/passed') + + +if __name__ == '__main__': + try: + main() + except ValueError as exc: + print('FAIL:', exc) + sys.exit(1)