Superseded by #1112

Makefile

@@ -618,3 +618,8 @@ phase-recipes-parallel-benchmark:
 frontier1042-verify: selected-record-check
 	@work=$$(mktemp -d "$${TMPDIR:-/tmp}/integer-mult-frontier1042.XXXXXX"); \
 	python3 -B scripts/verify_frontier1042.py --work "$$work/replay"
+
+.PHONY: frontier1042-invoice-audit-verify
+frontier1042-invoice-audit-verify:
+	python3 -I -B research/frontier1042-invoice-audit-seed81/verify.py
+	cd research/frontier1042-invoice-audit-seed81 && python3 -B -m unittest test_package -v

research/frontier1042-invoice-audit-seed81/README.md

@@ -0,0 +1,129 @@
+# Independent re-check of the selected PR1042 finite invoice and outer admission
+
+**Status: independent verification. No new κ, and the selected result is unchanged. No discrepancy was found.**
+
+- **Track and seed:** track 75–84 (independent verification), assignment seed **81** from the OS CSPRNG (Python `secrets`).
+- **Base commit:** `ba82555c64e1879e4b7decce28186f208fcb8262`.
+- **Audited record:** `research/community-frontier1042-audit/ASSEMBLY.json`, sha256 `093f3544…1e54e`. This is the `certificate_sha256` in `certificates/selected-result.json`, with κ = 1672188119205421/10¹⁸.
+- **Adds:** this directory and one Makefile target.
+
+## Why
+
+Existing independent checks of the current chain each stop at a stated boundary:
+
+- **#1049** checks the leaver local words.
+- **#1091** checks the T16 owner maps.
+- **#1069** checks the pricing chain, from profile through deficit and endpoint to κ. It explicitly excludes invoices.
+- **#1052** recomputes the 94 outer slacks and 14 bootstrap steps, but only for the historical #942 T37 record.
+- **#771** (theon199, open) independently reproduces the nine finite invoice guards and the 2,628-bit group order, but for the earlier #626 invoice (row coefficient 16,467), not the selected #1042 invoice (16,469).
+
+That left the finite invoice of the selected record without a check outside the retained `assemble.py`. The same was true of its seven-plus-seven bootstrap levels and its 47 + 47 outer slacks. The finite invoice covers the per-vertex envelope and the nine strict size guards (router, literal, precision, tape, row and the others listed below).
+
+## What `verify.py` checks
+
+It uses only the standard library. It imports and executes nothing from the repository. All inputs are pinned and read as data:
+
+- the committed assembly;
+- the members `t16/global/audit/OWNERS-AND-PROFILE.json` and `PREFIX-AND-INVOICE.json` from the committed `selected-replay.tar.gz`. Each is checked against the assembly's own `input_sha256`, and the archive's `t16/ASSEMBLY.json` must be byte-equal to the committed file;
+- PR589's `EXPECTED.json`, checked against git blob `e293ddc5…`.
+
+The verifier recomputes every quantity and compares it exactly with the record.
+
+1. **Profile composition.**
+   - There are exactly 144 calls, one per (stage, replica) in 9 × 16, with forward and backward orientations alternating.
+   - The per-call paid profiles sum to the selected local profile.
+   - The idle remainders `{1:2249, 2:1, 3:400, 7:3, 16:47, 48:4850}` are nonnegative and number 7550.
+   - Rank mass is 1,041,408 and the deficit is 73 · 14336 − mass = 5120.
+   - The halving guard holds: 73² = 5329 > 2 · 48² = 4608.
+2. **Per-vertex envelope.**
+   - Actual selected primitives: 28,625,376. Wrapper factors: 9,953,280.
+   - Adapter formula, compiler 64 · 74³, nonlocal item count, unhosted per-vertex 3,588,959,010,714,576 and hosted rebased per-vertex value.
+   - The retained prior overcharge gives a used allowance of 6,466,906,000,439,144.
+   - The physical stock identity sums to 14,826.
+3. **The nine strict finite guards.** The table below gives the headroom in bits; all nine recorded bit lengths match.
+   - **Group order.** The charged group order is computed in two independent ways: 2^(n²)∏(2^(2j)−1), and the orbit–stabilizer count of hyperbolic pairs. Both give n = 36, i.e. |Sp(72,F₂)|.
+   - **Interpretation.** In characteristic two, the orthogonal group of a nondegenerate quadratic form in odd dimension 2n+1 is isomorphic to Sp(2n,q). So this number is |O(73,F₂)| for the parabolic quadratic form, for m = 73. That is one reading of the "full finite orthogonal group" named in `research/native-complex-moment552/PROOF.md`.
+   - **Relation to #771.** #771 reads the same group as the isometry group of the standard dot product on F₂⁷³. It checks that reading by enumerating orthonormal bases in dimensions 1–7. That group has the same order, so the invoice is identical under either reading.
+   - **Brute-force check.** The verifier enumerates every invertible matrix preserving the parabolic form x₀² + Σ x₂ᵢ₋₁x₂ᵢ. It finds |O(3,2)| = 6 and |O(5,2)| = 720, matching the formula. This is a different object from #771's, so the two checks complement each other.
+
+   | Guard | Bound | Headroom |
+   |---|---|---|
+   | local primitive bound | 2⁴⁸ | **4 bits** (10,038,040,553,630 ≈ 2^43.19, about 28×) |
+   | logical (group · used + 64) | 2⁶⁰⁵⁰ | 3,370 bits |
+   | router | 2³⁰⁰⁰⁰ | 22,012 bits |
+   | literal | 2¹⁰⁰⁰⁰⁰ | 64,716 bits |
+   | mass (streamed mass vs 2¹⁰⁰⁰⁰⁰) | 2¹⁰⁰⁰⁰¹ total | 97,352 bits |
+   | precision 32·73·B² | 2²¹⁰⁰⁰⁰ | 9,988 bits |
+   | tape | 2²¹⁰⁰⁰⁰ | 109,998 bits |
+   | row coefficient 2·2642+9909+252+1024 | 20,161 | 16,469 < 20,161 |
+   | halving | — | 5329 > 4608 |
+
+   Prefix: the local maximum is 68 bits. The global prefix is 68+37+144+144+4 = 397, charged at 512; the row reserve is 2 · 512 = 1024.
+4. **Bootstrap and outer assembly, for both the native and the conservative endpoint.**
+   - **Bootstrap.** It has seven affine levels from 384599/10¹⁰, with target s = min(c, (1−β)b) − 10⁻²⁷ and η = β = 10⁻²⁴. All 14 (exponent, gap, cutoff) records match exactly.
+   - **Outer slacks.** All 47 + 47 slacks equal the recorded rationals exactly and are positive.
+   - **κ.** Each κ is the largest 10⁻¹⁸ grid point strictly below the absorption margin εq.
+   - **Controls.** The four recorded outer controls (`next_grid`, `zero_eta`, `zero_beta`, `unit_beta`) are re-derived as failures.
+5. **PR589 bit side.**
+   - The bit endpoint equals PR589's recorded `bit_lower`.
+   - The bit deficit is 32(2·4·111 − 9·63) = 10,272, and it equals 64·live − mass for PR589's profile.
+   - The endpoints are ordered conservative < native complex < bit.
+
+### Additional observations
+
+- **The bootstrap cutoffs do not depend on the prefix reserve.** At every one of the 14 steps the quadratic term ⌈36/gap²⌉ decides the cutoff. It keeps deciding it for any reserve P ≤ 6,566,539 in ⌈2(4+P)/gap⌉. So this lineage's 512-bit linear term, where T37 used 1024, does not affect the recorded cutoffs.
+- **The tightest finite guard is the local primitive bound, not precision.** Its value is dominated by local adapters × compiler (387,056 × 25,934,336). Future provider words with more macros or children consume this 28× margin first.
+- **The smallest outer slacks are η-scale.** For example, λ − τ = aη ≈ 1.7 × 10⁻²⁷, followed by β = 10⁻²⁴. They are positive by construction, not by numerical margin.
+
+### Negative controls
+
+There are 15 controls, and each must be rejected. Every one is rejected at its intended check:
+
+- one extra idle child;
+- one call's primitive count changed;
+- one call dropped;
+- one orientation swapped;
+- one extra physical register;
+- the retained prior overcharge dropped;
+- recorded router bits off by one;
+- row coefficient set to the bound;
+- κ + 10⁻¹⁸;
+- one outer slack edited by 10⁻⁴⁰;
+- one bootstrap cutoff off by one;
+- bit endpoint − 10⁻²⁴;
+- complex endpoint + 10⁻²⁴;
+- a count- and mass-preserving idle edit introducing a rank-52 child, which fails only the halving guard;
+- group |Sp(70,2)| in place of |Sp(72,2)|.
+
+## Reproduce
+
+```sh
+make frontier1042-invoice-audit-verify
+```
+
+Expected output:
+
+```
+PASS_FRONTIER1042_INVOICE_OUTER_INDEPENDENT | guards 9 | slacks 94 | bootstrap 14 | controls 15
+```
+
+Six unit tests should then pass. The run takes about 1.5 s on Python 3.10+, needs no network, and reads the committed archive without extracting it. `RESULT.json` is regenerated and compared byte for byte; `--write` rewrites it.
+
+## Scope and independence
+
+- **How the formulas were obtained.** The definitions of the envelope, the guards, the bootstrap and the 47 constraints exist only as code. They live in the retained `code/assemble.py` and the `engines/outer.py` engine (sha `c1ebb521…`). Their conceptual source is `notes/three-stage-cover-assembly.tex`, § "Full finite router and completed-child guard". I read those definitions and re-implemented them separately; nothing from them is imported or executed.
+- **What this does and does not catch.** It is an independent re-computation. It catches transcription, data-binding and arithmetic errors in the selected record. It does **not** independently justify why these particular formulas are the right charges.
+- **What is taken as data.** Taken as given are:
+  - the semantic content of the receipts: local words, Clifford phases, owner windows and hosting. Those are covered by #1049, #1091 and the maintainer replay;
+  - the two moment endpoints `complex_lower` and `conservative_complex_lower`. Those are certified by the two retained engines and independently by #1069.
+- **Inherited assumptions.** All the record's conditions remain: all-size/compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, exact recovery, analytic transfer and bit H1–H5.
+- **What this is not.** It is a finite check of one certificate. It is not a formal proof, and it is not a verification of the multiplication theorem.
+
+## Credit
+
+- **Construction:** Jeremy Kothe (#1042 and its chain), with Rohan Arun's #987 slot search, Hao Yan's #858 T16 controller and the full lineage credited in `research/gauge44-slots-t16`. The bit supplier is DreamingOfClouds' PR589 on eumemic's PR555.
+- **Assembly and guard engines:** the retained engines and their authors as named in their headers: icekylinx (PR144), Zhihao Chen (PR23), eumemic and hipotures' balanced transform.
+- **Predecessor guard audit:** theon199's #771 established the group order and the nine-guard recomputation for the #626 invoice, including the row-guard sensitivity to replacing the group with GL(73,2). This package extends that check to the selected #1042 invoice, the per-vertex envelope, the bootstrap chain and the outer slacks. It does not claim priority for the group-order identity.
+- **Neighbouring audits whose boundaries this complements:** #1069 and #1051 (Sagar Thakrar), #1052 (steph4n-gh), #1091 (JosieElliston), #1049 and #1009.
+
+Prepared by Wronskode (@Wronskode) with substantial AI assistance from Claude (Anthropic) via Claude Code. New material is Apache-2.0.

research/frontier1042-invoice-audit-seed81/RESULT.json

@@ -0,0 +1,130 @@
+{
+ "conservative": {
+  "absorption_gap_over_kappa": "1793928311450341652126462993975374676671683256294031944367298339641448680333297947674520128977613231324347522231563051943005447670744740636734105356607471601251222581214803571019825029913203279695345742919981429792583076478853465101276007386390276786228229649328049330609921201035442825722449400497914073088936420190160457482155640445049599711466132438405592016305107159844319457541720604316894233678604555971679/1956396462916165769309682536808093436689934574780270280446916092175260605646903318931488279624590912825481419335971634954607786158048438706514820685577142587829476892438231619356471295310816797342529520344714574237169211267396677595275125260339533406255485661319097702245671343609312671271273718812103362182602371672521649411400782639006003713263671653553007279171736886045321005448876417857050607022028321000000000000000000000000",
+  "all_quadratic": true,
+  "bootstrap_levels": 7,
+  "controls": [
+   "next_grid",
+   "zero_eta",
+   "zero_beta",
+   "unit_beta"
+  ],
+  "final_exponent_decimal": 0.001674989013076874,
+  "kappa": "836094058177091/500000000000000000",
+  "min_slack_names": [
+   "lambda_above_tau",
+   "lambda_above_internal",
+   "lambda_prime_above_lambda"
+  ],
+  "reserve_insensitive_up_to": 6566539,
+  "slacks": 47
+ },
+ "controls_rejected": {
+  "bit_endpoint": "bit endpoint differs from PR589 record",
+  "bootstrap_cut": "native bootstrap record",
+  "call_primitives": "call field real_component_primitives differs from provider orientation",
+  "complex_endpoint": "native bootstrap record",
+  "drop_call": "call count",
+  "extra_idle": "idle remainder count",
+  "group_Sp70": "stock bits",
+  "kappa_up": "native kappa",
+  "max_rank": "halving guard m^2 > 2 max^2",
+  "physical_plus": "physical stock identity",
+  "prior_dropped": "conservative per-vertex used",
+  "router_bits": "router bits",
+  "row_bound": "row coefficient",
+  "slack_edit": "native slack values",
+  "swap_orientation": "orientation alternation"
+ },
+ "envelope": {
+  "compiler": 25934336,
+  "hosted_rebased_pervertex": 3588959010114264,
+  "local_adapters": 387056,
+  "local_primitive_bound": 10038040553630,
+  "local_primitive_bound_bits": 44,
+  "nonlocal_items": 10330706,
+  "selected_primitives": 28625376,
+  "unhosted_pervertex": 3588959010714576,
+  "used": 6466906000439144,
+  "wrapper_factors": 9953280
+ },
+ "group_identity_small_cases": {
+  "3": 6,
+  "5": 720
+ },
+ "guards": {
+  "group": "|Sp(72,2)| = |O(73,2)|",
+  "group_bits": 2628,
+  "halving": [
+   5329,
+   4608
+  ],
+  "headroom_bits": {
+   "literal": 64716,
+   "local_primitive_bound": 4,
+   "logical": 3370,
+   "precision": 9988,
+   "router": 22012,
+   "streamed_mass_below_2E": 97352,
+   "tape": 109998
+  },
+  "prefix": {
+   "charged": 512,
+   "global_bits": 397,
+   "local_max": 68
+  },
+  "row": [
+   16469,
+   20161
+  ],
+  "stock_bits": 2642
+ },
+ "native": {
+  "absorption_gap_over_kappa": "5898870362994891634444604624472313490385041769044841029282436221394301619483331101300482774752713592828780555650775228372923267597658144681965494760827577052221368735004683884421179242961266214755879022040006321890865282747363951678071580189889102625080740060236293742745183773211712384497111999756119249695117541637231855734848960082400315928585470227084315404683984061633592339323874345677609144984126696159/7642173683288098696353206320533098397425303740389176568296792768321409694791227176758388940490772445254290891270282752927617617341749604846144822956754229220151880926832518672008638252454857338443493953390547083184027340315381008353350104455338847177256218236473459164407826365829096398886967631947514171400433110871808493474188166327784405693451719993241411307050337157486106732990992508508693812303841000000000000000000000000",
+  "all_quadratic": true,
+  "bootstrap_levels": 7,
+  "controls": [
+   "next_grid",
+   "zero_eta",
+   "zero_beta",
+   "unit_beta"
+  ],
+  "final_exponent_decimal": 0.0016749890159376724,
+  "kappa": "1672188119205421/1000000000000000000",
+  "min_slack_names": [
+   "lambda_above_tau",
+   "lambda_above_internal",
+   "lambda_prime_above_lambda"
+  ],
+  "reserve_insensitive_up_to": 6566539,
+  "slacks": 47
+ },
+ "profile": {
+  "calls": 144,
+  "deficit": 5120,
+  "halving": [
+   5329,
+   4608
+  ],
+  "idle": {
+   "1": 2249,
+   "2": 1,
+   "3": 400,
+   "7": 3,
+   "16": 47,
+   "48": 4850
+  },
+  "idle_children": 7550,
+  "live": 14336,
+  "local": {
+   "1": 347328,
+   "2": 60192,
+   "3": 62208,
+   "4": 20448,
+   "5": 11808,
+   "8": 1152
+  },
+  "rank_mass": 1041408
+ },
+ "status": "PASS_FRONTIER1042_INVOICE_OUTER_INDEPENDENT"
+}

research/frontier1042-invoice-audit-seed81/test_package.py

@@ -0,0 +1,53 @@
+"""Unit tests for the seed-81 PR1042 invoice/outer audit. Apache-2.0."""
+import json
+import subprocess
+import sys
+import unittest
+from fractions import Fraction as Q
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+sys.path.insert(0, str(HERE))
+import verify as V  # noqa: E402
+
+
+class GroupOrder(unittest.TestCase):
+    def test_formulas_agree(self):
+        for n in range(1, 40):
+            self.assertEqual(V.sp_order_product(n), V.sp_order_orbit(n))
+
+    def test_brute_force_small_odd_orthogonal(self):
+        self.assertEqual(V.orthogonal_odd_brute(1), 6)
+        self.assertEqual(V.orthogonal_odd_brute(2), 720)
+
+
+class Replay(unittest.TestCase):
+    @classmethod
+    def setUpClass(cls):
+        cls.data = V.load_inputs(V.ROOT)
+
+    def test_committed_result_regenerates(self):
+        r = subprocess.run([sys.executable, '-I', '-B', str(HERE / 'verify.py')], capture_output=True, text=True)
+        self.assertEqual(r.returncode, 0, r.stdout + r.stderr)
+        self.assertIn('PASS_FRONTIER1042_INVOICE_OUTER_INDEPENDENT', r.stdout)
+
+    def test_every_control_rejected(self):
+        res = V.controls(self.data)
+        self.assertEqual(len(res), 15)
+        self.assertEqual(res['max_rank'], 'halving guard m^2 > 2 max^2')
+        self.assertEqual(res['group_Sp70'], 'stock bits')
+
+    def test_kappa_is_last_grid_point(self):
+        out = V.run_all(self.data)
+        k = Q(self.data['asm']['kappa'])
+        self.assertEqual(out['native']['kappa'], str(k))
+        self.assertEqual(k, Q(1672188119205421, 10 ** 18))
+
+    def test_result_fields(self):
+        res = json.loads((HERE / 'RESULT.json').read_text())
+        self.assertEqual(res['guards']['row'], [16469, 20161])
+        self.assertTrue(res['native']['all_quadratic'] and res['conservative']['all_quadratic'])
+
+
+if __name__ == '__main__':
+    unittest.main()