Research audit: the selected #1094 local programs satisfy Lemma G's extended-label H1 (HPE-aware check, 0 violations); the selected chain runs no tag check (published checker needs a cold-HPE patch; the frame-only replay accepts three adapter mutants) (no new kappa)

[thakrarsagar]

Change and mathematical scope

Audit for the complex supplier. No new κ, and the selected record is
unchanged. This adds one registered package,
research/selected1094-extended-labels-seed65/.
No selected record, supplier, pinned file or upstream/ file changes.

(a) H1 holds for the selected programs. Lemma G's Theorem 1 (Lean
LemmaG.Stream.conj_matrix) needs two hypotheses:

• H1: the emitted stream is WellLabelled in the extended labels
  (tag × frame);
• H2: every recipe is exact.

The package regenerates the selected seven-slot word's emitted forward and
backward local programs from committed bytes, using the pinned PR635 tools. It
reproduces all four selected hashes: canonical 4ddb29fb, programs 071ecdac /
f36c5831, and CLIFFORD-RECIPES d0768f21.

An independent HPE-aware extended-label checker finds 0 violations in both
orientations. That covers 24,767 events each, including 1,497 / 3,924 source
writes and 240 wrapped helpers, 48 of them cold hyperplane-ended. The result
holds under both the literal and the most permissive Lean reading of private
clears.

• Lemma S. A structural lemma extends the tag part to every word the pinned
  transport and emitter accept.
• Theorem R. With conj_matrix, the H2 recipe pin (independently checked by
  my open Independent verification: every child record and endpoint adapter of the selected frontier1094 CLIFFORD-RECIPES exact with global phase (no new kappa) #1781) and an exact scalar shadow, this gives per-call common-label /
  mutable-source realization of the complex local programs. It holds on ℂ^{2^9}
  and ℂ^{2^9} ⊗ V for arbitrary dirty inputs.
• Still inherited, named and not discharged:
  • all-size recipe execution;
  • whole-call hosting (Lemma A (O′), (W));
  • cross-call composition;
  • precision and tape;
  • Lemma A (N);
  • the bit supplier's mutable-basis realization (Post-center rank-four kernels for conditional κ = 0.001584931111785787 #535's carryover note).

(b) The selected chain runs no tag check. Lemma G assigns the tag half of H1
to check_extended_labels.py, which cannot parse HPE words (see (c)). The HPE
package maps only G0 in cleanup_tail to the local audit, and every operand
there has tag T.

The chain's emitted-program check, PR635's frame-only hpe_audit_local.py,
does not substitute for a tag check. It accepts three scalar-neutral mutants
of the forward program (exit 0, PASS, 25 controls). Their scalar shadows equal
the honest data shear, yet each is physically wrong:

mutant	label_check permissive / strict	patched Lemma G checker	exact witness
X: exit straddle, target 112 at frame 778	2 / 4	4	target ends at a, not N_t⁻¹ a; at a = e_0, i³e_1 is expected
Y: entry straddle, source 0 at frame 9	2 / 2	4	M_0 skipped; wrong at h_0 = e_1 (M_0 e_1 = i e_10)
Z: exit adapters of registers 0..112 moved before a phase-B add on L_112	113 / 113	113 (50 capped)	honest − mutant = (I − A_t) b/2; target ends at (i³e_1 − e_0)/2 instead of 0

The pinned emitter cannot produce these mutants from any word, so κ is
unaffected. This is a coverage gap in admission.

Recommendation. Run an HPE-aware extended-label check next to the replay.
Forbidding scalars in the adapter phases is not enough, because Z has none
there. verify.py also includes a cheaper adapter_rule:

• every adapter and wrapper sits in its own phase at cur[r] == f;
• per-register adapter state is tracked.

The rule rejects all three mutants and accepts the selected programs. It is a
sketch, not proved sufficient.

(c) The published Lemma G checker on the selected word. Before this, only
#509 and #516 ran it, and never on an HPE word.

• As published: it fails with ValueError on the 5-field HPE wrapper events.
• With the 5th field stripped: 96 violations per orientation, which is the
  48 cold helpers × 2.
• With a three-line marked cold-HPE patch (rebuilt byte for byte from the
  pinned original): 0 violations. It still rejects its own five mutants and all
  three mutants of (b).

Task and overlap

• Base and track: base 0b1cccf8. Seed 65 → adversarial mathematical
  audit, card uniform-transfer-audit (catalogue priority revision 3), scope
  refined.
• Independent verification: every child record and endpoint adapter of the selected frontier1094 CLIFFORD-RECIPES exact with global phase (no new kappa) #1781 (mine, open) checks H2 on the same word. This package checks
  H1. They are complementary.
• Research audit: signed prefixes give 18/21-bit local bounds for selected PR1094 #1282 (merged) and [Lean] Prove unitary prefix bounds on the existing Lemma G semantics #1309 (open), bitplane, derive a Lemma G prefix-norm
  corollary on the same programs, with H1/H2 as premises.
  • This package discharges the H1 instance they assume, and the
    concrete-extended-label part of the Discussion Lean prefix norm corollary on the existing Lemma G stream interface #1291 / [Lean] Prove unitary prefix bounds on the existing Lemma G semantics #1309 handoff.
  • The row certificate and recipes stay theirs and Independent verification: every child record and endpoint adapter of the selected frontier1094 CLIFFORD-RECIPES exact with global phase (no new kappa) #1781's.
• Bind emitted k8 helper 450 to the retained Lean wrapper pair #1611 and Independent verification: bind all 511 cold hyperplane operators with phase and spectator #1697 bind wrapper pairs and cold operators (Lemma A / HPE (N)).
  They are used here only through the inherited helper-block evaluation.
• Independent verification: audit helper-frame lifetimes with a scalar-preserving regression #729 found a frame-history gap in a different component.
• Overlap searches of open and recent PRs for Lemma G, WellLabelled,
  check_extended_labels, hpe_audit_local, tag check, extended-label and
  exit adapter found nothing else on this proposition.

Validation

python3 scripts/research_package.py --package research/selected1094-extended-labels-seed65 --check-only
python3.12 scripts/research_package.py --package research/selected1094-extended-labels-seed65

verify.py uses only the standard library and takes about 85 s; recipe
generation dominates and runs concurrently. Its checks raise ValueError, and
it is registered plain and under -O. The pinned producer scripts run in
-I -B subprocesses from SHA-checked byte copies.

Failure controls. These test the checker; they do not prove it.

• Rejected under both readings: 28 forward and 27 backward edited programs.
  • Lemma G's five mutants() and two HPE edits.
  • Single-clause edits:
    • target exit and entry adapters at wrong frames or positions;
    • identity adapters added for wrapped or HPE helpers;
    • a post wrapper before the final climb;
    • a source entry adapter keyed away from its start;
    • centre steps and copies from wrong frames;
    • phase markers dropped or swapped;
    • unknown event kinds;
    • wrapper key and count edits.
• Rejected under the strict reading only: one edit, as Lean's Admissible
  intends.
• Clause weakenings. verify.py weakens each of the checker's 32 clauses
  alone and re-runs all 62 pinned inputs. 31 of 32 change a pinned value.
  The survivor is implied by the next clause and is pinned.

Pre-PR review. A three-lens review (proof, verifier, claims) returned
ship-with-fixes. It found mutant Z, which showed the earlier "forbid scalars in
adapter phases" fallback was insufficient. It also asked for the added
controls, the complex-supplier scoping, the credit corrections and the (b)
reframing. All are applied. Tested on Python 3.12.15.

Credit

• Lemma G / Lemma A Lean packages: DreamingOfClouds (Lemma G of #484: clean proof and Lean 4 formalisation of its core #509, Lemma A of #484: the realization of paid wrappers and spectators, proved in Lean 4 #516, and Complex supplier b ≈ 1.327·10⁻³ (+4.7%) on whole-residual hosting: shared-donor kernel and entrance gauges with paid residual wrappers (conditional on two lemmas) #484's
  Lemma G stage and lg_phys.py).
• HPE Lean packages: jeremykothe2 ([Lean] Hyperplane-ended helpers: Lemma A with an arbitrary terminal frame (no κ claim) #593) and DreamingOfClouds ([Lean] Hyperplane-end helpers: multi-gate cleanup tails and the cold specialisation (stacked on #593, no κ claim) #599).
• PR635 tools: jeremykothe2 (Conditional κ = 0.001636241501576388: h4a plus PR627's two factored jp8 cold ends #635). They adapt Split centres and source-basis reuse for conditional κ = 0.001120864952258278 #433 (icekylinx), building on
  κ = 1.048005508028206e-3: mutable-basis Hamming packets (≈2^-9.89814; conditional; complex +4.97%) #425 (Zhihao Chen / jacklightChen) and Conditional kappa 0.001391523459591829: partial-own factory, 92 pivots and asynchronous whole owners #514 (Dugongue). They include:
  • jeremykothe2's HPE changes (Conditional κ = 0.001609915765452068: hyperplane-ended helpers on the PR588 witness #591, Conditional κ = 0.001612719427075359: hyperplane-ended helpers with ck/atm3 dispatch #592, Conditional κ = 0.001614202339036103: 46 hyperplane-ended helpers per call via commuting-prefix cleanup #601);
  • DreamingOfClouds' GK (Complex supplier b ≈ 1.327·10⁻³ (+4.7%) on whole-residual hosting: shared-donor kernel and entrance gauges with paid residual wrappers (conditional on two lemmas) #484) and COLD-HPE (Conditional κ = 0.00162128508944984: cold factory-scratch helpers end at 4-dimensional frames on the PR601 witness (+0.439%) #604) changes;
  • phases_full.py (icekylinx, vendored via Conditional κ = 0.001592517889315014: eight rank-five kernel pivots #558, eumemic);
  • clifford_exact.py (Direct delivery with 504 helpers for conditional κ = 0.001517760977820331 #531, icekylinx).
• Slot / T16 lineage:
  • rohanarun (Conditional κ = 0.001662039077758742 — U10 (two new triangle-hybrid slots) on PR942's T37 owners #987; Conditional kappa 0.001672660197076918: rare-pattern T16 exchanges #1094, the selected record);
  • jeremykothe2 (Conditional κ = 0.001671387264390146: all eight mutable-leaver all-K cells, U8 hybrids and frame re-optimisation on PR799's word #1005, Conditional κ = 0.00167166528321877: seven triangle-hybrid slots (PR987 search) on the k8 leaver word #1018, Conditional κ = 0.001672081255752945: sixteen-replica owner controller on the seven-slot k8 word #1022, Conditional κ = 0.001672654541898561: improved T16 owner packing on the seven-slot k8 word #1087);
  • Hao Yan / FanPUYen (Research: T16 owner concentration raises conditional κ to 0.001661642255531641 #858 controller).
• Seven-slot word bytes: Ali Romman.
• Prefix-norm corollary: Gareth Davidson / bitplane (Research audit: signed prefixes give 18/21-bit local bounds for selected PR1094 #1282, [Lean] Prove unitary prefix bounds on the existing Lemma G semantics #1309).
• Bit-supplier carryover note: icekylinx (Post-center rank-four kernels for conditional κ = 0.001584931111785787 #535).

AI disclosure: prepared by Sagar Thakrar with substantial Anthropic Claude
assistance, including explorer, judge, builder and reviewer subagents. No
independent human review. New work is Apache-2.0. The patched checker keeps its
original attribution, and its changes are marked.

Open next questions

1. Wire an HPE-aware extended-label check into the selected local replay, with
   X, Y and Z as negative controls. Alternatively, prove that a cheaper rule
   like adapter_rule implies H1.
2. State the cross-call data-phase composition in Lemma G's event model.
3. Re-run the Lean builds of e8-lemma-g-lean and hyperplane-end-lean. This
   package checks statement text only.
4. Formalise Lemma S against an extended Lean emitter model.

[Mister-Meeseeks]

Batch review at 6f34af34efa178cc2dbe0612c094a1bda591d332.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Extended-label proof over the pinned complex emitter, both complete selected programs and scalar shadows, with targeted label mutants and an HPE-aware copy of the historical checker. Mutable sources and cold hyperplane-ended helpers are treated explicitly. Lean is cited but not rebuilt; all-size compilation, whole-call hosting, cross-call composition and bit realization remain inherited.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.