Audit (no κ): #2297/#2041 k-group port decoders are not scalar decoders — 6,608 parity-forced forbidden entries; k=5 needs a diagonal rank-112 map; 2-integral floor 554/334 exceeds every saving threshold

[thakrarsagar]

Audit / scoped negative result (no κ). Recursive-interfaces track, card coverage-law-change, seed 51.

#2297 (five-dimensional port groups, u=5) and #2041 (three-dimensional, u=3) each prove an exact F2 factorisation of the label pairing B0_ij = q_i·q_j and use it as the decoder of the k-unpaid endpoint. Merged #1889 showed this step is invalid for #1825's paired planes, and philippeVV ruled that the masked identity is the target for arbitrary label subspaces (Discussion 1587). This package replays both pinned certificates against that masked scalar identity.

	#2297 (k=5)	#2041 (k=3)
F2 identity Σ terms = B0 (positive control)	reproduced	reproduced
free ordered pairs under the group mask	0 (dim E^⊥ = 4 < 5)	102
literal lift: forbidden nonzero entries (parity-forced)	12,281 (6,608)	11,755 (6,608)
dirty source columns failing	112 / 112	112 / 112
rank of any valid scalar decoder vs published terms	≥ 112 (diagonal) vs 16	≥ 99 vs 11
2-integral floor Σ dim E_i (philippeVV's Theorem 1, port-space pricing)	554	334
zero-saving threshold (uniform u / exact)	497.8 / 492.4	298.7 / 296.9
incumbent tie (ceiling.py, child ranks 1–9)	455–460	256–261

Counterexample. Target port 0 (q=11) and source port 7 (q=21) have q_0·q_7 = 1. With target 0 dirty at 11, the literal coefficient moves it to 12 (#2297) or 14 (#2041); a valid endpoint must leave it at 11.

Consequence.

• Neither Research five-dimensional port decoder for P112 #2297's charge 118, its 157-unit allowance and its favourable a=1/99 screen, nor Research: exact tri-plane factorization for selected P112 (no new kappa) #2041's charge 85, certifies a k-port decoder.
• No decoder without even denominators gives any saving. A saving needs even-denominator (2-adic) gain above about 56 (k=5) or 35 (k=3); tying the incumbent needs about 94 or 73. The incumbent line decoder's gain is 48.
• The direct per-port decoder reaches the 554 / 334 floor. Its frame distance is k per port, using icekylinx's lemma (notes/general-clifford-frames.tex). Its exact deficit is −Σ dim E_i / 9.

Concurrent #2528 (ywz65) audits a different #2297 premise: uniform five unpaid coordinates, giving an allowance of 157 → 152. It keeps the binary factorisation as the decoder; this audit shows that factorisation is not a scalar decoder. The two audits are complementary, and #2528's weighted dimension 277/56 agrees with the exact accounting here.

Reproduce (standard library, about 7 s):

python3 -I -B research/kport-group-scalar-endpoint-audit/verify.py
# PASS_KPORT_GROUP_SCALAR_ENDPOINT_AUDIT PR2297:forbidden=12281,parity=6608,rank>=112,floor=554 PR2041:forbidden=11755,parity=6608,rank>=99,floor=334

• Inputs and pins. Labels come from the selected archive member used by Audit: paired-plane binary factors do not establish the scalar endpoint #1889. Both CANDIDATE.json files are vendored byte-for-byte and pinned by commit, blob and sha256; ceiling.py is pinned. The computed receipt must equal the committed RESULT.json.
• Controls. One positive fixture is accepted. Five negative controls are rejected, including a single-defect control with exactly one failing dirty column.
• Checks run. research_package.py --check-only and the research unit tests pass on CPython 3.14.4. The registered Python 3.12 replay was not run.

Scope.

• Not disputed: the binary algebra, the cover searches, and C_E² = X_(⊕q).
• Not ruled out: decoders with even-denominator gain (philippeVV's Smith lemma is the framework), operator- or block-valued interpretations including a Construct exact scalar identity fit for paired planes #2126-style block identity priced by label support, and other contracts.
• Base: main 0fdd7d82d.

Credits.

• Cinna Davis: Research five-dimensional port decoder for P112 #2297, Research: exact tri-plane factorization for selected P112 (no new kappa) #2041, Construction: paired plane-port decoder on selected E8 labels #1825.
• adamgall: Audit: paired-plane binary factors do not establish the scalar endpoint #1889.
• ctoth: plane-port endpoint, naive per-port decoder, masked-set term count.
• philippeVV: masked-identity ruling, Theorem 1, Smith lemma.
• icekylinx: frame-distance lemma.
• jeremydiviney: Account for both native payloads in paired-plane identity blocks #2203.

Prepared by Sagar Thakrar with substantial AI assistance (Claude Code, Claude Opus 5.5). Three adversarial AI reviewers recomputed every count independently; their fixes are included. No independent human review is claimed. Apache-2.0.

🤖 Generated with Claude Code