[1337isnot1337]

The coherent-frame route left open by PR4966 also needs scalar-gate compatibility. A shared potential commuting with an unchanged dyadic-unit ADD on arbitrary inputs must be additive. The independent source audit finds such an ADD on every one of the 1,002 active frames in each retained round-three orientation.

The package includes a written proof, exact reversible nonlinear and unitary-equivariant counterexamples, 2,004 source-event witnesses, and the paid graph's 2,297 fundamental closed-walk tests per orientation. Those cycle counts identify obligations; they do not show failures of a particular realization. This is a boundary theorem for the gatewise coherent-potential recipe, not a general exclusion of correlated-error implementations or a new κ.

Yiyang (@Lyy-iiis) supplies PR4966's same-realization inverse construction and independent-error precision census; Cao Yifan supplies the actual round-three word and its retained predecessor lineage. Nick Petalas's related binary symplectic graph transport work is credited. The exact pending predecessor proof is vendored with commit/blob/SHA256 pins; the scientific replay imports no predecessor implementation.

Validation on Python 3.12.3:

• Isolated normal and optimized source/certificate replays pass, including frame chronology, both persistent endpoint lists, owned-center macro separation, all frame witnesses and five specified rejection controls.
• Registered package replay passes with outcome=completed; metadata/source pins and committed-byte/source-history preflight pass.
• Canonical main and live open-PR/discussion overlap refreshed before publication. No selected cold replay, native physical suite, Lean build or full multiplication theorem is claimed.

The remaining task is an additive, fully priced coherent realization, or a changed scalar/caller argument with its own complete bill. See research/coherent-frame-additivity/PROOF.md and its Open next questions. Canonical investigation: #4611 (comment).

Prepared by Cinna Davis with substantial OpenAI Codex assistance in research, proof explanation, implementation, verification and writing. No independent human review claimed. Apache-2.0.

[jwr404]

Post-merge independent check of head acb28c0b. I used my own parser of research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz (compressed SHA-256 7679daa4…) and imported nothing from this package. Earlier I used the same word to recount #4966's census.

Census: both orientations reproduce exactly.

	forward	backward
events	21,449	21,449
active frames (scalar/climb/center/warp records)	1,002	1,002
frames with a distinct-register L→L ADD of unit dyadic coefficient ±2^k	1,002	1,002
paid occurrences (climb + center)	3,298	3,298
paid-graph components over active frames	1	1
non-tree occurrence tests (E − V + 1)	2,297	2,297
simple edges / cycle rank	2,855 / 1,854	2,855 / 1,854

Lemma. y = 0 gives cA(0) = 0, so A(0) = 0 because c is a unit. x = 0 gives A(cy) = cA(y). Then A(x+z) = A(x + c·c⁻¹z) = A(x) + A(z), which is additivity. The converse uses unique halving in a 2-torsion-free dyadic module. P(v) = ‖v‖²v is unitary-equivariant and bijective but not additive (P(2e) = 8e), as stated.

Not checked. I did not separately verify that each witness lies outside the owned-center macros; my count only confirms that every active frame has some qualifying ADD. Nor did I check the bijectivity premises that make the two witness fields independent.

This is an independent check, not acceptance, and κ is unchanged.

Reviewed by James Reed with substantial Anthropic Claude (Claude Code) assistance.

[Clear1nsight]

One exact loop evaluation for the open common-potential question, against #4983 head acb28c0b5708d0aee91e457050c973e3df476fa4:

• paid9896: helper352, frame0→85=[382];
• warp6275: X83, positive52, frame85→137=[45];
• inverse paid6276: Y126, frame137→0.

These are different roles and not a chronological program segment. The premise of a single A_f shared by all roles makes this a valid constraint loop. In exact source-frame semantics its holonomy is K52. Unchanged ideal paid and warp maps therefore require A0 K52 A0^-1=K52.

For the specific additive Gaussian proposal A_f=F_f D_A, take source portq=11 and D_A=∏C_a on the orthonormal transverse axes [13,14,7,16,32,64,128,256]. Paid-transition and dyadic-ADD equations hold, but the warp condition fails. SourceG52 is [1,2,4,16,392,128,162,68,401]; the canonical chirped native K has unsigned Pauli action (x,z)→(Gx,(G+G^-T)x+G^-Tz). It sends X1 to (1,264). The D_A action uses P=I+11·11^T, with P264=259, so D_A K52 and K52 D_A give X-address masks258 and1 respectively. They do not commute even projectively.

This is one candidate rejection, not a classification of additive potentials. No inference that additive implies complex-linear is used: the displayed Gaussian is an explicitly chosen complex-linear candidate. The actual signed frame guard holds here (G382=45); absolute phase and a modified warp's physical tariff remain separate. A Gaussian on truly new spectator axes commutes with K52, but cancels from all paid transitions and changes no invoice unless its nontrivial input boundary is actually supplied and priced.

Self-contained fixed reproduction, using only the public source object (fetch PR4983 first if needed):

python3 - <<'PY'
import gzip,hashlib,json,subprocess
H='acb28c0b5708d0aee91e457050c973e3df476fa4'
P='research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz'
b=subprocess.check_output(['git','--no-replace-objects','show',H+':'+P])
def need(t,s):
    if not t: raise ValueError(s)
need(hashlib.sha256(b).hexdigest()==
 '7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05','source')
a=json.loads(gzip.decompress(b)); p=a['programs']['forward']; c=a['canonical']
need(p[9896]==['climb','warp_retimed',352,0,85,1],'paid85')
need(p[6275]==['warp',['L',83],52,85,137],'warp52')
need(p[6276]==['climb','warp_retimed',126,0,137,1],'paid137')
G=next(w['G_columns'] for w in c['warps'] if w['op']==52)
def image(x):
    y=0
    for j,v in enumerate(G):
        if x>>j&1: y^=v
    return y
def dot(x,y): return (x&y).bit_count()%2
need(c['frames'][85]==[382] and c['frames'][137]==[45]
     and image(382)==45,'signed positive image')
q=c['ports'][0]; A=[13,14,7,16,32,64,128,256]; B=[q]+A
need(q==11 and all(dot(u,v)==int(i==j)
 for i,u in enumerate(B) for j,v in enumerate(B)),'orthonormal basis')
v=1; w=265
need(all(dot(col,w)==((v>>j)&1) for j,col in enumerate(G)),'G^-T v')
x=image(v); z=x^w; Pz=z^(q if dot(q,z) else 0)
need((x,z,Pz,x^Pz)==(1,264,259,258),'commutator witness')
print('PASS_ONE_UNSIGNED_COMMUTATOR_WITNESS: 258 != 1; phase/tariff not replayed')
PY

The canonical chirped-K formula used above is the actual Kop in research/warp-interface-20261022/verify_candidate.py at the same public head, lines78–81. This fixed calculation was run; it is not a new physical caller replay, general cycle census or κ claim.

The source calculation and fixed reproduction were separately checked by a second agent, including the literal signed Kop tableau; this is not proof-kernel or independent human acceptance. It is a distinct loop evaluation, alongside jwr404's separate census and additivity check above.

Credit Cinna Davis / 1337isnot1337 for the shared-potential boundary in #4983, Yiyang / Lyy-iiis for #4966's actual-inverse context, Cao Yifan and the retained native source lineage, Nick Petalas for related holonomy work, and James Reed / jwr404 and #4979 for the actual event-frame guard. Prepared by Chris R / Clear1nsight with substantial OpenAI Codex assistance from separate derivation and verification agents. No new κ or physical-cost claim.