[Clear1nsight]

Change and mathematical scope

The exact historical pre-record-13 helper cut in PR #5612 has restricted dyadic capacity exactly one. Its existing published channel attains that ceiling, and the left module orthogonal to the known right column is zero. The result closes the nominated one-extra-channel question on this exact object; it earns no additional target, paid saving, P–T gain or kappa.

The object is cut 12626, frame 267, pivot 225, support $E=(57,81,92,224,225,234)$, with the full original same-boundary helper group $H$ and boundary frames 3 and 127. It is reconstructed after delayed preparation and exactly the first 12 published splits. No full-bank, global, final PR #5613 or changed-source ceiling is claimed.

The five stored original independent constraints give $L=Dq$ over $D=\mathbb Z[1/2]$, with $q=(1,1,1,-1,-2,4)=4a_0$. The known pair has $a_0b_0=1$ and $qb_0=4$, so capacity one is attained and the residual left module is zero. The right module has dimension 5; its pairing is $(1,1,-1,-2,4)$ with Smith factor $(1)$. README contains the short elimination proof and exact matrix. The general theorem and Smith implementation are credited to PR #5615.

Task and overlap

Publication base: 32890bc5de034ab8fc93ac88ead7279a6a416d04, an available ancestor distinct from fresh canonical main 6cf7a683f447b9f1e2333791907fd92be5009a63. Source head: faa9f6dbe6b8cc4a996d3edeca71823056453e1a. Released capacity head: d914f77d948ac377bdb9823daca93d08913c3fa7. Task complex-new-helper-inventory, scope changed to one exact restricted-support feasibility test and source-bound ceiling.

The fresh bounded curator gate found no matching exact public certificate. That is bounded overlap evidence, not a guarantee of global novelty. The newer PR #5627, head ed4dc88a09a7d201971f6603b8c2074e95dd9c32, repeats the same literal pivot 225/frame 267 $a,b,c,d$ witness at cut 12603 on a different nine-split, changed-boundary word. Neither that witness nor the split method is claimed here, and this historical ceiling does not transfer to that changed stage.

PR #5627 claims conditional $\kappa=.00310440546$, tested $.003104405465$, with 66,546 paid jobs and 12,958 target fields. Its hosted run 40247590574 was recorded successful; selected or independent admission is not asserted. It removes 72 H5 from both sides of the invoice, preserving the signed recursive moment. Its small gain concerns funding/headroom, not a new raw crossing. See the pinned comparison proof.

Validation

Root executed one bounded normal/-O pair under 150 seconds and 512 MiB. The pair completed in 9.576948022993747 seconds, with 60,301,312 bytes sampled peak descendant RSS. Entire result bytes match with zero fields excluded. Five algebraic controls reject and one positive saturation control verifies the full kernel basis; these are not physical source-mutation experiments.

• Request: 58ba6570966c3af66822dca90d78a815c3d73bf7fa6fccef0b7a21e52b715994.
• Stage: 0ba81142bc47457490996c88d88c74849c7648922ff696e496f95bfb7afcf801.
• Result: ca4b71b20a3c1cf35aa0985cb6d4aeed05385bceaf66f1c1a5d5e8e21ad5db90.

The stage has 747 public inputs and 25,492 events. Its actual complete invoice is 66,690 paid jobs and 13,030 targets. The published one-channel comparison has 13,048 targets; the 13,066-target optimistic second-channel comparison is unrealized. All chart, empty-owned, endpoint and known-pair gates passed before the restricted capacity calculation.

Reproduce: python3 -B scripts/research_package.py --package research/p104-record13-capacity-ceiling. The portable wrapper retains all 49 original pins, 42 external inputs and the complete 24-file reconstruction export. It changes no checker or imported algorithm and executes only v2. The static v1 revision remains unrun provenance. Static v2 review and a post-result direct proof are preserved, without claiming independent numerical, human or formal acceptance.

Root portable qualification passed: metadata and source pins; eight custody rejections and one unchanged positive path in each mode; registered normal/-O replay in 10.072604689004947 seconds with 92,237,824 bytes sampled peak RSS; and exact committed bytes/source ancestry for all 97 package files. The relocated, read-only, Git-free optimized replay passed with an empty PATH in 4.727409606988658 seconds, using 65,236,992 bytes sampled peak RSS. All 98 exported files remained byte-identical and read-only. No retry, cap increase or scientific source revision was needed.

Public head: 5062af108566f765f753e83e8ba8ca4dd6711220, tree 738bbf296d81f5e165aa871b244ee561088252a6. The GitHub-created contribution and locally checked commit have the same complete tree and base; their commit identities differ. The frozen README records the preparer's unrun status; these are the subsequent root receipts. This is portable reproduction of the same restricted certificate, not independent physical/native admission.

Credit

Credit Ali Romman for PR #5599, PR #5602 and PR #5615; flyingviper for PR #5612 and PR #5608; Hexapode for PR #5565; and the retained source-word, private-word, controller, compiler, native, precision and analytic lineage. Rank and Smith-normal-form mathematics is classical. The bounded source binding, qualification, static proof/review and portable packaging were prepared for Chris R/Clear1nsight with substantial OpenAI Codex/Astra assistance. Apache-2.0 notices remain intact.

Open next questions

No further construction is justified on this unchanged $E_6$ interface: the published channel already exhausts it. A larger support, another cut, helper group, source or changed boundary is a fresh object requiring a new source-bound nomination and ownership gate. This result authorizes no next scan. Independent human/formal review of the five-row proof and stage binding remains welcome; no ordinary cap, native all-width admission, full compiler/outer/BIT conjunction or multiplication theorem is claimed.

[Clear1nsight]

1. Research discussion / PR / artifact: proposed research/p104-record13-capacity-ceiling, a focused source-bound restricted ceiling. Public fork commit: 5062af108566f765f753e83e8ba8ca4dd6711220. Upstream PR #5632; the source witness belongs to PR #5612, and the released general capacity method belongs to PR #5615.
2. Exact commit: contribution 5062af108566f765f753e83e8ba8ca4dd6711220, tree 738bbf296d81f5e165aa871b244ee561088252a6; source faa9f6dbe6b8cc4a996d3edeca71823056453e1a; theorem d914f77d948ac377bdb9823daca93d08913c3fa7; available ancestor base 32890bc5de034ab8fc93ac88ead7279a6a416d04; fresh canonical main 6cf7a683f447b9f1e2333791907fd92be5009a63. Stage SHA256 0ba81142bc47457490996c88d88c74849c7648922ff696e496f95bfb7afcf801.
3. What is established: exact pre-record-13 cut 12626/frame 267, $E=(57,81,92,224,225,234)$ and full original $H$ have $L=D(1,1,1,-1,-2,4)$, right dimension 5, unit Smith factor 1, total capacity 1 and residual capacity 0. The existing channel already attains the ceiling. The actual stage is 747 public inputs/25,492 events, with complete paid/target counts 66,690/13,030. No additional channel or P–T gain is earned. Complete normal/-O result SHA256 ca4b71b20a3c1cf35aa0985cb6d4aeed05385bceaf66f1c1a5d5e8e21ad5db90 matches; five controls reject and one positive saturation control passes.
4. What remains uncertain: no full-bank, global, final PR #5613 or current PR #5627 transfer is supplied. The latter repeats the same literal witness at a different cut 12603 on a changed nine-split word; its conditional .00310440546 claim is not selected or independently admitted. No new physical target, native all-width, ordinary-cost, compiler/outer/BIT or full kappa admission follows. Portable registered normal/-O, exact committed bytes/source-history and relocated read-only Git-free export passed; these checks reproduce the same certificate.
5. Smallest useful next task: stop construction on this unchanged $E_6$ object. A different support, cut, helper group, source or boundary needs a fresh exact nomination and ownership gate before any new science; there is no automatic next scan. A separate human/formal review can inspect the five-row elimination and source binding.
6. Reproduction command and expected runtime: python3 -B scripts/research_package.py --package research/p104-record13-capacity-ceiling. The original pair took 9.576948022993747 seconds with 60,301,312 bytes sampled RSS. The registered portable pair took 10.072604689004947 seconds (92,237,824 bytes sampled RSS); the optimized read-only Git-free replay took 4.727409606988658 seconds (65,236,992 bytes). All 98 exported files stayed unchanged; each isolated child is capped at 60 seconds/512 MiB under the 150-second serial root guard. Root qualification is complete; no new scientific object was run.
7. Predecessor credit: Ali Romman PR #5599, PR #5602 and PR #5615; flyingviper PR #5612 and PR #5608; Hexapode PR #5565; all retained source-word/private-word/controller/compiler/native/precision/analytic contributors; and classical Smith theory. Chris R/Clear1nsight qualification, static review and packaging used substantial OpenAI Codex/Astra assistance. No independent human/formal acceptance is implied.