[Clear1nsight]

Change and mathematical scope

Independently verify Ali Romman's PR5405 fixed equation-(1) FULL/QUERY prefix/suffix controller-family obstruction for 0.00302728825 <= κ < 1. The retained exchange reduction and strict discrete convexity on all nonnegative FULL counts reduce the fixed-exponent gate to C18>0, C18−C17<0 and C19−C18>0. A new directed-rational standard-library engine certifies all three signs. A separate normalized whole-invoice monotonicity proof extends the result through the stated saving interval.

This adds a small independent verification route to the author's unbounded-family ceiling. It supplies no κ gain, physical/native/compiler admission, global circuit optimum, formal-kernel proof, independent human acceptance, selected-record update or transfer to PR5402. Source equation (1), the fixed local profile and its controller-family interpretation remain explicit premises.

Task and overlap

Catalogue card independent-moment, priority revision 7, with scope_status: changed: the explicit donor task is an independent fixed-family ceiling check rather than a changed-mechanism κ improvement. Exact source PR5405 head 314b56a6c0056c2358538f072c6fde9d365be44d; canonical base 1ec1119972c9aefe42525172d07b332fcff81cb4. Root owns the canonical claim, live overlap refresh and publication.

The exact source proof blob is 5ad89d4ba1836d47798bdb856e3726c70a7b1922, SHA256 77dc9ce552be7dc9c9a32850c2f2cf0eff92cfe2e0a0e316db210a1667a8d32b, 10,029 bytes. The frozen 10,030-byte monitor representation is retained unchanged and checked as the source plus one LF. Git-free commit/tree/blob Merkle proofs authenticate the original source and canonical provenance. Original PR-head availability is separate from canonical ancestry; all consumed scientific bytes are self-contained in the new package.

Validation

Exact bounds are C18>0.000000014914967918767741908079, C18−C17<−0.271338621904872494155700553536 and C19−C18>0.022748156490424972863108432493, displayed as rationals over 10^30; finer endpoints over 2^256 are retained. The canonical minimum is at n=18. All-n coverage comes from the analytic exchange/convexity proofs, including the small-count junction. Numerical tiny-mask checks are controls, not the universal proof.

The engine independently derives paid/target histograms and exact equation-(1) coefficient identities, checks 456 tiny indexing cases and canonical counts n=0,...,5 and 16,...,20, and rejects changed bytes, reversed sign, omitted QUERY charge, omitted full-path targets and a changed paid-profile count. The favorable omitted-target mutant fails invoice identity. It imports no author engine and runs no original 10,290,000-state DP, native/cold replay or Lean.

The independent auditor found that v2 used assertion-based acceptance which would disappear under -O. Exact v1/v2 source, raw receipts and manifests remain preserved. V3 replaces all assertions with explicit require/raise predicates; normal/optimized scientific outputs and earlier numeric endpoints agree. The independent read-only audit and its exact freeze are retained. No raw receipt was silently repaired.

The registered wrapper authenticates immutable artifacts, actual Git Merkle origins and the LF bridge, exercises changed-source and forged-tree controls, reruns only the ~0.1-second independent arithmetic engine and compares every scientific field. Normal/O registered commands, committed-byte/source-history and Git-free export results are recorded in the final root handoff. Timing/environment are excluded from scientific equality. This package does not repeat the original expensive author replay. The sealed package commit is 0f98ba50cdc510fa9f6d1c2508bf84405ebbc801 (69 files); export SHA256 94b078333f1f1fdf0ae867e43afe36fe692c018a662b981307c93e9588320614 (1,505,280 bytes). The registered normal/O pair passed in 1.494 seconds with all 69 working inputs unchanged and empty stderr. Its initial Git commit omitted eight already authenticated raw log files because of repository ignore rules; final retention adds only those unchanged logs, with exact wrapper/inventory equality recorded in the mandatory execution-to-publication bridge. Final committed-byte/canonical source-history and export checks pass. The final Git-free normal/O pair passes with PATH empty, no .git, and all 70 extracted files unchanged (including transport receipt). The initial transport receipts/archive remain preserved locally.

python3 -B scripts/research_package.py --package research/controller-ceiling-convexity
python3 -B scripts/check_research_commit.py --package research/controller-ceiling-convexity --check-source-history

In a Git-free extraction run python3 -I -B research/controller-ceiling-convexity/verify.py and the same command with -O. --integrity-only authenticates frozen evidence without arithmetic replay. Hosted CI, maintainer review and selection are separately reported.

Execution-to-publication retention record (operational provenance, not an additional mathematical test):

{
  "status": "PASS_EXECUTED_BYTES_RETAINED",
  "registered_commit": "0f784cffd0842f147cabc6f408b7d049253272e3",
  "publication_commit": "0f98ba50cdc510fa9f6d1c2508bf84405ebbc801",
  "changes": [
    "A\tresearch/controller-ceiling-convexity/numerical/receipts/arithmetic-v1.stderr.log",
    "A\tresearch/controller-ceiling-convexity/numerical/receipts/arithmetic-v1.stdout.log",
    "A\tresearch/controller-ceiling-convexity/numerical/receipts/arithmetic-v2.stderr.log",
    "A\tresearch/controller-ceiling-convexity/numerical/receipts/arithmetic-v2.stdout.log",
    "A\tresearch/controller-ceiling-convexity/numerical/receipts/arithmetic-v3-optimized.stderr.log",
    "A\tresearch/controller-ceiling-convexity/numerical/receipts/arithmetic-v3-optimized.stdout.log",
    "A\tresearch/controller-ceiling-convexity/numerical/receipts/arithmetic-v3.stderr.log",
    "A\tresearch/controller-ceiling-convexity/numerical/receipts/arithmetic-v3.stdout.log"
  ],
  "integrity_same": true,
  "wrapper_same": true,
  "final_git_free_pair_pass": true
}

Credit

Preserve Ali Romman's PR5405 family, original ceiling/DP and owned/transposed local profile; Cinna Davis's controller/helpers; Cao Yifan's native source; zxv's interval/preflight/compiler/precision lineage; Chris R's controller screening and independent admission; Dugongue, Jacob Alan Sussman and all retained native/helper/compiler/analytic contributors and source notices. The root coordinator proposed the exchange and convexity conjectures; the sole Astra worker supplied the frozen analytic proofs. The successor worker independently reconstructed the invoice, rational arithmetic and normalized extension; a separate agent audited the proof and controls. New work by Chris R / Clear1nsight, with substantial OpenAI Codex assistance; Apache-2.0. No construction priority or human acceptance claimed.

Open next questions

A human or formal-kernel reviewer can inspect the exchange inequalities, small-count convexity junction and interval remainder derivations. Source equation (1) still requires separate binding to any claimed physical/native controller. Escaping the obstruction needs a changed provider/consumer contract, stage rank or idle law with a complete bill. This certificate grants no changed-profile PR5402 acceptance. Structured questions, relevance, first steps and blockers are in TASK.json.