research: sharp P104 consumer threshold and six/seven/six caller format

[Clear1nsight]

Change and mathematical scope

PR #3609 supplies an actual entrance completion, but its named consumer still fails and its arbitrary-grid caller format was unspecified. This focused package closes two local proof obligations without claiming a physical supplier or changing the selected frontier.

• Sharp conditional budget. For PR3609's actual full dual and the retained forward, every integer rank-unit deletion allowance at most 425 per dual fails for every integer pair count and every finite number of fully paid auxiliary banks in the named all-pair law. Strict convexity and outward rational intervals prove the all-pair statement. An abstract 426 rank-one deletion passes at seven pairs and a=1/596, but has only 4.557071360876949 total rank-normalised cost units of slack. Four added units pass; five fail. No deletion network is constructed. The full criterion includes replacement profiles, genuine coverage relief, and added cost.
• Sharp six / seven / six format. Arbitrary original-grid physical inputs need six added fractional bits for the 1,238-event entrance, seven for the 5,265-event exact execution, and six for all 358 final outputs. The proof combines Gaussian-ideal valuation, the exact scalar/frame trace, a literal 36-event necessity cone, and the required X0 endpoint. Sufficient stored and literal-scratch bounds are 3296H and 6592H, with signed widths b+20 and b+21 for the full word. This is one-layer refined ideal execution, not a coarse-grid rounded identity or all-depth theorem.

The calculator separately reproduces PR #3605's current T740 root bracket and PR #3574's 1126/1127 hosting separator. Their provider contracts are kept distinct from P104. Neither historical physical release is replayed here.

Package and proofs are in research/p104-caller-feasibility/. The remaining obligations are an actual producer, legal owners and writable/restored Y, zero stock, routing/control, a complete affordable invoice, and recursive admission. Unknown costs are not zero.

Task and overlap

User-assigned continuation of the PR3609 handoffs, recorded as changed scope under the unchanged p104-side-correction card, priority revision 6. Claim.

Frozen main and pre-submission fetch at 09:58 UTC remain 20ecf2891d80b5acf18d980b2164fb44ea7faa90. All checked guides and the selected record are unchanged. Entry coverage included all 330 open PR metadata/body records; the update-window refresh covered all eight PRs updated since 09:16, plus fresh P104/twiddle claims. Coverage excludes arbitrary historical diffs and all Discussion pagination.

Primary source is PR3609 at 13f974dae4af66027afb01f3ab42df9e830c2e90; comparisons use PR3605 at 3efbb5de06a49ffeea6684482f2d3fe48cdca3fb and PR3574 at eb11cd484c23990c250bdc67ae61829ebae35536. All 24 retained input files and source-specific notices are exact. Their public origins remain in the component manifests; this PR's source-retention ancestor makes clean-checkout provenance self-contained. No predecessor package is modified.

Validation

Public head 5a4354c669dc05a9368f58321b1951ebac36d80d, tree f35c792cb220b130646e783310c4c1b128495c69, changes only 39 files in this package. Local CPython 3.12.14 evidence includes registered normal/optimised commands, strict source/typed-receipt checks, disposable CLI mutations, and separate same-session proof and Git-free implementation review.

GIT_NO_REPLACE_OBJECTS=1 python3.12 -B scripts/research_package.py --package research/p104-caller-feasibility
GIT_NO_REPLACE_OBJECTS=1 python3.12 -B scripts/check_research_commit.py --package research/p104-caller-feasibility --check-source-history

Exact public commit bytes and declared-source ancestry pass. Two official exports are identical, SHA256 6318df0f60594c61778d474473687334a0f5de94abcfd44f346bbaf543a1455f, 972,800 bytes. Actual Git-free normal, optimised, and CLI-control runs all pass; all 40 exported files, including the export receipt, preserve bytes and modes. Consumer and physical receipts are respectively 21183cc7bed0aacfcac41345a39382ac993175ea27c98b086d9b8f733ee192fe and 9ce25af396a2f76a69f32409b3371e8a35ba4d912e9992535579ccfe4b7c3a0b.

No historical full-native census, full selected replay, production physical caller, formal proof kernel, or independent human acceptance is claimed. Hosted CI will be reported only after its actual result.

Credit

Credit Jose Manuel's consumer insight, Vasek's PR2744 audit, Nick Petalas's all-pair law and PR3462/3469/3416 lineage, Hiroki Kumazaki's projection, ywz65 and Arham Tahir's original physical inputs, the retained Newton/compiler/precision contributors, and Dumas and Grenet's earlier dirty-accumulation method. The stronger T740 construction remains Ross Richardson's work; PR3574 remains jwr's work with its native-channel and budget lineage. Detailed exact-source attribution and notices are retained.

Clear1nsight with substantial OpenAI assistance from a root agent and three concurrent specialists. New work is Apache-2.0. Same-session independent checks are described by their actual scope.

Open next questions

TASK.json supplies the structured handoff. Reopen P104 construction only with a realised changed profile or genuine coverage change, its actual source/return contract, and a favourable whole bill. A named caller must meet the proved formats and pay every remaining owner/conversion/routing/return cost. A separate audit of PR3605's complete release is justified by its stronger arithmetic candidate, without transplanting it into P104.

[Clear1nsight]

Publication verification complete

Public head 5a4354c669dc05a9368f58321b1951ebac36d80d and complete tree f35c792cb220b130646e783310c4c1b128495c69 are verified. The PR changes only the 39 declared package files. The committed-byte/source-history gate authenticates main 20ecf2891d80b5acf18d980b2164fb44ea7faa90 and this PR's unchanged-source ancestor 35cf06a9d35b20701550b5517f4d69afd43c0ca7.

Hosted workflow 39118460473 completed successfully on 18 October 2026 at 10:17:36 UTC. Both planning and package replay jobs pass. The actual checkout was GitHub's preview merge fd7f64472b3866fbcc5c0738aaa80afbf51871c5, with parents main 20ecf28 and this public head; its complete tree equals the head tree. Hosted CPython 3.12.15 ran the declared normal, optimised, and physical CLI-control entries, with both scientific/joint PASS sequences and PASS_REGISTERED_RESEARCH_PACKAGE research/p104-caller-feasibility outcome=partial. The final tracked working-tree diff check passed. This workflow is not a separate source-history or export gate.

The separately executed official committed-source export/check passes. Two exports are byte-identical at 972,800 bytes, SHA256 6318df0f60594c61778d474473687334a0f5de94abcfd44f346bbaf543a1455f. Actual Git-free normal, optimised, and physical-control commands pass, preserving all 40 exported file identities and modes, including the export receipt. Consumer and physical scientific receipts remain 21183cc7bed0aacfcac41345a39382ac993175ea27c98b086d9b8f733ee192fe and 9ce25af396a2f76a69f32409b3371e8a35ba4d912e9992535579ccfe4b7c3a0b. Separate same-session agents reviewed the mathematics, full-copy replay, and hosted logs.

The result remains a sharp conditional budget and one-layer finite-format contract. It does not supply a realised 426-deletion network, an actual physical caller, legal owners/routing/zero stock, a complete affordable invoice, recursive admission, or independent human/formal acceptance. The named retained P104 model remains a stopping screen. Unknown charges are not zero; the selected frontier is unchanged. The complete TASK.json handoff and predecessor credit remain in the package.