[Clear1nsight]

Change and mathematical scope

This composite adds a historical exact PR #5569 price certificate and a separate current PR #5580 analytic transfer/count certificate. For exact PR #5580 head 6efa248cf456d6101d757e9d09ba29711d18a13a, the optimistic strict-single-use isolated-tail class needs at least 146 ideal exchanges per FULL with the permitted controller law, or 147 with the submitted 18-FULL caller retained, at $C=.0033$ and $C=.0033000005$.

The source paid change is +H2−2H3+H4 per FULL, with targets unchanged. The current certificate transfers the authenticated PR #5569 B/J intervals through B5580=B5569−gD, where gD=2H3−H2−H4. At $C=.0033$:

$$ 2.95302944896150557847079 < B5580 < 2.95303581796150557847087. $$

The count proof charges the productive rank loss of every isolated tail. Granted multiset witnesses use 94H4+52H5 for 146/n17 and 94H4+53H5 for 147/n18, with complete paid/target/surplus 60604/12079/712 and 64206/12814/760. Their complete raw slack is positive but below one global H1; an added uncompensated global H1 defeats these particular witnesses. Every query, whole idle and main bank is charged. Ordinary costs and compiler reserve remain separate.

This is an exact two-point necessary-budget/count result in an explicitly optimistic accounting class. It finds no actual 146/147 contacts, establishes no compatible source edits, constructs no 17-call caller, certifies no new funded κ and changes no selected result. Frame/endpoint/native, uniform precision/tape and complete compiler/outer premises remain open. Balanced concavity and the PR #5554 all-n implication are paper arguments, not a proof-kernel theorem. There is no larger-C or general P104 ceiling claim.

Task and overlap

Publication head c8b49410fb31d107d8c85d160ac5ca737c403231, tested tree 7e102b38d64ca97c43f0648ac8e275a3918ed111, directly based on 32890bc5de034ab8fc93ac88ead7279a6a416d04. Current upstream main 5e0052ca0aa3036a3afa8b0438927377c8d97d53 and guidance were checked separately at the 21:09 UTC prepublication checkpoint. Both package byte sets and source history were checked against the exact remote commit; 87 files are added.

Task scalar-to-moment, priority revision 7, changed scope. The original construction-gain gate is not met. The useful contribution is a current complete aggregate budget that prevents one attractive isolated contact from being mistaken for a complete .0033 route.

• research/p104-successor-price-gate: immutable 37-file historical PR #5569 certificate at head af9f091ac6f30c6eaacb9c27777bfbe2d0e5ffdf.
• research/p104-current-tail-count: separate current certificate for Ali Romman's PR5580, exact head 6efa248cf456d6101d757e9d09ba29711d18a13a.

GamingPuzzled's PR #5569/PR #5472 supply the predecessor handoff/cost lineage; zxv's PR #5554 supplies the all-controller reduction. PR #5585's native work is distinct from this price/count artifact. PR #5579's fixed-anchor owned holder obstruction is tied to its PR #5561/PR #5569 sources and does not transfer automatically to PR #5580's changed anchor. Constructive inventories remain outside this package. A broader A/B/C/D accounting family is under separate paper assessment, outside isolated tails; no resulting theorem or physical composition is claimed here. No exhaustive novelty claim is made.

Validation

Original current qualification: one root-reviewed normal/optimized pair, 0.905806529 seconds and 63,401,984 bytes sampled descendant RSS under the unchanged 150 second / 512 MiB serial guard. All 25 classified controls rejected and every scientific output byte matched, with zero exclusions. Result: f0ab2ed10f91a5acd76c1c6753d970c59e51e83c3d0b96fe8a6a3a6c3f80e9de.

The current wrapper preserves check.py, finite.py, request, inputs, both results and guard/log byte for byte. It authenticates every package/input byte, executes only the current finite certificate in an isolated private child limited to 60 seconds / 512 MiB, compares complete original output, then reauthenticates. It imports no price engine, source constructor or native module. Both source RESULT serializations and their explicit custody revision are retained; the historical derived hash was not silently replaced by the exact author-text hash.

Current-package commands:

python3 -B scripts/research_package.py --package research/p104-current-tail-count --check-only
python3 -B scripts/research_package.py --package research/p104-current-tail-count
python3 -B scripts/check_research_commit.py --package research/p104-current-tail-count --check-source-history

Expected marker: PASS_P104_CURRENT_TAIL_COUNT. The historical package retains its own registered reproduction command and evidence unchanged; its science is not rerun as part of this static preparation.

Portable current normal/-O registered replay passed in 1.714 seconds, sampled 88.61 MiB, under the unchanged 150 seconds / 512 MiB guard. Separate read-only Git-free optimized export with spaces and empty PATH passed in .705 seconds, sampled 63.70 MiB; all 51 exported files remained unchanged. Three custody corruptions reject before science in both modes. Metadata and 50-file exact committed-byte/history checks passed.

The historical component independently passed its portable registered pair in 1.912 seconds, sampled 73.89 MiB, and read-only optimized export in .906 seconds, sampled 48.84 MiB; all 38 exported files remained unchanged. Its 37 scientific-package files are preserved exactly. Local checks are scoped; hosted CI is pending at submission.

The three portable source/result/raw-serialization corruptions use --integrity-only and must reject before science. Export execution should use read-only files, empty PATH, an absolute interpreter and complete before/after file hashes. VERIFY.inputs=[] is intentional: all runtime source bytes are inside each package, so no machine-local path is declared as a repository input.

Credit

Ali Romman for PR #5580/PR #5579 and PR #5544/PR #5545; zxv for PR #5554; GamingPuzzled for PR #5472/PR #5569; DreamingOfClouds for PR #5561/PR #5553 and tooling; thu-nmrc for PR #5551; Matarener's endpoint contract; Clear1nsight's original caller/native/price audits; all retained P104/native/controller/compiler/precision predecessors. The historical numerical engine retains its original authorship and notices; the current certificate imports no engine. Paper analysis, finite qualification and packaging for Chris R/Clear1nsight used substantial OpenAI Codex assistance. Apache-2.0. Root agent code/proof review and two-mode reproduction do not constitute independent human/formal acceptance.

Open next questions

See both packages' NEXT.md, especially research/p104-current-tail-count/NEXT.md. A physical proposal must supply distinct actual helper/terminal-MOVE IDs, legal source windows/charts, ownership, compatibility, all changed paid/target/ordinary costs and compiler reserves. Aggregate ideal counts alone are insufficient. Broader A/B/C/D economics need a separately defined complete family and review. Independent human/formal review of the retained analytic implications is useful; no construction or contact scan is dispatched by this publication.

Current overlap/context: PR5590, head 627160c5e39501b69603c3a1e03bbfdc50a53a86, reports a sharp price floor for fixed scalar contacts and arbitrary frame paths on PR #5580. We have not replayed that proof. It is distinct from this explicitly optimistic inventory class, which grants contacts/attachments and does not assert physical realization. Discussion5575 now owns the specified commuting-ADD/order plus intermediate-frame optimization; Discussion5125 owns joint input/output basis splitting. A future constructive task must coordinate with those owners; this publication reserves no contact search.

[Clear1nsight]

Seven-field research handoff

1. Research discussion / PR / artifact: PR5592, atomic publication of research/p104-successor-price-gate and research/p104-current-tail-count.
2. Exact commit: publication c8b49410fb31d107d8c85d160ac5ca737c403231, tree 7e102b38d64ca97c43f0648ac8e275a3918ed111, parent 32890bc5de034ab8fc93ac88ead7279a6a416d04; current PR base 5e0052ca0aa3036a3afa8b0438927377c8d97d53. Current reviewed source PR #5580 head 6efa248cf456d6101d757e9d09ba29711d18a13a; historical source PR #5569 head af9f091ac6f30c6eaacb9c27777bfbe2d0e5ffdf.
3. Established: original root-qualified current analytic transfer and strict-single-use isolated-tail inventory minima 146 across permitted controllers and 147 with fixed 18 FULLs, at C=.0033 and .0033000005. Both complete optimistic invoices retain every paid/productive/nonlocal line. Current B17(.0033) is between 2.95302944896150557847079 and 2.95303581796150557847087. All 25 classified controls reject; original normal/optimized scientific SHA f0ab2ed10f91a5acd76c1c6753d970c59e51e83c3d0b96fe8a6a3a6c3f80e9de.
4. Uncertain / outside: actual 146/147 compatible contacts, physical 17-call caller, frame/row/native semantics, precision/tape and full compiler/outer funding, human/formal acceptance. No new κ, selected result, larger-C theorem or global P104 ceiling. PR #5585's native scope and the ongoing A/B/C/D paper assessment are distinct. PR #5579's old fixed-anchor obstruction is not automatically PR #5580 evidence.
5. Smallest useful next task: an owner-supplied aggregate source packet with one-to-one actual helper/old terminal-job IDs, protected reads, ownership, legal frames/compatibility and every recursive/ordinary debit. Meeting ideal counts alone is insufficient. Broader families need their own complete budget; no scan is launched by this artifact.
6. Reproduction / runtime: Python 3.12/stdlib: python3 -B scripts/research_package.py --package research/p104-current-tail-count; historical component uses its separately registered package. Original current pair .906 s / sampled 60.46 MiB; portable current registered pair1.714s/sampled 88.61 MiB and read-only Git-free optimized export.705s/sampled 63.70 MiB, all 51 exported files unchanged. Historical portable pair1.912s/sampled 73.89 MiB and export.906s/sampled 48.84 MiB, all 38 files unchanged. Three current custody corruptions reject before science in both modes; all 25 original classified controls reject. Both packages pass metadata, exact remote-commit byte and source-history checks (87 files total). Guards retain 150 s / 512 MiB. Hosted CI is pending at this handoff; local success is not human/formal acceptance.
7. Credit: Ali Romman, zxv, GamingPuzzled, DreamingOfClouds, thu-nmrc, Matarener, Clear1nsight and all retained P104/native/controller/compiler/precision predecessors; substantial OpenAI Codex assistance, Apache-2.0. Root agent code/proof review and Astra paper analysis are not independent human or formal acceptance.

The raw/derived source RESULT serializations and explicit custody revision are retained. Current context: PR #5590 reports a fixed-contact price floor; it is distinct from this favorable inventory relaxation and was not replayed here. Discussion5575 owns the specified commuting-ADD/frame work; 5125 owns joint basis splitting. Coordinate before any constructive follow-up. This completed finding reserves no source/contact search.

{"schema":"integer-mult-coordination/v1","kind":"FINDING","task":"scalar-to-moment","scope":"Exact PR5580 two-point analytic budget and 146/147 strict-single-use isolated-tail histogram minima; no actual contacts, no funded kappa","base":"32890bc5de034ab8fc93ac88ead7279a6a416d04","expiry":null,"artifact":"https://github.com/CrocSwap/integer-mult-bounds/pull/5592"}