Selected PR1094: exact single whole-helper relocation census

[Arham-Tahir64]

DONE — PR #1343, contribution head 489f9011862dcd53a7785e151d3af0a1cd08250a on main bce54fb3f895cbe5cd4c0eb477c3afeed100190f. Claim released.

Exact single-whole-helper relocation obstruction on the selected PR1094 map: 336,456,862 capacity-feasible distinct-bin role/destination pairs, counted in 20 exact rank classes; 19 would improve the idle moment for every real 0<a<1, and all 19 lie outside their actual strict destination windows. No legal strict improvement, new kappa, supplier adoption or global optimum is claimed.

The opt-in package research/frontier1094-single-relocation/ includes exact pins, proof, every candidate/window, and a real positive fixture whose improving inverse 39+9 -> 48+0 passes the retained owner audit. Registered CPython 3.12 replay and optimized 3.14 checks pass, with six new test groups, eleven retained owner mutation controls, source/receipt corruptions, read-only offline relocation, metadata and selected-record integrity. Geometry/baseline admission reuse Josie Elliston's PR1091 audit explicitly.

Not checked: neutral-then-strict paths, swaps, multi-role repacking, different orders/words, idle-axis transfers, native/controller/chart/invoice admission, endpoint repricing, full cold replay or hosted CI. A concrete next task is to filter the 32,872 capacity-neutral pairs by legality and enumerate strict second moves on the two changed bins. Full inherited theorem obligations remain.

Credit: Rohan Arun's PR1094, Jeremy Kothe's packing lineage, Josie Elliston's audit, Douglas Colkitt's composition, Hao Yan's controller and the retained word/supplier ancestry. Prepared for @Arham-Tahir64 with substantial OpenAI Codex assistance; no independent human review claimed.

Original claim:

CLAIM

Question: On the selected PR1094 owner map, can any single whole-helper relocation between existing bins strictly reduce the idle moment? Complete census, with all call times, helper widths and source-event windows fixed; source/destination offsets may compact to retain occupied prefixes. Classify for every real 0<a<1 using exact concavity, then enforce strict windows and per-call physical-family uniqueness.

Base: main bce54fb. Selected PR1094 audited head 0fc329d; geometry and independent baseline owner audit credited to Josie Elliston / PR1091; packing credited to Rohan Arun and Jeremy Kothe.

Bounded domain: 69,120 roles, 144 calls, 16 replicas, existing owner/child/port bins only. Excludes swaps, multiple role moves, changed words/orders, split helpers and idle-axis repartitions. This complements PR1240's broad packing ceiling, PR1254's fixed-profile comparisons and PR1276's idle-axis repartitions.

Expected artifact: one opt-in standard-library census with exact source pins and positive/failure controls, or a precisely scoped handoff. No supplier adoption or new kappa without full admission.

Prepared for @Arham-Tahir64 with substantial OpenAI Codex assistance. Claim expires: 2026-10-14 00:55 UTC.

[bbMisk]

DONE — PR #1617, exact contribution head 536bc90ea2de310e0e08d2cb65f7add1d9de92b5. Claim released.

Complete neutral-then-improving two-relocation census on selected PR1094: 3,484 legal neutral prefixes, 78 improving sequences and 78 final bin allocations. Every attaining path has the same idle-profile delta -H1-H7+H8, uniformly for 0<a<1. All paths are listed in the receipt. PR1343's one-move exclusion and PR1407's prior longer constructions remain explicitly credited.

Local registered replay passed: two enumeration methods agree on all paths; a direct small-domain oracle checks 2,013 initial maps (147 positive); the retained owner auditor checks all 156 intermediate/final maps; six test groups include inherited and new fault controls. Twenty repository workflow tests and selected-record integrity also pass. Both enumeration implementations were written by one Codex agent; geometry is explicitly reused, with no independent human-review claim.

The package began at main ebedc089 and was rebased onto 81e81af6 without changing any live input. Priority revision 3 and the retained packing cap were checked separately. Final overlap at 2026-10-14 04:04 UTC covered 745 open PRs and 250 Discussion/body/comment records, with complete pagination and no warnings; this is a body/note search, not a novelty proof.

No new kappa, full native/controller/invoice replay, supplier adoption or all-size theorem is claimed. Reproduce with python3.12 -B scripts/research_package.py --package research/frontier1094-neutral-pair-census.

---

Original claim:

CLAIM — exact neutral-then-strict two-relocation census on selected PR1094.

Base: ebedc08. Task: selected-packing; chooser nonce 3e0b262946823b22781a11be3342622f, scope refined. I will enumerate every legal histogram-neutral whole-helper relocation followed by one strict improvement, with widths, calls, source-event windows and original child bins fixed. Affected bins may be repacked into occupied prefixes.

PR1343 (489f901) already excludes improving single relocations. PR1407 (d8640f5) already constructs useful neutral paths. This investigation credits both and asks for a complete two-move census, with exponent-uniform comparison and controls, rather than another seeded path search. Geometry and baseline admission will explicitly reuse Josie Elliston's retained owner audit; the enumeration is separately implemented.

Expected artifact: one scoped standard-library package or a precise handoff; no supplier adoption or new kappa without full admission. Time cap: remainder of one 60-minute session. Claim expires 2026-10-14 05:50 UTC. Prepared for Hanson Sun (@bbMisk), with substantial OpenAI Codex assistance.

[navinor]

DONE / released — Aaron Wang / navinor, with help from chatgpt.

Status: completed, priority revision4. Author-checked exact finite result,
separately corroborated by read-only AI review; not maintainer or human review.
Public artifact: #2145,
head d8d6244df98271c91f57de1e95d0599226839837, package
research/selected-crosscall-rank8-cycle/. All 21,886 supported cross-call
coalescing cycles are strict-window blocked; two constant timing failures
cover the entire domain. Full registered Python3.12 optimized replay and
four test groups pass, with both unchanged supplier budgets and bit surcharge
included. No supplier, full cold replay, global optimum or new κ claimed.
Next useful task: a different supported rank transition, not rerunning this
slice. The larger cross-call domain remains open. Original claim released
early; scope and reservation details are retained below as history.

Original reservation

Question: do any simultaneous cross-call three-role cycles on selected
PR1094's original owner map coalesce idle ranks {0,1,7}->{0,0,8} legally?
This takes the cross-call handoff in
#1873, narrowed to one
complete rank transition. Expiry: 2026-10-14T22:40Z.

Base 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, refreshed canonical main;
selected head 0fc329d0bec93ca7cd288eaea1295172e8789810.
Assigned incumbent-optimization / selected-packing, scope refined;
OS nonce 3474c3e21150f5db2b291dfc2989aac6;
catalogue scope key 2eb6f6918b10e182033b.

Domain: three existing whole-helper roles in three distinct occupied bins,
at least two invocation times; unique slack7 pivot anchors a directed cycle
A->B->C->A, both orientations included, cyclic rotations counted once.
Fixed scalar word, widths, calls/order, actual strict event windows, active
pair rules, simultaneous per-call physical-family uniqueness, and occupied
prefixes. Complete width/slack class prefilter then exact window/family join;
compact touched bins and run unchanged PR1091 audit on any attaining map.
Initial compute cap5minutes, joined-candidate cap1million; interruption is
partial coverage, never an exclusion. Independent toy direct-triple controls
check completeness and same-call vacancies. Approved bounded probe; no pivot.

Fully charged model delta is only -H1-H7+H8; by strict concavity it lowers
the idle moment for all0<a<1 if legal. Both complete supplier moments and
ceiling(local,73,896,9,64) will be recorded; no new physical fees waived.
Expected package: research/selected-crosscall-rank8-cycle/ exact certificate
and registered replay, or a precise handoff if no distinct result warrants PR.
No supplier/native/controller/invoice/outer admission or new kappa promised.

Overlap: #1790 is two-role
swaps, #1873 is same-call
3cycles, #1617 completes
neutral-then-strict relocations, and
#1407 is longer sequential
paths. The positive cycle in
#1154 uses a different word
and map. Fresh cached coverage388 openPRs /793 discussion records plus live
primary-source/hub follow-up found no matching cross-call census; not a novelty
guarantee. These predecessors keep credit. PR1094/Rohan Arun, retained
Jeremy Kothe/Hao Yan construction; PR1091/Josie Elliston audit; PR1240/Douglas
Colkitt ceiling/pricing. Selected frontier and frozen inputs remain unchanged.

[navinor]

FINDING / DONE — Aaron Wang / navinor, with help from chatgpt.

Artifact: #2145,
exact head d8d6244df98271c91f57de1e95d0599226839837 on base
0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, branch
research/donation-round4-navinor. Canonical claim
#1332 (comment)
is completed/released. Track/card incumbent-optimization/selected-packing;
nonce 3474c3e21150f5db2b291dfc2989aac6; scope refined, no reroll/pivot.

Exact finite result: no simultaneous directed cross-call three-role
cycle on original selected PR1094 coalesces idle slacks {0,1,7}->{0,0,8}
legally. Distinct occupied bins; unique slack7 pivot; both directions and
all supported widths; fixed word/calls/order/windows. All 21,886 arithmetic
candidates are blocked before active-pair or family restrictions:

• 17,567 cycles of types (7,8),(0,8),(1,7): C→A always tries event 181 of
  (stage,replica,helper)=(1,15,226) in the destination window (255,430).
• 4,319 cycles of types (7,8),(1,7),(0,7): A→B always tries event 417 of
  (7,14,296) in the window (-1,208).

The proposed -H1-H7+H8 moment delta is strictly favorable for all 0<a<1,
but no source candidate satisfies timing. This domain realizes zero of the
packing headroom. It is one slice of PR1873's cross-call handoff, not all
3cycles, a global packing optimum, a new mechanism, supplier or κ.

Evidence: primary type/indexed join and separate role-first direct
enumeration agree on all 21,886 candidates. Constant-block proof objects,
complete candidate digest, eleven unchanged PR1091 owner mutations and six
synthetic controls are in RESULT.json. A separate read-only AI review also
rebuilt raw source geometry independently, confirmed the counts/digest and
both window failures, and ran a 200-case family/cache differential check.
Its deadline-bypass finding was reproduced by a failing test and fixed;
the original bypass now rejects, confirmed by the same reviewer. No human
or formal-kernel review. Registered metadata/pins and full optimized replay
pass; four test groups, 7.024 seconds in the final pre-commit run.

python3.12 -B scripts/research_package.py --package research/selected-crosscall-rank8-cycle

Outputs PASS_SELECTED_CROSSCALL_RANK8_CYCLE_OBSTRUCTION candidates=21886 all_window_blocked direct_crosscheck=PASS owner_controls=11 new_kappa=NO
and PASS_REGISTERED_RESEARCH_PACKAGE ... outcome=completed.
Both complete unchanged supplier endpoint and next-tick signs pass exact
pricing checks, including the bit surcharge. The required
ceiling(local,73,896,9,64) reproduces a<0.001690054109089; PR1847's stronger
fixed-route ceiling is credited as context, not newly replayed or sharp.

HANDOFF: census another supported rank transition touching a slack7 bin,
including old slacks involving rank 3. First classify exact moment changes,
then join windows and simultaneous family vacancies. The blocker is that
general three-component changes need not be majorization-ordered. No larger
census or controller/native/invoice/outer/full cold admission is supplied.
All inherited realization/hosting/precision/tape/all-size/analytic/bit H1–H5
obligations remain; selected record and frozen inputs untouched.

Credit Rohan Arun/PR1094 and Jeremy Kothe/Hao Yan lineage; Josie Elliston/
PR1091 geometry/audit; #1873
same-call handoff; #1790
two-swap fixture; #1617,
#1819 and
#1407 distinct relocation
work; #1154 different-map
cycle; Douglas Colkitt/PR1240 ceiling; PR1012 coverage; PR1847 fixed-route
context; retained PR589/PR555 bit lineage. Apache-2.0. Substantial AI research,
implementation, writing and read-only review assistance disclosed.

[1337isnot1337]

RESULT / 2026-10-14 22:54 UTC — partial bounded join; claim released.

Correction: the preliminary type count and tuple counts in the claim were wrong because the slack update used the wrong sign. The correct directed update is new_slack[i] = old_slack[i] + departing_width[i] - incoming_width[i-1] (indices mod 4). On the pinned selected PR1094 map this yields 31 rotation-unique nonnegative type patterns that strictly majorize {1,3,7,7}; exact multiplicity counts are 226,561,920 tuples with distinct high-slack bins and 212,529,870 after requiring four distinct calls.

The bounded identity join stopped at its declared cap of 1,000,000 low-role pair checks. It processed the first 5/31 patterns in sorted order, with 14 distinct high-role pairs. All one million checks failed a strict source-event window; there were zero window survivors and no accepted owner-map witness. This is only a partial obstruction for the processed prefix. The remaining 26 patterns were not joined, and no whole-class impossibility, packing improvement, supplier change, or new κ is claimed. An earlier prototype false positive was rejected by the pinned owner audit and discarded.

The favorable fixed-word ceiling remains a < 0.001690054109089, κ < 0.001687202645325402, about 0.87% over the selected κ; no improvement is realized. Local reproducible handoff is on branch research/codex-loop-20261014-cycle25-agent, exact base 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, under research/selected-t16-four-cycle-seeda490466f/. Reproduce with:

python3 -m unittest discover -s research/selected-t16-four-cycle-seeda490466f -p 'test_*.py'
python3 -I -B research/selected-t16-four-cycle-seeda490466f/search.py --join-cap 1000000 --seconds 300 --out /tmp/RESULT.json

The original claim expiry has passed. This scope is released; the local handoff labels its incomplete coverage and exact source pins. No PR is submitted because this capped prefix does not establish the proposed full-domain construction or obstruction.