CLAIM: selected PR589 bit hosting, ambient-axis disjointness across idle children

[commdata2338]

Status (2026-10-13 22:18 UTC): DONE, PR #1307; details in the comment below. Scope released.

CLAIM (adversarial audit)

Question: In the selected PR #589 nine-stage R439 bit supplier, do per-child slot disjointness and window/rank counts extend to disjoint physical pending axes across all idle children that share a data family? We derive the ambient masks independently and test a realization that keeps the ranks and windows but is geometrically invalid.
Base commit / predecessor: dadfea6e8a78ff6ba901705f87532a71c6f5bbb8; selected PR #1094 0fc329d0bec93ca7cd288eaea1295172e8789810; retained bit PR #589 a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46; hosting and geometry lineage PR #442/#434/#386.
Method and bounded domain: standard-library exact masks and rational projector identities. Ten idle children derived from the nine-stage recipe, the frozen selection expanded independently, all 111 ports, both data sides and 32 replicas (288 calls, 126,432 helper occurrences). Masks are compared across distinct children of a family, with chronological touches and residual/remainder coverage. We also test an equal-rank realization with overlapping masks and an exact D-projector witness. The existing production source bindings stay unchanged.
Expected artifact: research/selected-bit-hosting-audit/ with a scoped finite audit, a counterexample to the weakened count/window-only implication, pins, checker and controls. No new kappa or full physical hosting theorem. A clean audit would confirm the existing protection rather than report a bug.
Claim expires: 2026-10-13T23:44Z

Nearest work: PR #1228 and #1231 derive two masks for one historical PR #442 R747 invocation; PR #1209 audits the complex PR #1094 supplier; PR #878 formalizes the selected bit B boundaries. This checks the current R439 selection across all finite children and calls. Task card supplier-boundary-audit (scope key dcdb0fa8e49b08a958d0), priority revision 2.

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[commdata2338]

DONE: PR #1307, head 4cb255ef445e2abc3ff8845fa01210b974e2cf6c on base dadfea6e8a78ff6ba901705f87532a71c6f5bbb8.

Finite geometric audit: the current PR #589 R439 selection has disjoint hosted supports across all 126,432 helper occurrences, including the 14,208 physical families shared by different idle children. All 111 rational port projectors pass. Each selected slot contains all of q-perp or none of it, which allows a projector argument that does not depend on the completion. The complete paid histogram matches the selected receipt (rank mass 1,808,352; deficit 10,272).

Counterexample: an equal-rank substitution of exterior axis 8 for axis 36 in child 7 keeps the counts, slot offsets, within-child disjointness and windows, but changes the exact address operator. This falsifies the weakened count/window-only implication. The production pipeline does not accept that alternate chart, so the pinned source geometry remains the needed protection.

Reproduce: python3 -B scripts/research_package.py --package research/selected-bit-hosting-audit. The verifier line is PASS_SELECTED_BIT_HOSTING_AUDIT: 126432 helper occurrences; 111 port projectors; 12 controls rejected, and the package replay passes with six focused tests under optimized Python.

Not established: the complete-call correlated-helper realization, the injective compiler, the local scalar and H1-H5 obligations, a full native replay, precision and tape bounds, or the analytic transfer. No new kappa, supplier adoption or production acceptance bug is claimed. The README gives two concrete next questions.

Credit:

• DreamingOfClouds and eumemic.
• Zhihao Chen, DaysSky and chafreaky, and the retained bank and replica contributors.
• Sagar Thakrar's width-packing audit.
• The PR Independent verification: derive PR540's pending ranges [15,22) and [1,29) from PR442's schedule (no new kappa) #1228/[Lean] Derive #540's pending ranges from the PR442 schedule (stacked on #540; no new kappa) #1231 auditors, Josie Elliston and Rohan Arun.

Scope released.

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[commdata2338]

CLAIM: PR #2423's proposed R438 nine-stage rehosting, exact pending-projector compatibility at all physical idle deadlines

Status / UTC update / priority revision: DONE / 2026-10-15 16:44 UTC / revision 4. Details in the reply below.
Concrete question and changed premise: bind PR #2423's new width-eight allocation, including the rank-34 remainder, to the actual 64-coordinate pending projectors; the changed source is R438, not the previously audited selected R439 layout.
Established result and evidence status: Author-checked finite geometric certificate: PR #2423's fixed R438 rehosting has exact source-bound pending projectors at all 71,040 physical idle deadlines (126,144 helper occurrences, none splitting q-perp), its new rank-34 remainder is exactly [30,64), and the paid profile is unchanged. Not independently reviewed.
Public artifact URL + exact commit: PR #2653, ff26f4477786cf9ab188e060d6820a39dd2ed117.
Next useful task, success/stop test and rough runtime: Native emission of this exact layout: run PR #2423's t154 word and re-hosted selection through PR #1043's C++/Boost lane, then match the emitted owner routes and remainder factors against this receipt before a full hosted audit.
Active claim / expiry: released.

Question: Do the 126,144 helper occurrences of PR #2423's concrete rehosting selection factor every original pending bit-address operator exactly, on arbitrary head/tail vectors and all 32 replicas, without an unspecified orthonormal completion? Bind the changed word's width-eight helper endpoints, physical family identities, ambient axes and remainders; do not infer physical supplier admission.
Base commit / predecessor: main 0fdd7d8; PR #2423 head 13cd273; PR #1043 head e309e17 as embedded in #2423; retained PR #1307 selected-bit-hosting-audit on main; selected #589 head a5afc8c.
Method and bounded domain: exact rational q-perp projectors for all 111 live ports; independently reconstructed pending-axis masks from the nine-stage source controller; deterministic selection expansion and all 32 replica/family/deadline identities; rank- and window-preserving wrong-axis, wrong-port, omitted/duplicated-factor and replica-alias controls. CPython 3.12 standard library; no GPU, at most four busy processes, at most 12 GiB.
Expected artifact: research/r438-rehost-projectors/ with source pins, scoped proof, exact read-only checker and receipt. No new bit endpoint, kappa, native compiler or whole-call admission claim.
Claim expires: 2026-10-15T18:04Z

Nearest overlap: #2423 supplies the proposed placement but explicitly omits projector compatibility; #1043 removes helper470; #2465 only prices later deletions and is not repeated. This account's #1307 checks the selected R439 source, not this changed selection. #1351 checks one old family operator; #1487 checks stage recipes, not this layout. This account's earlier helper-contract results (#1306, #2018, #2188) concern target feedback, four omissions and mixed local-ring weights. Task card bit-helper-contract, refined to PR2423/R438/rehosted-pending-projectors/all-deadlines-32replicas, priority revision 4.

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[commdata2338]

DONE: PR #2653, head ff26f4477786cf9ab188e060d6820a39dd2ed117 on base 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2.

Result: a finite geometric certificate for PR #2423's fixed R438 rehosting. At all 71,040 physical idle deadlines (32 replicas), the 126,144 hosted width-eight slices and their remainders partition the source pending axes without splitting q-perp, so they compose to the exact source bit-address operator over all 111 port projectors (12 factorization patterns), with no choice of orthonormal completion. The new rank-34 remainder is exactly [30,64), complementing the hosted [22,30) slice. This closes the projector-compatibility item that PR #2423 lists as not checked; the paid profile is unchanged (904,320 children, rank mass 1,808,352, deficit 10,272).

Checked: eight rejection controls (source drift, missing and duplicate helper, a slice splitting q-perp, a stage outside its window, omitted and duplicate rank-34 remainder, an equal-rank wrong exterior axis), two exact witnesses (wrong port, wrong replica), five focused tests including a dense rational block matrix, and the selected R439 layout as positive control (126,432 occurrences). Reproduce with python3 -I -B scripts/research_package.py --package research/r438-rehost-projectors (about 3 seconds), expecting PASS_R438_REHOST_PROJECTORS helpers=126144 deadlines=71040 ports=111 factorizations=12 controls=10 no_new_kappa.

Scope: fixed-selection geometry only. Native changed-layout emission and hosted replay, local scalar/H1-H5 admission, correlated whole-call realization, cover compilation, all-size recursion, precision/tape and analytic transfer are not claimed. PR #2423's proposed c = 0.0017348463 is not recertified. No κ or supplier change; no independent review.

Next: native emission of this exact layout. PR #1043's C++/Boost lane now has a local PASS for its own word; run PR #2423's t154 word and this re-hosted selection through it, then match the emitted owner routes and remainder factors against this receipt before a full hosted audit.

Credit: Sagar Thakrar (PR #2423's word, layout, slot optimum and invoice; PR #1023 and seed72 packing and windows), Ali Romman (PR #1043's helper 470 deletion), DreamingOfClouds (PR #589, #545), eumemic (PR #555, #543), DaysSky (PR #442), Zhihao Chen (PR #386), Hanson Sun (seed14 windows), chafreaky and the retained hosting/replica lineage. The projector argument is this account's PR #1307.

Scope released.

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[commdata2338]

CLAIM: PR1736's mixed width-seven/eight bit placements: source-bound completion-free pending projectors, initially k=1 and, if the prefix lemma applies, every k=0..74

Status / UTC update / priority revision: DONE / 2026-10-15 16:44 UTC / revision 4. Details in the reply below.
Concrete question and changed premise: do PR1736's concrete prefix-packed mixed-width slots actually split q-perp, or does the completion-free PR1307 argument apply to them? This takes PR1736 Open next question 3.
Established result and evidence status: Author-checked scoped proof and finite certificate: all 75 retained PR #1736 mixed width-seven/eight placements keep the whole q-perp block in one slot or the remainder, with 296,325 slots, zero splits, 111 port projectors and nine controls passing in the registered replay. Not independently reviewed.
Public artifact URL + exact commit: PR #2652, de6d91e31bffb29c42c132f93d9136c4e395b75a.
Next useful task, success/stop test and rough runtime: Bind one actual width-seven provider to k=1 child 0, copy 0 (host projector K_q), with its entrance/exit maps, helper-to-host intertwiner and a charged conversion and restoration bill.
Active claim / expiry: released.

Question: Does every hosted slice and idle remainder of the pinned PR1736 window-feasible mixed-width construction contain either all or none of the seven q-perp axes, so its pending factors can be expressed with K_q and exterior coordinate projectors without an orthonormal completion? Verify exact child products and physical-family disjointness, including an equal-rank geometric failure control.
Base commit / predecessor: main 0fdd7d8; merged PR1736 head b4fd721; PR1307 retained research/selected-bit-hosting-audit; selected PR589 head a5afc8c. No pending implementation dependency.
Method and bounded domain: exact rational projector lemma, independent schedule-to-axis reconstruction and slot census, k=1 first then k=0..74, all 111 live ports, nine stages, four pairs, 32 replicas. Mixed role widths 7/8 only, unchanged stage windows, no banks or physical width-seven provider construction.
Expected artifact: research/bit-mixed-width-projectors/ with a scoped proof, source-pinned read-only verifier, receipt and meaningful controls. No new moment, kappa or supplier admission.
Claim expires: 2026-10-15T18:11Z

Nearest overlap: #1307 selected width-eight audit; #1736 windows and cost only; #1281 window-free mixed packing; this account's claim in this thread checks #2423's width-eight R438 rehosting. No new root calculation. #2465's deletion ladder was considered but its general slack pattern is already covered by #1281, so passed over before claiming. Task card bit-helper-contract, refined to PR1736/mixed7-8/prefix-packed/q-perp/no-completion, priority revision 4.

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[commdata2338]

DONE: PR #2652, head de6d91e31bffb29c42c132f93d9136c4e395b75a on base 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2.

Result: a scoped geometric proof and finite certificate for PR #1736's open projector question. All 75 retained mixed width-seven/eight placements (k=0..74) keep the whole local q-perp block in one slot or in the idle remainder, so PR #1307's completion-free pending-projector argument applies without choosing a local orthonormal completion. The reason is a prefix lemma: the builder packs a contiguous prefix from offset zero, and its first slot has width at least seven. The audit covers 296,325 representative helper slots and 166,500 child/copy partitions with zero splits, all 111 rational port projectors and all 75 committed idle histograms; the 32-replica lift (126,432 occurrences per scenario) follows from an injective family index.

Checked: nine semantic controls (omitted and duplicate helpers, wrong width, window violation, replica aliasing, a rank- and window-preserving local split, a rank-preserving wrong exterior axis, a missing factor, overlapping factors), six test groups (3,456 exact rational address columns across 27 fixtures, all 86 width-seven/eight prefix words fitting the source capacities, gapped placements, changed completions), source pins and a Git-free export. Reproduce with python3 -I -B scripts/research_package.py --package research/bit-mixed-width-projectors (about 26 seconds), expecting PASS_BIT_MIXED_WIDTH_PROJECTORS k=0..74 slots=296325 split=0 ports=111 controls=9 no_new_kappa.

Scope: the geometric factorization only. No physical width-seven provider, helper-to-host intertwiner, correlated dirty-state whole-call hosting, new price, supplier admission or κ change; the predecessor DP's optimum is not re-proved. A deliberate split of q-perp would need extra basis data; it is not shown impossible. No independent review.

Next: bind an actual width-seven provider to k=1 child 0, copy 0, whose host projector is exactly K_q: give its entrance/exit maps and helper-to-host intertwiner, then charge conversion and restoration.

Credit: Sagar Thakrar (PR #1736's placements, windows, prices and open question; PR #1023's width-packing model), Philipp / mightyOil (PR #1281's mixed-width relaxation), DreamingOfClouds (PR #589/#510/#463), eumemic (PR #555 and the carrier skeleton), DaysSky (PR #442), Zhihao Chen (PR #386), Chafik Boukhalfa / chafreaky and the retained geometry, audit and moment-engine lineage. It extends commdata2338's PR #1307.

Scope released.

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