[Clear1nsight]

Change and mathematical scope

For the unchanged released two-FULL/one-query source, an arbitrary admitted FREE input encoder mixing both original main banks still supplies at most 112 independent rank-17 main Gaussian jobs at sufficiently large widths. The written capacity proof permits mixed target ranks, rectangular readout, owned clean scratch and saved-original FREE bypass. It does not require an invertible t0 or input encoder.

Controls, encoder, readout, bypass and target entry/exit charts require fixed finite columnwise complete-product supports independent of width (or the retained canonical native target charts). Outer scalar coefficients may vary with width. Fixed weighted generators with unbounded width-dependent products are not covered. The nonlinear route projects the finite coefficient identity onto the full-Gaussian monomial double coset before evaluation, then bounds evaluated capacity through 112 fields; it does not assume an infinite algebra is faithfully represented.

The best granted target is 112 H17 + 112 H16 + 816 H9. It and the retained paid profile have rank mass 11040, while target ranks are at least 9 and paid ranks at most 5. Thus the optimistic complete recursive moment loses strictly for every 0<C<1; at C=0 masses tie. This is an exact inequality, not a root or numerical scan. No physical supplier/compiler/caller or κ improvement is claimed.

Task and overlap

task_id: joint-query-controller. Scope change: allow FREE encoding across both 224 main inputs and mixed Gaussian targets, replacing the earlier unchanged-feed/all-H17 demand. Retain the exact source, two FULL calls, 112-H1 query bank, first three control memberships, autonomous 816 helpers and their billed completion.

Scientific source is 4c0a359d88f22f05189d51f48387750b801a45d4, research/coded-native-caller; #5126 context is 0e8a13c251a9be1029114cda8b4194f05f3a23ec; Clifford predecessor #5160 is 7800589ce99d932bdb063aafca1f501f1a38626d. The independently reviewed nonlinear partition proof is retained as exact source bytes and is now published in #5210 at bddbdfab1cdba27ce69ce4a83d9c92a5d9e66bd8; it does not itself prove this changed-input result. Publication base is ec2780e8aeb1c88acaf5e9e470ef8c68e7fbbb6c, rechecked live by the sole monitor at 2026-10-23 12:48:22 UTC with all nine governing/selected blobs unchanged. Complete created/updated PR pagination through 12:45:32 UTC, cursor #5215, found no matching mixed original-input capacity result; this bounded check is not a novelty guarantee. No duplicate feed intake was performed.

Nearby #5200, historical head f6fa6d1930069ef52fce431250129819a3931767, studies two pure calls with arbitrary/noncommuting q_i and reversible controls over a fixed finite monomial-Clifford algebra, restoring independent dirty workspace. Our retained billed 112-H1 query bank is an extra paid nonmonomial resource beyond that pure-two-call model. Its theorem is neighboring scope, not a dependency or a transfer used for this mixed-target capacity result.

Changed source O, native/history/helper paths, extra observations, paid controls, growing/noncolumnwise supports and changed target contracts are outside the result. Held investigations are not consumed. The original reports, pre-target-chart correction, conceptual feedback, both author metadata versions and independent freeze are preserved unchanged.

The subsequent #5200 head c5a75152105119a91887a90aad6ed41e191d1d2f now explicitly includes joint routing across arbitrary many main pairs, including 112. No bank-size gap is claimed. Its pure two-FULL theorem still excludes this package's extra 112-H1 query bank and mixed target demand.

Validation

python3 -I -W error -B research/mixed-target-capacity-ceiling/verify.py
python3 -I -O -W error -B research/mixed-target-capacity-ceiling/verify.py
python3 -B scripts/research_package.py --package research/mixed-target-capacity-ceiling --check-only
python3 -B scripts/research_package.py --package research/mixed-target-capacity-ceiling
python3 scripts/check_research_commit.py --package research/mixed-target-capacity-ceiling --ref HEAD --check-source-history

Normal/O, registered replay, metadata/pins, committed-byte/source-history checks and official export pass. Fresh Git-free normal/O replays regenerate both full scalar receipts byte for byte and leave exported bytes unchanged. The hook preserves all 26 author/review evidence files, reads the unchanged independent checker and privately mirrors the author checker's original source layout. It verifies 5,824 source edges, the mode Gram identity, source-row conventions, profile/census arithmetic and four scalar controls. The 113th-target mutation only checks a mass inconsistency; it is not a machine proof of the capacity bound. Written independent review supplies the capacity and all-C mathematics.

Standard-library CPython 3.12; about 1 second per direct run. No operator/native/source solver, compiler/Lean or historical helper suite is run. Raw source CRLF/LF bytes remain exact. Finite costs, raw-dual construction, precision/storage, helper-completion implementation and compiler/outer obligations remain open and cannot overturn the already negative optimistic necessary gate. Hosted first run 39956794777 passed at exact contribution head e51bd17de70e32ff37c653d392c6b00f13d4b277, tested merge ae2626b55e5d5c88d411e914ba148d60c13fc68b against base ec2780e8aeb1c88acaf5e9e470ef8c68e7fbbb6c. Plan job 120424518737 passed 414 tests with 17 skips in 207.029 seconds and selected this package alone. Replay job 120426531073 ran both normal/optimized hooks: PASS_SCALAR_SOURCE_AND_MIXED_INVOICE_ONLY, 26 evidence files, 5,824 source edges, four controls and equal 11,040 rank masses; complete author and independent receipts matched the frozen modes. Registered-package and committed-input checks passed. This is scalar source/invoice validation, not an operator/native/compiler/all-width capacity-theorem or κ replay.

Contribution head: e51bd17de70e32ff37c653d392c6b00f13d4b277.

Credit

Root source-edge/capacity derivation, conceptual paper-worker feedback and separate independent mathematical/scalar review; Chris R/Clear1nsight packaging, with substantial OpenAI Codex assistance. Retain Dillon's equations, Dugongue/mdumitrean code/profile, actual normalizer authors, Cinna Davis/1337isnot1337, Cao Yifan/intqwq, zxv, Jacob Alan Sussman, Ryanson Jonathan and the native/helper/Clifford/compiler lineage. Apache-2.0 and original notices preserved. No independent human or proof-kernel acceptance is claimed.

Open next questions

A useful reopening must change a source/control/observation or paid-invoice premise and exhibit an actual negative-bank rank-17 channel or cheaper complete bill, with source access, ownership, target charts and all finite costs. Merely changing the FREE input encoder, eigenbasis or mixed lower-rank list inside this scope cannot pass. Changed O and held native/history lanes remain separate; this submission neither searches nor stops those routes.

[Clear1nsight]

HANDOFF

Research discussion / PR / artifact:
PR #5223, module research/mixed-target-capacity-ceiling, branch research/mixed-target-capacity-ceiling-20261023. Published through Browser; completed investigation RELEASED, changed-contract follow-up remains open. Nonlinear partition predecessor is now #5210 at bddbdfab1cdba27ce69ce4a83d9c92a5d9e66bd8. Nearby #5200, now c5a75152105119a91887a90aad6ed41e191d1d2f, explicitly covers joint routing over all 112 main pairs in its pure-two-call arbitrary-q_i dirty-stability result; this word retains an additional billed 112-H1 query bank, so no theorem transfer is used. Task ID joint-query-controller, changed scope allows both-bank FREE input encoding and mixed target ranks on the fixed released provider.

Exact commit:
e51bd17de70e32ff37c653d392c6b00f13d4b277; base ec2780e8aeb1c88acaf5e9e470ef8c68e7fbbb6c; scientific source 4c0a359d88f22f05189d51f48387750b801a45d4; context 0e8a13c251a9be1029114cda8b4194f05f3a23ec; predecessor #5160 7800589ce99d932bdb063aafca1f501f1a38626d. Reviewed report 11c0e2a0...; independent review aa573b3...; freeze 83903097... and files 102b6ba9....

What is established:
Under fixed finite columnwise complete-product support for controls, encoder, readout, bypass and target entry/exit charts (or retained native charts), at most 112 independent main rank-17 jobs at sufficiently large widths. Granting 112 H17+112 H16+816 H9 still loses the unchanged complete optimistic recursive invoice for all 0<C<1 by rank-mass/support gap. All 1040 original inputs and 816 helpers counted once, no dependent-query reward. Written proof review PASS; scalar source/invoice normal/O, registered, source history, committed bytes, export and Git-free read-only replay PASS. Hosted first run 39956794777 passed at exact contribution head e51bd17de70e32ff37c653d392c6b00f13d4b277, tested merge ae2626b55e5d5c88d411e914ba148d60c13fc68b against base ec2780e8aeb1c88acaf5e9e470ef8c68e7fbbb6c. Plan job 120424518737 passed 414 tests with 17 skips in 207.029 seconds and selected this package alone. Replay job 120426531073 ran both normal/optimized hooks: PASS_SCALAR_SOURCE_AND_MIXED_INVOICE_ONLY, 26 evidence files, 5,824 source edges, four controls and equal 11,040 rank masses; complete author and independent receipts matched the frozen modes. Registered-package and committed-input checks passed. This is scalar source/invoice validation, not an operator/native/compiler/all-width capacity-theorem or κ replay.

What remains uncertain:
Changed source O, native/paid/helper history, extra observations or paid controls, growing/noncolumnwise support, changed target charts/contracts, actual operator/raw-dual/precision/storage/helper completion/compiler/outer admission. Fixed weighted generators alone do not ensure the finite-product premise. Scalar hooks are not capacity or all-width theorem verifiers. No universal provider/decoder barrier, physical supplier, caller or new κ.

Smallest useful next task:
Name one changed premise that admits a genuine negative-bank rank-17 component or cheaper complete paid bill. Specify actual source access, arbitrary-input ownership, target chart program and full finite/recursive cost before construction. Do not repeat FREE encoder/eigenbasis or lower-rank target scans within this stopped model; respect held native/history investigations.

Reproduction command and expected runtime:
python3 -I -W error -B research/mixed-target-capacity-ceiling/verify.py, repeat with -O; about 1 second, standard-library CPython 3.12. Registered: python3 -B scripts/research_package.py --package research/mixed-target-capacity-ceiling. The wrapper authenticates 26 evidence files, runs unchanged scalar checks and compares full author/independent receipts to frozen modes. Actual 5,824 source edges and mode identity are scalar checks; the 113th-target control is mass arithmetic only. Package and exported bytes remain read-only; no full 414 helper suite or native/compiler replay.

Predecessor credit:
Dillon, Dugongue/mdumitrean, normalizer authors, Cinna Davis/1337isnot1337, Cao Yifan/intqwq, zxv, Jacob Alan Sussman, Ryanson Jonathan and retained native/helper/Clifford/compiler lineage. Root report, conceptual paper feedback, separate independent mathematical/scalar review and Chris R/Clear1nsight packaging; substantial OpenAI Codex assistance. Original licenses/notices preserved.

{
  "schema": "integer-mult-coordination/v1",
  "kind": "HANDOFF",
  "task": "joint-query-controller",
  "scope": "Completed fixed-provider both-bank input-encoder mixed-target capacity ceiling, including fixed finite complete-product support of target charts; changed-contract reopening only.",
  "base": "ec2780e8aeb1c88acaf5e9e470ef8c68e7fbbb6c",
  "expiry": null,
  "artifact": "https://github.com/CrocSwap/integer-mult-bounds/pull/5223"
}