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201 changes: 201 additions & 0 deletions research/fixed-caller-query-and-host-limits/LICENSE
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81 changes: 81 additions & 0 deletions research/fixed-caller-query-and-host-limits/PROVENANCE.json
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{
"upstream_files": [
{
"pr": 7000,
"head": "93effe2a135bf57b9e484cb630d8dd057159aec9",
"path": "research/shared-wire-split-composition/data/caller.json",
"vendored": "PR7000-CALLER.json",
"sha256": "3828d53e80ea97e8b866320f081af20b6b93bfebd58b95b56b85a7afe151af5e"
},
{
"pr": 7001,
"head": "d777f3a0aa2878bea0478918923dabcf86b9878b",
"path": "research/paired-query-only-bit/EFREE-RESULT.json",
"vendored": "PR7001-RESULT.json",
"sha256": "a46b6c6040f75184cab5467656811ad988c216e3bc8e44d595a5015b6e49620b"
},
{
"pr": 7002,
"head": "ed1a0a83dfe5d28db9a971bcfc1403bcdc03a49b",
"path": "research/connected-l18-root-caller/COALESCING-WINDOW.json",
"vendored": "connected7002/COALESCING-WINDOW.json",
"sha256": "86eb8ec70f899637089a741548659f433854fa3a8b2532937eb0679d89e8114f"
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{
"pr": 7002,
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"scope": "Normalized generated word. Replay checks all endpoints and the paid and helper histograms against the retained #7002 invoice. The hook uses the generated word as its input."
}
}
29 changes: 29 additions & 0 deletions research/fixed-caller-query-and-host-limits/README.md
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# Fixed caller query and native HOST repair limits

This follow-up to [PR #7098](https://github.com/CrocSwap/integer-mult-bounds/pull/7098) records three bounded results from the search for κ = .005 and ultimately .01. The results are about the specified normalized operators and tariffs. There is no new exponent claim.

## Results

- **Fixed central interval of #7000.** Between the first and last central QUERY in each branch there is no native J. The required operator difference at q and −q has rank four in each branch under the exact finite-field specialization. Any sign-even step contributes zero to the telescoping product difference, and each permitted QUERY contributes rank at most one. Four QUERYs per branch are therefore necessary to preserve those interval operators over the dyadic formal ring. All eight literal omissions change the operator. A separate prefix-transport screen found zero proportional source or range directions among 300 tested query/query and query/native pairs. That screen addresses the directions at their original prefixes.
- **Whole #7000 caller and the #7004/#7001 tariffs.** At unit stage weights the sign-relative map is −I on 38 roles in each branch. It requires at least 39 rank-one transvections. Eighteen native J calls contribute at most 36, leaving a global floor of three QUERYs per branch under the retained factorization. Even a hypothetical saving of one QUERY in each branch leaves the complex signed moment at approximately −462.571 at .005. The unchanged BIT moment is approximately −444.063. At .004 those values are −48.708 and −57.182. The two deletions are granted for pricing only.
- **Fixed-chronology #6824 HOST repair.** For the specified same-port rank-one repair, no insertion of up to two distinct-register coframed ADDs achieves the normalized endpoint on any of the 104 ports. Replay first checks the original endpoint and the paid and helper histograms. The first-order census excludes all direct X←Y sensitivity. The two-add expansion then forces the mixed term to supply this entry. If both intervening factors survive, the change has rank two. Exact cancellation and scratch reachability checks cover the remaining degenerate cases. This uses the fixed scalar chronology and endpoint.
- **Connected #7002 idle schedule.** The revised projector allocation reduces 181 idle jobs to 75 per port in the normalized 18-stage schedule, versus 76 in #7098. Exact commutation and both signed role-level controls are replayed. The additional saving across 104 ports is about 5.697 at .005. The composed F+H1 raw complex moment still encloses −814.90413 at .005 and −502.85167 at .004. A strictly positive raw .005 moment would require at least 815 further rank-one cost equivalents at fixed targets. Physical packing and ordinary work, BIT, precision and the outer reduction remain separate obligations.

## Reproduction

```sh
python3 -B scripts/research_package.py --package research/fixed-caller-query-and-host-limits
```

The three registered checks hash the inputs and replay the operator bounds, projector allocation and rational price checks, and the fixed-chronology census. They compare regenerated JSON with the archived receipts. The normalized #6824 word is a pinned generated input. The replay checks its endpoint and inventory directly. It does not regenerate that word from the upstream construction chain. These checks do not reproduce the complete physical suppliers or the conditional multiplication theorem.

For the 39-factor bound, rank of −I minus I first forces at least 38 factors. With exactly 38, their update directions must form a basis. In this basis only the first-applied transvection updates the first coordinate, and its square-zero condition keeps that diagonal entry at +1. All subsequent transvections leave that coordinate unchanged, contradicting −I.

## Open next questions

- Can a changed native macro supply more independent sign-sensitive directions? Start by certifying the full arbitrary-input operator of one replacement macro in both signs and inventory every paid step. Retaining the current two-shear macro leaves the global query floor.
- Can a changed entrance implement the HOST boundary within budget? Start with a new chronological frame path and recheck the full normalized word before lowering it. Two added coframed ADDs on the current word are excluded, and the concrete idle savings leave a substantial deficit.

## Credit

Rohan Arun with substantial OpenAI Codex assistance. [#7000](https://github.com/CrocSwap/integer-mult-bounds/pull/7000), [#7001](https://github.com/CrocSwap/integer-mult-bounds/pull/7001), [#7002](https://github.com/CrocSwap/integer-mult-bounds/pull/7002) and [#6980](https://github.com/CrocSwap/integer-mult-bounds/pull/6980) are by Jerry Chen / CubeJerry. [#6824](https://github.com/CrocSwap/integer-mult-bounds/pull/6824) is by DreamingOfClouds and retains the native verifier and constructive lineage credited upstream. [#7004](https://github.com/CrocSwap/integer-mult-bounds/pull/7004) is by ToikY. See the vendored notices and exact inputs in `PROVENANCE.json`. Apache-2.0.
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