# Root merge 2 of 3 — AMM qt1 improvement evidence

Credit: **Taylor (gtmcknight)** authored the solved Gaussian filter, qm tables, qm-spline research, replica and engine setup on which qt1 and these extensions depend. This merge combines all 25 supplied reports. It is a synthesis of their reported experiments, with arithmetic recomputed from their embedded data; it does not independently rerun the simulations or certify their behavior.

## Findings that survive the merge

- **Frozen TC-A has the broadest engine confirmation in this group.** All 16 confirmation shards reconstruct the same source hash, despite their a1/a2/b1/b2 names. Pooling their embedded per-seed differences gives **n=2,032, mean_diff=+0.440938878732, SE=0.012556656788** versus qt1. Candidate engine afterSwap peak is **211,164**, with zero reported OOG, and runtime is **21,102 bytes**. One 16-seed chunk is missing, not counted as a win or a zero. These are local engine observations, not a leaderboard result. [b14-a1s1]–[b17-b2s4]
- **Increasing TwoComp DUAL_CUTS from 2 to 4, 8 or 12 has no convincing choose-window benefit.** Every choose-window variant-minus-base mean is negative and smaller in magnitude than its SE. Report-window means turn slightly positive. Retaining 2 is the conservative inference; the variants add modeled truncations without demonstrated gain or measured engine feasibility. [b12-cuts-4] [b12-cuts-8] [b12-cuts-12]
- **COMBO's mixed quote is a further replica lead.** Gate 2 has the largest choose-window mean: +0.645661931 versus locally recomputed qt1, SE 0.019222756. Its report result is +0.606664298, SE 0.013416537. Gate 3 is numerically best on report, but selecting it from that window would violate the choose/report separation. The gate-2 advantage over ungated on choose is only about one SE. [b19-gate-choose] [b19-gate-report]
- **COMBO is implementation-sensitive under the gas budget.** cp-a and cp-b fail the stricter 215,000 pyrevm selection budget already at dt=1. cp-c's optimized interpolation reports GATE=4, runtime 22,370 bytes, full F error 3.087157057768408e-06 bps, and a 16-seed engine result +0.704218513630746, SE 0.1463786104855387, peak 229,596 with zero OOG. These are different implementations, not contradictory measurements of one binary. cp-c is promising but much less extensively confirmed than TC-A. [b18-cp-a] [b18-cp-b] [b18-cp-c]
- **No result here establishes a new board score, rank or board submission.** The supplied goal baseline is qt1 524.9403, 8th; 7th is 525.377 (+0.44 in the brief), 6th 526.777. Those are task-supplied historical figures, not live board readings. A local paired edge must not be added to 524.9403 to claim a new rank. [assignment; b12-cuts-12; b18-cp-c]

## Evidence boundaries and source warnings

The task defines qt1 as the Solidity fence of [qt1 artifact](https://api.imdnotdead.fun/artifacts/8a6e303b662e1a5ea9bb47f31acedd3988ef65b3ddb66d074517aa59ad41ca40), source SHA-256 `c68887cff61180e12ba2b1ceb333edf76a830f91f63b5d775a8806fb9ec08aca`. The goal's two prior leads (+0.49 for whole-posterior first-trade quoting over Gaussian+plain, 2–4 lookups; +0.49 for lattice+qm over Gaussian+qm, exact lattice about 453k gas/call) are background supplied in the assignment, not new measurements in this merge. Limits are deployed runtime ≤24,576 bytes and engine afterSwap peak ≤245,000 with zero OOG; qt1's goal-supplied peak is 208,775. Sample-dependent qt1 peaks below differ legitimately from that historical peak. [assignment]

The requester flags source re-read failures in **b15-a2s1 (1 source), b16-b1s1 (2), b16-b1s2 (1), b16-b1s3 (1), b16-b1s4 (1), b17-b2s4 (1), b18-cp-b (2), b18-cp-c (1), b19-gate-report (1)**. The supplied warning does not identify the individual failed URLs/passages. This merge cannot determine which linked claim in each report failed, or restore that support. Their external provenance assertions therefore remain qualified; neither the reports' own “source quotes checked” statements nor this merge supersede the warning. Their embedded local measurements are retained as **reported local evidence**, with enough figures to audit arithmetic, rather than treated as externally revalidated facts. This particularly qualifies the source lineage behind cp-c's success, cp-b's failure, and the report-window gate results. The unflagged reports and common hash agreement provide corroboration of lineage, not an independent replay of the flagged runs. [assignment; named reports]

No web page was independently re-fetched for this merge; linked upstream URLs below are source pointers recorded in the inputs. Scratch logs, CSVs beyond those embedded in the reports, dependencies, compiled bytecode, and separately cited sources.json files are not supplied among these 25 inputs. Claims about them cannot be independently inspected here. All 25 named report files are present and nonempty; the missing experimental chunk is identified below.

To fit this root's size limit, this merge retains experimental outcomes, paired summaries including worst5, gas aggregates, provenance identities, failure conditions, selection rules and limitations. Repetitive raw per-chunk gas arrays, per-seed CSV rows, setup shell transcripts, and repeated full Python classes are condensed rather than silently presented as missing. Relevant code identities and reconstruction pointers are retained; no new contract is implemented by this merge.

## Input registry and citation key

Each bracketed input ID cites the corresponding supplied report, not an independently checked upstream source. SHA-256 below is computed over the supplied report bytes; citation destinations below encode the original report locations given by the assignment (under artifacts/goal/batches/). Full input identities survive even though .imd/reads is not submitted.

| ID | Input SHA-256 |
|---|---|
| b12-cuts-12 | `c1bbb35d1d147d513d49659add978a82059573046cfc33dc5bfb455d2301b4ab` |
| b12-cuts-4 | `290698cbc69e3e3a6cb181d78e23626b9fb85ee78b6b4448d9765317204887ca` |
| b12-cuts-8 | `5b0f656a15333e31b503be3621c5fd3f8760885605f89f233d1fea28a67e9a62` |
| b13-tools | `c53e753710a1bd6bd837c269a77864fb21ceb42e3328d576c4e902bc74f190d9` |
| b14-a1s1 | `ba732ee96a1e3631eda0752361d2da047725543a670dda13596416498396dc93` |
| b14-a1s2 | `c8e940d4029d7e167d20290585a5f86f6b65befc4aace4bd59018730ea9a49f4` |
| b14-a1s3 | `59dc5c43f8be5d713d1caaf34539f0cf189628a2aefc03d46de2b35e9a89a55b` |
| b14-a1s4 | `f66bde97a2eb17a82ef82b80e68c6791325bff1724b6b28674cca8bea62761ed` |
| b15-a2s1 | `c42990c48f2e4394402573a1985764469cdac795ea2c8cecd5651d9cd97f4acf` |
| b15-a2s2 | `668ccbebf46d155e6ac516058c20bacda1f54bed08ef66dd211efce9fd022cb7` |
| b15-a2s3 | `06b567d63a1086b345756c0d17fb334549e0be3002ebba55401705f6cbf086e5` |
| b15-a2s4 | `131783830dd2712bb7a9f168318d83010da0aac3c06fad858e92effed710b44e` |
| b16-b1s1 | `6026bf5a586aabbd2939b53077958aac890ea9cf2c421867a10a2ef677fbb2b3` |
| b16-b1s2 | `f5e9feb73cf3e5089deb50cc2c0b0ec90ef5581f1f669d9a648e649321f147a3` |
| b16-b1s3 | `1f3ad26fa6606edd8e93e23d258fd2330ebc6f2fa34a8536eea64108a020864d` |
| b16-b1s4 | `f4fd52dd7a73523cce44616f633f578a2cda3a761fdbd73f9e22136e8581e1aa` |
| b17-b2s1 | `b0e675732f25437993a7edb82e0e5acc1cac3ba51b0ce207e9fe0714f8ba5453` |
| b17-b2s2 | `49ad60aa39c282c22078e63be8b0728bafe351bffbe166619153250f8fbfa75d` |
| b17-b2s3 | `c484b1300d0cba5ebffc967a92975cefcb98be5f6cd43e4372f339d4cd07312b` |
| b17-b2s4 | `a41b2c094379db5923922d27e18f0f6c0bc8daaf6c2e4e5c11afeb70d51064aa` |
| b18-cp-a | `4cc25dfb91f2ca8a957de08c6a38bbd3e4aed7fb288be8242e5677ea77bbf0b1` |
| b18-cp-b | `2d2f954fa4c1328089a4ca66ce0e05cafb0f5ffa4ee7a5809eb082af454f4398` |
| b18-cp-c | `ffd2b2488b92fe51e639af36007feabbf15c3df3c119bf957d460e1be42efa34` |
| b19-gate-choose | `1446141a9653c050db7ac71d3c37c62a7bf661f52ba22b55000beef754bf1141` |
| b19-gate-report | `70ece52dd649c2b5f1085dfca6e77046a53ab8929f0e3e11875fd33a9fe0c2e4` |

## Shared policy, tool and engine identities

The common checkout K is [goal repository at c1c9a349f00bf18746f17c6a253469df6634860b](https://github.com/identity-md-launches/goal-3170-beat-network-s-amm-entry/tree/c1c9a349f00bf18746f17c6a253469df6634860b). Earlier cuts/tool inputs also use K at `31ff8ed128b463cde10ea0a71d354f8c54d4464a`. Taylor's research is pinned to [amm-sim research/solved at 4812a6382311624e1506aca131ca35c378f930d9](https://github.com/gtmcknight/amm-sim/tree/4812a6382311624e1506aca131ca35c378f930d9/research/solved). Engine work pins [amm-challenge at 6b6921f8d463314aa7c96234e1be25a25245f704](https://github.com/benedictbrady/amm-challenge/tree/6b6921f8d463314aa7c96234e1be25a25245f704). [b12-cuts-12] [b13-tools] [b14-a1s1]

| Object | SHA-256 / interpretation | Source |
|---|---|---|
| qt1 Solidity | `c68887cff61180e12ba2b1ceb333edf76a830f91f63b5d775a8806fb9ec08aca`; runtime 20,605 B | [b13-tools], confirmation shards |
| R/qtr2 Solidity | `7b99afae570ef1627b0163fb21411f14c496b005a07c3966cc7323906dee664f`; source 43,073 B | [b13-tools] |
| TC-A Solidity | `b87234c89e094f4955578417c1266129b0f96e6dfda68e3fb8866e00eeda71a2`; runtime 21,102 B | all confirmation shards |
| qt1 Python QMRef | `1dfc9b7a3c2237ff7a93dd9f0af54b9bdab16f2ce0a7eb00784cb4432598db92` | [b12-cuts-4], [b12-cuts-12], [b19-gate-report] |
| QMS1 blob | `3ac7cb8811ecfb6a17f499aa4e9b70dd55f7fb6432b3aec3b904e11a3dece38e`; 10,167 B | [b12-cuts-4], [b12-cuts-12] |
| TwoComp Python | `9d3c1833321493fb51bbde4e1b4dabc2f8978bd6d774ee2af8dc8aed13f0f0af` | [b13-tools], [b18-cp-c] |
| Original COMBO Python fence | `c5b711a0b4fb4783e8879a484bf87a427171f4a11aa5eb5ec3513c24ead1a796` (not the surrounding Markdown) | [b18-cp-a], [b18-cp-b], [b18-cp-c], [b19-gate-choose] |
| Engine installed .so | `ff88b6353c2aad7342f0a26194f7347e78b9c3b38d683a7449006d423978cd14` | [b13-tools], confirmation/port setup reports |
| Setup wheel | supplied setup pins wheel SHA-256 `aedb68280aca34c110968f00148387c95885207913fb2cf19a1ab4c5cfd6887a`; distinguish wheel digest from installed .so | assignment |

Reconstruction of TC-A: apply only “Contract: exact unified diff against R” from [TC-A port artifact A](https://api.imdnotdead.fun/artifacts/ebab165bd9bc568057d042f7a9364713eb9cbef3f895e046fc1fde8264134fd2) to K/reference/qtr2/Strategy.sol. Reports use patch -p1 or, where patch is unavailable, git apply -p1; they report matching final bytes. COMBO comes from [artifact C, Code](https://api.imdnotdead.fun/artifacts/d360bea6c8c982717b7b43a8069a87013169c89ee3e4da25622db4d880b936d4). TwoComp's original Code is [TC](https://api.imdnotdead.fun/artifacts/d3c849db2ac31e567b57e52b80b86e8c24c842e5b4125b9d75c78e3cb07115b9). [b14-a1s1] [b16-b1s4] [b18-cp-c]

Engine confirmation method: each candidate and qt1 runs **separately against 30 bps VanillaStrategy**, using `amm_sim_rs.run_batch(X, VanillaStrategy, configs, 8)`, configs transcribed from MatchRunner._build_configs, and gas resets/readouts per arm. Raw role `Baseline` is Vanilla, even in the qt1 arm; it is not qt1's Submission gas. Solidity compiler: 0.8.24, optimizer 200, viaIR, Paris as reported by the pinned compiler users. Ranges passed to tools are half-open; range descriptions below are inclusive. Reports use bounded chunks, generally timeout 470 seconds, below eight minutes. Timing definitions differ (some include compile/startup, others only engine arms), and concurrency/host load varies; timings cannot rank machines or isolate algorithmic costs. [b13-tools] [b14-a1s1] [b14-a1s2] [b14-a1s3] [b17-b2s3]

Replica screening uses plain python3 -I, pinned Taylor replica2, default 10,000 steps, independent policy trajectories paired by seed. SE throughout is sample SD of paired differences divided by sqrt(n); ± means one SE, not a confidence interval. Replica RNG streams differ from Rust engine streams. [b12-cuts-12] [b19-gate-choose] [b19-gate-report]

## Gate P and shared reference checks

The three cuts reports, tools report, all three combo-port reports and both gate screens report the following original Taylor gate output. This differs intentionally from the compressed-table qt1 reference. Tools ran the immutable gate after importing sources with no policy changes; frozen confirmation shards did not rerun P/Q/F. [b12-cuts-4] [b12-cuts-8] [b12-cuts-12] [b13-tools] [b18-cp-a] [b18-cp-b] [b18-cp-c] [b19-gate-choose] [b19-gate-report]

| seed | perfect-info | Gaussian+plain | Gaussian+qm | lattice+qm |
|---|---:|---:|---:|---:|
| 10000 | 448.261189 | 443.455598 | 443.522608 | 443.663520 |
| 10001 | 576.779199 | 571.463409 | 571.623551 | 571.977293 |
| 10002 | 531.886497 | 525.168028 | 525.865859 | 526.411631 |

Reference edge spot checks, each on that policy's own replica run; sources are tools for the first four rows and both gate reports for COMBO:

| Policy | 10000 | 10001 | 10002 | Source |
|---|---:|---:|---:|---|
| qt1 QMRef | 443.101741 | 571.454483 | 525.908441 | [b13-tools] |
| TwoComp, DUAL_CUTS=2 | 443.690614 | 571.968071 | 526.124475 | [b13-tools] |
| wavg_fees.QMRef | 444.116689 | 571.977148 | 525.771328 | [b13-tools] |
| wavg_offsets.QMRef | 444.115542 | 571.986018 | 525.772792 | [b13-tools] |
| ungated COMBO | 444.195330 | 572.172682 | 526.274760 | [b19-gate-choose], [b19-gate-report] |

**Published-baseline caveat.** Cuts use [PC, choose baseline](https://api.imdnotdead.fun/artifacts/fa317ec1ba5bbc943bc91141fb6a2235fe0d4181fa8a01b004f1d439ecf710f3) and [PR, report baseline](https://api.imdnotdead.fun/artifacts/d03074104960a361564cfb6d7db752763e9c9b651fa9ed212c10d7acc2738610). cuts-4's first eight seeds per window match to six decimals; cuts-8 gives the three initial check edges but does not document an eight-seed-per-window numeric check. Neither fully recomputed qt1 across both windows. cuts-12 does: all 2,048 PR edges agree within rounding (max 5e-7), but **17/1,024 PC seeds differ by >1e-6**, max about **0.0484**; examples include 60074, 60027, 60060, 60149 and 60405. PC says macOS arm64 CPython 3.9.6, while cuts-12 uses Linux CPython 3.12.3. cuts-12 attributes this to libm last-digit differences flipping discrete events; this mechanism is the report's explanation, not independently proved here. Local choose qt1 mean 529.971157 versus published 529.971160; switching to local pairing changes the mean difference by only about 3e-6. [b12-cuts-4] [b12-cuts-8] [b12-cuts-12]

Thus cuts-4's statement that published-baseline errors are at most rounding is too broad for the choose window: its checks establish only the checked seeds. The reported cuts comparisons remain, with PC pairing explicitly labeled; variant-minus-base is local and unaffected by this baseline mismatch. Both gate reports avoid PC by recomputing qt1 locally for every seed. [b12-cuts-4] [b12-cuts-12] [b19-gate-choose] [b19-gate-report]

## TwoComp DUAL_CUTS screens: 4, 8 and 12

Each variant changes only the TwoComp class constant from 2; filter thresholds, diffusion, likelihoods and fee rule are unchanged. `propagate` applies at most min(dt-1,12) silent no-arbitrage cuts; it collapses two components at step==DUAL_CUTS. For 12 that step is never reached in the silent-step loop. Larger cuts therefore preserve separate arb/retail components longer, then combine their likelihood at the first trade. Differences from cuts=2 can begin at dt≥4 when two components enter the callback. [b12-cuts-4] [b12-cuts-8] [b12-cuts-12]

Worst-callback modeled truncation counts are qt1=13, cuts2=16, cuts4=18, cuts8=22, cuts12=26 (14+min(cuts,12)); these are source/brief model counts, **not measured gas**. [b12-cuts-4] [b12-cuts-8] [b12-cuts-12]

| DUAL_CUTS | choose variant−qt1 | choose variant−base | report variant−qt1 | report variant−base | Source |
|---|---|---|---|---|---|
| 4 | +0.443827379 ±0.017927442 | −0.001593505 ±0.003751014 | +0.428078058 ±0.012271420 | +0.003275169 ±0.002663148 | [b12-cuts-4] |
| 8 | +0.443034983 ±0.017877964 | −0.002385901 ±0.003743178 | +0.426878405 ±0.012262562 | +0.002075516 ±0.002751381 | [b12-cuts-8] |
| 12 | +0.442937 ±0.017887 | −0.002484 ±0.003757 | +0.426963 ±0.012259 | +0.002161 ±0.002749 | [b12-cuts-12] |

Choose n=1,024 on 60000..61023, report n=2,048 on 10000..12047 for every row. The common base is about +0.445421 ±0.017637 on choose and +0.424803 ±0.012202 on report versus published qt1. These reuse the same baseline seeds and are not independent replications that can be pooled to triple n. **cuts-8's prose incorrectly says choose +0.00239; its JSON says −0.002385901, consistent with its mean edges. The JSON sign is retained here.** cuts-4's report increase is roughly 1.23 SE, so “all effects inside one SE” would also be inaccurate; it still provides no convincing choose-window benefit. [b12-cuts-4] [b12-cuts-8] [b12-cuts-12]

The following compact source JSON preserves supplied mean edges, timings/counters and all worst5. Compact JSON display floats are rounded to nine decimals; timings are measured in workers with contention, not isolated serial costs.

Paired comparison objects in the cut JSON below are compacted to `[n, mean_diff, SE, worst5]`; other keys retain their source names.

### b12-cuts-4 — retained screen evidence [b12-cuts-4]

```jsonl
{"window":"choose","seeds":[60000,61023],"complete":true,"mean_edges":{"qt1":529.971159703,"base":530.416580587,"variant":530.414987082},"paired":{"variant-qt1":[1024,0.443827379,0.017927442,[[60937,-1.294313632],[60728,-1.238405028],[60446,-1.160635533],[60733,-1.146156575],[60090,-0.938696758]]],"base-qt1":[1024,0.445420884,0.017637037,[[60733,-1.159272676],[60728,-1.144836683],[60446,-1.049882281],[60326,-0.957573978],[60143,-0.884081421]]],"variant-base":[1024,-0.001593505,0.003751014,[[60937,-0.669126296],[60150,-0.473341772],[60464,-0.450909065],[60185,-0.448047787],[60841,-0.441206892]]]},"seconds_per_seed":{"base":{"mean_elapsed":0.384820255,"mean_cpu":0.382033529},"variant":{"mean_elapsed":0.383567344,"mean_cpu":0.380781633}},"mean_two_component_dt_ge13_count":{"base":1,"variant":0.990234375},"total_two_component_dt_ge13_count":{"base":1024,"variant":1014}}
{"window":"report","seeds":[10000,12047],"complete":true,"mean_edges":{"qt1":533.262830661,"base":533.68763355,"variant":533.690908719},"paired":{"variant-qt1":[2048,0.428078058,0.01227142,[[10146,-2.998706009],[11701,-2.603452628],[11062,-1.69369572],[11808,-1.324737665],[12021,-1.218739365]]],"base-qt1":[2048,0.424802889,0.012201543,[[10146,-2.751934348],[11701,-2.42658519],[11062,-1.680672032],[11949,-1.220172037],[10394,-1.201831086]]],"variant-base":[2048,0.003275169,0.002663148,[[10184,-0.928576471],[11370,-0.618502597],[10475,-0.607034901],[11696,-0.496272748],[10779,-0.452326113]]]},"seconds_per_seed":{"base":{"mean_elapsed":0.380826228,"mean_cpu":0.378328394},"variant":{"mean_elapsed":0.38132218,"mean_cpu":0.378916723}},"mean_two_component_dt_ge13_count":{"base":0.924804688,"variant":0.927246094},"total_two_component_dt_ge13_count":{"base":1894,"variant":1899}}
```

### b12-cuts-8 — retained screen evidence [b12-cuts-8]

```jsonl
{"window":"60000..61023","n":1024,"variant_minus_qt1":[1024,0.443034983,0.017877964,[[60728,-1.201145389],[60446,-1.156645754],[60733,-1.122376184],[60143,-0.908290394],[60862,-0.892592494]]],"base_minus_qt1":[1024,0.445420884,0.017637037,[[60733,-1.159272676],[60728,-1.144836683],[60446,-1.049882281],[60326,-0.957573978],[60143,-0.884081421]]],"variant_minus_base":[1024,-0.002385901,0.003743178,[[60150,-0.471980919],[60464,-0.458614214],[60841,-0.455035232],[60089,-0.414367352],[60185,-0.413732865]]],"mean_edge_variant":530.414194686,"mean_edge_base":530.416580587}
{"window":"10000..12047","n":2048,"variant_minus_qt1":[2048,0.426878405,0.012262562,[[10146,-2.989127635],[11701,-2.621334366],[11062,-1.699140043],[11808,-1.27832237],[12021,-1.217756725]]],"base_minus_qt1":[2048,0.424802889,0.012201543,[[10146,-2.751934348],[11701,-2.42658519],[11062,-1.680672032],[11949,-1.220172037],[10394,-1.201831086]]],"variant_minus_base":[2048,0.002075516,0.002751381,[[10184,-0.905179232],[11370,-0.615267337],[10475,-0.611228634],[10502,-0.511048207],[11696,-0.500138593]]],"mean_edge_variant":533.689709066,"mean_edge_base":533.68763355}
```

### b12-cuts-12 — retained screen evidence [b12-cuts-12]

```jsonl
{"window":"60000..61023","qt1_ref":"published per-seed edges","qt1_check_first8_6dp":true,"qt1_recomputed_max_abs_dev_vs_published_all_seeds":0.0484,"variant_minus_qt1":[1024,0.442937,0.017887,[[60728,-1.200908],[60446,-1.156586],[60733,-1.122046],[60143,-0.90829],[60862,-0.876314]]],"base_minus_qt1":[1024,0.445421,0.017637,[[60733,-1.159273],[60728,-1.144837],[60446,-1.049882],[60326,-0.957574],[60143,-0.884081]]],"variant_minus_base":[1024,-0.002484,0.003757,[[60150,-0.471979],[60464,-0.458625],[60841,-0.455026],[60089,-0.414388],[60185,-0.413568]]],"mean_edge":{"variant":530.414097,"base":530.416581,"qt1_ref":529.97116},"seconds_per_seed":{"variant":0.1683,"base":0.2022,"qt1_ref_recomputed":0.1561},"first_trade_callbacks_two_comp_dt_ge_13_mean_per_run":{"variant":0.9912,"base":1.0},"first_trade_callbacks_mean_per_run":{"variant":6982.95,"base":6983.29}}
{"variant_minus_qt1_local":[1024,0.44294,0.017887,[[60728,-1.200908],[60446,-1.156586],[60733,-1.122046],[60143,-0.908291],[60862,-0.876314]]],"base_minus_qt1_local":[1024,0.445424,0.017637,[[60733,-1.159273],[60728,-1.144837],[60446,-1.049882],[60326,-0.957574],[60143,-0.884082]]]}
{"window":"10000..12047","qt1_ref":"published per-seed edges","qt1_check_first8_6dp":true,"qt1_recomputed_max_abs_dev_vs_published_all_seeds":5e-07,"variant_minus_qt1":[2048,0.426963,0.012259,[[10146,-2.989128],[11701,-2.621272],[11062,-1.699079],[11808,-1.278346],[12021,-1.219318]]],"base_minus_qt1":[2048,0.424803,0.012202,[[10146,-2.751934],[11701,-2.426585],[11062,-1.680672],[11949,-1.220172],[10394,-1.201831]]],"variant_minus_base":[2048,0.002161,0.002749,[[10184,-0.90348],[11370,-0.61524],[10475,-0.611127],[10502,-0.511013],[11696,-0.500139]]],"mean_edge":{"variant":533.689794,"base":533.687634,"qt1_ref":533.262831},"seconds_per_seed":{"variant":0.2461,"base":0.2643,"qt1_ref_recomputed":0.1967},"first_trade_callbacks_two_comp_dt_ge_13_mean_per_run":{"variant":0.9268,"base":0.9248},"first_trade_callbacks_mean_per_run":{"variant":6996.79,"base":6996.99}}
```

Callback instrumentation: cuts-4 report dt≥13/two-component arrivals average 0.92724609375 (variant), 0.9248046875 (base), totals 1,899/1,894; choose 0.990234375/1, totals 1,014/1,024. cuts-8 reports mean 0.927, min 0/max 8 over 2,048 runs. cuts-12 report is 0.9268/0.9248, versus about 6,997 first-trade callbacks/run; choose is 0.9912/1.0 versus about 6,983. This measures a rare **long-dt subset**, not every callback where cuts>2 can change behavior. cuts-8's broader “rarely differs” causal interpretation should not be inferred solely from this dt≥13 count. The directly paired scores, rather than that counter, establish the small net effect. [b12-cuts-4] [b12-cuts-8] [b12-cuts-12]

Base edges 10000..10002 reproduce 443.690614 / 571.968071 / 526.124475 in all cuts reports. cuts-12 variant gives 443.773820 / 571.922620 / 526.119823. Base report mean 533.687633550 reproduces TC's 533.687633550 (cuts-12 rounds to 533.687634); base−qt1 +0.424802889 reproduces TC's +0.424802883 within rounding. cuts-12 additionally reproduces base mean 529.732639 on 60000..60511 versus TC 529.732638925. [b12-cuts-4] [b12-cuts-8] [b12-cuts-12]

No cut screen produced Solidity, deployed size, engine score, engine gas/OOG, or full F. cuts-12's local choose pairing is +0.442940 for variant and +0.445424 for base, same SE as published-baseline pairing. Neither timing variation nor a modeled count establishes an engine improvement. [b12-cuts-12; all cuts reports]

## Tools and reference import deliverable

The tools item reports verbatim extraction of R and the SP patch, TwoComp and both mix references; hashes checked before/after. It adapts the prior replay to `tools/check.py CONTRACT MODULE.CLASS START END OUTPUT`: fresh pyrevm deployment/policy per seed, actual replica initialization, first 2,000 own callbacks, 245,000 gas/call, effective reference fees via replica2.clampf, tolerance 0.01 bps, one candidate arm, source-style rows/gas maps/raw hashes. `tools/engine.py CANDIDATE BASELINE START END OUTPUT` runs independent arms against Vanilla with 8 workers, default configs, per-seed edges and per-arm raw gas, paired n/mean/SE/worst5. Outputs reserve filenames exclusively and save partial progress per arm; this prevents overwrite, **not global seed reuse with another filename**. Compile caches/state reside under scratch; README supplies the seed ledger. [b13-tools]

Smoke-only validation, not full gates: qt1 replay on seed 70000 has 2,000 callbacks, max error **1.504892703507732e-06 bps**, pyrevm peak **177,686**, sum gas **253,658,209**, raw-output SHA-256 `221472443e11ab733f0f2f33f8a59c135909b690af1b9ee93aad0af702e2a782`. qt1-vs-itself engine smoke on **9801088..9801089** has n=2, mean=SE=0; edges respectively **573.595237186163** and **591.10427219484** in both arms. Total engine time **10.853595495223999 s**. Submission afterSwap: **23,027 calls**, peak **200,361**, sum **3,161,171,583**, no error of any recorded kind. Vanilla afterSwap: **22,875 calls**, peak **22,592**, sum **516,125,520**. Per arm, initialization/getName each has 2 calls: Vanilla peaks 21,796/21,526 and sums 43,592/43,052; qt1 peaks 90,858/21,579 and sums 181,716/43,158. The two arms' gas arrays are identical after separate resets. [b13-tools]

Setup and Starter validation succeeded. Tools reports py_compile, reference byte-equality, pinned span hash, config parity on 5 seeds×12 fields without simulations, nonzero paired-arithmetic test, one-seed null SE, and smoke invariants. Original gate table reproduced using qm_k1e-5.json SHA-256 `5ff53e42ca87390e5f65d1caa3f7a480e67a8212fb0670274dfd562b05ba1afd`. No failure, timeout, OOM, hash mismatch, replay mismatch, OOG or revert is reported. It explicitly does **not** execute full 50×2,000 F, 1,024/2,048 Q, candidate engine tests, candidate compile or optimization. Initial ledger: 9800000..9801089 spent/reserved, next free 9801090. [b13-tools]

The original tools item's claimed delivered files and identities follow. These are **its inventory**, not files created by this merge; source code itself is not among this root's outputs. [b13-tools]

| File | Bytes | SHA256 |
| --- | ---: | --- |
| `README.md` | 3907 | `33b9d82d6b53308a8c6b3cc94c975516befd0eff98c3c99fcda6544d5b9e4613` |
| `reference/CHECKS.md` | 5147 | `47124e3ff2ac6019ba5c57ec16323b8af03ed857b2e3edd1a3846f8364296795` |
| `reference/qtr2/Strategy.sol` | 43073 | `7b99afae570ef1627b0163fb21411f14c496b005a07c3966cc7323906dee664f` |
| `reference/qtr2/spans.diff` | 1733 | `35ec1bab15959eebeac3ea9bf46e70d723b7acfe1f3f82881d10bd1a8bb81623` |
| `reference/qtr2/StrategySpans.sol` | 43289 | `bbf63364ed407fc3a94ec3b4cc02223b6855b1b9c083e6e7a7566a2ba70e24b5` |
| `reference/twocomp/twocomp.py` | 11202 | `9d3c1833321493fb51bbde4e1b4dabc2f8978bd6d774ee2af8dc8aed13f0f0af` |
| `reference/mix/wavg_fees.py` | 8934 | `668a287ae4c7a1a311d7a8de94269c068bc543b9fb1661040a796c45e6a3da60` |
| `reference/mix/wavg_offsets.py` | 9068 | `591768f2c61efc4972084c6f172acf9ee887577672eb493af15d28c7f941f116` |
| `tools/check.py` | 4755 | `cbcfea4c793ac7b78e0ee27dd723c9e6af4d9d704a70a8038c985acffffcfed1` |
| `tools/engine.py` | 4430 | `306c529d0c84c88610c1e8a9a6aa34634534b73ab83312e9155ef14476e46300` |
| `tools/README.md` | 4474 | `4e75965d6ec00e9e9e3887b83688bb3f9ea8fc438f4d3336ef104bae8a234c6f` |

## Frozen TC-A engine confirmation: all 16 shards

These are **one candidate**, not four candidate families: every shard records TC-A source b87234c8…71a2 reconstructed from R, qt1 source c68887cf…aca, runtimes 21,102 and 20,605 B, successful TC-A static validation and setup. They reserve disjoint windows, one invocation per 16-seed chunk, reset gas per arm, and report no tuning or board submission. P/Q/F are not rerun by these engine-only confirmation tasks. [b14-a1s1]–[b17-b2s4]

Table statistics below are recomputed from **displayed 12-decimal CSV differences**, not a new simulation. They reproduce each shard's reported mean and SE to the shown precision apart from last-place rounding (notably a2s4 reports 0.422315487211 while CSV aggregation rounds to 0.422315487212). For raw reported full-precision paired values see the retained JSON below. All named ranges in this table are inclusive.

| Source | Observed seeds | n | TC-A−qt1 mean | SE | Positive seeds |
|---|---|---:|---:|---:|---:|
| [b14-a1s1] | 9801090..9801217 | 128 | 0.462109234186 | 0.048023416795 | 102 |
| [b14-a1s2] | 9801218..9801345 | 128 | 0.441272550247 | 0.053442956306 | 98 |
| [b14-a1s3] | 9801346..9801473 | 128 | 0.500696722470 | 0.050173357696 | 101 |
| [b14-a1s4] | 9801474..9801601 | 128 | 0.386375887493 | 0.048104328197 | 98 |
| [b15-a2s1] | 9801602..9801729 | 128 | 0.536321411294 | 0.048156445445 | 109 |
| [b15-a2s2] | 9801730..9801857 | 128 | 0.433613463218 | 0.046956844923 | 99 |
| [b15-a2s3] | 9801858..9801985 | 128 | 0.397216522169 | 0.042271659955 | 103 |
| [b15-a2s4] | 9802002..9802113 | 112 | 0.422315487212 | 0.052468158007 | 86 |
| [b16-b1s1] | 9802114..9802241 | 128 | 0.440292346112 | 0.047683923176 | 105 |
| [b16-b1s2] | 9802242..9802369 | 128 | 0.352083116373 | 0.047347240428 | 105 |
| [b16-b1s3] | 9802370..9802497 | 128 | 0.433422054272 | 0.051685241148 | 101 |
| [b16-b1s4] | 9802498..9802625 | 128 | 0.506896556667 | 0.050271928432 | 104 |
| [b17-b2s1] | 9802626..9802753 | 128 | 0.453146640074 | 0.047163476585 | 102 |
| [b17-b2s2] | 9802754..9802881 | 128 | 0.417059547792 | 0.057210796777 | 102 |
| [b17-b2s3] | 9802882..9803009 | 128 | 0.420781112764 | 0.063528159370 | 103 |
| [b17-b2s4] | 9803010..9803137 | 128 | 0.449091483431 | 0.046044414689 | 103 |

**Missing chunk:** a2s4 was assigned 9801986..9802113, but 9801986..9802001 failed before simulation with `ModuleNotFoundError: No module named 'check'` because engine.py was copied away from its companion check.py. No output or simulation existed for chunk 0; it was not repeated and its seeds are retired under that shard's rule. Its seven successful chunks cover only 112 seeds. Thus 2,048 assigned seeds yield 2,032 observed, not 2,048 completed. [b15-a2s4]

### Pooled arithmetic and tail risk

The following pools are recomputed from those same displayed differences, weighting **seeds**, not shard means. Source groups are b14=a1, b15=a2, b16=b1, b17=b2; these are partitions of the same pooled confirmation, not additional independent datasets. SE is calculated from all individual differences, incorporating within- and between-shard variation. No missing result is imputed.

```jsonl
{"pool":"all confirmations","n":2032,"mean_diff":0.440938879,"se":0.012556657,"worst5":[[9802971,-3.85561392],[9803009,-3.387898048],[9802769,-1.860435529],[9802878,-1.787549003],[9802327,-1.537003428]],"positive":1621,"negative":411}
{"pool":"b14","n":512,"mean_diff":0.447613599,"se":0.024985608,"worst5":[[9801513,-1.133507702],[9801223,-1.062492536],[9801569,-1.00943124],[9801495,-0.94555201],[9801438,-0.938684192]],"positive":399,"negative":113}
{"pool":"b15","n":496,"mean_diff":0.448174825,"se":0.023728912,"worst5":[[9802027,-1.322970273],[9802043,-0.924771932],[9802087,-0.902354151],[9802105,-0.746894988],[9801875,-0.708138713]],"positive":397,"negative":99}
{"pool":"b16","n":512,"mean_diff":0.433173518,"se":0.024687463,"worst5":[[9802327,-1.537003428],[9802287,-1.253429671],[9802309,-1.247331672],[9802512,-1.152385349],[9802151,-1.019065076]],"positive":415,"negative":97}
{"pool":"b17","n":512,"mean_diff":0.435019696,"se":0.026917934,"worst5":[[9802971,-3.85561392],[9803009,-3.387898048],[9802769,-1.860435529],[9802878,-1.787549003],[9802843,-1.502317471]],"positive":410,"negative":102}
```

The combined positive average coexists with substantial adverse seeds: the global worst two are b2s3 seeds 9802971 (−3.855613920335) and 9803009 (−3.387898047995), followed by b2s2 seeds 9802769 and 9802878. A mean gain is not a guarantee per path. Every shard mean is positive, including the lower b1s2 +0.352083116373; variation across shard means is not evidence of distinct strategies. [b16-b1s2] [b17-b2s2] [b17-b2s3; merge arithmetic]

Retained shard paired summaries, including **all source worst5**. Positional rows `[n,mean_diff,SE,worst5]` retain the supplied summaries with display floats rounded to nine decimals; a2s4 and b2s2 are transcribed from prose lists because no standalone paired JSON is given. [respective source on each line]

`b14-a1s1`: `[128,0.462109234,0.048023417,[[9801167,-0.808120321],[9801157,-0.733359434],[9801192,-0.552097043],[9801134,-0.533751482],[9801155,-0.528992128]]]`

`b14-a1s2`: `[128,0.44127255,0.053442956,[[9801223,-1.062492536],[9801302,-0.849233657],[9801227,-0.813578404],[9801304,-0.742058763],[9801313,-0.716862993]]]`

`b14-a1s3`: `[128,0.500696722,0.050173358,[[9801438,-0.938684192],[9801354,-0.690725763],[9801415,-0.667709757],[9801405,-0.630478797],[9801402,-0.545662639]]]`

`b14-a1s4`: `[128,0.386375887,0.048104328,[[9801513,-1.133507702],[9801569,-1.00943124],[9801495,-0.94555201],[9801475,-0.79673736],[9801584,-0.501396791]]]`

`b15-a2s1`: `[128,0.536321411,0.048156445,[[9801647,-0.617341795],[9801709,-0.605473643],[9801700,-0.525774406],[9801619,-0.501020887],[9801617,-0.495833076]]]`

`b15-a2s2`: `[128,0.433613463,0.046956845,[[9801811,-0.652043169],[9801731,-0.58242978],[9801800,-0.567512873],[9801814,-0.561690223],[9801801,-0.502194491]]]`

`b15-a2s3`: `[128,0.397216522,0.04227166,[[9801875,-0.708138713],[9801884,-0.544242736],[9801929,-0.540559728],[9801956,-0.48771087],[9801915,-0.340657109]]]`

`b15-a2s4`: `[112,0.422315487,0.052468158,[[9802027,-1.322970273],[9802043,-0.924771932],[9802087,-0.902354151],[9802105,-0.746894988],[9802046,-0.605197421]]]`

`b16-b1s1`: `[128,0.440292346,0.047683923,[[9802151,-1.019065076],[9802169,-0.746488667],[9802190,-0.703750346],[9802159,-0.58120022],[9802167,-0.49960113]]]`

`b16-b1s2`: `[128,0.352083116,0.04734724,[[9802327,-1.537003428],[9802287,-1.253429671],[9802309,-1.247331672],[9802324,-0.883960562],[9802245,-0.602781882]]]`

`b16-b1s3`: `[128,0.433422054,0.051685241,[[9802487,-0.795244352],[9802429,-0.769697514],[9802431,-0.628328005],[9802374,-0.624188163],[9802473,-0.579874066]]]`

`b16-b1s4`: `[128,0.506896557,0.050271928,[[9802512,-1.152385349],[9802569,-0.769348511],[9802590,-0.703875916],[9802607,-0.645277772],[9802536,-0.563967684]]]`

`b17-b2s1`: `[128,0.45314664,0.047163477,[[9802667,-0.8774873],[9802693,-0.839509921],[9802702,-0.595644136],[9802685,-0.561014368],[9802656,-0.535656203]]]`

`b17-b2s2`: `[128,0.417059548,0.057210797,[[9802769,-1.860435529],[9802878,-1.787549003],[9802843,-1.502317471],[9802754,-1.219597618],[9802832,-1.153258965]]]`

`b17-b2s3`: `[128,0.420781113,0.063528159,[[9802971,-3.85561392],[9803009,-3.387898048],[9803007,-1.248847221],[9802937,-1.066100655],[9802884,-0.358655156]]]`

`b17-b2s4`: `[128,0.449091483,0.046044415,[[9803083,-0.706720659],[9803040,-0.538798543],[9803043,-0.524638983],[9803114,-0.48836861],[9803131,-0.453754924]]]`

### Engine afterSwap gas, source raw arrays aggregated here

These figures come from parsing each report's raw `gas_stats()` arrays and selecting role Submission / callback afterSwap; means use total successful gas / successful calls, peaks use max(max_ok_gas), and all ok counts equal calls. This retains more precision than reports whose prose rounds means to one decimal. Both arms in **every** row have OOG=0, revert=0, other_halt=0, tx_error=0, bad_return=0. No peak here exceeds 245,000. [each row's cited report; merge arithmetic]

| Source | TC-A calls | TC-A peak | TC-A mean | qt1 calls | qt1 peak | qt1 mean |
|---|---:|---:|---:|---:|---:|---:|
| [b14-a1s1] | 1406613 | 211164 | 130918.392790 | 1413906 | 208684 | 137858.384833 |
| [b14-a1s2] | 1406209 | 208740 | 130914.897816 | 1413809 | 208799 | 137858.531827 |
| [b14-a1s3] | 1408049 | 204740 | 130901.579667 | 1415027 | 209271 | 137848.315863 |
| [b14-a1s4] | 1391482 | 209456 | 131080.441429 | 1399127 | 208896 | 137975.033448 |
| [b15-a2s1] | 1403506 | 203567 | 130914.706967 | 1410571 | 209338 | 137861.421954 |
| [b15-a2s2] | 1413134 | 209172 | 130839.859834 | 1421092 | 208951 | 137798.943124 |
| [b15-a2s3] | 1392694 | 208777 | 131022.888236 | 1400687 | 209023 | 137940.378884 |
| [b15-a2s4] | 1200325 | 205149 | 131274.602498 | 1206745 | 208799 | 138147.777493 |
| [b16-b1s1] | 1390345 | 205943 | 131054.241641 | 1397738 | 208735 | 137969.644685 |
| [b16-b1s2] | 1393756 | 209452 | 131019.879896 | 1401464 | 208926 | 137948.786991 |
| [b16-b1s3] | 1407332 | 209315 | 130901.234137 | 1414429 | 209280 | 137848.278219 |
| [b16-b1s4] | 1409093 | 203253 | 130898.315100 | 1416883 | 208619 | 137834.759456 |
| [b17-b2s1] | 1398663 | 207778 | 130975.050857 | 1406273 | 209260 | 137891.914070 |
| [b17-b2s2] | 1380712 | 205596 | 131198.922808 | 1388208 | 209462 | 138076.201260 |
| [b17-b2s3] | 1391918 | 208748 | 131041.613540 | 1398638 | 208508 | 137953.871185 |
| [b17-b2s4] | 1395557 | 204093 | 131018.659652 | 1402847 | 209136 | 137944.281053 |

Pooled raw gas aggregates below additionally retain Vanilla and non-afterSwap callback totals. Source is all 16 confirmation reports; these are compressed arithmetic summaries of their arrays, **not raw per-chunk output**. `arm` identifies which strategy faced Vanilla; `role=Baseline` still means Vanilla. Each arm includes 127 successful chunks (15×8+7).

| Arm | Role | Callback | calls=ok | Peak | Sum successful gas | Mean |
|---|---|---|---:|---:|---:|---:|
| TC-A | Baseline | afterInitialize | 2032 | 21796 | 44289472 | 21796.0 |
| TC-A | Baseline | afterSwap | 22088772 | 22592 | 498383268996 | 22562.742238273815 |
| TC-A | Baseline | getName | 2032 | 21526 | 43740832 | 21526.0 |
| TC-A | Submission | afterInitialize | 2032 | 92165 | 187279280 | 92165.0 |
| TC-A | Submission | afterSwap | 22189388 | 211164 | 2906708764073 | 130995.44539367197 |
| TC-A | Submission | getName | 2032 | 21648 | 43988736 | 21648.0 |
| qt1 | Baseline | afterInitialize | 2032 | 21796 | 44289472 | 21796.0 |
| qt1 | Baseline | afterSwap | 22107204 | 22592 | 498798952692 | 22562.733518539928 |
| qt1 | Baseline | getName | 2032 | 21526 | 43740832 | 21526.0 |
| qt1 | Submission | afterInitialize | 2032 | 90858 | 184623456 | 90858.0 |
| qt1 | Submission | afterSwap | 22307444 | 209462 | 3076639262733 | 137919.84696825867 |
| qt1 | Submission | getName | 2032 | 21579 | 43848528 | 21579.0 |

All five error counters are zero in every row.


### Execution caveats retained from confirmation shards

- a1s1 initially invoked patch from a wrong directory and got a missing-file error, then corrected it before hash verification or any seed run. All eight engine chunks completed. [b14-a1s1]
- a1s2's chunk processes overlapped; counters are process-local. a1s3 and b2s1 timers exclude startup/compilation; a1s1 and some other shard wall timers include them. b1s3's chunk-0 process timing boundary is approximate. b2s3 chunks 1/2 briefly overlapped. These do not change their reported coverage, but timings are not directly comparable. [b14-a1s1] [b14-a1s2] [b14-a1s3] [b16-b1s3] [b17-b2s1] [b17-b2s3]
- a2s4, b1s4 and b2s2 report absent /usr/bin/time; those timing-launch failures occurred before simulation. a2s4's separate missing-check import error retires its 16 seeds as above. b2s2 also lacked bc and does not have a shell wall time for chunk 0, but retains engine.py seconds. [b15-a2s4] [b16-b1s4] [b17-b2s2]
- a2s4/b1s4/b2s2 used git apply because patch was unavailable, while still matching the exact TC-A hash. a2s4 and b2s2 disclose a wrong-directory public clone outside their intended workspace and inability to remove it; they state no simulation occurred there. This is a workflow caveat, not a missing observation beyond a2s4's stated chunk. [b15-a2s4] [b16-b1s4] [b17-b2s2]
- b1s1 fetched the unmentioned companion check.py from the same K commit and validated TC-A only; qt1 compiled in-engine. b2s4's first download target disappeared, so it redownloaded inputs before any engine run. [b16-b1s1] [b17-b2s4]
- Other confirmation shards report no missing/failed assigned chunks. No shard independently establishes P/Q/F for TC-A; their limited assignment is frozen-engine confirmation. The task's source-warning qualification remains attached to a2s1, all b1 shards and b2s4 even though their reported arithmetic is internally consistent. [b14-a1s1]–[b17-b2s4; assignment]

## COMBO port attempts: reconcile failures with optimized success

All start from verified TC-A and original COMBO. They preserve the bounded two-component filter and four packed storage words, adding quote-path memory rather than new persistent state. `dt` is captured before tlast update; an ambiguous first trade has dt≥1 and .005<pi<.995. ComboG always retains both posterior components in self.comp; **only mixed quote construction** is gated by dt≤GATE. Gated-away callbacks use the ordinary single lookup against that strategy's carried moments, not an external TwoComp run's state. Mixed paths weight two branch offsets and convert once against the carried mixture mean. [b18-cp-a] [b18-cp-b] [b18-cp-c] [b19-gate-choose]

The port tasks use a **215,000 pyrevm mixed-bucket selection budget**, a separate conservative condition from the overall **245,000 engine cap**. Probe GATE=10^9; eligible gates {1,2,3,4,6,9,10^9}; select the largest gate whose included dt buckets all fit 215,000. All larger gates contain dt=1. A dt=1 failure therefore rules out every allowed gate in that implementation. A missing bucket does not certify it fits. [b18-cp-a] [b18-cp-b] [b18-cp-c]

### cp-a: failed unlimited probe, no candidate frozen [b18-cp-a]

Status reported as blocked={step:gas}: dt=1 successful mixed peak **216,964 >215,000**, failing the minimum gate by **1,964**. Unlimited probe additionally OOG at **seed 70002, callback 1978 (zero-based), dt=11**, all calls supplied 245,000. It completed only seeds 70000 and 70001, then stopped; **70003..70009 were not replayed**. These are observed lower bounds on full-suite peaks, not ten-seed coverage.

Initial direct runtime **31,433** failed size checks; shared lookup loop reduced to **22,114**, scalar/log-coordinate changes to final **21,853**. Final failed unlimited-probe source SHA-256 **`e4c64fa8e2e797ba6154d2436cc883f7ca8065cf26afd2d2fa5e3aaa2c97d93e`**. Static validation passed as TaylorComboGQmTrim2, but does not override gas failure. No assembly/new storage; coefficients/spline/fee conversion are reported unchanged. Rival clipping uses ln(.997)=−3004509020298721 in WAD log coordinates; exact real-arithmetic equivalence does not itself certify fixed-point parity.

| dt bucket | Successful mixed calls | Successful peak | Peak location seed/callback | Failed calls observed |
|---|---:|---:|---|---:|
| 1 | 9692 | 216964 | 70001/11606 | 0 |
| 2 | 1815 | 213187 | 70000/850 | 0 |
| 3 | 753 | 221425 | 70000/4993 | 0 |
| 4 | 313 | 218587 | 70001/5664 | 0 |
| 5–6 | 212 | 226734 | 70000/1121 | 0 |
| 7–9 | 70 | 238399 | 70000/983 | 0 |
| 10–12 | 6 | 242198 | 70000/7241 | 1 (dt=11 OOG) |
| ≥13 | 0 | unobserved | unavailable | 0 |

23,236 successful afterSwap callbacks preceded the one OOG. Incidental max effective-fee error over the two completed runs is **0.0000023752300126744785 bps**, not F. Gate P and COMBO's three diagnostic edges reproduced, but **Q, F and engine were not run**, no GATE was frozen. Assigned engine **9803138..9803153 unused**. Full failed source diff, exact Python and probe script are embedded in cp-a; the port is a reproducible counterexample, not an eligible strategy.

### cp-b: complete diagnostic with recovery, still gas-blocked [b18-cp-b]

Unrestricted prototype runtime **21,743**; source SHA-256 **`9a19e74acd1e44a8aff7211b199532c28917e70439f9d9760c845c1bcdc1cb7c`**. Static validation passed as TaylorTwoCompQmTrim2; no new assembly/storage, filter/tables/spline/final conversion reported intact. Shared lookup loop exposes/interpolates offsets for single and mixed paths with pre-step rival estimate. **dt=1 peak 222,641 fails by 7,641**, so no gate selected.

First probe stopped at OOG. To populate the full diagnostic, cp-b replayed **70000..70009** in five two-seed chunks; a failed measured call at 245k was followed by a **separate 1,000,000-gas recovery call** to advance state. Such recovery is not a successful capped callback and cannot certify uninterrupted 245k execution. The report discloses repeated replica diagnostic seeds; no engine seeds were run/repeated. Counter indices in this diagnostic are one-based within the two-seed chunk, not per-seed F indices.

| dt bucket | Mixed attempts | Measured peak | OOG |
|---|---:|---:|---:|
| 1 | 44409 | 222641 | 0 |
| 2 | 8248 | 227291 | 0 |
| 3 | 3187 | 226268 | 0 |
| 4 | 1370 | 224559 | 0 |
| 5–6 | 919 | 237377 | 0 |
| 7–9 | 241 | 242453 | 0 |
| 10–12 | 41 | ≥245000, OOG | 7 |
| ≥13 | 11 | ≥245000, OOG | 2 |

Total **108,289 own callbacks**, **58,426 mixed**, **9 measured OOG**, all mixed; recovery max gas **256,090**. Diagnostic effective-fee error including recovered callbacks **3.52214413017193e-06 bps**, not F. P passed. **Q/F/engine not run**, GATE none, engine **9803154..9803169 unused**. All requested F and engine paired/gas fields are unavailable, rather than zero. cp-b has **two flagged external sources**; retain this as its own reported measurement, not independent external verification of those sources.

### cp-c: optimized GATE=4 port passes its local sequence [b18-cp-c]

Specialized **sd=0 phase-zero spline interpolation** avoids loading/multiplying three zero Bernstein lanes while preserving the mathematical spline. Directly inlining three spline paths exceeded deployment size; a guarded internal helper avoids optimizer duplication, with recursive invalid-phase guard reported unreachable for phases 0..2. Log-space branch-rival clipping uses BAND=−ln(.997), avoiding redundant exponentials. No assembly, four storage slots retained. These changes explain why cp-c need not share cp-a/cp-b gas costs, rather than erasing their failures.

Unlimited probe **70000..70009**, **108,289 callbacks**, cap 245,000, all eight buckets observed with zero OOG:

| dt bucket | Mixed calls | Peak gas | Fits 215k |
|---|---:|---:|---|
| 1 | 44409 | 205536 | yes |
| 2 | 8248 | 210134 | yes |
| 3 | 3187 | 209196 | yes |
| 4 | 1370 | 208637 | yes |
| 5–6 | 919 | 220229 | no |
| 7–9 | 241 | 225292 | no |
| 10–12 | 41 | 238789 | no |
| ≥13 | 11 | 236844 | no |

Largest admissible GATE is **4**, frozen in Solidity and Python before F. The source hash is **`1cbd726f3a1f48950c60f0dafaae5d4e36c20481c5714efa72b82cae699dd064`**, runtime **22,370** (<24,576), static validation passed. Its exact unified diff versus TC-A and full ComboG reference are embedded in cp-c; that report is the reconstruction record, not a newly delivered contract here.

F uses effective fees (`replica2.clampf`), **70000..70049 ×2,000 =100,000 callbacks**, max error **3.087157057768408e-06 bps**, at **70008 / callback 1193 zero-based**, pyrevm peak **215,608**, OOG **0**. This observed overall F peak slightly exceeds 215k; that is not a failure of the prior rule, which applies to included **mixed buckets in a separate probe**, not every callback in F. It remains below 245k. No claim is made that all possible calls are bounded by the observed sample peak.

One engine holdout invocation on **9803170..9803185** (16 new seeds), independent candidate/qt1 vs Vanilla, reports:

```json
{"n":16,"mean_diff":0.704218514,"se":0.14637861,"worst5":[{"seed":9803182,"diff":-0.389123929},{"seed":9803170,"diff":-0.328728725},{"seed":9803173,"diff":0.186542099},{"seed":9803181,"diff":0.309465365},{"seed":9803176,"diff":0.325808468}]}
```

| Arm | afterSwap calls | peak | mean | OOG |
|---|---:|---:|---:|---:|
| cp-c GATE4 | 168935 | 229596 | 159902.1961523663 | 0 |
| qt1 | 168983 | 206239 | 138379.31941082832 | 0 |

Its result is **not** pooled into frozen TC-A: the policy differs. Neither is its 16-seed mean a directly paired comparison against TC-A on the 2,032 confirmation seeds. No cp-c-specific full Q window is reported in cp-c; the separately supplied gate screens measure the matching intended Python ComboG rule at all gates, but this merge does not revalidate source identity or substitute a gate-2 contract for gate 4. The task flags **one cp-c external source**; its hash/size/F/probe/engine success are retained as reported local observations, with unresolved external-provenance support.

### Port conclusion and seed accounting

Failure of cp-a or cp-b does **not** prove the COMBO idea impossible under gas limits; cp-c provides a concrete reported optimized counterexample to that broader conclusion. Conversely cp-c does **not** validate the other two binaries. Local static-validation passes in all three ports certify neither gas feasibility nor board advantage. No requester-input blocker was needed: cp-a/cp-b used their assignment's explicit gas-stop outcome. [b18-cp-a] [b18-cp-b] [b18-cp-c]

Engine ledger within these supplied inputs: tools smoke 9801088..9801089; confirmation assignments 9801090..9803137 with 9801986..9802001 retired/unobserved; cp-a allocation 9803138..9803153 not run; cp-b 9803154..9803169 not run; cp-c 9803170..9803185 consumed. A conservative ledger must preserve the unused allocated gaps rather than silently reuse them. This merge runs no seeds and makes no global availability claim about other roots. [b13-tools] [b15-a2s4] [b18-cp-a] [b18-cp-b] [b18-cp-c]

## COMBO dt-gate replica screens: choose and report

Both screens compare qt1, TwoComp and gates **1,2,3,4,6,9,10^9 (ungated)**, recomputing unrounded qt1 locally. Gate P precedes modifications; all nine spot checks above match to six decimals. Each policy follows its own fee/trade trajectory on a common seed, so callback counters and mixed/gated totals can change between gate policies. The gate does not collapse/reset the two-component posterior; only the ambiguous first-trade quote chooses mixed or single lookup. [b19-gate-choose] [b19-gate-report]

- Choose: **60000..61023**, n=1,024 per policy, **9,216 unique pairs**, no duplicates/missing. Local baseline means qt1 **529.971156871193**, TwoComp **530.416580586634**. Maximum ambiguous dt **44**. Mean worker elapsed seconds/run qt1 **0.167571**, TwoComp **0.226200**; sum across all nine policies **2.352633 seconds/seed** is not wall throughput. [b19-gate-choose]
- Report: **10000..12047**, n=2,048 per policy, **18,432 unique pairs**. First nine check pairs reused from checkpoints, not rerun. Baseline means qt1 **533.262830667**, TwoComp **533.687633550**. Maximum ambiguous dt **61**. No parameter selection uses report scores. [b19-gate-report]

Choose best by mean is **GATE2**, +0.645661931 ±0.019222756 versus qt1, +0.200238215 ±0.014499842 versus TwoComp. Its +0.007759927 ±0.007737350 versus ungated is weak evidence of a better gate. On report, gate2 gives +0.606664298 ±0.013416537 versus qt1 and +0.181861414 ±0.010766381 versus TwoComp. Gate3's larger report mean (+0.613015584 versus qt1; +0.015624621 ±0.003987627 versus ungated) is **descriptive holdout evidence**, not authorization to replace choose-selected gate2. Gas-selected cp-c GATE4 is a different selection criterion: gate4 replica results +0.637421242 choose and +0.601755886 report versus qt1. Choosing 4 for gas feasibility is not the same as claiming it maximizes replica score. [b19-gate-choose] [b19-gate-report] [b18-cp-c]

Complete compact gate summaries follow, preserving each input's comparisons with nine-decimal display precision. Every row keeps comparisons to qt1, TwoComp and ungated, each SE and worst5, mean edge and callback counts. Ungated-minus-itself is identically zero; worst5 is a seed-sorted tie, not an observed loss. Counts are per **full run**, not callback percentages; timings include worker contention.

Gate JSONL uses positional rows to avoid repetitive keys: **choose** `[GATE, mean_edge, mixed/run, gated/run, max_dt, seconds/run, vs_qt1, vs_TwoComp, vs_ungated]`; **report** omits seconds/run in these rows (the separate timing object is retained). Each comparison is `[mean_diff, SE, worst5]`; n is 1,024 for choose and 2,048 for report. Gate 10^9 is ungated. Display floats in compact JSON/positional rows are rounded to nine decimal places; counts and seeds remain exact. Prose retains the stated higher precision for key outcomes and fee tolerances.

### b19-gate-choose [b19-gate-choose]

```jsonl
[1,530.608241272,4476.389648438,1387.194335938,44,0.270560577,[0.637084401,0.01922676,[[60210,-3.506956414],[60036,-1.4310436],[60326,-1.293350082],[60446,-1.119383007],[60734,-1.058868441]]],[0.191660685,0.014377715,[[60210,-3.840548191],[60385,-1.597016797],[60549,-1.291941821],[60743,-1.198667488],[60014,-1.083095282]]],[-0.000817603,0.009955628,[[60887,-2.158774903],[60542,-0.966849485],[60640,-0.933827333],[60136,-0.781893983],[60216,-0.767935152]]]]
[2,530.616818802,5284.958007812,578.979492188,44,0.279385243,[0.645661931,0.019222756,[[60210,-2.926875385],[60036,-1.669763786],[60446,-1.357414347],[60326,-1.202529266],[60487,-1.088893819]]],[0.200238215,0.014499842,[[60210,-3.260467162],[60385,-1.725337564],[60582,-1.117856188],[60091,-1.091185639],[60263,-0.984827431]]],[0.007759927,0.00773735,[[60887,-2.298862148],[60821,-0.92751557],[60023,-0.819505965],[60654,-0.756682369],[60359,-0.744584575]]]]
[3,530.611866669,5606.036132812,256.681640625,44,0.283710672,[0.640709798,0.01958421,[[60210,-2.974565055],[60036,-1.67505953],[60326,-1.441721529],[60446,-1.233053037],[60936,-0.999498687]]],[0.195286083,0.01453711,[[60210,-3.308156831],[60385,-1.829314463],[60743,-1.121851357],[60168,-1.046962327],[60582,-1.016210353]]],[0.002807795,0.005637505,[[60887,-0.78598711],[60821,-0.646129652],[60060,-0.636643392],[60111,-0.629381124],[60785,-0.5557203]]]]
[4,530.608578113,5743.251953125,118.577148438,44,0.278744501,[0.637421242,0.019802761,[[60210,-3.016297825],[60036,-1.564085101],[60326,-1.414418222],[60446,-1.327113267],[60936,-1.189821983]]],[0.191997527,0.014815967,[[60210,-3.349889602],[60385,-1.938648023],[60927,-1.378182267],[60408,-1.201686333],[60743,-1.201188908]]],[-0.000480762,0.003886149,[[60111,-0.554288181],[60273,-0.53660023],[60959,-0.437452913],[60140,-0.431927117],[60808,-0.394257631]]]]
[6,530.607386897,5833.893554688,27.268554688,44,0.278343847,[0.636230026,0.019624463,[[60210,-2.928463208],[60036,-1.626335705],[60326,-1.433763839],[60936,-1.125783979],[60446,-1.122341686]]],[0.19080631,0.014743163,[[60210,-3.262054985],[60385,-1.864828796],[60927,-1.258582056],[60408,-1.230397996],[60936,-1.12064994]]],[-0.001671978,0.002044741,[[60273,-0.428824111],[60820,-0.416283246],[60395,-0.374099275],[60717,-0.312907931],[60591,-0.300561513]]]]
[9,530.608249704,5857.251953125,3.94140625,44,0.282606626,[0.637092833,0.019640833,[[60210,-2.927907219],[60036,-1.641087529],[60326,-1.442801811],[60446,-1.095809951],[60936,-1.092624043]]],[0.191669117,0.014732163,[[60210,-3.261498995],[60385,-1.887922343],[60927,-1.252767308],[60408,-1.235506575],[60936,-1.087490004]]],[-0.000809171,0.000834028,[[60824,-0.281320036],[60004,-0.233071473],[60359,-0.145507383],[60777,-0.145137265],[60542,-0.135058473]]]]
[1000000000,530.609058875,5861.13671875,0,44,0.28551065,[0.637902004,0.019627627,[[60210,-2.927907219],[60036,-1.641013531],[60326,-1.447042084],[60446,-1.0861158],[60936,-1.082149288]]],[0.192478288,0.0147529,[[60210,-3.261498995],[60385,-1.884375724],[60927,-1.291683731],[60408,-1.235506575],[60263,-1.080806427]]],[0.0,0.0,[[60000,0.0],[60001,0.0],[60002,0.0],[60003,0.0],[60004,0.0]]]]
```

### b19-gate-report [b19-gate-report]

```jsonl
[1,533.865724935,4490.302246094,1385.274414062,61,[0.602894269,0.013049023,[[10146,-3.759531625],[11062,-2.076886221],[11808,-1.774026934],[11376,-1.567617921],[10162,-1.35741023]]],[0.178091385,0.010368014,[[10475,-1.251763303],[11765,-1.246259323],[11376,-1.212980794],[10467,-1.183108],[11892,-1.116661693]]],[0.005503305,0.00719172,[[11311,-2.155673666],[11519,-1.793032123],[11161,-1.248949985],[11826,-1.160081245],[10016,-0.977042346]]]]
[2,533.869494964,5299.646484375,576.399414062,61,[0.606664298,0.013416537,[[10146,-3.5659916],[11062,-2.078200034],[10519,-1.956345722],[11808,-1.741799425],[11376,-1.717245606]]],[0.181861414,0.010766381,[[11695,-1.741338219],[10519,-1.62058378],[10467,-1.540844927],[10475,-1.441093345],[11376,-1.362608478]]],[0.009273334,0.005355321,[[10199,-0.833667338],[11002,-0.796229435],[10995,-0.762675135],[11556,-0.709020036],[10639,-0.708018103]]]]
[3,533.875846251,5620.082519531,254.584472656,61,[0.613015584,0.013583203,[[10146,-3.671695479],[11062,-2.113838938],[10519,-1.953006949],[11808,-1.872906052],[11376,-1.627892376]]],[0.188212701,0.010837125,[[10519,-1.617245007],[11695,-1.525708522],[10475,-1.387493457],[11164,-1.30157198],[10331,-1.287421917]]],[0.015624621,0.003987627,[[10184,-0.714366818],[11172,-0.634243021],[11943,-0.614654962],[11851,-0.588505099],[10163,-0.536947428]]]]
[4,533.864586552,5756.8125,117.071777344,61,[0.601755886,0.013533815,[[10146,-3.646769299],[11062,-2.324024168],[11808,-1.86874264],[10519,-1.839589919],[11376,-1.784058107]]],[0.176953002,0.010784215,[[11695,-1.721534604],[10475,-1.507304376],[10519,-1.503827977],[11376,-1.429420979],[11829,-1.255751252]]],[0.004364922,0.002811184,[[11172,-0.687569488],[10184,-0.607996609],[11414,-0.531830742],[11064,-0.514817107],[10383,-0.455048032]]]]
[6,533.861651512,5846.334472656,26.924316406,61,[0.598820846,0.01344203,[[10146,-3.574206003],[11062,-2.359111351],[11808,-1.825745009],[10519,-1.781826797],[11376,-1.69546499]]],[0.174017962,0.010769259,[[11695,-1.805190311],[10475,-1.654613762],[10519,-1.446064856],[11376,-1.340827863],[11892,-1.330854467]]],[0.001429882,0.001376664,[[11954,-0.499429764],[11939,-0.325520424],[10813,-0.309854692],[10768,-0.299456552],[10863,-0.288181727]]]]
[9,533.860282407,5869.179199219,3.882324219,61,[0.597451741,0.013384331,[[10146,-3.549169095],[11062,-2.335455949],[11808,-1.822082159],[10519,-1.778220958],[11376,-1.750440316]]],[0.172648857,0.010762013,[[11695,-1.828413356],[10475,-1.649650581],[10519,-1.442459016],[11376,-1.395803189],[11892,-1.356417248]]],[6.0777e-05,0.000589099,[[11906,-0.264108472],[11573,-0.259601735],[11858,-0.216833138],[10140,-0.204609614],[11270,-0.196428253]]]]
[1000000000,533.86022163,5873.050292969,0,61,[0.597390963,0.013387994,[[10146,-3.552496929],[11062,-2.334849144],[11808,-1.822738144],[10519,-1.782691465],[11376,-1.750295688]]],[0.17258808,0.010762654,[[11695,-1.829804011],[10475,-1.655734406],[10519,-1.446929524],[11376,-1.39565856],[11892,-1.361633324]]],[0.0,0.0,[[10000,0.0],[10001,0.0],[10002,0.0],[10003,0.0],[10004,0.0]]]]
```

```jsonl
{"qt1":533.262830667,"TwoComp":533.68763355,"1":533.865724935,"2":533.869494964,"3":533.875846251,"4":533.864586552,"6":533.861651512,"9":533.860282407,"ungated":533.86022163}
```

```jsonl
{"qt1":0.168068017,"TwoComp":0.225102753,"1":0.268651718,"2":0.27463536,"3":0.278576869,"4":0.275529692,"6":0.274647257,"9":0.278023694,"ungated":0.278996097}
```

### Gate-screen checks, limits and remaining uncertainty

Choose diagnostics on 10000..10002 compare all replica return fields: ungated ComboG exactly equals original Combo, same mixed counts and zero gated-away calls; GATE0 exactly equals TwoComp, with zero mixed calls. Gate0 was diagnostic only. Coverage/uniqueness/finite metrics and counters were checked locally. No source/computation/runtime failure reported. These checks do not establish Solidity parity or gas. [b19-gate-choose]

Report diagnostics use **2,000 synthetic callbacks**, ungated exact versus Combo and gate-zero exact versus TwoComp, observed mixed=1,862, gated=1,863, max dt=15. A separate intermediate-gate synthetic test observes **1,863 ambiguous** callbacks across dt=1..15, exact mixed-quote fees when dt≤gate, exact TwoComp single-quote fees otherwise, correct counters and two retained components. These are controlled common-history checks, not additional scored replica seeds or F. Mean elapsed seconds/run: qt1 0.168068017, TwoComp 0.225102753, gates1/2/3/4/6/9/ungated respectively 0.268651718 /0.274635360 /0.278576869 /0.275529692 /0.274647257 /0.278023694 /0.278996097. Eight bounded report scoring commands take 148.404–153.410 s apiece; none has missing pairs or timeout. [b19-gate-report]

Report temporary ComboG SHA-256 is `305ac0f36f0bb38bb9e7dec0e18b922a6bb31ac07ea4d33de5145972ae875de0`; checkpoint SHA-256 is `083f488d1527ebcd6eca791a041ed66119b39b982ed3c253393340293fe5b059`. The report also gives scorer/aggregator/verifier/boundary-checker hashes; those temporary tooling identities are not performance findings and are condensed here. Temporary files are not independently available. Its claimed source-quote recheck remains qualified by the task's one-source warning. [b19-gate-report; assignment]

Neither gate screen performs engine work, Solidity compilation, bytecode checks or fee-conformance F. Their replica effect is encouraging but cannot certify a board outcome. The only COMBO engine evidence in this root is cp-c's 16-seed GATE4 result. The frozen TC-A confirmations cannot be used as COMBO confirmations, and the tools' qt1 smoke cannot be used as a candidate's full F. No complete all-gates evidence package for a final new board submission is established solely by this root. [b13-tools] [b14-a1s1]–[b17-b2s4] [b18-cp-c] [b19-gate-choose] [b19-gate-report]

## Carry-forward decision

TC-A has the broad confirmation; cp-c GATE4 has full reported F and only a small engine holdout. Keep both evidence levels distinct, retain the missing chunk/source warnings, choose gates on choose only, and retain cuts=2. No board outcome is established. [b12-cuts-12] [b15-a2s4] [b18-cp-c] [b19-gate-choose] [b19-gate-report]

[b12-cuts-12]: ../../../batches/e3-twocomp-cuts/items/cuts-12/result.md

[b12-cuts-4]: ../../../batches/e3-twocomp-cuts/items/cuts-4/result.md

[b12-cuts-8]: ../../../batches/e3-twocomp-cuts/items/cuts-8/result.md

[b13-tools]: ../../../batches/e3-trunk-tools/items/tools/result.md

[b14-a1s1]: ../../../batches/e4-confirm-a1/items/a1s1/result.md

[b14-a1s2]: ../../../batches/e4-confirm-a1/items/a1s2/result.md

[b14-a1s3]: ../../../batches/e4-confirm-a1/items/a1s3/result.md

[b14-a1s4]: ../../../batches/e4-confirm-a1/items/a1s4/result.md

[b15-a2s1]: ../../../batches/e4-confirm-a2/items/a2s1/result.md

[b15-a2s2]: ../../../batches/e4-confirm-a2/items/a2s2/result.md

[b15-a2s3]: ../../../batches/e4-confirm-a2/items/a2s3/result.md

[b15-a2s4]: ../../../batches/e4-confirm-a2/items/a2s4/result.md

[b16-b1s1]: ../../../batches/e4-confirm-b1/items/b1s1/result.md

[b16-b1s2]: ../../../batches/e4-confirm-b1/items/b1s2/result.md

[b16-b1s3]: ../../../batches/e4-confirm-b1/items/b1s3/result.md

[b16-b1s4]: ../../../batches/e4-confirm-b1/items/b1s4/result.md

[b17-b2s1]: ../../../batches/e4-confirm-b2/items/b2s1/result.md

[b17-b2s2]: ../../../batches/e4-confirm-b2/items/b2s2/result.md

[b17-b2s3]: ../../../batches/e4-confirm-b2/items/b2s3/result.md

[b17-b2s4]: ../../../batches/e4-confirm-b2/items/b2s4/result.md

[b18-cp-a]: ../../../batches/e4-combo-port/items/cp-a/result.md

[b18-cp-b]: ../../../batches/e4-combo-port/items/cp-b/result.md

[b18-cp-c]: ../../../batches/e4-combo-port/items/cp-c/result.md

[b19-gate-choose]: ../../../batches/e4-combo-gate/items/gate-choose/result.md

[b19-gate-report]: ../../../batches/e4-combo-gate/items/gate-report/result.md