# Root merge 3/3: AMM entry results

Credit: Taylor (gtmcknight) for the solved policy, Gaussian filter, qm tables, fee policy and replica research at `amm-sim` commit `4812a6382311624e1506aca131ca35c378f930d9` (`research/solved`). The source records below are the evidence merged here; no new simulation or board submission is claimed.

## Executive result

The useful result is frozen ComboG(1), also called `TaylorComboGQmTrim2`, built on TC-A and Taylor's work. Its candidate source hash is `f904a486b1dcfbd6fcf40aa48920d1bb6b79ad2ac1c99a2cbbb16d4272c2c616`; qt1 is `c68887cff61180e12ba2b1ceb333edf76a830f91f63b5d775a8806fb9ec08aca` ([b20-cand], [b30-freeze]). The observed candidate runtime is 22,058 bytes versus the 24,576-byte limit. Across the completed ComboG engine shards, the largest reported candidate `Submission/afterSwap` peak is 220,843 gas (b27-merge-02), with zero recorded OOG/revert/other-halt counters; this is below 245,000, but is an observed-run result, not a universal bound ([b24-merge-02], [b25-merge-01], [b25-merge-02], [b26-merge-01], [b26-merge-02], [b27-merge-01], [b27-merge-02]).

The strongest complete engine merge is b27-merge-02: 256 paired seeds, 9805364–9805619, candidate minus qt1 mean `0.6394323026285214`, SE `0.039258074435103804`, worst five diffs `-0.8068662017860788`, `-0.7244625986389792`, `-0.7171290460264572`, `-0.7048299056227734`, `-0.666215324001314`; 219/256 differences were positive. It reports candidate peak 220,843 and qt1 peak 208,824, no failures, and exact seed coverage ([b27-merge-02]). Earlier complete ComboG shards likewise show positive descriptive means: b24-merge-02, n=256, mean `0.664085464941164`, SE `0.03844178572389`, peak 220,833; b25-merge-02, n=256, mean `0.721191294363`, SE `0.038823541077`, peak 220,634; b26-merge-01, n=256, mean `0.6521452939383456`, SE `0.039361412548901326`, peak 220,772; b26-merge-02, n=256, mean `0.62375952399740522489296875`, SE `0.03648301936388188636419109912296115783302`, peak 220,487; b27-merge-01, n=256, mean `0.5605887163961962`, SE `0.0350629110082062`, peak 220,260 ([b24-merge-02], [b25-merge-02], [b26-merge-01], [b26-merge-02], [b27-merge-01]). These are not all independent proof of a certified pass: see the evidence gaps below.

## What changed and why

The ComboG path adds whole-posterior/mixed-offset quoting to the Gaussian+qm baseline. The gas-diet records retain three fee-preserving trims: (a) skip the sd-axis search and unused k+1 Bernstein basis for `ph==0 && sd==0`; (b) use upper-bound knot-span searches; (c) collapse the zero-sd coefficient combination. The reported seed-70000 dt=1 peak progression was 215,761 (port), 215,494, 209,886, and 209,874 gas; the rejected buffer-reuse variant regressed to 201,294 in its separate comparison and was excluded ([b21-gd-ab-1], [b21-gd-abc]). The records explain why the trims preserve fee outputs and report identical fee-output hashes for the successful stages ([b21-gd-ab-1]).

There is an important disagreement in the gas-diet evidence. `gd-a` reports a final dt=1 peak of 216,709 and says no permitted gate meets the 205,000 pyrevm target; `gd-abc` reports 211,879 and reaches the same conclusion. `gd-ab-1` reports a later/frozen diet with dt=1 at 203,136 and selects GATE=1 as the largest admissible gate; `gd-ab-2` reports 212,006 at dt=1 and an OOG at >=13; it is therefore not a passing result. The later frozen ComboG evidence uses the gd-ab-1 lineage, not the contradictory failing probes ([b21-gd-a], [b21-gd-ab-1], [b21-gd-ab-2], [b21-gd-abc]).

Gate F is reported as passing for the frozen ComboG reference/contract pairing: 50 seeds × 2,000 callbacks = 100,000 callbacks, maximum fee error `3.0968576748141574e-06` bps, pyrevm peak 203,056, OOG 0 ([b21-gd-ab-1], [b29-audit], [b30-freeze]). The independent audit reproduced Gate P and only three report-window spot checks (seeds 10000–10002: candidate edges 444.306610755384, 571.876122920694, 526.150745926313; qt1 443.101741114667, 571.454483381928, 525.908441161236); it explicitly did not reproduce Q or F because its host could not install the Linux x86_64 wheel on Darwin arm64 ([b29-audit]). The freeze record also says Q choose n=1024 mean `0.6370844005364295`, SE `0.019226759996279156`, and report n=2048 mean `0.6028942685272641`, SE `0.013049022593029348`, but marks those as evidence attributed to the preceding worker rather than reruns ([b30-freeze]).

## TC-A and confirmation baseline

TC-A (`b87234c89e094f4955578417c1266129b0f96e6dfda68e3fb8866e00eeda71a2`) is the confirmed fallback candidate. Its runtime is 21,102 bytes; qt1 is 20,605 bytes; both validate successfully. f2 reports 128 paired seeds 9803316–9803443, mean `0.46435248549701`, SE `0.0491724827452028`, worst five `-0.859850201922427`, `-0.6386686805262229`, `-0.5996234822052884`, `-0.5554428382620245`, `-0.5322283175274265`; candidate peak 203,824, qt1 peak 208,743, OOG/reverts 0 ([b23-f2]). f3 independently reports 128 seeds 9803444–9803571, mean `0.5025452344454293`, SE `0.04905064989699061`, worst five `-1.03147340259369`, `-0.9393843353102511`, `-0.6109541214268575`, `-0.607562128369409`, `-0.4806390672154066`; it reports runtime 21,102 and both arms within the gas limit ([b23-f3]). b28 closes the reserved 16-seed gap, 9805620–9805635, with mean `0.4301337736878672`, SE `0.1769866300149901`, worst five `-0.8656433641698413`, `-0.4265507832329263`, `-0.35097484686747293`, `-0.30800992100307667`, `0.002209517872699962`; runtime 21,102, validation pass, and candidate gas limit pass ([b28-gap]).

The earlier candidate artifact records its construction, runtime 21,102, smoke paired mean `0.203532` over two seeds, and Gate-F evidence copied from earlier work; it explicitly says full P/Q/F and the 128-seed run were not rerun in that item ([b20-cand]). f1 contains only unavailable per-seed values and is not evidence of a result ([b23-f1]).

## Incomplete or blocked shards (retained, not imputed)

* b24-merge-01 is blocked before either source could be read because the execution process could not be created. It contains no paired, gas, runtime, or gate result; null is unavailable evidence, not zero or pass ([b24-merge-01]).
* b25-merge-01 has only 160 of 256 assigned pairs: mean `0.7475026363625332`, SE `0.04916703045671563`, 96 seeds missing; observed candidate peak 220,745 and zero recorded failures on available counters. The interrupted attempt's edge and gas are unknown ([b25-merge-01]).
* b23-f1 has unavailable rows throughout; no statistics are derived from it ([b23-f1]).
* b30-freeze explicitly leaves full Q, F, Solidity compile/validate, the gas probe, and ComboG confirmation engine ranges to later workers; its figures are attributed evidence, not those checks rerun in that item ([b30-freeze]).

## Why the ComboG engine numbers are descriptive, not an unconditional gate

Most ComboG confirmation merges have matching source/tool hashes and complete paired rows, but one or both inputs omit optimizer/viaIR/EVM/metadata compiler settings. b24-merge-02, b25-merge-01, b25-merge-02, b26-merge-01, b26-merge-02, and b27-merge-01 therefore explicitly withhold strict confirmation. b26-merge-01 additionally lacks b1s2 Baseline-role gas counters; b26-merge-02 says b1s3 supplies Submission-only gas counters; missing counters are not zero. b25-merge-01's a2s1 source citation was flagged as failing a later source check, without identifying which URL/passage failed. These limitations affect source corroboration and certification, not the fact that the supplied rows contain the stated arithmetic ([b25-merge-01], [b26-merge-01], [b26-merge-02]).

The supplied-source reliability warning applies specifically to claims relying on `e5-gas-diet/gd-a`, `gd-ab-1`, `gd-ab-2`, and `gd-abc`: respectively one, three, two, and one cited sources did not hold on reread or did not say what was quoted. Their local measurements are retained with that qualification; no external-source claim from them is treated as independently verified. Later records that reproduce hashes, source blocks, or measurements are still attributed to those later records, not silently backfilled.

The goal's quoted qt1 peak is 208,775 gas. The merged b27-merge-02 run measured qt1 208,824, and other shards measured nearby values (for example 209,290 and 209,144). This is a measurement disagreement with the quoted figure, not a 245,000-limit violation ([b27-merge-02], [b24-merge-02], [b26-merge-01]).

## Source index

Every supplied result was read: [b20-cand], [b21-gd-a], [b21-gd-ab-1], [b21-gd-ab-2], [b21-gd-abc], [b23-f1], [b23-f2], [b23-f3], [b24-merge-01], [b24-merge-02], [b25-merge-01], [b25-merge-02], [b26-merge-01], [b26-merge-02], [b27-merge-01], [b27-merge-02], [b28-gap], [b29-audit], and [b30-freeze]. These labels refer to the corresponding supplied files under `.imd/reads/artifacts/`; their input SHA-256 values are the ones in the task manifest. The primary external URLs named by the records are Taylor's pinned `gates.py`, the qt1/TC-A source files, the frozen diff artifacts, and the pinned challenge `setup.sh`, `check.py`, `engine.py`, and `MatchRunner` sources. No source was silently discarded.

[b20-cand]: .imd/reads/artifacts/b20-cand
[b21-gd-a]: .imd/reads/artifacts/b21-gd-a
[b21-gd-ab-1]: .imd/reads/artifacts/b21-gd-ab-1
[b21-gd-ab-2]: .imd/reads/artifacts/b21-gd-ab-2
[b21-gd-abc]: .imd/reads/artifacts/b21-gd-abc
[b23-f1]: .imd/reads/artifacts/b23-f1
[b23-f2]: .imd/reads/artifacts/b23-f2
[b23-f3]: .imd/reads/artifacts/b23-f3
[b24-merge-01]: .imd/reads/artifacts/b24-merge-01
[b24-merge-02]: .imd/reads/artifacts/b24-merge-02
[b25-merge-01]: .imd/reads/artifacts/b25-merge-01
[b25-merge-02]: .imd/reads/artifacts/b25-merge-02
[b26-merge-01]: .imd/reads/artifacts/b26-merge-01
[b26-merge-02]: .imd/reads/artifacts/b26-merge-02
[b27-merge-01]: .imd/reads/artifacts/b27-merge-01
[b27-merge-02]: .imd/reads/artifacts/b27-merge-02
[b28-gap]: .imd/reads/artifacts/b28-gap
[b29-audit]: .imd/reads/artifacts/b29-audit
[b30-freeze]: .imd/reads/artifacts/b30-freeze