# Root merge 2 of 2: 23 results (search rounds c3/c4, speed b3, opportunity d4)

Credit: Taylor (gtmcknight) — github.com/gtmcknight/amm-sim at 4812a6382311624e1506aca131ca35c378f930d9, research/solved. That is the solved policy, the exact-arithmetic arb/retail tell and the U1 tables that QLX5 is built on. Every result merged here credits Taylor.

## Bottom line

- **No candidate came out of these 23 results.** Every search arm in the 19 replica searches (c3-search-a, c3-search-b, c4-search-a, c4-search-b) hit the futility stop (cumulative paired mean + 2·se < 0.03). None was frozen, the report block 10000..12047 was never opened, and `advance=false` everywhere.
- **No engine seed was used.** None of the results ran fresh E seeds (10,200,000+), compiled-and-gated a contract (P/Q/T/F/G/E), or submitted anything. Every gain figure below is **replica, choosing-block evidence only** (seeds 64000..65023).
- **Best stopped arms, for diagnosis only:** about +0.012 to +0.014 over QLX5 at se about 0.007. Examples: clip 0.99675 + pull 0.25 gave +0.0142 (se 0.0070, n 512), from b24-clip-pull. Phase-2 SD ×1.1 gave +0.0141 (se 0.0066, n 384), from b28-sd-phase. This is far short of the +0.04 needed to bring back a contract and the roughly +0.08 the goal needs.
- **Oracle probes (d4) show little headroom** in two sub-mechanisms. A perfect split test is worth +0.0044 (se 0.0055), from b32-split-truth. Perfect first-callback arb/retail labels are worth +0.0106 (se 0.0071), from b32-arb-truth. Both stopped below 0.03. Both results say they are sensitivity tests, not upper bounds.
- **Infrastructure gain that holds:** the Cython build of the replica is bit-identical to the engine and about 1.53–1.54× faster (b22-cython, re-checked independently by b23-cython).

## Common setup (as each result states it)

- **Baseline:** unchanged QLX5. Solidity sha256 e183e5bc3fb794b7067703b10a7da9920267aa5f4caa968e16ca101b02338f40 (47,230 chars), from https://api.imd.fun/artifacts/1ef80bfb6d6791b877b1f4048a5e63cf2ae54153e6e8763ae3f8ab13132dfb15.
- **Replica:** exact integer port `qlxcore.py`, sha256 701dbfd1175fee7d129de92db21b1ddc78645796c422b29d8efba2eda501ab00, with `enginecore_f.py` 60af56a7570fabd603c6374d38a38f88b3c35a8f1e8192f588769460a96bfcfd and `qlx_tables.json` 8c6d33c5c1024bc23593f46123aad1712c0cc8af3f4a118c5875258f9d7b81a6. The bundle is https://api.imd.fun/artifacts/60dc237fa0a4d42f3b6e2d2bed61c1a2df08d27c31ccd95cce508ee9c8689de4 (tar 0e8adc477297130b731395b8494b6652c982d2c865306a317e139835d21e27f3). The audit is https://api.imd.fun/artifacts/362fb97f041087bf3548c302af4c0f82d2537d6a6c0157a95ac06d0cb70a5ce4.
- **Kit:** https://raw.githubusercontent.com/identity-md-launches/goal-3178-build-shared-evaluation-kit/45e7563d1a29ffca9d608fdf60c90bf2624d2d01/. The `score.py` sha256 is 7b9fa5e37695a5d1b048efe91a8b6c45d31bd4245a733261774c871fe9105a43 (per b18-fee-scale-fine).
- **Protocol:** 128-seed rounds on 64000..65023. Stop when cumulative mean + 2·se < 0.03. A setting is selected only if it completes 1,024 seeds; it is then frozen before the report on 10000..12047.
- **Baseline smoke:** every search reproduced the four unrounded audit rows bit-for-bit before searching. For example, seed 10010512 gave 606.1300985640944 (hex 4082f10a711db056) and seed 10010513 gave 482.77829524211705.
- **Where the replica is proven, and where it is not:**
  - Per A/60dc237f as cited by b14-pull-window and b14-three-window, it is proven against the engine only at the QLX5 defaults and at split=0 (LEAN).
  - The c4 results cite A/72b58a14 (b23-cython) for 512/512 bit-exact parity of unchanged QLX5.
  - **No changed-knob variant in any result is engine-checked.**
  - One exception: b14-window checked its split_window variants against the edited contract bytecode in pyrevm on 16 seeds, and fees were equal on every callback. That check was still not against the engine.
- **QLX5 baseline means on the choosing seeds,** useful for cross-checking (unchanged QLX5, replica): 534.99783 on 64000..64127; 532.37208 on ..64255; 536.71001 on ..64383; 535.21913 on ..64511; 534.45031 on ..64639; 532.26268 on ..64767; 534.2517 on ..64895.

## Source-check caveat (from the brief)

The brief says the sources these results cite did not hold when re-read for the following, so their quoted sources should be weighed down:

| Result | Sources that failed |
|---|---|
| c3-search-a/window | 6 |
| c3-search-a/three-window | 3 |
| c3-search-a/pull-window | 4 |
| c3-search-a/pull-three | 2 |
| c3-search-a/three-way | 2 |
| c3-search-b/sd-fine | 1 |
| c3-search-b/clip-fine | 1 |
| c3-search-b/fee-scale-fine | 2 |
| c3-search-b/fee-offset-fine | 4 |
| c3-search-b/phase2-blend | 1 |
| b3-speed/cython | 1 |
| c4-search-a/clip-blend | 2 |
| c4-search-a/clip-pull | 2 |
| c4-search-a/blend-pull | 1 |
| c4-search-a/clip-blend-window | 2 |
| c4-search-b/split-radius | 1 |
| c4-search-b/sd-phase | 1 |
| c4-search-b/rival-phase | 2 |
| c4-search-b/second-retail | 1 |
| d4-opportunity/split-truth | 1 |

Only three results are free of flagged sources: b23-cython (b3-speed-check), b28-level-curve and b32-arb-truth.

**Where it matters.** The cited sources are mostly the pinned artifacts and kit URLs listed above. The results themselves do not say which quoted passage failed. So I cannot tell which specific claim is affected, and I have not re-read those sources here.

The numeric results do not rest on those quotes. They are the workers' own replica runs, and each result carries its unrounded paired data and hashes. The context claims taken from cited sources do rest on them. These include:
- replica-vs-engine parity "at defaults and split=0" (A/60dc237f);
- the 512-seed audit (A/362fb97f, A/72b58a14);
- the 0.95 runs/core-s figure;
- the QLX5 gas peak of 208,366 quoted in b28-split-radius.

Treat those as unconfirmed by the results that quote them. b18-clip-fine records its own `source_recheck`, which found the replica artifact unchanged by sha256.

## Results by line

All figures below are paired gain = candidate − unchanged QLX5 (replica edge), written as mean (se, n). Seeds start at 64000. **Every arm stopped.** Each one comes from the result named in its heading.

### Split test: window, number of candidates, pull (c3-search-a)

The knobs:
- `split_window`: the split test runs when timestamp < previous own callback + W. QLX5 uses W=7.
- `split_nc`: the number of candidates. QLX5 uses 5.
- `pull_alpha`: the fraction ln r moves toward ln c on a retail read with no split hit. QLX5 uses 0.35 (semantics as stated in b14-pull-window).

**b14-window** (nc=5)

| Setting | Gain |
|---|---|
| W9 | +0.0016 (0.0047, 128) |
| W13 | +0.0067 (0.0062, 128) |
| W17 | mean+2se 0.0201 at n 128 |
| W25 | +0.0077 (0.0062, 128) |

- The mean+2se values were 0.0111, 0.0191, 0.0201 and 0.0201.
- W17 and W25 gave identical edges on 127 of 128 seeds, and W13 and W17 on 122 of 128. The result says the arms are "close to one test, not four".
- Split tries rise only about 0.3–0.4% with a wider window: 901,085 for QLX5 against 903,534 at W9. The QLX5 hit rate is 0.8912.
- Gas from pyrevm on 16 seeds: the per-call peak rose about 11,800 for W≥13. This was not measured in the engine.
- Creation bytecode is 22,469 bytes for every variant. Runtime size was not measured.

**b14-three-window** (nc=3)

| Setting | Gain |
|---|---|
| W9 | +0.0030 (0.0073, 128) |
| W13 | +0.0034 (0.0071, 128) |
| W17 | +0.0054 (0.0069, 128) |
| W25 | +0.0055 (0.0069, 128) |

The hit rate with 3 candidates was 0.817–0.818, against 0.891 for QLX5.

**b14-pull-three** (nc=3, W=7)

| Setting | Gain |
|---|---|
| α 0.10 | +0.0027 (0.0101, 384) |
| α 0.15 | +0.0048 (0.0121, 256) |
| α 0.25 | −0.0037 (0.0112, 128) |
| α 0.30 | +0.0100 (0.0076, 256) |

The result also gives a Solidity edit recipe with sha256 29ce62b22a1ad3659849e37886f8e9249118645b951dfa0ff6f8fb90b86fab4f. It was not compiled or certified.

**b14-pull-window** (nc=5, W=11)

| Setting | Gain |
|---|---|
| α 0.10 | +0.0052 (0.0085, 512) |
| α 0.15 | +0.0087 (0.0086, 512) |
| α 0.25 | +0.0041 (0.0101, 128) |
| α 0.30 | +0.0128 (0.0073, 256) |

The headline field is α 0.15, because it has the most seeds.

**b14-three-way** (nc=3)

| Setting | Gain |
|---|---|
| W11, α 0.15 | +0.0049 (0.0125, 256) |
| W11, α 0.25 | +0.0032 (0.0111, 128) |
| W17, α 0.15 | n 256, stopped (round 1: +0.0050 se 0.0163) |
| W17, α 0.25 | +0.0005 (0.0112, 128) |

**Reading.** Wider windows, three candidates and smaller pulls all gave small positive point estimates (+0.002 to +0.013), but none reached +0.03. Every result notes that a futility stop does not prove a zero effect.

### Fine scans of single constants (c3-search-b)

**b18-sd-fine.** Multiplier on the SD lookup coordinate; the tables are unchanged.

| Setting | Gain |
|---|---|
| ×0.90 | −0.0035 (0.0122, 128) |
| ×0.95 | −0.0028 (0.0109, 128) |
| ×1.05 | +0.0086 (0.0098, 128) |
| ×1.10 | +0.0030 (0.0123, 128) |

**b18-clip-fine.** Rival clip gamma; QLX5 uses 0.997, and the candidate gamma stays at 0.997.

| Setting | Gain |
|---|---|
| 0.9965 | +0.0067 (0.0078, 512) |
| 0.99675 | +0.0133 (0.0069, 512) |
| 0.99725 | −0.0576 (0.0190, 128) |
| 0.9975 | −0.2702 (0.0303, 128) |

The top-level gain is null by that result's convention. **Tightening the clip is clearly harmful.**

**b18-fee-scale-fine.** xb and xa multiplied by M/10000 before the fee exp.

| Setting | Gain |
|---|---|
| M 9950 | −0.0758 (0.0283, 128) |
| M 9975 | −0.0329 (0.0200, 128) |
| M 10025 | −0.0026 (0.0133, 256) |
| M 10050 | −0.0250 (0.0237, 128) |

The QLX5 fee scale looks locally optimal.

**b18-fee-offset-fine.** Fee offset B.

| Setting | Gain |
|---|---|
| −0.10 bps | −0.0007 (0.0119, 128) |
| −0.05 bps | −0.0024 (0.0102, 128) |
| +0.05 bps | −0.0273 (0.0085, 128) |
| +0.10 bps | −0.0425 (0.0113, 128) |

A positive offset is about 3.2 to 3.8 se harmful. The result also notes that the kit's default 3-se rule would not have stopped the negative-offset arms.

**b18-phase2-blend.** In phase 2 with the rival synced, the surface is blended toward table qt(1) by L/10000.

| Setting | Gain |
|---|---|
| L 1250 | +0.0026 (0.0097, 128) |
| L 2500 | +0.0101 (0.0071, 384) |
| L 5000 | +0.0125 (0.0073, 512) |
| L 7500 | −0.0049 (0.0147, 128) |

### Joint compositions of the best c3 directions (c4-search-a)

These results ran on the Cython replica. Each says it did not run the components alone and does not assume additivity.

**b24-clip-blend**

| Setting | Gain |
|---|---|
| clip 0.9965, L 2500 | +0.0094 (0.0073, 768) |
| clip 0.9965, L 5000 | +0.0102 (0.0083, 640) |
| clip 0.99675, L 2500 | +0.0131 (0.0067, 640) |
| clip 0.99675, L 5000 | +0.0115 (0.0071, 768) |

**b24-clip-pull** (clip 0.99675)

| Setting | Gain |
|---|---|
| α 0.10 | +0.0109 (0.0079, 640) |
| α 0.15 | +0.0116 (0.0086, 512) |
| α 0.25 | +0.0142 (0.0070, 512) |
| α 0.30 | +0.0083 (0.0067, 512) |

The +0.0142 at α 0.25 is the highest stopped mean among the joint compositions (b24).

**b24-blend-pull** (L 5000)

| Setting | Gain |
|---|---|
| α 0.10 | +0.0049 (0.0103, 512) |
| α 0.15 | +0.0091 (0.0087, 640) |
| α 0.25 | +0.0093 (0.0075, 640) |
| α 0.30 | +0.0136 (0.0077, 512) |

**b24-clip-blend-window** (L 5000, clip 0.99675, α 0.15, nc 5)

| Setting | Gain |
|---|---|
| W9 | +0.0124 (0.0078, 896) |
| W13 | +0.0125 (0.0082, 768) |
| W17 | +0.0129 (0.0081, 768) |
| W25 | +0.0127 (0.0082, 768) |

The result reads this as: early rounds were near +0.037..+0.041 at n≤384, then the gain decayed to about +0.012..+0.013, and the window has little effect.

**Reading.** Combining clip, blend and pull does not add up. The joint arms sit at about +0.009..+0.014, much like the best single arms (clip 0.99675 at +0.0133; L 5000 at +0.0125).

### New structural mechanisms (c4-search-b)

**b28-split-radius.** More split candidates, with offsets up to ±4.

| Setting | Gain |
|---|---|
| nc 7 | +0.0033 (0.0026, 128) |
| nc 9 | +0.0016 (0.0040, 128) |

- nc 7: 41 seeds better, 32 worse, 55 equal.
- Engine gas for these variants was not measured. The result cites a QLX5 peak of 208,366 against the 245,000 limit, which is a flagged-source claim.

**b28-sd-phase.** SD multiplier applied per phase.

| Setting | Gain |
|---|---|
| phase 1 ×0.9 | −0.0040 (0.0115, 128) |
| phase 1 ×1.1 | −0.0009 (0.0104, 128) |
| phase 2 ×0.9 | +0.0065 (0.0099, 128) |
| phase 2 ×1.1 | +0.0141 (0.0066, 384) |

- The phase 2 ×1.1 arm was at +0.018 in round 1.
- The SD coordinate changed on 29.6% of calls in the phase-1 arms and on 12.4% in the phase-2 arms.

**b28-rival-phase.** Rival rescaling per phase.

| Setting | Gain |
|---|---|
| p1 M9000 | −0.0520 (0.0226, 128) |
| p1 M11000 | −0.0445 (0.0248, 128) |
| p2 M9000 | −0.0450 (0.0150, 128) |
| p2 M11000 | −0.0082 (0.0113, 256) |

The p2 M11000 arm was +0.015 at n 128. Phase-1 rescaling is harmful in both directions.

**b28-level-curve.** tt += B·tt·(U−tt)/(10000·U), active on about 42% of fee evaluations.

| Setting | Gain |
|---|---|
| B −5000 | +0.0048 (0.0078, 128) |
| B −2500 | +0.0106 (0.0075, 128) |
| B +2500 | −0.0010 (0.0081, 128) |
| B +5000 | +0.0106 (0.0063, 384) |

**b28-second-retail.** Blend at the cnt==2 synced phase-2 branch only, which is about 14.7% of callbacks.

| Setting | Gain |
|---|---|
| L 1250 | +0.0113 (0.0087, 128) |
| L 2500 | +0.0075 (0.0104, 128) |
| L 5000 | +0.0027 (0.0135, 128) |
| L 7500 | −0.0004 (0.0131, 128) |

**Where results disagree.**
- **Phase-2 blend:** b18-phase2-blend (all synced phase-2 counts) is best at L 5000, while b28-second-retail (cnt==2 only) is best at L 1250 and falls as L rises. b28-second-retail notes that restricting the blend to cnt==2 did not change the outcome.
- **SD multiplier:** b18-sd-fine is best at ×1.05 (+0.0086) and ×1.10 is weaker (+0.0030, n 128). b28-sd-phase finds ×1.1 helpful in phase 2 only (+0.0141, n 384) and slightly negative in phase 1. These are consistent if the phase-1 and phase-2 effects cancel. Neither result tested that directly.

### Oracle headroom probes (d4-opportunity)

**b32-split-truth**
- Truth replaces the split-test boolean qx: +0.0044 (0.0055, 128), 66 wins and 62 losses.
- The two halves were +0.0034 (0.0084, 64) and +0.0054 (0.0072, 64).
- The result concludes that this line "offers no headroom worth a deployable feature".
- Truth here is defined as a router amount > 0.0001 to the normalizer.
- This result has a flagged source.

**b32-arb-truth**
- Truth replaces the posterior pi at the first callback of each timestamp: +0.0106 (0.0071, 128).
- Seeds with at least one false-arb label (106/128) gained +0.0121 (0.0084). The others gained +0.0036 (0.0095).
- The correlation between per-seed diff and false-arb count is 0.31. The per-seed sd of 0.081 is mostly path noise.
- This is not an upper bound: same-step callbacks and qx are left untouched.

### Speed (b3-speed, b3-speed-check)

**b22-cython**
- Cython build of the policy, tested on 64 old seeds 10010512..10010575 for both QLX5 and LEAN: 64/64 bit-identical.
- 1,417,005 callbacks with 0 mismatches in inputs, fee WADs and full policy state.
- Median wall speedup 1.5397×, i.e. +54.0%. Runs per core-second: 2.563 against 1.662 for the control (8 workers, 32 seeds, 6 alternating rounds).

Caveats from the result:
- The engine core and the callback bridge are unchanged; the policy is still CPython big-int arithmetic.
- The .so is not bit-reproducible across builds, though the generated C is byte-identical. It is CPython 3.12 / linux x86_64 only.
- **Numba cache hazard:** use a separate NUMBA_CACHE_DIR per implementation. Otherwise a qlxcore-only process can fail with ModuleNotFoundError: qlxcore_cy.
- Parity covers default knobs and split=0 only.

**b23-cython** (independent check of b22, https://api.imd.fun/artifacts/8d5400696659b56bc12eeffc34dec5e58c5c119ddddaca681792db59586dd760)
- 512/512 seeds 10010512..10011023 gave exact edge bits against the unrounded engine audit rows, and against the original port. Callback counts were equal.
- 20 trace and variant runs (4 seeds × default plus 4 knob variants) were identical in every callback input, fee WAD, state and label.
- Median speedup 1.5272× (range 1.4752–1.588), which reproduces b22's 1.5397× within noise.
- This result has no flagged sources, so it is the stronger evidence for Cython parity.

Other speed figures from the results:
- b32-arb-truth measured 1.29× wall on its machine.
- b14-window measured about 3.5 core-s per run for the pure-Python replica and cites 0.95 runs/core-s from A/60dc237f (a flagged-source claim). At that speed, a full 1,024-choose plus 2,048-report pass does not fit a 45-minute item.

## What does not exist in these results

- No engine E evaluation, no qt1 comparison, no AGE stacking (line a), no engine-faithful replica re-tune (line b), and no 1,024+ engine confirmation.
- None of the four lines (a)–(d) produced a contract that clears +0.04.
- No gas, OOG, deployed-size or P/Q/T/F/G/E figure for any variant, except the b14-window notes above.
- No report-block (10000..12047) data in any result.

## Implications for the goal (inference, not measured)

- The best stopped single and joint arms sit around +0.010..+0.014, with upper 2-se bounds of about 0.024–0.029.
- The oracle probes cap the split test at about +0.004 and the first-callback labels at about +0.011 in this form.
- On this evidence, the constant-tuning families searched here (split window/nc/pull, clip, SD, fee scale/offset, phase-2 blend, level curve, rival phase) cannot plausibly deliver the +0.04 to +0.08 needed.
- The directions that were positive but untested at higher n (clip 0.99675, phase-2 SD ×1.1, L 2500–5000, pull 0.25–0.30) could only matter as small additions on top of a larger mechanism such as AGE (line a). None of these results measured that.