# Root merge 7 of 8: 25 results (batches t5-d, t5-e, confirm-k01, t6-a, t6-b)

Goal: train the network's best fee policy for paradigm.xyz/puzzles/amm. The policy is T plus a learned 19-8-2 fee correction. Weights are carried from relay leg to relay leg. Board entry IB = 522.00.

Every figure below comes from the result named in brackets, for example `[n25]` = input `b39-n25-s04-h60-p24`. Input files are at `.imd/reads/artifacts/<id>`, and their originals are at `artifacts/goal/batches/<batch>/items/<item>/result.json`. All 25 inputs were present, parsed as JSON and matched their stated SHA-256. None was missing or empty.

The merger (this step) computed only the pooled figures marked **[pooled]**. They come from the per-item `n`, `sum` and `sumsq` fields over disjoint seed blocks, using the sample variance. Everything else is copied from the results, rounded to 4 decimals where marked ≈.

All performance numbers are the workers' own local measurements. None is a leaderboard score. The results say this themselves, for example the notes in [n16], [n20] and [q07].

## 0. Source-check warning (applies throughout)

The requester reports that every one of these 25 results cites 1–3 sources that did not hold when re-read. Counts:

- 3 sources each: q04 and q06.
- 2 sources each: n18, n24 and q07.
- 1 source each: all the others.

The sources files themselves are not among the inputs, so this merge cannot tell which URL failed in each result. The URLs that appear inside the results are listed below:

- The artifact pages for IB (`afd5183e…`), KIT-B (`48cd6a10…`), t5 START (`b4669de3…`, cited only by [n20]), t6 START / k01 CAND (`12606d82…`) and T03 (`3d001532…`).
- The pinned engine tree `github.com/benedictbrady/amm-challenge/tree/6b6921f8…`, cited by [k01-c2].

How to weigh them:

- **Engine measurements are not quoted from sources.** That covers the gates, speed, search curves, holdout, real-engine runs and gas. The workers made these measurements locally, and the failed sources do not directly undercut them.
- **Provenance claims are what the failed sources touch.** These are claims that a file is "the" IB/START/T03, that a hash matches an artifact page, that the configs follow `MatchRunner._build_configs`, and the brief's reference gains (+0.797, +0.793). Treat them as the worker's say-so, not as independently checked.
- Several results cross-check the same hashes and get the same answers. The IB code SHA-256 `301941829a…` matches the brief in [n19], [n22], [n21], [k01-c1..c6], [k07-c1..c2] and [q02..q07]. That agreement is the best evidence available here.

## 1. Headline findings

1. **No new weights in this root are confirmed better on the real engine at a precision that matters.**
   - Of 17 searches, 13 returned their START unchanged ("nothing beat START on the monitor").
   - [n25] beat its START on both replica and real, but only by about 2 SE on the real engine. Replica holdout: +0.0082, se 0.0041, n=8192. Real: +0.0456, se 0.0220, n=256.
   - [q01] beat START on the replica holdout (+0.0207, se 0.004) but **not** on the real engine (−0.0056, se 0.0157, n=512). The two engines disagree here.
   - [q04] showed the largest replica gain (+0.0450, se 0.0051, n=8192). It ran **replica-only** (no Solidity, EVM, gas or real engine), so it is unconfirmed.
   - [n24] was also replica-only and returned START.
2. **The k01 and k07 candidates are both real-confirmed ahead of IB and of T03** (gas-valid, 0 OOG):
   - k01 CAND (code `9253b6f3…`): +0.8221 vs IB (se 0.0163, n=3072) and +0.0678 vs T03 (se 0.0086, n=3072). **[pooled from k01-c1..c6]**
   - k07 CAND (code `039fa1a3…`): +0.8838 vs IB (se 0.0493, n=1024) and +0.0734 vs T03 (se 0.0147, n=1024). **[pooled from k07-c1..c2]**
   - The two CANDs were never paired with each other. Their gains over T03 differ by 0.006 ± ~0.017, which is indistinguishable.
3. **Both START policies used here beat IB by about +0.81 to +0.82 on the real engine:**
   - t5 START (code `1be16eb8…`): +0.8085, se 0.0147, n=3008 **[pooled, n16–n23 + n25 start_vs_IB]**.
   - t6 START (code `9253b6f3…`, the same code as k01 CAND): +0.8204, se 0.0182, n=2368 over the q items. Including k01 it is +0.8214, se 0.0121, n=5440 **[pooled]**.
   - The two STARTs were never run head-to-head, and their gains over IB are on different seeds. The +0.012 gap between them is well inside noise.
4. **The searches mostly lost ground over 35–80 minutes.** Most CMA-ES means drifted below START, with final monitor gains of −0.013 to −0.26.
   - Only three searches crossed above START: [n25] at sigma0 0.4 with population 24, [q04] at 1114 generations and a 30-minute sigma half-life, and [q01] after about 77 minutes.
   - The sister goal saw "+0.33 in 210 gens, +0.59 in 910". This root does not reproduce that. Its long run [q04] (1114 generations) gained only +0.045 on the replica. Note that the sister-goal figures are the brief's; no result here measured them.
5. **Gates were reproduced identically across machines, which shows determinism.**
   - Every t5 item measured Gate B at +0.8782 (se 0.0500, n=256) against the reference +0.797.
   - Every t6 item measured Gate B at +0.9156 (se 0.0439, n=512) against the reference +0.793. The absolute error of 0.1226 is under the 0.15 tolerance but close to it: the replica overstates START−IB by about 0.12.
   - The replica holdout values match exactly across items on the same seeds.
6. **Gas:** no OOG, revert, halt, tx error or bad return in any measured run.
   - The highest afterSwap peak seen is 238,289 (T03, [k01-c6]); the highest for a candidate is 238,271 (k01 CAND, [k01-c6]). Both are ≤ 245,000.
   - afterInitialize peaks are 243,227 (IB) and 243,234 (CAND/T03/START) [k01-c1..c4]. The brief's 245k limit names afterSwap only.
7. **No result measured anything against HA.** The brief's "+0.59 over HA" for IB was not re-measured in this root.

## 2. What each result started from

| Group | Results | START artifact | START code SHA-256 | START port SHA-256 |
|---|---|---|---|---|
| t5-d / t5-e | n16–n25 | `b4669de39651a749…` (cited in [n20].inputs) | `1be16eb82ba3170aef776d5f4061fb8c882ca52210628d97fd17f2dfe1096b9c` | `572bb0e6b7eb78ce84d95a48730ba05e699914643c0a062892a5a73970e1f372` |
| t6-a / t6-b | q01–q07 | `12606d82ec57ee9fe351945ec520b1ab8d79c8a472ff46b3bce6c5c0693b7b49` | `9253b6f3a49eafc1ed21ad19d9e2c0761c2ff151a6a7aa81e16de83834ad6a1b` | `732c0fb615480020795039a111e4a49a46f851e6f29720b092665b247d79006b` |
| confirm k01-c1..c6 | CAND = artifact `12606d82…` (same as t6 START) | — | `9253b6f3…` | — |
| confirm k07-c1..c2 | CAND (artifact URL not given in the results) | — | `039fa1a3fcab7d33a03457284bdb8858beea581eaddcd904631e8c0d91855608` | — |
| comparator T03 | artifact `3d001532cce4c2885307bb007a5170f77dd4b2f8151d041696e04a1c60a0f475` | — | `cb6d945511e1e10af78baa64c2a6cb25806f0998403ce6440654bfc3c70092d9` | — |
| IB | artifact `afd5183e…` | — | `301941829a44bb60977bb28181a5e4bfa6544f3696763f987054789b2611d686` | `f63227c5e0f63633efd132d6fb402ede665e5c9cb24481911471e8dc20a3362d` ([q02], [q04], [q06]) |

Gaps in provenance:

- The results do not say how t5 START, t6 START, k07 CAND and T03 are related, or which earlier leg produced each one.
- The `9253b6f3…` code is used both as the t6 relay START and as the k01 confirmation CAND. That identity is stated by hash in [q02], [q03] and [q05]–[q07], and in [k01-c1..c6].
- [n25]'s frozen output (`9b9d7e09…`) is **not** `9253b6f3…`, so it is not the k01 CAND.

Weight layout (consistent across [n16], [n17], [n19], [n20], [n21], [q01], [q03], [q05], [q06]):

- W = [enabled, 19 feature multipliers, 19 offsets, W1 8×19, b1 8, W2 2×8, b2 2, ANCHOR_COUNT_CAP, ANCHOR_LINEAR_K, ANCHOR_QUADRATIC_K, then TH_VALUES with the named constants replaced]. NW = 217.
- The search space is 219 dimensions: 178 head weights plus 41 constants.
- Weight transform: `start + 0.05·RMS(block)·z`. Constant transform: `start·2^(0.03 z)`, with integer constants rounded.
- Exceptions:
  - [n25] applied the constant transform to (1−d) for *_DECAY constants.
  - [q04] capped decay/alpha constants at 0.9995.
  - [q06] clamped decay/alpha/frac constants at ≤ 0.999.
  - [n24] clipped decays at 0.9999 and says the clip was never active.
  - [n20], [n21], [n23] and [q01] rejected infeasible decays instead.

## 3. Gates (A: START Solidity vs port; B: replica gain vs real reference; C: frozen Solidity vs frozen port)

A and C each replay the first 2,000 afterSwap callbacks from each of 50 replica markets: seeds 9,200,000–9,200,049 for A and 9,200,100–9,200,149 for C. No result used synthetic stress sequences.

| Result | A max bps (≤0.01) | C max bps (≤0.1) | B mean_diff (se, n) | B reference | Pass |
|---|---|---|---|---|---|
| n16, n18, n22 | 5.5488e-05 | 5.5664e-05 | 0.8782 (0.0500, 256), seeds 8,116,736–8,116,991 | 0.797 | yes |
| n17, n19, n20, n21, n23 | 5.5488e-05 | 5.5664e-05 | 0.8782 (0.0500, 256) | 0.797 | yes |
| n25 | 5.5488e-05 | 6.5461e-05 | 0.8782 (0.0500, 256) | 0.797 | yes |
| n24 | **not run** (no EVM on an aarch64 host) | **not run** | 0.8782 (0.0500, 256) | 0.797 | B only |
| q01 | 6.0336e-05 | 6.3531e-05 | 0.9156 (0.0439, 512), seeds 8,097,280–8,097,791 | 0.793 | yes |
| q02, q03, q05 | 6.0336e-05 | 6.1209e-05 | 0.9156 (0.0439, 512) | 0.793 | yes |
| q06, q07 | 6.0336e-05 | 6.1209e-05 | 0.9156 (0.0439, 512) | 0.793 | yes |
| q04 | **not run** (macOS arm64 host) | **not run** | 0.9157 (0.0439, 512) | 0.793 | B only |
| k01-c1..c6, k07-c1..c2 | not in scope ("confirmation only") | — | — | — | — |

- Gate B split: replica retail edge −0.1071 and arb edge +0.9853 on t5 START [n20], [n24], [n25]; −0.3121 and +1.2277 on t6 START [q01], [q03], [q05].
- [q04] also re-ran its START artifact's own holdout on seeds 41,030,000–41,038,191. It got +0.834 (se 0.0098, n=8192), equal to the artifact-reported 0.834.
- [n19] and [n22] state that freezing the unmodified START reproduced the START Solidity byte for byte.

## 4. Replica speed and the ≥ 300 markets/s rule (disagreement)

The goal says "search only at >= 300 markets/s". Nine of the 17 searching results measured below 300 and searched anyway. They used a lower branch (M=256, stop 45 minutes before the end), apparently from their item briefs:

| Result | markets/s (setup) |
|---|---|
| n16 | 453.6 (8 workers) |
| n17 | 462.6 |
| n18 | **227.5** |
| n19 | **190.0** |
| n20 | 456.0 at first, **137.6** after generation 44, **135.4** after generation 61 (BLAS limited to one thread from generation 41) |
| n21 | **94.7** (contended), **110.7** (isolated) |
| n22 | 356.9 at first, **145.7** from generation 52 |
| n23 | 845.5 |
| n24 | 890.1 (aarch64, replica-only) |
| n25 | 300.7 |
| q01 | 549.9 |
| q02 | **282.7** |
| q03 | **213.7** (8 workers); 131.0 with 24 workers |
| q04 | 1886.8 (macOS arm64, 10 processes) |
| q05 | **187.5** |
| q06 | **236.6** (4 CPUs) |
| q07 | 511.1 (24 workers) |

Treat the below-300 searches as weaker evidence. All of them returned START, so no weights depend on them.

## 5. Search legs (CMA-ES, population 16 unless noted; monitor = fixed seeds 30,000,000–30,002,047; selection = ES mean vs START on the monitor)

| Result | ES seed | sigma0 / cap | M | Generations | Search minutes | Final monitor gain vs START (se) | Best monitor | Training seeds | Returned |
|---|---|---|---|---|---|---|---|---|---|
| n16 | 20261516 | 0.3; 0.3·2^(−min/60) | 512 | 161 | 78.0 | −0.0369 (0.0101) | 0 (START) | 720,000,000–720,082,431 | START |
| n17 | 20261517 | 0.4; 0.4·0.5^(min/60) | 512 | 327 | 80.4 | −0.0825 (0.0094) | 0 (best non-START −0.0667) | 728,000,000–728,167,935 | START |
| n18 | 20261518, restarted with 20261522 at generation 4 | 0.5 | 256 | 116 | 46.2 | −0.0659 (0.0117) | 0 | 736,000,000–736,029,695 | START |
| n19 | 20261519 | 0.3; 0.3·0.5^(min/90) | 256 | 218 | 63.4 | −0.0508 (0.0102) | none beat START | 744,000,000–744,055,807 | START |
| n20 | 20261520 (population 24) | 0.4; 0.4·0.5^(min/45) | 512→256 | 86 | 64.2 | −0.0127 (0.0081) | 0 | 752,000,000–752,033,279 | START |
| n21 | 20261521 | 0.5; 0.5·0.5^(min/60) | 256 | 56 | 35.3 | −0.1167 (0.0085) | 0 | 760,000,000–760,014,335 | START |
| n22 | 20261522 | 0.4·0.5^(min/75) | 512→256 | 99 | 64.2 | −0.0644 (0.0092) | 0 | 768,000,000–768,038,399 | START |
| n23 | 20261523 | 0.3; 0.3·0.5^(min/45) | 512 | 357 | 61.5 | −0.0170 (0.0092) | 0 | 776,046,080–776,228,863 | START |
| n24 | 20261524 | 0.6; 0.6·0.5^(min/60) | 512 | 239 | 37.1 | −0.2564 (0.0129) | 0 (best non-START −0.139) | 784,000,000–784,122,367 | START (replica-only) |
| **n25** | 20261525 (population 24) | 0.4; 0.4·0.5^(min/60) | 512 | 97 | 68.3 | +0.0086 (0.0083) | **+0.0159 (0.0081), generation 78, 55.0 min** | 792,000,000–792,049,663 | **new, code `9b9d7e09…`** |
| **q01** | 20261601 | 0.3; 0.3·0.5^(min/45) | 512 | 322 | 78.7 | +0.0048 (0.0082), terminal | **+0.0100 (0.0077), 77.1 min** | 100,000,000–100,164,863 | **new, code `1d90b211…`** |
| q02 | 20261602 | 0.2; 0.2·0.5^(min/45) | 256 | 135 | 58.1 | −0.0166 (0.0087) | 0; all 12 checks between −0.035 and −0.017 | 108,000,000–108,034,559 | START |
| q03 | 20261603 | 0.4; 0.4·0.5^(min/45) | 256 | 123 | 59.3 (64.4 wall) | −0.0555 (0.0084) | 0 | 116,000,000–116,031,487 | START |
| **q04** | 20261604 | 0.3; 0.3·0.5^(min/30) | 512 | **1114** | 78.7 | +0.0180 (0.0101) | **+0.0206 (0.0101), generation 1000, 70.7 min** | 124,000,000–124,570,367 | **new params, no code (replica-only)** |
| q05 | 20261605 | 0.3; 0.3·0.5^(min/60) | 256 | 124 | 43.0 | −0.0551 (0.0085) | 0 | 132,000,000–132,031,743 | START |
| q06 | 20261606 | 0.2; 0.2·0.5^(min/60) | 256 | 144 | 36.3 | −0.0195 (0.0079) | 0 | 140,000,000–140,036,863 | START |
| q07 | 20261607 | 0.5; 0.5·0.5^(min/45) | 512 | 322 | 80.8 | −0.0134 (0.0095) | 0 | 148,000,000–148,164,863 | START |

Totals **[merger's sums of the table]**: t5 ran 1,756 generations over about 598.6 search minutes; t6 ran 2,284 generations over about 434.9 minutes. That is 4,040 generations in all.

Search irregularities the results report themselves:

- [n17]: generation 131 executed twice. The duplicate was not counted as independent, and reserved seed block 728,067,072–728,067,583 was skipped.
- [n18] restarted CMA at generation 4 with seed 20261522, the same ES seed [n22] used. They ran on different training seeds, so no data is shared.
- [n20]: 89 candidates were rejected by the domain check, and the terminal monitor was skipped to keep the confirmation reserve.
- [n23]: the first 90 exploratory generations used a wrong decay transform. They were excluded, and their seeds were not reused.
- [q01]: rejected decay/blend constants ≥ 1 after the first segment, to avoid unsigned underflow.
- [q04]: at the selected point, STEP_COUNT_CAP moved 64→62 and ANCHOR_COUNT_CAP 713→666. TOX_DECAY and LAMBDA_DECAY sat at the 0.9995 cap, so the search pushed past it. The largest relative changes were LAMBDA_COEF +0.1182, MIN_GATE −0.0998, ACT_DECAY −0.0984, TOX_DECAY +0.0732, PHAT_ALPHA_RETAIL −0.0718, DIR_COEF +0.0673, ANCHOR_COUNT_CAP −0.0659 and TOX_CAP +0.0537.
- [n24]: its final ES mean (information only) scored −0.2163 (se 0.0062) vs START on the holdout.
- [q06] claims the "previous leg used 0.5 with M=512 over 470 gens". No result in this root shows that leg, so the claim is unverified here.

## 6. Replica holdout (evaluated once per arm; not used for selection)

The t5 items used seeds 41,070,000–41,078,191 and the t6 items 41,090,000–41,098,191, both with n=8192. All items in a group share the same holdout seeds.

| Result | frozen − START (se) | frozen − IB (se) | START − IB (se) | frozen − IB retail / arb edge Δ |
|---|---|---|---|---|
| n16–n23 (frozen = START) | 0 | 0.7897 (0.0095) | 0.7897 (0.0095) | −0.2263 / +1.0160 (se 0.0103 / 0.0055 per [n18], [n19]) |
| n24 (replica-only; frozen = START) | 0 | 0.7897 (0.0095) | 0.7897 (0.0095) | −0.2263 / +1.0160 |
| **n25** | **+0.0082 (0.0041)**; retail +0.0670, arb −0.0588, retail volume +47.01 | 0.7978 (0.0098) | 0.7897 (0.0095) | −0.1594 / +0.9572 |
| **q01** | **+0.0207 (0.0040)**; retail +0.494, arb −0.4733 | 0.8688 (0.0095) | 0.8481 (0.0098) | +0.1213 / +0.7475 |
| q02, q03, q05, q06, q07 (frozen = START) | 0 | 0.8481 (0.0098) | 0.8481 (0.0098) | −0.3727 / +1.2208 |
| **q04** | **+0.0450 (0.0051)**; retail +0.3926, arb −0.3476, retail volume +72.46 | 0.8931 (0.0098) | 0.8481 (0.0098) | +0.0199 / +0.8731 |

Replica mean edges:

- t5: START 525.9183, IB 525.1287, n25 frozen 525.9265 [n24], [n25].
- t6: START 529.2876, IB 528.4395, q04 frozen 529.3326 [q02], [q04], [q05].
- Worst seed in the t5 holdout: −4.4725 (seed 41,072,956) [n17]. In the t6 holdout: −6.3158 (seed 41,092,519) [q03].

The three positive candidates all trade arb edge for retail edge relative to START: retail goes up and arb goes down.

## 7. Real engine (`amm_sim_rs.run_batch(X, VanillaStrategy, configs, 8)`, each arm alone, 64-seed commands)

### 7a. Search items: frozen vs START and vs IB

| Result | Seeds | n | frozen − START (se) | frozen/START − IB (se) | worst5 vs IB | retail / arb **volume** Δ vs IB | retail / arb **edge** Δ vs IB | valid |
|---|---|---|---|---|---|---|---|---|
| n16 | 8,163,840–8,164,351 | 512 | 0 | 0.7550 (0.0336) | −1.376, −1.349, −1.150, −1.040, −0.973 | +264.47 / −41.24 | null | yes |
| n17 | 8,164,864–8,165,375 | 512 | 0 | 0.7713 (0.0386) | −1.408, −1.192, −1.137, −1.072, −1.004 | +228.45 / −50.86 | null (IB reconstruction mismatch) | yes |
| n18 | 8,165,888–8,166,143 | 256 | 0 | 0.8653 (0.0441) | −0.731, −0.726, −0.670, −0.574, −0.526 | +242.84 / −49.91 | null | yes |
| n19 | 8,166,976–8,167,167 (IB) | **192** | 0 (n=256) | 0.8178 (0.0667) | −2.338, −2.224, −1.329, −1.157, −1.002 | +245.77 / −45.94 | null | **no** (see §8) |
| n20 | 8,167,936–8,168,191 | 256 | 0 | 0.8019 (0.0483) | −1.678, −1.665, −1.250, −0.877, −0.702 | +256.76 / −39.43 | −0.2224 (0.0562) / +1.0243 (0.0279) | yes |
| n21 | 8,168,960–8,169,215 | 256 | 0 | 0.8798 (0.0464) | −1.258, −1.132, −0.845, −0.772, −0.589 | +248.84 / −38.15 | −0.1367 (0.0477) / +1.0166 (0.0274) | yes |
| n22 | 8,169,984–8,170,239 | 256 | 0 | 0.8401 (0.0461) | −3.928, −1.162, −0.721, −0.701, −0.638 | +263.02 / −30.72 | null (decomposition on 8,170,240–8,170,303 failed, error 0.0212) | yes |
| n23 | 8,171,008–8,171,519 | 512 | 0 | 0.8188 (0.0386) | −5.31, −1.347, −0.901, −0.847, −0.813 | +258.96 / −31.29 | −0.1745 (0.0442) / +0.9933 (0.0205) | yes |
| n24 | not run (x86_64-only wheel on an aarch64 host) | — | — | — (reports START's own item figure +0.7968, se 0.0521, as *inherited*, not measured) | — | — | — | null |
| **n25** | 8,173,056–8,173,567 | frozen 512; START **256** | **+0.0456 (0.0220)**, n=256; worst5 −1.28, −1.007, −0.935, −0.781, −0.721 | frozen 0.8386 (0.0360), n=512; START 0.8091 (0.0491), n=256 | frozen −1.371, −1.26, −1.221, −1.197, −1.075 | frozen +324.37 / +54.71 | frozen −0.107 / +0.9456; vs START retail +0.0954, arb −0.0498 | yes |
| **q01** | 8,178,176–8,178,687 | 512 | **−0.0056 (0.0157)**; retail +0.476, arb −0.4816 | frozen 0.7997 (0.0381); START 0.8053 (0.0387) | frozen −2.391, −1.422, −1.145, −1.013, −0.908 | frozen +442.57 / +151.15 | frozen +0.0552 / +0.7445 | yes |
| q02 | 8,179,200–8,179,263 | **64** (768 planned) | 0 (identical code) | 0.7682 (0.0983) | −1.217, −0.521, −0.427, −0.392, −0.318 | +339.33 / −78.16 | null (reconstruction failed on some seeds) | yes, but incomplete |
| q03 | 8,180,224–8,180,479 | 256 | 0 | 0.7403 (0.0500) | −1.027, −0.835, −0.813, −0.745, −0.678 | — | −0.4772 / +1.2175 | yes |
| q04 | not run (macOS arm64) | — | — | — | — | — | — | null |
| q05 | 8,182,272–8,183,039 | 768 | 0 (identical code) | 0.8652 (0.0342) | −2.944, −2.728, −2.053, −1.815, −1.388 | +327.68 / −72.20 | null | yes |
| q06 | 8,183,296–8,183,551 | 256 | 0 (identical code) | 0.7844 (0.0477) | −1.583, −1.227, −0.933, −0.782, −0.698 | +318.27 / −72.98 | null | yes |
| q07 | 8,184,320–8,184,767 and 8,184,832–8,184,895 | 512 | 0 | 0.8330 (0.0398) | −1.681, −1.658, −1.628, −1.312, −1.260 | +342.49 / −62.95 | null | yes |

**[pooled]** t5 START (`1be16eb8…`) − IB over n16–n23 and n25's start_vs_IB: **+0.8085, se 0.0147, n=3008**. t6 START (`9253b6f3…`) − IB over q01–q03 and q05–q07: **+0.8204, se 0.0182, n=2368**.

Real mean edges per arm:

- [n21]: IB 520.3843, START 521.2642.
- [n25]: frozen 532.1461, START 532.0121, IB 531.3075.
- [q05]: frozen 528.8339, IB 527.9688.
- [q06]: frozen 528.2389, IB 527.4546.

These levels differ by seed block. They are not comparable to the board's 522.00 except by coincidence.

### 7b. Confirmation items (no search, port or replica; three arms, 512 seeds each)

| Result | Seeds | CAND − IB (se) | CAND − T03 (se) | T03 − IB (se) | CAND − IB worst5 | CAND − IB retail / arb volume Δ | Mean edge IB / CAND / T03 |
|---|---|---|---|---|---|---|---|
| k01-c1 | 8,174,080–8,174,591 | 0.7567 (0.0412) | 0.0366 (0.0187) | 0.7201 (0.0394) | −2.534, −2.495, −1.52, −1.375, −1.362 | +340.32 / −66.75 | 529.996 / 530.7527 / 530.7161 |
| k01-c2 | 8,174,592–8,175,103 | 0.8259 (0.0384) | 0.0566 (0.0183) | 0.7693 (0.0369) | −2.482, −1.432, −1.376, −1.306, −1.135 | +319.97 / −72.72 | 532.4717 / 533.2975 / 533.241 |
| k01-c3 | 8,175,104–8,175,615 | 0.8156 (0.0392) | 0.0855 (0.0200) | 0.7300 (0.0379) | −3.055, −2.835, −1.749, −1.192, −1.155 | sums +178,185.68 / −35,478.95 (≈ +348.0 / −69.3 per market **[merger ÷512]**) | 541.7443 / 542.5599 / 542.4744 |
| k01-c4 | 8,175,616–8,176,127 | 0.8469 (0.0380) | 0.0772 (0.0199) | 0.7697 (0.0369) | −2.25, −1.797, −1.719, −1.141, −1.108 | +327.62 / −79.72 | 530.9107 / 531.7576 / 531.6804 |
| k01-c5 | 8,176,128–8,176,639 | 0.8408 (0.0433) | 0.0661 (0.0286) | 0.7747 (0.0452) | −2.222, −2.213, −1.779, −1.701, −1.406 | +332.93 / −71.24 | 529.4248 / 530.2656 / 530.1995 |
| k01-c6 | 8,176,640–8,177,151 | 0.8471 (0.0390) | 0.0850 (0.0191) | 0.7621 (0.0356) | −1.877, −1.546, −1.415, −1.217, −1.05 | +314.61 / −77.18 | 522.3674 / 523.2145 / 523.1295 |
| **k01 [pooled]** | 8,174,080–8,177,151 | **0.8221 (0.0163), n=3072** | **0.0678 (0.0086)** | **0.7543 (0.0158)** | | | |
| k07-c1 | 8,177,152–8,177,663 | 0.8589 (0.0390) | 0.0724 (0.0178) | 0.7865 (0.0397) | −1.535, −1.483, −1.224, −0.974, −0.936 | +289.09 / −33.60 | 525.0403 / 525.8992 / 525.8268 |
| k07-c2 | 8,177,664–8,178,175 | 0.9087 (0.0906) | 0.0744 (0.0234) | 0.8343 (0.0838) | −2.383, −1.972, −1.291, −1.277, −1.155 | +271.15 / −53.60 | 523.3535 / 524.2622 / 524.1878 |
| **k07 [pooled]** | 8,177,152–8,178,175 | **0.8838 (0.0493), n=1024** | **0.0734 (0.0147)** | **0.8104 (0.0464)** | | | |

Further confirmation findings:

- k07-c2 has one outlier seed: CAND − IB best5 includes +43.457 (and T03 − IB +40.187). That inflates its se to 0.0906; the median is 0.777.
- [k01-c1]: CAND led IB in all 8 chunks, with chunk means 0.62–0.98. CAND was positive on 429 of 512 seeds vs IB and 273 of 512 vs T03.
- CAND vs T03 was negative in only a few chunks (k01-c1: 2 of 8; c2, c4, c5, k07-c1 and k07-c2: 1 of 8 each).
- Most of k01 CAND's gain over T03 comes with higher retail volume and lower arb volume: +32.7 to +45.7 retail and −23.5 to −32.7 arb [c2], [c4]–[c6]. k07 CAND instead has about zero volume change vs T03: −3.85 / +0.73 [k07-c1] and −0.72 / +7.28 [k07-c2]. So the two candidates beat T03 in different ways.
- The confirmations do not split real retail/arb edge. They say the engine exposes only edge, PnL and volumes.

## 8. Validity problems and protocol deviations (kept, not dropped)

- **n19, valid=false.** The first IB 64-seed block (8,166,912–8,166,975) ran, but postprocessing read IB `BASE_FEE = 4*BPS` as 4 raw WAD units. The block failed its arb-volume check and its aggregates and gas stats were lost. It was not re-run, so IB has n=192. No OOG was observed in the saved blocks.
- **n24, valid=null, replica-only.** The host was aarch64 Linux and setup failed with exit 133 on the x86_64 uv binary. There was no Solidity, EVM, gas or real engine. 50×2,000 gate-A sequences were recorded for later replay (sha256 `fae8b6d4…`). The worker used the Linux aarch64 uv instead of the macOS uv that the fallback brief named.
- **q04, valid=null, replica-only.** The host was macOS arm64, and installing the x86_64 wheel failed. code_sha256 is null and its params have never been frozen to Solidity or gas-checked. Its START artifact reports its own gate A at a 3.7e-05 bps maximum, which q04 quotes rather than measures.
- **q02: real engine only n=64 of 768 planned.** Running two arms concurrently slowed each chunk from 40 s to 240 s, and host load reached about 67. IB also ran an extra 8,179,264–8,179,327.
- **n25: START arm only n=256 of 512**, for lack of time. frozen_vs_START is therefore on 256 seeds.
- **n21: seed re-runs.** The first IB and START 64-seed runs completed but failed to serialize, and were repeated. One IB retry hit the 450-second command timeout. Baseline chunks were replayed to extract edge components, with replay edges matched to saved edges within 1e-9. This is a re-run of the same arm on the same seeds, which the brief forbids ("never reused"). The engine is deterministic, so the reported values should not change. 384 START/IB seeds were run, but only the first 256 are reported.
- **q07:** IB block 8,184,768–8,184,831 hit the 470-second limit without saving. It was excluded and replaced by the fresh block 8,184,832–8,184,895.
- **q03:** a reporting-helper probe ran IB and START on seeds 8,000,000–8,000,007, which are excluded from its results. Those are the lowest seeds of the brief's "fresh from 8000000 up" range. Whether another item also used them cannot be checked from these results.
- **Retail/arb edge reconstruction failures:**
  - [n17]: IB arms mismatched by 0.016–0.029.
  - [n22]: error 0.0212 against tolerance max(0.01, 1e-7·volume).
  - [q02]: some seeds failed.
  - These items report null real edge splits. Successful reconstructions report a maximum arb-volume error ≤ 1e-4: [n20], [n21], [n23], [q01], [q03].
- **No synthetic stress sequences** were run in any result. The brief's gates do not require them; several results set `stress: null`.
- **Real seed blocks are disjoint across all 25 results**, as far as the reported ranges show, running from 8,163,840 to 8,184,895. The replica holdout and Gate B seeds are deliberately shared within each group.

## 9. Gas (`amm_sim_rs.gas_stats()`; submission afterSwap peak; all OOG = 0)

| Result | Frozen/CAND | START | IB | T03 |
|---|---|---|---|---|
| n16 | 235,563 | 235,563 | 237,803 | |
| n17 | 237,421 | 237,421 | 234,825 | |
| n18 | 237,654 | 237,654 | 237,069 | |
| n19 | 235,406 | 235,406 | 232,014 (192 seeds) | |
| n20 | 235,247 | 235,247 | 234,704 | |
| n21 | 235,480 | 235,480 | 237,149 | |
| n22 | 237,600 | — | — | |
| n23 | 237,449 | 237,449 | 236,916 | |
| n25 | 237,433 | 237,421 | 234,965 | |
| q01 | 238,108 | 238,102 | 234,868 | |
| q02 | 232,641 (64 seeds) | = frozen | 237,710 | |
| q03 | 235,453 | — | — | |
| q05 | 237,479 | = frozen | 236,940 | |
| q06 | 235,454 | = frozen | 234,865 | |
| q07 | 237,676 | — | — | |
| k01-c1 | 237,594 | | 234,965 | 237,600 |
| k01-c2 | 235,550 | | 234,958 | 235,564 |
| k01-c3 | 235,423 | | 234,872 | 235,417 |
| k01-c4 | 238,102 | | 234,953 | 238,088 |
| k01-c5 | 235,739 | | 237,088 | 235,480 |
| k01-c6 | 238,271 | | 237,699 | 238,289 |
| k07-c1 | 237,455 | | 236,928 | 237,449 |
| k07-c2 | 237,691 | | 236,977 | 237,641 |

- The same code produces different peaks on different seed blocks: 235,423–238,271 for `9253b6f3…`. A peak therefore depends on the seeds as well as the code.
- The highest peak seen is 238,289, which leaves 6,711 gas below the 245,000 limit. The baseline Vanilla afterSwap peak is 22,592.
- [n24] and [q04] measured no gas. [n24] quotes START's item at 235,417 with 0 OOG as *inherited*.

## 10. Where results disagree

1. **Replica vs real for q01.** Replica holdout +0.0207 (se 0.004) against real −0.0056 (se 0.0157, n=512). The real-engine figure should govern. [q01]'s own note says no real improvement over START was shown.
2. **Replica vs real for n25.** Both are positive: replica +0.0082 (0.0041) and real +0.0456 (0.0220, n=256). The real gain is larger than the replica gain but has a wide se.
3. **Replica vs real level of START − IB.** Gate B overstates the real gap by about 0.08 (t5: 0.8782 vs 0.797) to about 0.12 (t6: 0.9156 vs 0.793). The pooled real gap in this root is +0.8085 for t5 and +0.8204 for t6 START. The ≈0.12 bias is close to the 0.15 tolerance, so small replica gains (< ~0.02) cannot be trusted to transfer.
4. **Per-item real START − IB estimates** range from 0.7403 [q03] to 0.8798 [n21] for essentially the same comparison. That spread is consistent with se ≈ 0.04–0.05 per 256–512 seeds.
5. **Speed rule.** See §4: nine items searched below 300 markets/s, against the goal's rule.
6. **Search outlook.** [q06] says a larger M, more generations or a larger sigma0 is "likely needed". [n24] (sigma0 0.6) and [n21] (0.5) drifted the furthest below START. [q04] (sigma0 0.3, fast host, 1114 generations) and [n25] (population 24) were the only ones to gain. More generations at moderate sigma fits these results better than a larger sigma0 does.

## 11. What the write-up can use

- **Best real-confirmed policies in this root:**
  - k01 CAND `9253b6f3…` (artifact `12606d82…`): +0.8221 vs IB (se 0.0163, n=3072). It also served as t6 START.
  - k07 CAND `039fa1a3…`: +0.8838 vs IB (se 0.0493, n=1024).
  - Both beat T03 by about +0.07. Neither has been compared with the other.
- **New weights produced in this root:**
  - [n25], code `9b9d7e098b185de26b98202e36a0513b30bd35e5997911ad2e8fc35102b5cd5a` with port `572bb0e6…`. Built from t5 START, real +0.0456 (0.0220, n=256) over it. It has never been compared with the k01/k07 CANDs or T03. Its START chain (`1be16eb8…`) is a different lineage from `9253b6f3…`.
  - [q01], code `1d90b211332d12978ee7737a0cfc134296ab0110a0d271defad0f95a2b33c853` with port `732c0fb6…`. Real −0.0056 vs `9253b6f3…`, so not an improvement.
  - [q04], params only. Replica +0.0450 (0.0051) over `9253b6f3…`. It needs freezing, gates A/C, gas and a real confirmation on a Linux x86_64 host before it counts.
- The full code, port and params for each are in the original result files (paths in the header). Appendix A copies the [n25] and [q04] parameters so this root carries them.
- **Not established in this root:** any comparison with HA; the sister-goal figures; the identity and lineage of T03 and k07 CAND; which cited sources failed (§0).

## Appendix A: parameters of the two candidates with a measured gain over their START

Copied from the results as written. Each block is compact JSON of the result's `params` (with `constants_wad` for [q04]). The port uses the W layout in §2.

### A.1 [n25] params (code `9b9d7e09…`, port `572bb0e6…`)

```json
{"W1":[[0.000422,0.574759,-0.796694,3.050619,-2.342248,0.729405,-1.26267,2.251104,-5.3754,-1.742979,-0.733145,-0.24914,0.216465,-2.238647,-0.338758,-0.399742,-1.261657,-0.100035,1.615155],[0.759754,0.891498,1.995728,2.699825,-0.199431,-0.592798,-0.428185,0.346759,-0.326248,0.251385,-0.070745,-1.844263,0.054356,-0.125856,0.001634,0.855388,0.14711,0.052218,1.113525],[0.869495,3.820601,-1.339245,0.695623,1.044956,2.305508,-1.839043,1.008444,1.257236,-0.74742,0.5556,0.039057,-0.214186,0.365886,0.181859,1.231518,-2.499867,-0.424445,-2.283589],[0.278556,-1.477117,1.075177,-0.374273,-1.160361,-0.360319,0.0342,-0.009635,0.76571,0.126386,0.176704,-1.944633,-0.275334,0.2825,0.22475,-1.078344,1.082104,-0.139126,-0.900989],[1.233612,0.600913,4.685786,0.02418,-2.041538,-1.320059,-1.078735,-0.664245,-0.42032,0.674221,-0.061985,-2.326161,-0.064476,-1.13653,0.412377,-0.745753,2.451993,-0.024598,0.590084],[1.317749,-1.749466,0.392823,-1.388934,3.967242,1.355755,4.079569,0.438071,-0.671893,-0.121588,-0.01403,3.726684,0.574392,-1.086409,0.042033,0.361233,-1.786501,-0.273296,-1.855875],[-1.087537,1.107008,0.082955,-0.608992,2.423701,0.605986,-1.193624,2.20977,1.314509,-1.51857,1.48696,1.217677,1.548595,-1.062323,-1.107055,-1.321703,0.966972,-0.924654,2.455277],[-2.479078,-2.757487,3.372963,3.675849,-0.225184,-0.807457,-1.889673,2.592366,0.582295,-0.847137,2.509357,-1.904566,1.316115,0.193038,0.675106,1.059467,-0.382273,-1.724914,1.225998]],"b1":[2.1544,-1.822274,-4.141372,-0.887778,-1.432278,-2.03544,-0.606873,0.422751],"W2":[[0.083451,-2.210759,1.003664,-0.652252,-3.165663,-0.598823,-0.895736,1.023424],[0.433156,-1.95763,-1.813964,3.604778,0.296439,-2.21434,0.815193,-0.295727]],"b2":[1.417671,3.04818],"constants":{"ELAPSED_CAP":7,"SIGNAL_THRESHOLD":0.001154014953967601,"DIR_DECAY":0.7221778099636065,"ACT_DECAY":0.3723876003163257,"SIZE_DECAY":0.495809761975746,"TOX_DECAY":0.9302310182818359,"SIGMA_DECAY":0.7212005921428287,"LAMBDA_DECAY":0.9920359922058728,"SIZE_BLEND_DECAY":0.8441947198768979,"TOX_BLEND_DECAY":0.26834412421849607,"ACT_BLEND_DECAY":0.987177999854639,"PHAT_ALPHA":0.2504805256964007,"PHAT_ALPHA_RETAIL":0.05356234376123943,"PHAT_ALPHA_SAME":0.14795575285335405,"DIR_IMPACT_MULT":4,"GATE_SIGMA_MULT":6.633036069633707,"MIN_GATE":0.029567091982864516,"TRADE_TOX_BOOST":0.2975184990833133,"STALE_ATTRACT_FRAC":0.6646343639473498,"RET_CAP":0.023292273390871303,"TOX_CAP":0.20034701733265145,"TRADE_RATIO_CAP":0.18482817870446008,"LAMBDA_CAP":1.1446064786296324,"STEP_COUNT_CAP":65,"BASE_FEE":0.000402840316818657,"SIGMA_COEF":0.20888233304711368,"LAMBDA_COEF":0.001261002488863107,"FLOW_SIZE_COEF":0.5132313532220983,"TOX_COEF":0.03180321375667443,"TOX_QUAD_COEF":1.6333451741218183,"ACT_COEF":8.96471566333491,"DIR_COEF":0.001861335687539192,"DIR_TOX_COEF":0.007726992221419456,"STALE_DIR_COEF":0.7483813325415388,"SIGMA_TOX_COEF":0.05625829813121399,"TAIL_KNEE":0.05609777555843318,"TAIL_SLOPE_PROTECT":0.8287237696094074,"TAIL_SLOPE_ATTRACT":0.8202754952647076,"ANCHOR_COUNT_CAP":737,"ANCHOR_LINEAR_K":0.6658526848821095,"ANCHOR_QUADRATIC_K":1.1271118524151191},"scaling":{"feature_order":["sigmaHat","lambdaHat","sizeHat","toxEma","actEma","direction","(spot-staleHat)/staleHat","signed_trade_ratio","arb_probability","first_in_step","uncertainty","min(silent,8)/8","anchor_mean","raw_size","step_trade_count","prev_bid_fee","prev_ask_fee","steps_since_arb_like_print","router_implied_vanilla_spot_dev"],"feature_multipliers":[1000.0,2.0,500.0,500.0,500.0,1.0,500.0,500.0,2.0,2.0,1000000.0,1.0,500.0,647.054817,1.395287,220.617911,228.148131,0.412565,274.335453],"feature_offsets":[-1.0,-1.0,-1.0,-1.0,-1.0,-1.0,0.0,0.0,-1.0,-1.0,-1.0,0.0,-1.0,-0.618293,-2.037262,-0.803057,-0.808615,-0.823811,0.001772],"weight_fixed_point_scale":1000000,"input_clip":[-4,4],"hidden_relu_clip":[0,4],"output_unit_fee":0.0001,"note":"unchanged from CG"}}
```

### A.2 [q04] params and constants_wad (replica-only; port `732c0fb6…`; never frozen to Solidity)

```json
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from CG"}},"constants_wad":{"ELAPSED_CAP":"7","SIGNAL_THRESHOLD":"1125308361604317","DIR_DECAY":"703822500092087296","ACT_DECAY":"327008801295396352","SIZE_DECAY":"522067713654493568","TOX_DECAY":"999500000000000000","SIGMA_DECAY":"708089297700016000","LAMBDA_DECAY":"999500000000000000","SIZE_BLEND_DECAY":"829509323200493952","TOX_BLEND_DECAY":"252162279704856992","ACT_BLEND_DECAY":"987082701807639808","PHAT_ALPHA":"254212609044790272","PHAT_ALPHA_RETAIL":"48288689347380728","PHAT_ALPHA_SAME":"144335273914019040","DIR_IMPACT_MULT":"4","GATE_SIGMA_MULT":"6548329805715864576","MIN_GATE":"26246176043254044","TRADE_TOX_BOOST":"290983026818146304","STALE_ATTRACT_FRAC":"716373657155241984","RET_CAP":"20006324379826696","TOX_CAP":"216740550128086976","TRADE_RATIO_CAP":"178512999771622176","LAMBDA_CAP":"1004217390930032256","STEP_COUNT_CAP":"62","BASE_FEE":"379782019282540","SIGMA_COEF":"201365316324133152","LAMBDA_COEF":"1445532582739514","FLOW_SIZE_COEF":"539440224292905472","TOX_COEF":"31708227365041504","TOX_QUAD_COEF":"1612447998607022080","ACT_COEF":"8404636857759447040","DIR_COEF":"2040474894586742","DIR_TOX_COEF":"8227241110479091","STALE_DIR_COEF":"743887462126047744","SIGMA_TOX_COEF":"59727649630712328","TAIL_KNEE":"57090633771310872","TAIL_SLOPE_PROTECT":"837536536710408960","TAIL_SLOPE_ATTRACT":"814805699243822976","ANCHOR_COUNT_CAP":"666","ANCHOR_LINEAR_K":"647750051598237824","ANCHOR_QUADRATIC_K":"1121263271129021184"}}
```