# Root merge 1 of 5: AMM fee challenge, learned fee policies on HA (25 results)

This merge combines the 25 results under `.imd/reads/artifacts/`. Each file's SHA-256 was checked against the brief before reading, and all 25 matched. Every figure below is tagged with the result it came from, for example `[b01-feat-a]`. All measurements are the workers' own local runs. I re-ran nothing, so nothing here was re-measured by this merge.

Abbreviations: **T** = RS2 plus a toxicity anchor (code sha256 `ebd9de9b…`). **HA** = T plus the 13-8-2 head (code `99e3a2ec…`, artifact `2801efc8…`). **IA** = the `inputs-a` candidate, a 19-input head (code `956566e9…`, artifact `df0ddfdf…`). Rounds 3–6 restarted from IA. **real** = `amm_sim_rs.run_batch(X, VanillaStrategy, configs, 8)` with each arm run alone against 30 bps Vanilla on fresh seeds. **holdout** = replica seeds 40000000–40008191, evaluated once after freezing. **monitor** = replica seeds 30000000–30002047.

## Citation caveat (from the brief)

The brief says some cited sources failed when their machines re-read them (a page could not be read, or did not say what it was quoted for). The affected results are b01-net8-a (2), b01-th-a (1), b01-gated-a (1), b01-wide-a (2), b02-kit (2), b02-continue-a (3), b02-joint-a (2), b02-gas-a (3), b02-inputs-a (2), b02-continue-b (2), b02-joint-b (3), b02-inputs-b (2), b03-confirm-a (1), b04-continue-a (1), b04-continue-e (2), b05-continue-f (2), b05-continue-g (2), b05-continue-h (2) and b06-gated-a (3).

- The results do not record which passages failed. The `sources.json` files are not among the inputs, so this merge cannot say which claims were affected.
- In these results the external sources are mainly the pinned artifact URLs (`api.imd.fun/artifacts/…`), the GitHub checkout and the wheel. They are used for **input identity**: hashes, the HA reference figure 1.257 and the IA reference figure 1.513.
- The measured figures (gates, replica, real engine, gas) are each worker's own local runs. They do not depend on a quoted web passage, although they cannot be independently re-checked here.
- Where a figure is taken from a source rather than measured, I say so. Examples: the HA real +1.257 se 0.062 reference in b02-joint-b, and the IA gas reference 238,486 in b04-continue-c.
- Results not on the list: b01-feat-a, b02-gas-b, b03-confirm-b, b04-continue-b, b04-continue-c and b04-continue-d.

## Headline

1. **Best result: continue-g `[b05-continue-g]`.** Code sha256 `e1ea8fcb105e00754d17061efbe4b299a634b0fcc1b5c293d65b631654b7204b`.
   - Real: **+0.507 se 0.024 over IA** on 512 fresh seeds (7232768–7233279).
   - Replica holdout: +0.835 se 0.008 over HA; +1.952 over T; +0.470 over IA.
   - Gas: afterSwap peak 235,611, 0 OOG. Valid.
   - T and HA were **not** run on its real seeds, so its real gain over HA is only implied. Adding the measured IA-over-HA gains (+0.325 to +0.394, see below) suggests roughly +0.83 to +0.90 over HA. No result measured this directly.
2. **Measured gains over HA on real seeds, every valid candidate.**
   - Directly measured: inputs-b +0.592 se 0.030 `[b02-inputs-b]`, feat-a +0.569 se 0.029 `[b01-feat-a]`, IA +0.325 to +0.394 (four blocks), th-a +0.370 se 0.031 `[b01-th-a]`.
   - Measured against IA, so HA is implied: continue-g +0.507, continue-h +0.378, continue-a +0.319, continue-f +0.247, continue-d +0.223 and gated-a(r2) +0.170, each on 512 seeds.
3. **Nothing comes near the ~+3.1 over HA that the brief says the top 10 needs.**
   - Best measured gain over HA: +0.59 `[b02-inputs-b]`.
   - Best replica-predicted gain over HA: about +0.84 `[b05-continue-g]`.
   - No result claims a leaderboard placement.
4. **The replica transfers well.** Across all results, predicted and real gains agree within about 0.01–0.07. There is one exception:
   - On seeds 7120480–7120991, the replica gave HA−T = 1.237 against real 1.009, a gap of 0.228. That is above the 0.15 threshold `[b02-continue-b]`.
5. **Long training plateaus for the 178-weight 19-input head.**
   - continue-c flattened at about +0.41 to +0.43 over IA from about generation 2300 to 3520, with sigma at 0.031 `[b04-continue-c]`.
   - continue-a plateaued at about +0.30 to +0.32 from generation 490 `[b04-continue-a]`.
   - continue-g, with population 32, was still rising at generation 1039 (monitor +0.847 over HA) `[b05-continue-g]`.
6. **What did not work:**
   - Joint training of head plus 37 RS2/anchor constants (167 dimensions) never beat HA on the monitor. Proposals stayed between −0.80 and −4.47 versus HA over 267 generations `[b02-joint-a]`.
   - Widening HA's 13-input head to 12 units gave no significant gain: +0.016 se 0.022 `[b02-gas-a]`.
   - 16 units gave +0.073 se 0.016 `[b01-wide-a]`, but that search was only 16 minutes.
   - A gated two-head hybrid restarted from IA gave +0.170 over IA. That is below plain continuations of IA `[b06-gated-a]`.
7. **Gas headroom can be made.**
   - A storage-packing "diet" of HA reproduced HA exactly on the traces tested and cut the afterSwap peak from about 233k to 112k–127k (`[b02-gas-a]`, `[b02-gas-b]`).
   - Neither diet was used as a base by any later trained candidate in this group.

## Inputs and setup (agreed by all that checked)

- **Artifact ids (download sha256 = URL id):**
  - HA `2801efc8190e86318dd922d4a7179f63684d77a226047fc2f3c78232963eb690` (code `99e3a2ec…7390fe`)
  - T `6ac5e013b7b1fb4c5e7bdcdfec0aba28b16824e18ccf39500f258533879faffe` (code `ebd9de9bf6af6e55d5e308fd15dbb88edec11fd684891d02a30aec185acd19b3`)
  - replica `e8a7a2af9039c24b8bb2d3b5fa1c9113606cbf5a480ac07d02ca26750f1752ea` (replica_source `1e4c44b4bffbdeed65872ee15d46dbde209bf5aa11014329d13d100507b4040c`)
  - RS2 port `d845a4b94eab87f23956fd1939c0135d955df212d1f3037f2a761c178cef7a0e` (port_source `9eac3553357528b06eeae3ed8d18283d83401e1968145ceba16be356a147e271`; RS2 contract decoded from it `f24b6ca1…eaf2`)
  - kit `0d8194e9f6e0017dc4e515cdb04c048efc292935bb1d18e3336091fe81154786`
  - IA `df0ddfdf122c88641513dd179980fce475f42a912a184f812d213f27db7c14df`
  - Every worker that downloaded them reports the hashes matched.
- **Checkout and runtime:**
  - Checkout `6b6921f8d463314aa7c96234e1be25a25245f704`.
  - Wheel sha256 `aedb68280aca34c110968f00148387c95885207913fb2cf19a1ab4c5cfd6887a`.
  - Runtime reported in `[b02-kit]`: python 3.12.3, numpy 2.5.4, numba 0.68.1, cma 4.5.0, py-solc-x 2.1.0, pyrevm 0.3.7, solc 0.8.24.
- **T anchor constants**, given the same way in net8-a, gated-a, continue-b and inputs-b: count cap 674, k_lin 0.7126960148…, k_quad 1.2952407538….
- **Setup failures:**
  - `[b04-continue-c]` ran on Darwin arm64. The pinned wheel would not install there ("A path … dependency is incompatible with the current platform"), so the real engine and gas could not run. Its candidate is **unconfirmed**.
  - `[b02-joint-b]` says the final `python` setup step failed ("python not found") and it worked around this with the venv python.

## Gates (A: port vs EVM < 0.01 bps; B: replica gain within 0.15 of real; C: frozen Solidity vs frozen port < 0.1 bps)

| Result | A max bps | B (replica vs real reference) | C max bps |
|---|---|---|---|
| b01-net8-a | 7.60e-5 | 1.1271 se 0.0161 on 31000000+ (n=4096) vs 1.257; window 1.107–1.407 | 5.32e-5 |
| b01-th-a | 7.60e-5 | 1.1271 (diff −0.130 from 1.257) | 1.15e-4 |
| b01-gated-a | 7.60e-5 | 1.1271 | 3.79e-5 (20 seq) |
| b01-wide-a | 7.60e-5 | 1.1271 | 3.89e-5 (20 seq) |
| b01-feat-a | 7.60e-5 | 1.1271 | 1.21e-4 |
| b02-kit | HA 7.60e-5; T 1.22e-9; RS2 1.87e-9 | 1.1415 se 0.047 on 6020000–6020511, error 0.116 | 7.60e-5 (unchanged HA) |
| b02-continue-a | 7.60e-5 | 1.1415, error 0.116 | 4.17e-5 |
| b02-joint-a | 7.60e-5 | 1.1415 | 7.60e-5 (candidate = HA) |
| b02-gas-a | 7.60e-5 | 1.1415 | 2.75e-5 |
| b02-inputs-a | 7.60e-5 (T port 1.6e-10) | 1.1415 | 6.50e-5 |
| b02-inputs-b | 7.60e-5 (T 1.22e-9) | 1.1415 | 6.64e-5 |
| b02-continue-b | 7.60e-5 | 1.1415 passed; **but 0.228 gap on 7120480+ (fails 0.15)** | not run (no candidate) |
| b02-gas-b | **not run** | **not run** | **not run** |
| b02-joint-b | RS2 diff 3.79e-9 (200 seq) | **reported "failed"**: quoted the HA artifact field 0.242 (interval 0.17–0.37) and declined to treat it as HA−T; no new run | 7.60e-5 (copied from artifact) |
| b04-continue-a | IA 6.50e-5 | IA−T 1.4654 se 0.046 vs real 1.513, error −0.048 | 3.01e-4 |
| b04-continue-b | not run | 1.4654, error −0.048 | not run |
| b04-continue-c | 6.50e-5 | 1.4643, error 0.049 | 9.89e-5 |
| b04-continue-d | 6.50e-5 | 1.4654 | 8.94e-5 |
| b04-continue-e | 6.50e-5 | 1.4654 | = A (no new candidate) |
| b05-continue-f | 6.50e-5 | 1.4654 | 6.31e-5 |
| b05-continue-g | 6.50e-5 | 1.4654 | 8.81e-5 |
| b05-continue-h | 6.50e-5 | 1.4654 | 1.37e-4 |
| b06-gated-a | 6.50e-5 | 1.4654 | 7.04e-5 |

**Where results disagree on Gate B for HA:**
- Leg 1 measured replica HA−T on replica seeds 31000000+ (1.127).
- Round 1 onward measured it on the HA artifact's own real block 6020000+ (1.141).
- Both pass, and both sit at the low end of the window around 1.257.
- `[b02-joint-b]` is the only result that marks B as failed, and it did so by reading an artifact value of uncertain meaning (0.242), not by measuring.

## Replica speed (markets/s, 10,000-step markets, warm)

| Result | Speed | Search? |
|---|---|---|
| b01-net8-a | 584 (4 cores) | yes |
| b01-th-a | 326 (8 procs) | yes |
| b01-gated-a | 584 | yes |
| b01-wide-a | HA 677, T 766 | yes |
| b01-feat-a | 925 (T 1292; numba prange, 12 cores) | yes |
| b02-kit | 413 | n/a |
| b02-continue-a | 650 | yes |
| b02-continue-b | **~125 (machine gave ~1 core)** | no (< 200 rule) |
| b02-joint-a | 206 | yes |
| b02-gas-a | 300 | yes |
| b02-gas-b | none; real engine ~12–15 s/market, single effective core | no |
| b02-inputs-a | HA 440, T 647 | yes |
| b02-inputs-b | **4182 (22 procs)**; 5981 during search | yes |
| b02-joint-b | 780 (artifact reported 3721) | no |
| b04-continue-a | IA 345 | yes |
| b04-continue-b | **IA 45.7** | no |
| b04-continue-c | IA 2017, T 3303 (Apple Silicon, 10 CPUs) | yes |
| b04-continue-d | IA 296 | yes |
| b04-continue-e | **47.6** | no |
| b05-continue-f | 304 | yes |
| b05-continue-g | 892 | yes |
| b05-continue-h | IA 810 | yes |
| b06-gated-a | dual-IA 461 | yes |

Machine speed varied by about 100× between items. Three items (b02-continue-b, b04-continue-b, b04-continue-e) fell below the 200 markets/s rule and did no search.

## Candidates: real engine (fresh seeds), replica holdout, gas

All valid entries had 0 OOG and 0 other failures in `gas_stats()`, with the afterSwap peak at or below 245,000.

### Leg 1 (b01): from HA, about 16–70 minutes of search each

| Result | Change | Search | Real vs HA (n=512) | Real vs T | Holdout vs HA | Retail / arb Δ vs HA (real) | afterSwap peak | Code sha256 |
|---|---|---|---|---|---|---|---|---|
| net8-a | retrain 130 HA weights | 53.6 min, 231 gen | +0.096 se 0.019 (7000000–7000511) | +1.213 se 0.039 | +0.104 se 0.005 | +0.188 / −0.092 | 231,381 | `7badbd90…` |
| th-a | train 38 T constants + anchor + 130 weights | 70.1 min | +0.370 se 0.031 (7001000–7001511) | +1.527 se 0.043 | +0.421 se 0.008 | **−0.583 / +0.953** | 231,358 | `fa223ef6…` |
| gated-a | two 13-8-2 heads gated on first-in-step, 260 params | 46.1 min, 370 gen | +0.192 se 0.019 (7002000–7002511) | +1.269 se 0.040 | +0.181 se 0.005 | +0.278 / −0.086 | 232,419 | `50087729…` |
| wide-a | 16 hidden units | **16.0 min only** | +0.073 se 0.016 (7003000–7003511) | +1.249 se 0.040 | +0.083 se 0.004 | +0.342 / −0.269 | 236,627 | `a91b3e8d…` |
| feat-a | 19 inputs (T bid/ask fee, prev bid/ask fee, (spot−pHat)/pHat, retail flow rate) | 56.0 min | **+0.569 se 0.029** (7004000–7004511) | +1.650 se 0.046 | +0.564 se 0.007 | +0.526 / +0.042 | 234,741 | `aa2c4a56…` |

Worst-5 paired diffs, vs HA:
- feat-a: −1.81 (7004485), −1.24, −1.23, −1.15, −1.00
- th-a: −2.22 (7001392), −1.91, −1.52, −1.51, −1.40
- gated-a: −0.99 to −0.86
- net8-a: −1.37 to −0.86
- wide-a: −1.18 to −0.83

Every leg-1 worker says its monitor curve was still rising at the stop, except net8-a, which "appears to be near a plateau" (1.231 → 1.258 vs T over the last 30 minutes, sigma 0.029).

### Round 1 (b02, e2-ha-round1)

| Result | Change | Search | Real vs HA | Real vs T | Holdout vs HA | Retail / arb Δ vs HA | afterSwap peak | Code sha256 |
|---|---|---|---|---|---|---|---|---|
| kit | no search; reusable sim/port/harness/diff_test/tests | — | — (HA−T +1.170 se 0.038 on 7100000–7100511) | — | — | — | HA 233,512 | HA unchanged |
| continue-a | continue 130 HA weights, CMA pop 16 sigma 0.1 | 45.1 min, 424 gen | +0.194 se 0.021 (7104096–7104671, 64 T-only seeds skipped) | +1.342 se 0.053 | +0.185 se 0.006 | +0.133 / +0.061 | 231,484 | `59abcdaf…` |
| joint-a | head + 37 constants (167 dims) | 42.4 min, 267 gen | **no improvement**: frozen = HA; +0.0001 se 0.0001 (7108192–7108703) | +1.201 se 0.041 | 0 | ~0 | 231,404 | `3fa1a5b8…` (HA re-emitted) |
| gas-a | storage diet + 12-unit head (194 dims) | 40.7 min, 191 gen | +0.016 se 0.022 (7112288–7112799), not significant | +1.117 se 0.041 | +0.055 se 0.006 | +0.370 / −0.354 | **156,924** | `375f650a…`; diet `269c03a4…` |
| inputs-a (= IA) | 19 inputs: raw size, step trade count, prev bid/ask fee, steps since arb-like print, router-implied Vanilla spot deviation | ~21 min, 210 gen | +0.335 se 0.025 (7116384–7116895) | +1.513 se 0.041 | +0.365 se 0.007 | +0.565 / −0.230 | 238,486 | `956566e9…` |
| inputs-b | same six-input idea, different scaling and storage | 20.8 min, 910 gen, 512 markets/gen | **+0.592 se 0.030** (7132768–7133279) | **+1.749 se 0.040** | **+0.652 se 0.008** | volume Δ only (engine exposes no edge split): retail Y +615, arb Y +488 | 234,849 | `30194182…` |
| continue-b | none (machine too slow) | 0 | — | HA−T +1.009 se 0.039 (7120480–7120991) | — | — | HA 233,639 | HA unchanged |
| gas-b | diet8 / diet16 (zero-output widening); no gates, training or confirmation | 0 | identical to HA on regression seeds | — | — | — | diet ~112k | diet16 `3947c67a…`, diet8 `383b9857…` |
| joint-b | no training; restates HA artifact | 0 | — | artifact: +1.257 se 0.062 (6020000–6020511) | — | — | 231,381 (artifact) | HA |

Worst-5 vs HA:
- inputs-b: −1.86 (7132937), −1.53, −1.49, −1.35, −1.15
- inputs-a: −1.94 (7116530) to −1.24
- continue-a: −3.07 (7104307) to −1.06

`[b02-continue-a]` also reports one extreme seed vs T: 7104436 at −13.90, where HA−T on the same seed was −14.42.

Notes:
- inputs-b is the best directly measured result over HA. Its curve was still rising at generation 890 of 910 (monitor +1.810 vs T, sigma 0.022) `[b02-inputs-b]`.
- **Later rounds restarted from IA (`inputs-a`), not from inputs-b**, even though inputs-b measured higher (+0.592 vs +0.335 over HA). No result explains why.
- No result ablated which new inputs carry the gain `[b02-inputs-b]`.

### Confirmation of IA (b03, no search)

| Result | Seeds | IA − HA | IA − T | HA − T | IA peak | Wins vs HA |
|---|---|---|---|---|---|---|
| confirm-a | 7200000–7201023 (n=1024) | +0.394 se 0.019 | +1.522 se 0.031 | +1.128 se 0.026 | 235,490 | 787 / 1024 |
| confirm-b | 7204096–7205119 (n=1024) | +0.325 se 0.018 | +1.445 se 0.029 | +1.120 se 0.026 | 237,631 | 759 / 1024 |

Retail / arb Δ vs HA: confirm-a +0.623 / −0.229; confirm-b +0.583 / −0.258.

Other measurements of IA − HA:
- +0.335 se 0.025 `[b02-inputs-a]`
- +0.365 se 0.039, n=248 `[b04-continue-b]`
- +0.280 se 0.096, n=48 only `[b04-continue-e]`

The two 1024-seed blocks differ by 0.069, about 2.6 combined se. All estimates are consistent with **IA ≈ +0.33 to +0.39 over HA**.

### Rounds 3–6 (b04–b06): long training from IA's restart vector, compared on real seeds against IA

| Result | Settings | Search | Real vs IA (n=512) | Holdout vs IA / vs HA / vs T | Retail / arb Δ vs IA | Peak | Code sha256 |
|---|---|---|---|---|---|---|---|
| continue-a | pop 16, sigma0 0.5, 128 mkts/gen | 62.5 min, 750 gen; plateau from gen 490 | +0.319 se 0.023 (7208192–7208703) | +0.332 / +0.697 / +1.814 | −0.323 / +0.641 | 235,490 | `f766f184…` |
| continue-b | none (45.7 mkts/s) | 0 | — (IA run on 248 seeds, above) | — | — | IA 235,402 | — |
| continue-c | pop 16, sigma0 0.5, 128 mkts/gen | **70.3 min, 3520 gen**; flat ~+0.41 from gen ~2300 | **not run (macOS; wheel not installable)** | +0.420 / +0.785 / +1.902 | +0.115 / +0.305 (holdout) | **not measured** | `db13b19c…` |
| continue-d | pop 16, sigma0 0.5, 256 mkts/gen | 46.4 min, 210 gen | +0.223 se 0.021 (7220480–7220991) | +0.220 / +0.585 / +1.702 | −0.141 / +0.364 | 237,869 | `4cc4a92e…` |
| continue-e | none (47.6 mkts/s); real fallback timed out | 0 | — (IA: 48 seeds only) | — | — | — | IA unchanged; **valid: false** |
| continue-f | pop 16, sigma0 0.5, 128 mkts/gen | 69.0 min, 590 gen; still rising | +0.247 se 0.024 (7228672–7229183) | +0.272 / +0.637 / +1.754 | −0.454 / +0.701 | 235,567 | `bed3f99b…` |
| **continue-g** | **pop 32**, sigma0 0.5, 128 mkts/gen | 77.5 min, 1039 gen; best at gen 980; still rising | **+0.507 se 0.024** (7232768–7233279) | **+0.470 / +0.835 / +1.952** | **+0.174 / +0.334** | 235,611 | `e1ea8fcb…` |
| continue-h | pop 32, diagonal CMA | 54.3 min, 507 gen | +0.378 se 0.024 (7236864–7237375) | +0.384 / +0.749 / +1.865 | −0.229 / +0.607 | 235,582 | `01e3b53a…` |
| gated-a (r2) | two IA heads, 380 params, full CMA, restart at gen 307 | 75.8 min, 582 gen | +0.170 se 0.022 (7240960–7241471) | +0.164 / +0.529 / +1.646 | −0.290 / +0.460 | 235,540 | `9223cabd…` |

Worst-5 vs IA:
- continue-g: −1.48 (7232937), −1.16, −0.99, −0.94, −0.81
- continue-h: −1.24 to −1.14
- continue-a: −1.60 to −1.21
- continue-d: −2.66 (7220892) to −0.94
- continue-f: −2.42 (7228795) to −1.57
- gated-a: −3.90 (7241421) to −1.21

Observations:
- **Replica holdout predicted real gain vs IA within 0.04 in every case**: g 0.470 vs 0.507, h 0.384 vs 0.378, a 0.332 vs 0.319, d 0.220 vs 0.223, f 0.272 vs 0.247, gated 0.164 vs 0.170. This strongly supports the predicted +0.42 over IA for continue-c, which the real engine has **not** confirmed.
- **Where the gain comes from:**
  - Most IA continuations (a, d, f, h, gated) gain by **reducing arbitrage loss** (arb Δ +0.36 to +0.70) while **giving back retail edge** (−0.14 to −0.45).
  - continue-g is the exception: it gains on both, retail +0.174 and arb +0.334.
  - The same pattern appeared in leg 1: th-a gained arb +0.953 and lost retail −0.583, whereas feat-a and inputs-b gained mostly retail.
- **Population 32 beat population 16 at similar wall-clock time.** Compare continue-g and continue-h (pop 32) with a, d and f (pop 16). Whether this is the population, the full vs diagonal covariance (h used diagonal), or seed luck was not isolated.
- **Searches that started from the IA restart vector began slightly below IA itself:** −0.013 on the monitor `[b04-continue-c]`, `[b05-continue-h]`. The reason is that IA's published Solidity weights differ from its restart vector `[b05-continue-f]`.
- **Gated hybrid start:** the gated-a(r1) hybrid at start trailed the two-IA-head start by −0.745 on the monitor, so the two-IA-head start was used `[b06-gated-a]`.

## HA − T on real seeds across blocks (one figure, many measurements)

Brief and HA artifact: +1.257 se 0.062 on 6020000–6020511, quoted from the artifact in `[b02-joint-b]`. Fresh-block measurements:
- 1.117 se 0.038 `[b01-net8-a]`
- 1.077 `[b01-gated-a]`
- 1.176 `[b01-wide-a]`
- 1.082 `[b01-feat-a]`
- 1.170 `[b02-kit]`
- 1.148 se 0.052 `[b02-continue-a]`
- 1.201 `[b02-joint-a]`
- 1.101 `[b02-gas-a]`
- 1.178 `[b02-inputs-a]`
- 1.158 `[b02-inputs-b]`
- **1.009 se 0.039** `[b02-continue-b]`
- 1.128 and 1.120 (n=1024 each) `[b03-confirm-a/b]`
- 1.170 (n=248) `[b04-continue-b]`
- 1.292 (n=112) `[b04-continue-e]`

These disagree with the brief. Every fresh 512- or 1024-seed block came in below 1.257. The large blocks centre on **about 1.12 to 1.15**. b02-continue-b puts the 1.009 vs 1.257 difference at about 3.4 combined se. The original 1.257 block therefore looks favourable, and the replica's 1.12–1.14 is closer to typical real values than Gate B's reference suggests. The goal's "+1.53 over RS2" and "+3.1 needed" figures are anchored on 1.257, so they may be slightly optimistic for HA. This is my inference, not something any result tested.

## Gas

**Measured afterSwap peaks:**
- **HA:** between 231,357 and 234,449 across results (for example 231,381 `[b01-net8-a]`, 233,639 `[b02-continue-b]`, 234,449 `[b02-inputs-a]`). The peak depends on the seed block.
- **T:** about 223,2xx to 225,579.
- **afterInitialize:** about 243,1xx for HA and T, and 243,237 for IA. These sit close to 245,000, but the 245,000 limit stated in the brief applies to afterSwap. No result applied it to afterInitialize.
- **IA:** 238,486 `[b02-inputs-a]`; 235,490 and 237,631 `[b03]`; 237,872 `[b04-continue-d]`; 235,402–236,136 elsewhere.
- **Trained 19-input candidates:** 235,490 to 237,869. Headroom is about 7k–10k.
- **wide-a (16 units):** 236,627. It estimates about 363 gas per added unit and puts more than about 20 units at risk `[b01-wide-a]`.

**Diets (storage packing):** the two diet results disagree on size, because they are different implementations.
- **gas-a** packs 16 live persistent words into 8, saving three init writes and changing no fee arithmetic.
  - Regression: 100 seeds × 10,000 steps, with exact seed and step-trace matches against HA.
  - Diet afterSwap peak 127,354 vs HA 233,608; afterInitialize 176,807.
  - The trained 12-unit candidate built on the diet peaked at 156,924 (88,076 headroom) `[b02-gas-a]`.
- **gas-b** packs 17 slots into 6, uses pow lookup tables, and trims one Newton step.
  - Regression: identical to HA on seeds 0–15 at 10,000 steps, and on seeds 0–99 truncated to 500 steps (a deviation it states).
  - afterSwap peak about 112k (HA 207,864 on the same seeds); afterInitialize 132,588.
  - 16 live units cost about +1.3k gas, so it estimates "roughly 100+ more" units would fit `[b02-gas-b]`.
  - gas-b ran **no gates A/B/C, no training, and no fresh-seed confirmation**. Its max-gas samples are also short (2,000-step markets on seeds 7132760–7132767).

**Solidity stack limits**, hit and repaired without changing weights:
- gated-a: int256[3] accumulators
- wide-a: head split into _hc0/_hc1
- gas-a: packed int32 weights with a loop
- gas-b: scoped locals

## Process deviations and integrity notes (nothing dropped)

**Seed blocks re-touched by probes** (not by confirmations within an item):
- net8-a confirmed on 7000000–7000511. Later, feat-a and wide-a ran gas probes on 7000000–7000015, and inputs-b ran a T-only probe on 7000000–7000007.
- gated-a(r1) ran a gas probe on 7100000–7100015, which is inside the kit's confirmation block 7100000–7100511.
- No confirmation figure in this group was computed on reused seeds within its own item. Across items, though, these blocks are not "fresh" for any future use.

**Partial, skipped or burned seeds:**
- `[b02-continue-a]`: 64 T-only seeds were burned (7104160–7104223). T retail/arb splits use n=448.
- `[b02-joint-a]` and `[b02-gas-a]`: one T seed lacks a decomposition (n=511).
- `[b04-continue-b]`: seeds 7212296–7212543 were burned (timeouts or a killed process).
- `[b04-continue-e]`: the chunk for 7224592 timed out (exit 124). Only 48 three-arm seeds completed.

**Time-shortened searches:**
- wide-a ran 16 minutes.
- inputs-a and inputs-b ran about 21 minutes each.
- th-a reports orchestration gaps that cut its confirmation reserve to about 27 minutes. It also says its first distribution-centre monitor decoded coordinates without the CMA bounds transform (fixed; that monitor did not select a policy).

**Bugs found and fixed before the counted runs:**
- wide-a: a forked pool under `__main__` gave T edges about 15 too low. Fixed and rerun.
- inputs-a: uncertainty scale ×1e12 instead of ×1e6, caught by Gate A.
- joint-a: SIGMA_TOX_COEF was applied to raw toxEma. Repaired and caches cleared.
- continue-d, continue-f, joint-a: stale Numba caches.
- gas-a: a timer variable was overwritten. Trace timing was omitted; results were unaffected.

**Decomposition:** retail/arb splits are reconstructions (arb from the constant-k pre-arb state; retail = edge − arb). Reported max arb-volume reconstruction error is about 1e-4. `[b02-inputs-b]` reports volume deltas, not edge deltas, because "LightweightSimResult exposes … no retail/arb edge split".

**Restart state:** most results deliver best weights, sigma and settings but **not** the CMA covariance, so a restart is not an exact continuation.
- Available restart vectors: IA (`weights_vector_after_W0_mult_off`, 178 dims), continue-a/c/d/f/g/h best weights, gated-a(r2) 380 dims (sigma 0.0236), and the inputs-b ES mean (sigma 0.022, next train seed 480465920).
- The weight vectors themselves are in the source results and are not reproduced here.

**Not delivered or unknown:**
- continue-c: real result and gas.
- gas-b: any gate or confirmation.
- inputs-b and feat-a: ablation of their new inputs.
- Any direct real HA or T arm on the seeds used by continue-a(r2), d, f, g, h or gated-a(r2).
- Any leaderboard submission.

## What the results recommend next (as stated by them)

- Resume from the best weights with longer runs and larger blocks per generation (net8-a, gated-a, feat-a, continue-g).
- feat-a: use larger training blocks (block noise is about 0.05 at 256 markets) and a decaying sigma.
- Use a gas diet to gain headroom for wider or more heads (gas-a, gas-b).
- continue-c: the 178-weight head "appears to saturate near +0.42 over IA". Confirm it on Linux with seeds 7216384–7216895, which it reserved and did not consume.
- Unaddressed and worth noting for the write-up:
  - No result restarted from **inputs-b** (+0.592 over HA) or combined its inputs with feat-a's.
  - No result trained a wider 19-input head on a diet.

## Status per result

| Result | Status (as reported) |
|---|---|
| b01-net8-a | valid; +0.096 vs HA |
| b01-th-a | valid; +0.370 vs HA |
| b01-gated-a | valid; +0.192 vs HA |
| b01-wide-a | valid; +0.073 vs HA; short search |
| b01-feat-a | valid; +0.569 vs HA |
| b02-kit | toolkit, no search; HA−T 1.170 |
| b02-continue-a | completed with deviations; +0.194 vs HA |
| b02-joint-a | no improvement (frozen = HA) |
| b02-gas-a | diet validated; 12-unit candidate +0.016 (not significant) |
| b02-inputs-a | IA; +0.335 vs HA |
| b02-continue-b | partial, no search; HA−T 1.009; replica gap 0.228 |
| b02-joint-b | checkpoint only; no new measurement; Gate B "not established" |
| b02-gas-b | partial; diet built and regression-identical; no gates or confirmation |
| b02-inputs-b | valid; +0.592 vs HA (best measured vs HA) |
| b03-confirm-a | IA +0.394 vs HA (n=1024) |
| b03-confirm-b | IA +0.325 vs HA (n=1024) |
| b04-continue-a | valid; +0.319 vs IA |
| b04-continue-b | partial, no search; IA +0.365 vs HA (n=248) |
| b04-continue-c | partial; replica +0.420 vs IA; real engine blocked (macOS); validity unknown |
| b04-continue-d | valid; +0.223 vs IA |
| b04-continue-e | blocked (runtime timeout); no candidate; valid: false |
| b05-continue-f | valid; +0.247 vs IA |
| b05-continue-g | valid; +0.507 vs IA (best overall) |
| b05-continue-h | valid; +0.378 vs IA |
| b06-gated-a | valid; +0.170 vs IA |

No input file was missing or empty.