# Root merge 1/02: 25 results (batches e04, e05, e06)

The goal is to take the network from 8th to 1st on paradigm.xyz/puzzles/amm. C0 (seat #1268, Gaussian + qm, artifact `8a6e303b…`) scores 524.94. 5th place is C0 + 3.16 and 1st is C0 + 3.48.

This root merges 25 results. 24 are complete and 1 is blocked. Each figure below carries the input id it came from (`b13-p3` = `.imd/reads/artifacts/b13-p3` = `artifacts/goal/batches/e04-a-u1-paired/items/p3/result.json`, and so on). Figures marked **[merge]** were not in any single result. This merge computed them from the per-seed rows embedded in the results (`rows_zb64`, `per_seed_zb64`, `data_zb64`). It ran no engine or replica seeds.

## 0. Short version

- **Contract carried forward: "u1-give."** Source sha256 `99d031f4…`, runtime `b6f3c2c2…`, 21,055 B. Artifact `https://api.imd.fun/artifacts/fd2f147e94f3523e4c4f91e43dc98b88e9ce8ef1060d2939367445711154a16a`, which is the body of result `b14-copy-b` (c02 and c03 give this URL; c05 gives its body hash). It is the frozen "lookup-u1" contract (`69c361ef…`, 20,977 B) plus one rule: a two-sided rival pull with alpha = 0.35 on retail callbacks where the bound does not bind (`b14-copy-b`).
- **Engine, u1-give vs C0.** Each contract ran alone against VanillaStrategy on fresh seeds. 12 valid 256-seed items, 3,072 seeds (14002600..14005927, minus the unused block noted in §2.4): mean_diff **+3.3504, se 0.0190** [merge, pooled from rows of g1, g3–g8, c01–c05]. u1-give beat C0 on 3,068 of the 3,072 seeds [merge].
- **Engine, u1 vs C0.** 2,304 seeds: **+3.2695, se 0.0211** [merge, from p3, p4 and g-series ref column]. The README's replica figure for the tell policy over C0 is +3.21 se 0.02.
- **Engine, u1-give vs u1.** 1,792 seeds: **+0.0868, se 0.0071** [merge, g1, g3–g8]. The replica forecast was +0.0904 se 0.0072 (`b15-stack-u1-give`), so engine and replica agree.
- **Against the leaderboard (inference, not a measurement).** If a leaderboard score moves by the engine paired mean, u1-give lands at about C0 + 3.35. That is above 5th (C0 + 3.16) and about 0.13 short of 1st (C0 + 3.48), roughly 7 se below 1st on this sample. Nothing here has been submitted. Every result says `submission: false` or makes no submission claim.
- **Gates for u1-give all pass** (`b14-copy-b`):
  - isArb matches 11,856/11,856 vectors.
  - Closed-loop fees are within 4.58e-7 bps of the GivePolicy shadow (tolerance 0.01).
  - The rule-off sanity check passes.
  - `amm-match validate` passes.
  - 21,055 B against a 24,576 limit, so 3,521 B are free.
  - 6 of 32 storage slots are used, with no assembly.
  - Engine afterSwap peak is at most **209,315** across all paired items (`b17-g7`) against a 245,000 cap, with 0 OOG or other failures in every item.
- **4,096-seed carry is not finished in this root.** There are 3,072 valid seeds. A 13th item (`b16-g2`) is invalid and partial, covering 64 seeds.
- **Track C (replica): nothing reached the +0.2 bar.** Best holdout gains over the constant-pull BASE:
  - coarse 31-cell lattice: +0.0191 se 0.0049
  - rise-fast stale-rival pull: +0.0121 se 0.0039 [merge]
  - exact 0.25-bps lattice (vs no-pull baseline): +0.0102 se 0.0037

  The closed-form filter, sd calibration and offset residual are level or negative. Rival band cut is blocked.
- **Track P (probe on the unpatched engine): no item in this root.** Nothing here reports "arbitrage trades read / retail read as arbitrage over 8 runs" on the real engine. The nearest figures are replica and vector counts (§4).

## 1. Contracts in play

| name | source sha256 | runtime sha256 | runtime B | where |
|---|---|---|---|---|
| C0 `TaylorGaussianQMSpline` | `c68887cf…` | `79c8d6c3…` | 20,605 | api.imd.fun/artifacts/8a6e303b… (`b13-p3`, `b19-c02`) |
| min-lookup `TellMinLookup` (p3/p4 "ref") | `3a799de0…` | `b3f69b61…` | 22,499 | api.imd.fun/artifacts/755f4fc0… (`b13-p3`) |
| lookup-u1 `TellMinLookup` (p3/p4 "cand"; g-series "ref") | `69c361ef…` | `4ee7c49f…` | 20,977 | api.imd.fun/artifacts/fd38823c… (`b13-p3`, `b14-copy-b`) |
| u1-give, copy-b (g-series and c-series "cand") | `99d031f4…` | `b6f3c2c2…` | 21,055 | api.imd.fun/artifacts/fd2f147e… (`b14-copy-b`, `b19-c02`, `b19-c03`) |
| u1-give, copy-a (not engine-scored) | `6fd86a65…` | `e8557318…` | 21,077 | `b14-copy-a` |

All are compiled with solc 0.8.24, optimizer runs 200, viaIR, paris, through the pinned amm_competition SolidityCompiler (`b13-p3`, `b14-copy-a`, `b14-copy-b`). The C0 creation hash is `0af76fa6…` and the u1-give creation hash is `41a9c2c7…` (`b19-c01`, `b19-c02`). The VanillaStrategy creation hash is `3bcbd8a2…` (`b13-p4`, `b19-c02`, `b19-c03`, `b20-c05`).

Every engine item used the same setup:

- amm-challenge @ `6b6921f8d463314aa7c96234e1be25a25245f704`
- setup.sh sha256 `dc7fa6a1…` from gtmcknight/amm-sim **main**
- wheel `amm_sim_rs-0.1.0.post1…whl` sha256 `aedb6828…`, unpatched
- `amm_sim_rs.run_batch(X, VanillaStrategy, configs, 8)`, configs per `MatchRunner._build_configs` with `default_rng(actual seed)`, 10,000 steps

(`b13-p3`, `b13-p4`, g-series `setup`, `b19-c02`, `b20-c05`.) `b19-c01` and `b20-c05` also record the native `amm_sim_rs.abi3.so` sha256 `ff88b635…`.

### 1.1 Two independent copies of the "give" rule (b14-copy-a, b14-copy-b)

Both copies add the same single rule to lookup-u1, alpha = alpha2 = 0.35, untuned. They produced different sources.

- **copy-b** (`b14-copy-b`): the diff is two lines after the existing one-sided bound: `else if(c!=r){int256 lr=ln(r);r=exp(lr+mul(35e16,ln(c)-lr));syn=true;}`. Its gates:
  - vectors 11,856/11,856 matched;
  - tx gas min 37,256, max 43,166, mean 40,000.53, including the 21,000 base;
  - execution gas min 14,352, max 20,242, mean 17,064.49;
  - closed loop on replica seeds 60000..60007: 90,802 callbacks, max_bps [4.48e-7, 4.58e-7], rule_moves 7,470, bound_binds 52,340, pyrevm peak tx gas 181,935, 0 guard shifts;
  - raw (unclamped) shadow max 458.6 bps, which the result attributes to the unchanged 10% cap, "as reported for lookup-u1";
  - rule-off sanity pass: 90,448 callbacks, max 4.58e-7 bps;
  - discrimination check (new contract vs alpha = 0 shadow, seed 60000) fails as intended: max 18.9 / 39.3 bps, which shows the gate sees the rule;
  - validate pass; 21,055 B (+78 B vs u1); 6 of 32 slots; 0 assembly tokens;
  - engine gas smoke: 8 runs, 88,509 afterSwap calls, peak 207,569, 0 failures.
- **copy-a** (`b14-copy-a`): the same rule as copy-a describes it ("replace r with exp(ln(r)+0.35*(ln(cand)-ln(r))) and set synced=true"). Its gates:
  - isArb 11,856/11,856, same tx-gas min/max/mean;
  - closed loop: 90,802 callbacks, the same max_bps [4.48e-7, 4.58e-7] and 7,470 rule moves;
  - rule-off pass; validate pass; 21,077 B; 6 of 32 slots; no assembly;
  - engine smoke on seeds 14002584..14002591: peak 207,455, 0 failures.
- **Where they differ.** copy-a and copy-b have different source and runtime hashes and differ by 22 B of runtime. They report identical closed-loop numbers (same callbacks, max_bps and rule moves), so on the replica they behave the same. Only copy-b was carried into the engine pairs. No result compares the two directly on the engine.
- **Engine configs in the smokes.** copy-b says its smoke drew configs with `default_rng(i)`, i = 0..7, and sim seeds 14002592+i. That is "the lookup-u1 bundle convention", not `_build_configs`' same-seed tie, and copy-b says so itself under `not_done`. copy-a's smoke configs show distinct per-seed draws (for example gbm_sigma 0.000887 for 14002584). Neither smoke read a score.

## 2. Track A: engine paired results

Every item ran each arm alone against VanillaStrategy on the same seeds, in 64-seed blocks. d = edge(first) − edge(second). se = sqrt((sumsq − sum²/n)/(n−1)/n).

### 2.1 Per item

| item | seeds | u1-give − C0 (mean, se) | u1-give − u1 | u1 − C0 | peak afterSwap gas: u1-give / C0 / u1 | fails |
|---|---|---|---|---|---|---|
| `b16-g1` | 14002600..14002855 | 3.4145, 0.0650 | 0.1146, 0.0189 | 3.2999, 0.0627 | 208,638 / 209,123 / 204,363 | 0 |
| `b16-g2` **invalid** | 14002856..14002919 (block 0 only) | 3.4010, se null (n 64) | n 0 | n 0 | — | — |
| `b16-g3` | 14003112..14003367 | 3.3570, 0.0604 | 0.0837, 0.0202 | 3.2733, 0.0591 | 208,942 / 209,413 / 205,309 | 0 |
| `b16-g4` | 14003368..14003623 | 3.3268, 0.0612 | 0.0909, 0.0200 | 3.2360, 0.0601 | 208,976 / 208,775 / 204,933 | 0 |
| `b17-g5` | 14003624..14003879 | 3.2302, 0.0650 | 0.0883, 0.0180 | 3.1419, 0.0645 | 208,150 / 209,553 / 204,486 | 0 |
| `b17-g6` | 14003880..14004135 | 3.3616, 0.0774 | 0.0507, 0.0177 | 3.3109, 0.0771 | 209,086 / 209,270 / 204,455 | 0 |
| `b17-g7` | 14004136..14004391 | 3.4408, 0.0641 | 0.0947, 0.0187 | 3.3461, 0.0608 | 209,315 / 208,938 / 205,358 | 0 |
| `b17-g8` | 14004392..14004647 | 3.3441, 0.0616 | 0.0852, 0.0181 | 3.2590, 0.0610 | 208,344 / 209,271 / 205,299 | 0 |
| `b19-c01` | 14004648..14004903 | 3.3306, 0.0635 | — | — | 208,474 / 209,132 / — | 0 |
| `b19-c02` | 14004904..14005159 | 3.3338, 0.0682 | — | — | 208,527 / 209,206 / — | 0 |
| `b19-c03` | 14005160..14005415 | 3.3858, 0.0696 | — | — | 208,713 / 209,276 / — (per block, [merge]) | 0 |
| `b19-c04` | 14005416..14005671 | 3.2319, 0.0695 | — | — | 208,524 / 209,453 / — | 0 |
| `b20-c05` | 14005672..14005927 | 3.4475, 0.0602 | — | — | 208,820 / 209,360 / — | 0 |

Earlier items with u1 as the candidate (`b13-p3`, `b13-p4`, batch e04-a-u1-paired):

| item | seeds | u1 − C0 | u1 − min-lookup | min-lookup − C0 | peak u1 / C0 / min-lookup | fails |
|---|---|---|---|---|---|---|
| `b13-p3` | 14002072..14002327 | 3.3388, 0.0619 | 0.0738, 0.0160 | 3.2650, 0.0634 | 204,961 / 209,445 / 228,745 | 0 |
| `b13-p4` | 14002328..14002583 | 3.2197, 0.0619 | 0.1053, 0.0175 | 3.1145, 0.0617 | 205,003 / 209,169 / 228,521 | 0 |

Notes on the tables:

- **Recomputation.** The merge recomputed each item's mean and se from its embedded rows. They match the reported values to 4 dp for all 14 complete items [merge].
- **c03 peak.** `b19-c03` reports a single `submission_afterSwap_peak` of 209,276. Its per-block rows show that this figure is C0's. The u1-give per-block maximum is 208,713 [merge].
- **p3 post-processing fix.** `b13-p3` notes that its runner's peak-gas check first read the wrong gas_stats key. The post-processing was fixed and result.json rebuilt from saved per-arm checkpoints, with no arm rerun.
- **Mean edges.**
  - `b13-p3`: u1 535.42, C0 532.08, min-lookup 535.35.
  - `b19-c02`: u1-give 533.84, C0 530.51.
  - `b19-c04`: 536.41 / 533.18.
  - `b20-c05`: 530.45 / 527.01.
  - Pooled over the 3,072 u1-give seeds: u1-give 530.93, C0 527.58 [merge].

### 2.2 Pooled [merge]

All pools are from per-seed rows. No seed appears twice: 3,584 scored seeds, all unique.

| comparison | items | n | mean_diff | se | sum | sumsq | worst5 (seed, d) |
|---|---|---|---|---|---|---|---|
| u1-give − C0 | g1, g3–g8, c01–c05 | 3,072 | **3.3504** | **0.0190** | 10292.371 | 37873.552 | (14003953, −7.050), (14005601, −3.957), (14004016, −0.205), (14005461, −0.160), (14003918, 0.095) |
| u1-give − C0, g-series only | 7 | 1,792 | 3.3536 | 0.0246 | 6009.606 | 22102.052 | (14003953, −7.050), … |
| u1-give − C0, c-series only (e06 "fresh confirm") | 5 | 1,280 | 3.3459 | 0.0297 | 4282.765 | 15771.500 | (14005601, −3.957), … |
| u1 − C0 | p3, p4, g1, g3–g8 | 2,304 | **3.2695** | **0.0211** | 7532.967 | 27001.589 | (14003953, −7.129), (14004016, −0.439), (14004119, 0.153), (14003918, 0.197), (14003663, 0.506) |
| u1-give − u1 | g1, g3–g8 | 1,792 | **0.0868** | **0.0071** | 155.623 | 175.905 | (14003352, −1.105), (14004242, −1.028), (14003301, −0.985), (14004012, −0.890), (14003241, −0.808) |
| u1 − min-lookup | p3, p4 | 512 | 0.0895 | 0.0119 | 45.846 | 40.915 | (14002193, −0.857), (14002503, −0.728), … |
| min-lookup − C0 | p3, p4 | 512 | 3.1897 | 0.0443 | 1633.138 | 5723.543 | (14002301, 0.367), … |

- **Win rates.** u1-give beat C0 on 3,068 of 3,072 seeds. It beat u1 on 1,097 of 1,792 [merge].
- **Two large losses to C0, kept rather than trimmed.**
  - Seed 14003953 (`b17-g6`): C0 717.129, u1-give 710.079, u1 710.000. Both tell contracts lose about 7 on the same seed, so this is something u1 and u1-give share, not the pull.
  - Seed 14005601 (`b19-c04`): C0 548.711, u1-give 544.754.

  No result investigates either seed.
- **Gas.** Peak afterSwap for u1-give is at most 209,315 over the 12 items. For C0 it is at most 209,553 (`b17-g5`), for u1 at most 205,358 (`b17-g7`), for min-lookup at most 228,745 (`b13-p3`). Mean Submission afterSwap gas per call [merge, sum_ok_gas/calls]:
  - u1 ≈ 129.8k (`b13-p3`, `b17-g5`)
  - u1-give ≈ 130.8k–130.9k (`b17-g5`, `b19-c02`, `b20-c05`)
  - C0 ≈ 137.9k–138.0k (same items)
  - min-lookup ≈ 152.2k (`b13-p3`)

  Submission afterInitialize peaks at 137,205 for u1 and u1-give and at 90,858 for C0 (`b13-p3`, `b17-g5`). OOG, revert, other_halt, tx_error and bad_return are 0 for every arm in every valid item.
- **The pull costs about +4k gas at the peak** (u1 ≈ 205k → u1-give ≈ 209k). That is inside the +3k..6k on affected calls that `b15-stack-u1-give` estimated before measuring.

### 2.3 b16-g2: invalid and incomplete

`b16-g2` reports `valid: false`. Only block 0 ran (cand and C0), with paired n 64, mean 3.4010, sum 217.662, sumsq 804.044, se null, worst seed 14002884 at d = 0.194. The ref arm did not run, and 256 seeds from 14002856 are listed as remaining. Its contracts block also has defects: C0 `runtime_sha256: null`, and ref `runtime_bytes: 20605`, where every other result gives 20,977 for that source hash. Its rows field decodes to an empty list. It is excluded from every pool above. Its seeds 14002856..14002919 count as used, and 14002920..14003111 were not run by anyone in this root.

### 2.4 The 4,096-seed carry

The brief asks for the best candidate carried to 4,096 seeds. This root holds 3,072 valid u1-give vs C0 seeds (12 items × 256), 1,024 short. Whether other roots cover the rest is not known here. The unused seeds in this root's range are 14002920..14003111, plus the smoke seeds 14002584..14002599 that were run for gas only and not scored (`b14-copy-a`, `b14-copy-b`). Fresh seeds for further items would start at 14005928.

## 3. Track A: what C0 gives up to table compression

- **Replica, `b15-stack-u1-give`, holdout 10000..12047, n 2048.**
  - u1 tables (V0) − corrected qm baseline (C): −0.0046 se 0.0043.
  - The integer-observation wrapper plus this machine's libm (C − tell_qm): −0.0038 se 0.0015.
  - V0 − tell_qm: −0.0084 se 0.0043.

  On the replica, the u1 compressed tables cost almost nothing against the full qm_k1e-5 tables.
- **Engine.** u1 beats min-lookup by +0.0895 se 0.0119 over 512 seeds [merge from `b13-p3`, `b13-p4`] and is 1,522 B smaller (20,977 vs 22,499).
- **Not answered here.** No result in this root measures how much of C0's own "about 0.24 to table compression" (the brief's figure) u1 wins back on the engine. The engine u1 − C0 of +3.27 includes the tell itself.
- **Free space.** u1-give leaves 3,521 B free under 24,576 (`b14-copy-b`). No result in this root uses that space.

## 4. Track A(1) port, and what stands in for Track P

- **Solidity isArb against vectors.json.gz** (sha256 `7483623d…`): 11,856/11,856 match (`b14-copy-a`, `b14-copy-b`).
  - Gas per call, tx including the 21,000 base: min 37,256, max 43,166, mean 40,000.53.
  - Execution gas only: min 14,352, max 20,242, mean 17,064.49 (`b14-copy-b`).
  - Per-vector uint16 gas arrays are embedded in both results.
- **Python vectors** (`b15-exact-filter-bound`, `checks`): all 4,661 arbitrage vectors read as arbitrage, 9 of 7,195 retail vectors read as arbitrage, and 0 vector mismatches through the integer wrapper. `b15-stale-rival-pull` also reports "11856/11856 reference vectors matched through integer wrapper".
- **Replica truth diagnostics.** These come from the harness after each callback and are never passed to the policy. They are not the engine probe.
  - `b15-stack-u1-give`, seeds 61600..61663:
    - V0: 445,955 first trades; 239,704 arbitrage first trades, of which 27 were read as retail; 103 retail read as arbitrage.
    - V1: 447,455 first trades; 32 arbitrage read as retail; 94 retail read as arbitrage.
  - `b15-stale-rival-pull`, holdout 10000..12047: 14,401,705 first trades, 4,236 misread (rate 2.94e-4), of which 3,131 false positives and 1,105 false negatives.
  - First-trade misread rates on the holdout:
    - V0 2.93e-4, V1 2.89e-4, C 2.89e-4, shipped tell_qm 2.38e-4 (`b15-stack-u1-give`)
    - exact lattice 2.19e-4 (`b15-exact-filter-bound`)
    - coarse lattice 2.49e-4 and BASE 2.96e-4 (`b18-coarse-lattice`)
- **Track P (unpatched-engine probe, episode 1): missing.** No result in this root runs it or reports the 8-run counts the brief asks for.

## 5. Track C: replica items

Every item is plain Python on the replica, blind through run.py (sha256 `54d19a91…`, unmodified), tuned on seeds ≥ 60000, and scored once on 10000..12047 (n 2048) against tell_qm.json (sha256 `ad382c07…`).

Two baselines appear:

- **"corrected Gaussian" / C**: TellPolicy soft = 1 with the integer wrapper and no pull. C − tell_qm = −0.0038 se 0.0015.
- **"BASE"**: `stalerival:Policy` a0 = ainf = 0.35, i.e. a constant 0.35 pull. Code sha256 `176f8115…`, the code of `b15-stale-rival-pull` at artifact f5a140f5…. BASE − tell_qm = **+0.0886 se 0.0071**, reported identically by `b18-coarse-lattice`, `b18-closed-form-filter`, `b18-sd-calibration` and `b18-offset-residual`.

| item | idea | frozen choice | holdout vs its baseline | holdout vs tell_qm | verdict |
|---|---|---|---|---|---|
| `b15-stack-u1-give` | forecast: u1 tables (V0); u1 + give pull alpha 0.35 (V1) | nothing tuned | V1 − V0 +0.0904 se 0.0072; V0 − C −0.0046 se 0.0043; V1 − C +0.0859 se 0.0077 | V0 −0.0084 se 0.0043; V1 +0.0821 se 0.0077 | pull stacks on u1 with its full gain; below 0.2 alone |
| `b15-exact-filter-bound` | full Bayes lattice, 0.25 bps cells, no .995 collapse, all silent steps | `exactfast:Policy` | filter-only vs corrected Gaussian +0.0102 se 0.0037 | total +0.0064 se 0.0036 | keep the Gaussian; no lattice port |
| `b15-stale-rival-pull` | alpha(age) = a0 + (ainf − a0)·age/(age + tau) | rise_fast a0 0, ainf 0.7, tau 2 | tuning vs constant +0.0107 se 0.0094; **holdout vs constant +0.0121 se 0.0039 [merge]** | +0.1007 se 0.0073 | below 0.2 |
| `b18-coarse-lattice` | 10 bps, 31-cell lattice with pull | width 10, 31 cells, cap 12 | vs BASE +0.0191 se 0.0049 | +0.1077 se 0.0077 | largest Track C gain here; below 0.2 |
| `b18-closed-form-filter` | smoothed-box (form 2) / truncated normal (form 1) belief | sb, kappa 0.25 | vs BASE +0.0034 se 0.0029 | +0.0920 se 0.0073 | NEGATIVE |
| `b18-sd-calibration` | sd′ = c0 + c1·sd by phase for the lookup | c0 −1, c1 1.1, phases 1+2 | vs BASE −0.0010 se 0.0025 | +0.0876 se 0.0071 | NEGATIVE |
| `b18-offset-residual` | ±0.25 bps phase offset on both table sides | [0, 0, 0] (no change selected) | 0 (identical) | +0.0886 se 0.0071 | NEGATIVE: every ±0.25 trial lost |
| `b18-rival-band-cut` | — | — | — | — | **BLOCKED** |

### 5.1 Details kept per item

**b15-stack-u1-give**

- vs_HA on the holdout (mean, se): V0 6.9664, 0.0441; V1 7.0569, 0.0433; C 6.971, 0.044; tell_qm 6.9748, 0.044. For comparison, the README's solved policy is +6.98 over HA.
- Price rms (bps): V0 7.1551, V1 7.1131, C 7.1585, tell_qm 7.1494.
- Tuning smoke on 61600..61855: V1 − V0 +0.0604 se 0.0177; V0 − C −0.0014 se 0.0119.
- libm: this machine gives 446.79826 / 574.32668 / 529.637987 on seeds 10000..10002, against the README's 446.7525 / 574.32668 / 529.609154.
- Solidity estimate for V1, made before any contract existed: +60..150 B and +3k..6k gas on affected calls. The measured result in `b14-copy-b` is +78 B, and peak gas rose about 4k (§2.2).

**b15-exact-filter-bound**

- Tuning on 61900..62155: +0.0152 se 0.0122. 44-bit precision audit (n 40): +0.0376 se 0.0214. Packing pilot (n 64): +0.0204 se 0.0168.
- Holdout worst seeds: 10843 (−1.648), 11949 (−1.140).
- By common-clock pin age the lattice gives back edge near pins (steps 0–2: −0.0228) and gains later (steps 5+: +0.0321). Steps "1" alone: −0.0170 se 0.0012.
- At own-clock age 17+, Gaussian rms 12.97 bps against a claimed sd of 12.24; lattice rms 12.88 against 12.88. The lattice is better calibrated but barely more accurate.
- Solidity: not implemented. Estimates only: about 16 kB of state (2,256 B packed) and on the order of 10^6 gas per step.
- Poisoned-truth test: outputs are identical, so the policy is blind.

**b15-stale-rival-pull**

- Tuning on 62200..62455, vs corrected no-pull: constant +0.1055 se 0.0196; rise_fast +0.1161 se 0.0186; rise_slow +0.0934; decay +0.0810.
- Tuning vs constant: rise_fast +0.0107 se 0.0094; rise_slow −0.0121; decay −0.0245.
- The result itself says the holdout does not isolate staleness from the constant pull, because no constant arm was run. **[merge]** closes that gap: the result's own rows (candidate, tell_qm, binary64) paired with the BASE column in `b18-offset-residual`'s rows give rise_fast − constant **+0.0121 se 0.0039**, n 2048. This assumes BASE in the e05 items is the same constant-0.35 policy, which they state (same code sha `176f8115…`). The BASE columns of `b18-offset-residual` and `b18-coarse-lattice` agree to 5e-9, and BASE − tell_qm recomputed from these rows is +0.0886 se 0.0071, matching the reported figure.
- Solidity estimate, unmeasured: +100..300 B and +3.5k..9k gas on affected callbacks. Versus the constant pull, the staleness part alone is +30..100 B and +30..150 gas plus one stored timestamp.

**b18-coarse-lattice**

- Selection is one-SE: the fewest cells within 1 se of the tuning winner (5 bps, 121 cells: +0.0384 se 0.0146 vs BASE). The selected 10 bps / 31 cells scored +0.0312 se 0.0122 in tuning. 16 cells loses about −0.48; 21 cells about −0.02 to −0.03.
- Holdout: misread rate 2.49e-4 against BASE 2.96e-4; price rms 7.095 against 7.118 bps.
- Worst seeds: 11701 (−2.648), 11949 (−1.230).
- Solidity: unmeasured. 31 uint64 masses (248 B, 8 slots); at most 3,367 multiply-adds per worst callback (13 convolutions × 259 pairs); gas not benchmarked.
- **[merge]** coarse lattice − rise_fast on the holdout: +0.0069 se 0.0037, so the two are not clearly different. The coarse lattice's frozen pull is the constant 0.35. No item tried lattice and rise_fast together.

**b18-closed-form-filter**

- Form 2 (smoothed box), tuning on 62800..63055, by kappa: 0: −0.0118; 0.25: +0.0018; 0.5: +0.0015; 1: −0.0002; 2: −0.0047. All se are about 0.003–0.009.
- Form 1 (truncated normal) loses: kappa 0 −1.46 (32 seeds), 3 −0.71 (16 seeds), 12 −0.37, 60 −0.30. Misreads rise about 8× (874 against 127 on 64 seeds).
- latt.py's exact lattice with the tell and pull loses −1.086 se 0.355 on 32 seeds. Its price rms at 0 steps since pin is 6.26 bps against 0.754 for BASE, because the pin is smeared over 2.5 bps cells.
- This disagrees with `b15-exact-filter-bound`, whose 0.25-bps lattice gained +0.0102. The two lattices differ: 2.5 bps cells in latt.py against 0.25 bps in exactfast. The fine lattice keeps the pin and the coarse one smears it, so the results are consistent with cell size mattering.
- Conclusion stated in the result: the price error by steps since pin is the same for BASE and the smoothed box to 0.1 bps at every age, so "the 1.73 left to the true price is not in the shape of the belief between pins."

**b18-sd-calibration**

- 20 tuning variants on 63100..63355, all within 1.7 se of 0, except losses for c1 = 1.5 (−0.065) and c0 = +2 on all phases (−0.044).
- 99.999% of lookups fall inside the table's S grid (34 bps max). Only 224 of 24.2M fall past it.
- Realized rms exceeds the claimed sd by 1–2% for 1–2 steps after a pin and by 3–6% from 3 to 33 steps (for example 12.66 against 12.11 bps at 5–7 steps), and by 10% at ≥ 34 steps (n 4,185).
- The holdout's last chunk ran in a second command after a 10-minute timeout. The result says no chunk ran twice.

**b18-offset-residual**

- Coordinate sweep on 63400..63655 vs BASE:
  - phase 0: −0.25 → −0.0101 se 0.0086; +0.25 → −0.0599 se 0.0096
  - phase 1: −0.25 → −0.0115 se 0.0100; +0.25 → −0.0611 se 0.0110
  - phase 2: −0.25 → −0.0124 se 0.0071; +0.25 → −0.0236 se 0.0081
- The selected point is zero, so the holdout equals BASE exactly.
- One phase-0 +0.25 trial was interrupted and rerun, and the phase-0 −0.25 trial is listed twice with identical numbers.
- Price rms by steps since hard pin: 0 → 0.444, 1 → 6.98, 2 → 9.72, 3 → 11.24, 4 → 12.03, 5 → 12.46, 6+ → 12.77 bps.

**b18-rival-band-cut: blocked**

- step: "replica tuning execution: multiprocessing.Pool(8) startup before any seed completed"
- error: "PermissionError: [Errno 1] Operation not permitted; Python multiprocessing forkserver failed creating socket.socket(socket.AF_UNIX). No tuning or holdout results were produced."

That is a sandbox failure, not a negative result. The idea is untested.

### 5.2 Track C summary

- Nothing reaches the +0.2 bar the brief sets for moving an idea into A's next contract.
- The ideas with positive holdout gains over BASE are the coarse lattice (+0.019) and rise_fast (+0.012). The exact lattice (+0.010) is measured against the no-pull baseline instead.
- No item combined them, and summing them would be a guess. The coarse lattice already carries a constant pull, and rise_fast and the lattice act on different parts (the rival vs the price belief), but no stacking was measured.
- Results that bear on "a better price between pins (1.73 is left to the true price)": `b18-closed-form-filter`, `b18-sd-calibration` and `b15-exact-filter-bound` all find that the belief's shape and calibration between pins recover ≤ 0.02. Inside the e05 replica items, between-pin price rms is about 10–13 bps from step 2 on for every filter.

## 6. Sources that did not hold on re-read

The plane flagged one cited source each in `e05-a-u1g-paired-1/g3` (`b16-g3`), `e05-a-u1g-paired-2/g6` (`b17-g6`), `e05-c-replica/coarse-lattice` (`b18-coarse-lattice`) and `e05-c-replica/sd-calibration` (`b18-sd-calibration`). None of these four result files names the flagged URL or passage inline; they hold no sources list. So this merge cannot say which claim the source backed.

How much rests on them:

- **g3 and g6.** Their engine figures are local measurements. The merge recomputed them from the embedded per-seed rows and they match. Their contract hashes match every other item. The g6 outlier seed 14003953 is in its rows. Their numbers stand on their own rows, but whatever the flagged source was cited for should not be relied on.
- **coarse-lattice and sd-calibration.** Their BASE − tell_qm figure (+0.0886 se 0.0071) matches `b18-closed-form-filter` and `b18-offset-residual`, which were not flagged. The coarse-lattice BASE rows agree with offset-residual's to 5e-9 [merge]. Their own variant figures are local and unconfirmed by any other item. Treat any cited outside claim in them, such as published-file content, as unverified.

Other results that recorded source checks: `b15-exact-filter-bound` re-verified 13 quotes; `b14-copy-b` and `b15-stack-u1-give` report fetch.sh 34 files, 0 mismatched, and artifact bodies matching their URL digests. `b13-p3` notes that setup.sh came from gtmcknight/amm-sim **main**, as the brief says, not the pinned `66604b34` research commit.

## 7. Disagreements and open points

1. **copy-a vs copy-b**: two different 1-rule sources with identical gate numbers. copy-b is the one carried forward (§1.1). This is not a conflict in results, only a duplicate.
2. **Lattice sign**: +0.0102 for the 0.25-bps exact lattice (`b15-exact-filter-bound`) against −1.086 on 32 seeds for latt.py's 2.5-bps lattice (`b18-closed-form-filter`). This is explained by cell size, not by a contradiction (§5.1).
3. **Stale-rival isolation**: the result says the holdout cannot isolate staleness from the constant pull. The merge's row-level pairing with the BASE rows gives +0.0121 se 0.0039 (§5.1). The figure is derived, not run as its own arm.
4. **b16-g2 metadata** conflicts with every other item: ref runtime bytes 20,605 against 20,977, and C0 runtime hash null. The item is invalid and excluded.
5. **Engine smokes in copy-a/copy-b** did not use `_build_configs`' seed tie (copy-b says so itself). They are gas-only and carry no score.
6. **Missing from this root**: the Track P probe; the 4,096-seed carry (3,072 of 4,096 here); any engine measurement of the coarse-lattice or rise_fast ideas; any use of the 3,521 B free in u1-give; and any explanation of seeds 14003953 and 14005601.

## 8. Input index

| id | path | status |
|---|---|---|
| b13-p3 | artifacts/goal/batches/e04-a-u1-paired/items/p3/result.json | complete, valid |
| b13-p4 | artifacts/goal/batches/e04-a-u1-paired/items/p4/result.json | complete, valid |
| b14-copy-a | artifacts/goal/batches/e04-a-u1-give/items/copy-a/result.json | gates pass |
| b14-copy-b | artifacts/goal/batches/e04-a-u1-give/items/copy-b/result.json | gates pass; carried forward |
| b15-stack-u1-give | artifacts/goal/batches/e04-c-replica/items/stack-u1-give/result.json | complete |
| b15-exact-filter-bound | artifacts/goal/batches/e04-c-replica/items/exact-filter-bound/result.json | complete |
| b15-stale-rival-pull | artifacts/goal/batches/e04-c-replica/items/stale-rival-pull/result.json | complete |
| b16-g1 | artifacts/goal/batches/e05-a-u1g-paired-1/items/g1/result.json | complete, valid |
| b16-g2 | artifacts/goal/batches/e05-a-u1g-paired-1/items/g2/result.json | **invalid, partial (64 seeds)** |
| b16-g3 | artifacts/goal/batches/e05-a-u1g-paired-1/items/g3/result.json | complete, valid; 1 source flagged |
| b16-g4 | artifacts/goal/batches/e05-a-u1g-paired-1/items/g4/result.json | complete, valid |
| b17-g5 | artifacts/goal/batches/e05-a-u1g-paired-2/items/g5/result.json | complete, valid |
| b17-g6 | artifacts/goal/batches/e05-a-u1g-paired-2/items/g6/result.json | complete, valid; 1 source flagged |
| b17-g7 | artifacts/goal/batches/e05-a-u1g-paired-2/items/g7/result.json | complete, valid |
| b17-g8 | artifacts/goal/batches/e05-a-u1g-paired-2/items/g8/result.json | complete, valid |
| b18-coarse-lattice | artifacts/goal/batches/e05-c-replica/items/coarse-lattice/result.json | complete; 1 source flagged |
| b18-closed-form-filter | artifacts/goal/batches/e05-c-replica/items/closed-form-filter/result.json | complete |
| b18-sd-calibration | artifacts/goal/batches/e05-c-replica/items/sd-calibration/result.json | complete; 1 source flagged |
| b18-offset-residual | artifacts/goal/batches/e05-c-replica/items/offset-residual/result.json | complete |
| b18-rival-band-cut | artifacts/goal/batches/e05-c-replica/items/rival-band-cut/result.json | **blocked** |
| b19-c01 | artifacts/goal/batches/e06-a-fresh-confirm-1/items/c01/result.json | complete, valid |
| b19-c02 | artifacts/goal/batches/e06-a-fresh-confirm-1/items/c02/result.json | complete, valid |
| b19-c03 | artifacts/goal/batches/e06-a-fresh-confirm-1/items/c03/result.json | complete, valid |
| b19-c04 | artifacts/goal/batches/e06-a-fresh-confirm-1/items/c04/result.json | complete, valid |
| b20-c05 | artifacts/goal/batches/e06-a-fresh-confirm-2/items/c05/result.json | complete, valid |

External references as the results give them:

- C0: https://api.imd.fun/artifacts/8a6e303b662e1a5ea9bb47f31acedd3988ef65b3ddb66d074517aa59ad41ca40
- lookup-u1: https://api.imd.fun/artifacts/fd38823c16c850438759b77387cecd713241ff3f0b6d5280ef161c6717375ed8
- min-lookup: https://api.imd.fun/artifacts/755f4fc0a7b028497ad9ddf23ea568071192341e192335cb7f31174d066d4df0
- give.py: https://api.imd.fun/artifacts/e931451c8e4b3ace70dbcde4910728e086fb292489bccaab0bf9c5c3be72fe14
- u1-give: https://api.imd.fun/artifacts/fd2f147e94f3523e4c4f91e43dc98b88e9ce8ef1060d2939367445711154a16a
- stalerival: https://api.imd.fun/artifacts/f5a140f51df99423d6ede60b618dbc6eabc37a3050ac439c80dc3824191e9f59
- tell_qm.json: https://raw.githubusercontent.com/gtmcknight/amm-sim/66604b3426d8e97a73e2c39940b9b4dece51cc73/research/tell/tell_qm.json
- engine: https://github.com/benedictbrady/amm-challenge @ 6b6921f8d463314aa7c96234e1be25a25245f704
- setup.sh: https://raw.githubusercontent.com/gtmcknight/amm-sim/main/research/setup.sh