# Root merge 3 of 3: 23 results combined

Each figure carries its source as `[item]` (the input name, e.g. b20-c06 = batch e06-a-fresh-confirm-2 item c06). "Pooled" figures are my own arithmetic from the `n`, `sum`, `sumsq` the items reported; they are marked as such. Nothing was re-run.

## 0. Status of the 23 inputs

| Input | Status |
|---|---|
| b20-c06, b20-c07, b20-c08, b21-c09, b21-c11, b21-c12, b22-c13 | complete, 256 paired seeds each (engine, candidate vs C0) |
| b22-c14 | `complete:false`; only n=96 paired seeds (chunked 8-seed runs) |
| b24-r1, r2, r3, r4 | complete, 256 paired seeds each (engine) |
| b23-band-evidence-retry, b23-retail-price-likelihood, b23-silent-retail-evidence | complete replica (Track C) experiments |
| b25-quotient-on-base | complete replica experiment |
| b25-config-oracle | complete, null result, stopped at step 1 |
| b26-copy-b | complete Solidity port + gas of `isSplit`/`isSplitLite` (a split/quotient test, not the tell test) |
| **b21-c10** | **blocked** `cand:0`: "engine arm was interrupted after its in-flight checkpoint before results were saved". No data. |
| **b22-c15** | **blocked** `compile`: Solidity compile of frozen sources consumed >6m40s CPU, no time for the 8 engine blocks. No data. |
| **b22-c16** | **blocked** at checkpoint of candidate arm block 0: driver looked up `Submission` edge as `edges["Submission"]` while the engine exposes `submission`; arm not checkpointed. No data. |
| **b27-copy-a** | **blocked**: `python3 -m venv` exited 1, ensurepip unavailable; no profiling or replica gate run. |
| **b27-copy-b** | **blocked**: `python3: command not found`. |

The five blocked results (b21-c10, b22-c15, b22-c16, b27-copy-a, b27-copy-b) contribute no measurements. The two b27 "gas-profile" items were the only ones aimed at a gas profile / replica gate, so that is missing (see section 6).

### Sources that did not hold
The brief says three results cite a source that failed re-reading: "e06-a-fresh-confirm-2/c06" (b20-c06), "e06-c-new-evidence/silent-retail-evidence" (b23-silent-retail-evidence), "e07-a-confirm-fill/r1" (b24-r1). The result files do not say which source failed or what it was quoted for, so I cannot say which claim it backed. Handling:
- b20-c06 and b24-r1: every figure they give (candidate/C0 hashes, artifact URLs, paired stats) is consistent with the other engine items (same source/runtime hashes, same wheel and setup hashes, mean_diff within 3.28–3.44 of the others), so the engine conclusion does not rest on them alone; treat their individual figures with lower weight.
- b23-silent-retail-evidence: its claims are replica figures; its `base_vs_tell_qm` +0.0886 (se 0.0071) matches the same figure in b23-retail-price-likelihood and b25-quotient-on-base, so that baseline is corroborated. Its own variant figures have no second source and are weighed as one-source.

## 1. Headline: Track A engine confirmation of the candidate

**Candidate** = "frozen u1-give", contract name `TellMinLookup`, source sha256 `99d031f4…334b72`, artifact https://api.imd.fun/artifacts/fd2f147e94f3523e4c4f91e43dc98b88e9ce8ef1060d2939367445711154a16a, runtime 21,055 bytes (runtime sha `b6f3c2c2…1d05`, creation 21,083 bytes) [b20-c06, b20-c07, b20-c08, b21-c09, b21-c11, b22-c13, b24-r1..r4 — same hashes in all].
**C0** = seat #1268 Gaussian+qm (`TaylorGaussianQMSpline`), source sha256 `c68887cf…08aca`, artifact https://api.imd.fun/artifacts/8a6e303b662e1a5ea9bb47f31acedd3988ef65b3ddb66d074517aa59ad41ca40, runtime 20,605 bytes (creation 20,633) [b20-c06, b20-c07, b20-c08].
So the candidate is +450 runtime bytes over C0; the runtime limit is 24,576 [b20-c06 `gates.runtime_limit`], leaving 3,521 bytes.

Engine/setup used by all items: amm-challenge commit 6b6921f8d463314aa7c96234e1be25a25245f704, `setup.sh` sha256 `dc7fa6a1…c4d` (…`2f300d4`), unpatched wheel `amm_sim_rs-0.1.0.post1-cp310-abi3-manylinux2014_x86_64` sha256 `aedb6828…6887a`, solc 0.8.24 (optimizer 200, viaIR, paris), `run_batch(X, VanillaStrategy, configs, 8)`, 10,000 steps, score = `edges['submission']`, d = candidate − C0, each arm alone vs VanillaStrategy, se = sample SD/√n [b20-c06, b20-c07, b21-c11, b24-r3, b24-r4]. Validation `amm-match validate` rc 0 for candidate (`Strategy 'TellMinLookup' validated successfully!`) [b20-c06, b21-c09, b21-c11, b22-c13]; C0 validates as `TaylorGaussianQMSpline` [b22-c14, b24-r4].

### Per-item paired results (candidate − C0, n=256 unless noted)

| Item | Seeds | mean_diff | se | sum | sumsq |
|---|---|---|---|---|---|
| b20-c06 | 14005928–14006183 | 3.3475 | 0.0670 | 856.960 | 3161.304 |
| b20-c07 | 14006184–14006439 | 3.2824 | 0.0664 | 840.296 | 3045.801 |
| b20-c08 | 14006440–14006695 | 3.3319 | 0.0645 | 852.974 | 3113.375 |
| b21-c09 | (range not stated; inferred 14006696+) | 3.2796 | 0.0630 | 839.590 | 3013.010 |
| b21-c11 | 14007208–14007463 | 3.3181 | 0.0599 | 849.432 | 3052.755 |
| b21-c12 | starts 14007464 | 3.2901 | 0.0627 | 842.263 | 3027.589 |
| b22-c13 | starts 14007720 | 3.3685 | 0.0651 | 862.335 | 3181.201 |
| b22-c14 | from 14007976, **n=96 only** | 3.4313 | 0.0784 | 329.407 | 1186.383 |
| b24-r1 | (range not stated) | 3.4331 | 0.0661 | 878.874 | 3302.368 |
| b24-r2 | starts 14009000 | 3.3949 | 0.0605 | 869.097 | 3189.309 |
| b24-r3 | 14009256–14009511 | 3.3800 | 0.0651 | 865.268 | 3200.911 |
| b24-r4 | 14009512–14009767 | 3.4426 | 0.0587 | 881.297 | 3258.573 |

Arm means where reported: b20-c07 cand 531.2533 / C0 527.9709; b20-c08 540.3439 / 537.0120; b24-r3 529.0740 / 525.6941; b24-r4 542.3757 / 538.9331 (arm means differ by seed block; only the paired d is comparable).

**Pooled (my arithmetic from sum/sumsq):** 8 earlier items (b20-c06..b22-c14; 1,888 seeds): mean +3.3227, se 0.0233. All 12 engine items (**2,912 seeds**): **mean +3.3543, se 0.0187, per-seed SD 1.0098**. Seed ranges appear disjoint and never reused, as the brief required, but this is 12 separate 256-seed (one 96-seed) items, not a single 4,096-seed run: **no result carried the candidate to 4,096 seeds** [b20-c07 `not_done`: "No 4,096-seed carry"].

Outliers: b20-c06 seed 14006041 has d = −3.153 (cand 514.442 vs C0 517.595), the only negative per-seed d any item lists; every other reported worst-5 is positive (lowest 0.1748 in b21-c12, seed 14007655; 0.3098 in b24-r1; 0.3886/0.4386 in b20-c07). b24-r4 reports `wins_cand: 256` of 256 [b24-r4]. 

**Reading against the goal (my inference, not any item's claim):** the goal states C0 = 524.94, 5th = C0+3.16, 1st = C0+3.48. The pooled engine gain +3.354 (se 0.019) is above the 5th-place gap (+3.16) by ~0.19 and below the 1st-place gap (+3.48) by ~0.13, i.e. ≈ 528.29 if the paired gain transferred one-to-one to the leaderboard. Individual items straddle +3.48 (b24-r4 +3.4426 and b24-r1 +3.4331 are closest; none reached 3.48). The replica predicted +3.21 se 0.02 over C0 (brief); the engine shows ~+0.14 more. No item entered anything or measured an actual leaderboard rank.

### Gas, failures, size (candidate vs C0)
- Zero OutOfGas/revert/other_halt/tx_error/bad_return in every complete engine item, all callbacks and roles [b20-c06, b20-c07, b20-c08, b21-c11, b21-c12, b22-c13, b22-c14, b24-r1..r4]. b21-c09 reports its failure counters; no non-zero is shown in what I read.
- Submission `afterSwap` peak, candidate (gate 245,000 [b20-c06 gates]): 208,890 (c06), 208,672 (c07), 208,437 (c08), 209,159 (c09, arm unspecified), 208,835 (c11), 208,610 (c12), 208,897 (c13, single figure), 208,002 (c14, partial), 208,262 (r1), 208,666 (r2), 208,459 (r3), 208,338 (r4). Max 209,159, ≈35.8k under the limit.
- C0 peak: 208,693 (c06), 209,652 (c07), 208,971 (c08), 209,078 (c11), 209,100 (c12), 208,876 (c14), 208,974 (r1), 208,782 (r2), 209,677 (r3), 209,028 (r4). Candidate peak is slightly below C0's in each paired item that reports both except c06 (+197).
- Mean afterSwap gas, r4: candidate 369,641,790,915 / 2,828,354 calls ≈ 130.7k vs C0 390,281,739,971 / 2,831,631 ≈ 137.8k [b24-r4, my division]. Other items' totals are in their `gas_stats` (not reproduced).
- Submission `afterInitialize` max 137,205 (candidate) vs 90,858 (C0) [b20-c06, b20-c08].

### Operational notes on the engine runs
- b22-c14: arms ran ~19 min per 64 seeds on that machine; two whole-arm attempts (cand, 14007976–14008039) were killed by the 10-minute command limit, then re-run as 8-seed chunks; remaining unrun: cand 14008080–14008231, C0 14008072–14008231 (so n=96, `complete:false`).
- b24-r3: C0 block b2 (14009384–14009447) was run twice because the first run was killed before its edges were written; no saved block was rerun.
- Other items report no reruns. The b21-c10/b22-c16 blocks above are the same environment's failures (interruption; driver key bug); b22-c15 (compile CPU) is a related slowness symptom.

## 2. Track A not covered by any result
- (1) Solidity port of `tellref.is_arb` against `vectors.json.gz`, gas per call: **no result reports it.** b26-copy-b ported a *different* test (`isSplit`, from `quotient.py consistency()`), see section 4.
- (2) Whether the candidate meets the README gates "fees within 0.01 bps of tellpol.TellPolicy" and whether table-compression loss (~0.24) was won back: **not reported by any of these 23.** What is known: validates; size 21,055 bytes; peak ≤209,159; 0 failures; the candidate is labelled "frozen u1-give", with no description of its policy in these files.
- Which of the candidate's changes relative to C0 produce the +3.35: not stated in the results.

## 3. Track P (probe on unpatched engine)
No result reports the arbitrage-read / retail-read-as-arbitrage counts over 8 engine runs. Closest data are **replica** vectors, not the engine: in b23-band-evidence-retry's checks, `integer_vectors` n=11,856: `arb_read` [4661, 4661] (all arbitrage trades read as arbitrage), `retail_read_as_arb` [9, 7195] (9 of 7,195 retail trades), `expected_mismatches` 0. The wheel was verified unpatched byte-for-byte in b20-c06 (`__init__.py` de6ddf77…f81f, `amm_sim_rs.abi3.so` ff88b6353c…978cd14), but that was for scoring, not a probe.

## 4. Track C and side experiments (Python replica; none ran on the engine)
All scored on seeds 10000..12047 (n=2048) against `tell_qm.json` (sha256 `ad382c07…0634f`); the brief's bar for going to A is **+0.2** over tell_qm. BASE = `stalerival:Policy` (a0=ainf=0.35, soft=1, qm_k1e-5.json; source sha256 `176f8115…cc6a2b3`, artifact https://api.imd.fun/artifacts/806404e8de0d3fee0641a55560fee2001cdf19cceefd05c7b23b9b486faa263f). **BASE − tell_qm = +0.0886 (se 0.0071)**, identical in b23-retail-price-likelihood, b23-silent-retail-evidence, b25-quotient-on-base (the last states it equals the published +0.0886 to every digit). **None of the five experiments reaches +0.2; none is recommended for A's next contract.**

| Experiment | variant − BASE (se) | variant − tell_qm (se) | Verdict |
|---|---|---|---|
| band-evidence-retry (stale-rival 30 bps band likelihood; frozen noise_bps 5, strength 0.25) [b23-band-evidence-retry] | −0.00047 (0.0031) | +0.0881 (0.0074) | `eligible_for_A:false`; tuning gains were all negative (−0.006 … −0.046) |
| retail-price-likelihood (retail paid amount/side vs router allocation; chosen rival_sd 0.0002, strength 0.5) [b23-retail-price-likelihood] | +0.0058 (0.0028) | +0.0944 (0.0072) | `passes_threshold:false`; tuning best +0.0079 (se n/a) on 64300..64555 |
| silent-retail-evidence (no-fill evidence on silent steps; strength 1.0) [b23-silent-retail-evidence] | −0.0012 (0.0021) | +0.0874 (0.0071) | `qualifies:false` |
| quotient-on-base (quotient.py consistency test added to BASE; pull=1) [b25-quotient-on-base] | **+0.0443 (0.0039)** | **+0.1329 (0.0083)** | below the 0.2 bar; overlaps with BASE's gain (alone: +0.1229 on TellPolicy; sum would be +0.2115) |
| config-oracle (non-blind oracle of true sigma, lam, size) [b25-config-oracle] | tuning-only −0.0012 (0.0088) on 65500..65755 | not scored | NULL: oracle bound < 0.04; step 2 and holdout not run |

Details and caveats kept per experiment:
- **band-evidence-retry** [b23-band-evidence-retry]: protocol deviation disclosed — before freezing, published `tell_qm.json` was read for schema validation (first 350 bytes shown, values said not to guide tuning); "strict unopened-reference compliance is not claimed". Diagnostics: misreads 4,260 (BASE) vs 3,943 (variant), price log-error RMS 7.118 vs 7.114 bps. Limitations: correlated estimates can double-count evidence; no engine or rank measurement. Cost *estimate only* (unmeasured): +600–1,800 runtime bytes, 0 extra slots.
- **retail-price-likelihood** [b23-retail-price-likelihood]: BASE-vs-variant diagnostics misreads 4,260 → 4,091, RMSE 7.118 → 7.104 bps. Parameter-commitment caveat: the selected-parameter hash was materialised after holdout scoring began (the driver hash committing to all settings and the deterministic selection rule was recorded before). Unmeasured cost estimate: ≈384 constant bytes, ≈512 temp bytes, ~400 scalar ops plus up to 5+15 exp per update; no Solidity built.
- **silent-retail-evidence** [b23-silent-retail-evidence]: tuning on 64600..64855 best strength 1.0 (+0.0133, se 0.0062); holdout gain vanished (−0.0012). It discloses a numerical limitation: the 16-node quadrature has +0.9423% flat-likelihood variance error at ±8 sd (~1e-8 at ±4 sd), so any effect cannot be attributed purely to the likelihood. One-source weighting applies (section 0).
- **quotient-on-base** [b25-quotient-on-base]: tuning seeds 64900..65155: pull=1 vs BASE +0.0440 (se 0.0095), pull=0 +0.0271 (se 0.0167). Hit rate 0.8934 over 14,591,188 tested callbacks; hits that move the rival estimate are only 2.29% of hits (mean move 6.57 bps). Cost: ~79.8 binary64 ops per tested callback (worst 189), would need soft-float in Solidity; gas not measured by this item. Replica-only.
- **config-oracle** [b25-config-oracle]: best of 30 coordinate-search trials was cz=+0.03125 bps/unit size; every larger offset lost, down to −0.18 (cl=−4: −0.1751). Run parameter ranges: sigma 8.82–10.07 bps, lam 0.601–0.999, size 19.00–21.00. The contract never receives sigma/lam/size, so no port would be possible without blind estimators. Nothing goes into a contract.

Not answered by any result: "tables for a belief that knows its flags" and "a better price between pins (1.73 left to the true price)"; no item addresses them explicitly (the closest are the band and retail-price experiments above, which did not win).

## 5. b26-copy-b: Solidity port of the quotient "split" test [b26-copy-b]
(Related to the quotient-on-base idea, not the tell test of item (1).) Solidity 0.8.24, no inline assembly, binary64 emulated with integer significands/exponents, reusing TellMath gamma/WAD.
- Vectors: 32,115 (30,115 replica from seeds 66200–66203 via `quotient:Policy`, soft=1, qm_k1e-5; 2,000 synthetic); 26,965 hits, 5,150 misses.
- `isSplit`: 0 mismatches, 0 reverts. `isSplitLite`: 7 hits lost, 1 false hit, 0 reverts (sample includes all 8 discrepancies).
- Gas per call (execution gas minus 21,000 and calldata intrinsic; pyrevm 0.3.7): `isSplit` hits mean 140,330 (min 113,244, max 298,298), misses mean 141,573 (min 36,674, max 359,320); `isSplitLite` hits mean 98,709 (90,816–173,253), misses mean 161,262 (96,276–215,396). Costliest vector index 7405: 359,320 (profile: preimages/setup 45,781; ratios and dedup 160,000; forward tests 155,723).
- Runtime bytes: TellMath baseline 2,070; +3,264 for `isSplit` (5,334 total), +2,562 for `isSplitLite` (4,632), both +3,853 (5,923).
- Extra checks: 250 edge cases, 100 uint128/fee-cap cases, 3,000 bundle sample vectors, 0 mismatches for isSplit (sample isSplitLite: 7 lost, 1 false). Inputs ≥2^128 or zero reserves return false; fee_w clamped to 1e17.
- Not done: no contract integration, no engine run, no speed gate.
- **My inference:** the worst-case `isSplit` gas (359,320) alone exceeds the 245,000 afterSwap peak limit, and the candidate's afterSwap already peaks near 209k, so porting it in full would not fit the gas gate without the Lite variant or other savings; with the replica showing the quotient gain is only +0.044 over BASE (section 4), this item gives no reason to port it.

## 6. What could not be found / open items
- No engine run of the candidate with 4,096 seeds as a single carry; the pooled 2,912-seed figure is the substitute.
- No tell-test Solidity port gas/vector report (Track A item 1); no gates report on fee closeness to TellPolicy; no replica gate (b27-copy-a, b27-copy-b blocked).
- No Track P engine probe counts.
- No Track C result reached +0.2; the best (quotient-on-base) is +0.1329 vs tell_qm / +0.0443 vs BASE.
- Four engine items (b21-c10, b22-c15, b22-c16 plus partial b22-c14) were lost or truncated to environment limits (interrupted run, compile CPU, driver key bug, 10-minute command cap).
- Disagreements: none between engine items beyond sampling noise (range of mean_diff 3.28–3.44, with per-item se ≈0.06; the range is consistent with a single true gain near 3.35). Replica results do not conflict with each other (all show ≈0 to +0.04 over BASE) but differ in sign for band-evidence (−0.0005) vs retail-price (+0.0058), both within about 2 se of zero.