# Root merge 3 of 4: 25 results (e08-lean-a/b, e08-same-label, e08-lattice-tell, e09-confirm, e09-refit-port, e09-refit-q, e09-gap-oracles)

Credit: Taylor (gtmcknight) for the replica, the Gaussian and lattice filters, the solved policy and the qm tables (github.com/gtmcknight/amm-sim @4812a6382311624e1506aca131ca35c378f930d9, research/solved). Every result below builds on that work, and on the seats qt1, TC-A #770, o1-a #541, o1-b #1497, tca-path and buy-grid. The refit items also build on e07 visit-refit.

Goal context, from the brief: the target is #1 at 528.42. Ours is qt1 at 524.94, about +3.5 short.

How to read the figures:
- A paired figure is "mean_diff (se), min" against the named base, per seed.
- A replica figure comes from Taylor's replica through the o1-b engine-order port (10,000 steps per seed).
- An engine figure comes from `amm_sim_rs.run_batch(X, VanillaStrategy, configs, 8)`, with each arm run alone against the 30 bps VanillaStrategy.
- No result made a leaderboard submission. Every result says its replica and engine levels are local measurements, not board scores.

Inputs: all 25 files are present and non-empty. Each matched the SHA-256 given in the brief (checked by this merge with `sha256sum`). Each result's embedded base64 source bundle was not unpacked or re-run here. Its figures are taken as the result reports them.

Flagged source: one source in **lat-b** (e08-lattice-tell) did not hold when its machine read it again. The result file does not name which quote failed. The only claim in lat-b drawn from an outside source is "+0.5 lattice-over-Gaussian without the tell in Taylor's README". Weigh that comparison in lat-b accordingly. lat-b's own measurements are local runs and do not depend on it. lat-a, which is not flagged, states the same README comparison independently and also measures it locally (+0.542 se 0.028, LatticePort − qt1).

---

## 1. Headline findings (what holds across results)

1. **The arb-or-retail call on a step's first own trade is effectively solved by a wad tell. The true flag is now worth almost nothing on top of it.**
   - Taylor's filter alone (LatticePort) is wrong on 16.22% of first trades. TellPolicy with the tca-path tell is wrong on 0.222%, and LatticeTell on 0.192% (lat-a, diagnostic on 32 choose seeds 64000..64031).
   - The true flag adds +0.0066 (se 0.0056) over LEAN, the lb-4 lean tell (go-1, ORACLE A1, seeds 64000..64511, n=512).
   - The true flag adds +0.034 (se 0.006) over LatticeTell (lat-a report 10000..10511), and +0.033 (se 0.0095) in lat-b (10512..10831, n=320).
   - So the remaining gap is no longer the flag.
   - A merge-side note from the brief's own figures: true flag +6.98 over HA minus qt1's +3.8 over HA is about +3.2 over qt1. That is the same size as LEAN's measured +3.16 over qt1. The two come from different measurement setups, so this is a consistency check only.

2. **The lean tell (lb-4 contract `a243bb35…`, runtime `dab7d69d…`, 22,946 bytes) is the best qualified contract in this group.** Its gain over qt1 is about +3.16 on the replica and +3.19 on the engine:
   - Replica Q, lb-4 report 10000..12047 (n=2048): +3.1599 (se 0.0222), min −1.360 (seed 11062), no seed under −2.
   - Engine, lb-4 E (n=512, 9978100..9978355 and 9978400..9978655): +3.163 (se 0.043), min +0.573. afterSwap peak 224,481, 0 out-of-gas.
   - cf-1, cf-2, cf-3 and cf-4 independently confirmed identity, T, F and gas on fresh seeds. Engine pairings vs qt1: cf-1 +3.213 (se 0.043, n=512), cf-2 +3.195 (se 0.040, n=512), cf-3 +3.130 (se 0.054, n=320), cf-4 +3.223 (se 0.044, n=512).
   - All five engine runs pooled (lb-4 plus cf-1..4, n=2368 fresh engine seeds): **+3.189 (se 0.020)**. This is computed by this merge as an n-weighted mean of the five reported means, with the se combined from the block se's. It is not a figure any single result reports.
   - Highest engine afterSwap peak seen for this contract in any of these runs: 225,355 (cf-1). That leaves about 19.6k gas of margin, with 0 out-of-gas everywhere.

3. **The REFIT blob (e07 visit-refit, `ca5a606d…`) inside the lean tell (arm "R") adds about +0.05: real, but small.**
   - Replica R − LEAN, from the four rq report blocks, which tile 10000..12047: +0.0448, +0.0417, +0.0416, +0.0592.
   - Merge-derived pooled replica figure (equal-n mean of the four blocks, n=2048): **+0.0468 (se 0.0036)**. Same pooling gives R − qt1 +3.2067 (se 0.0224) and LEAN − qt1 +3.1599 (se 0.0222). The last one equals lb-4's own 2048-seed figure, so the four blocks reproduce lb-4.
   - Engine R − LEAN: +0.052 (rp-1), +0.048 (rp-2), +0.049 (rp-3). Merge-derived pooled figure over n=768: **+0.050 (se 0.006)**.
   - The R contract (StrategyR, 22,953 bytes) passed T, F and G in rp-1, rp-2 and rp-3. Peak 222,787, 0 out-of-gas.
   - R gives about +3.2 over qt1, still short of the +3.5 the goal needs.

4. **Swapping the Gaussian belief for Taylor's lattice adds about +0.11 under the tell, and that gain is table fidelity, not belief shape (lat-a).** In lat-a:
   - LatticeTell − TellPolicy is +0.107 (se 0.013).
   - TellPolicy quoting from Taylor's full pol_mid/qm tables instead of the spline blob ("TellFull") is +0.099 (se 0.013) over TellPolicy.
   - LatticeTell − TellFull is +0.008 (se 0.008).
   - lat-b, whose one source is flagged, measures LatticeTell − TellPolicy at +0.123 (se 0.017) but has no TellFull control.
   - Both estimate the lattice would not fit 245,000 gas. Neither measured it, because no contract was written.
   - Lead from lat-a: full-table fidelity under the tell is worth about +0.10. The lattice itself is not worth porting.

5. **Most of the headroom left in these oracle tests is price inference between tell pins (go-1).**
   - The true price at every callback (A4) is +1.183 (se 0.030) over LEAN, and +4.273 over qt1, on 64000..64511.
   - The true flag (A1) is +0.007.
   - Over the 128 seeds 64000..64127, A4 − A0 per seed is +1.113 (se 0.065). Of that, +1.066 falls at pin age 0, phase 0 (the arb pass), and +0.269 at pin age 6 or more. The age-0 retail phase is −0.289.
   - LEAN's belief error grows from about 0.04 bps at a fresh pin to 5.4, 7.7, 9.6 and 10.6 bps as the pin ages.
   - The rival-state oracles A2, A3 and A5 are strongly negative (−7.51, −8.66, −5.28 vs A0). go-1 itself says these are artifacts: the port calls our callback before the rival executes its leg. They do not measure what exact rival tracking is worth.

6. **Same-label Yul rewrite of the tca-path tell (sl-3) fully passes.** It runs at +3.098 (se 0.042, n=512) over qt1 on the engine, with peak 227,577 and 24,521 bytes. Its replica Q is inherited from tca-path: +3.1335 (se 0.0223, n=2048). The lean tell is a little better on both:
   - Replica: lb-4 +3.1599 against tca-path +3.1335 on the same seeds 10000..12047. These are two separate runs, not paired with each other.
   - Engine: lb-4 +3.163 against sl-3 +3.098 on different seeds.
   - The lean contract is also smaller and lighter: 22,946 bytes, and the tell alone costs about 6.2k gas on average.

7. **Gate status by family.** Many lean and same-label contracts sit within a few hundred gas or a few bytes of the limits:

   | Result | Gas margin (peak vs 245,000) | Byte margin (vs 24,576) | Notes |
   |---|---|---|---|
   | la-4 | over: 249,025 | — | 1 out-of-gas, fails E on gas |
   | la-5 | over: 249,087 | 72 | marked pass despite the peak (see §4) |
   | lb-2 | 687 | — | |
   | lb-5 | — | 2 (24,574 B) | |
   | sl-4 | — | 4 (24,572 B) | |
   | sl-1 | — | 1,440 over | fails size, cannot deploy |

   lb-4, and R built on it, are the only contracts here with comfortable margins on both gas and size.

---

## 2. Disagreements and points to weigh

- **la-5 marks E "pass", but its own first E window shows afterSwap peak_ok_gas 249,087**, over the 245,000 limit (9974100..9974355, contract `f4018bcf…`, 0 out-of-gas). Its second window peaked at 243,441. On its own data, la-5's contract does not meet the "peak ≤ 245,000" requirement, whatever its status line says.
- **la-4 fails E on gas:** peak 249,025 and 1 out-of-gas call, with only 64 E seeds completed (+3.062, se 0.130). It says the contract "needs a gas trim before submission".
- **lb-4 says "the tell alone costs at most 9800 gas" (mean 6196) on 74200..74249.** On other seeds the same contract's tell peaked higher: cf-1 12,811, cf-2 12,737, cf-3 12,592, cf-4 12,579, and rp-3 12,800 on the R stream. rp-2 gives 13,055 for its R stream. So 9,800 is that sample's maximum, not a bound. The means agree (about 6.2k). Whole-callback engine peaks stayed at or below 225,355.
- **T first-trade count:** tca-path reported 350,662 first trades on 74200..74249. lb-4, sl-1, sl-2 and sl-3 counted 350,657 on the same seeds. lb-4 and sl-3 suggest libm or platform float differences as the likely cause; neither checked it. lat-a adds a related, measured point: moving `exp()` by one ulp shifts a tell arm's single-seed edge by 0.01–0.12, against 2e-10 for qt1. Its seed 64109 differs from tca-path's by 0.088. Paired means are not affected. Single-seed edges and row hashes of tell arms reproduce only on the same libm and CPython build.
- **Lattice size of effect:** lat-a +0.107 (n=512, 10000..10511) and lat-b +0.123 (n=320, 10512..10831) agree within error. lat-a's TellFull control explains the gain as table fidelity. lat-b has no such control, has the flagged source, chose "mix" vs "pin" on only 64 seeds (+0.009 se 0.014 between them, so indistinguishable), and ran 320 of 512 planned report seeds.
- **Selection caveats on R (refit):**
  - rq-4's choose block 64768..65023 lies inside 64512..65023, the seeds REFIT used to select its regularisation weight under a different base.
  - rq-3 notes REFIT itself used overlapping validation and report ranges, so its report block is not newly unseen to the upstream refit work.
  - rp-1, rp-2 and rp-3 chose nothing; R has no free parameter. Their Q seeds (10000..10767) lie inside the report window that lb-4 and REFIT had already scored.
  - R was fitted on visits of REFIT's BASE policy (TwoComp plus o1-b Bayes tell), not on LEAN's (rq-4).
  - Choose and report agree in every rq item: choose +0.052, +0.037, +0.060, +0.061 against report +0.045, +0.042, +0.042, +0.059.
- **Seed-level spread of R − LEAN:** it is negative on 182 of 512 report seeds in rq-4 (worst −0.822). rq-2's worst seed is −1.588. It is a mean gain, not a per-seed one. rq-4 gives the per-seed sd of R − LEAN as 0.169.
- **Protocol deviations, as each result reports them (no seed reused in any case):**
  - lb-2 ran 64 E seeds (9976100..9976163) on its first contract, which had already failed G (+3.401). These are excluded from E.
  - lb-3 launched E before reading a failed G. 9977100..9977163 were interrupted and excluded.
  - lb-1's first E block (v1) peaked at 245,210, over by 210. The final revision was evaluated only on 9975400..9975655.
  - lb-5 ran mixed gas-only revisions over 9979100..9979259. Two of them peaked over the limit (245,179 and 246,960).
  - sl-4's primary E is incomplete: superseded source with 2 out-of-gas calls, then a qt1 arm that timed out.
  - rp-2 ran G before Q.
  - rp-3's F was first started with a patch bug and rerun from the start.
- **StrategyR stale metadata (rp-3):**
  - The header comment still names the original blob `3ac7cb88…`.
  - `getName` still returns `TaylorTCALeanTell`, the same as LEAN.
  - The runtime is 7 bytes longer than LEAN's (22,953 vs 22,946) although only constants changed. The cause was not investigated.
- **go-1 oracle defects (its own):**
  - A3 has a one-ulp band-boundary defect: 1,623 dominant point components rejected within 8.9e-16 log units on 8 check seeds. Treat A3 as a raw diagnostic, not a ceiling.
  - A2, A3 and A5 use callback-time rival state, which comes before the rival's leg. Their timing audit shows the mismatch averages about 20 bps (max about 992 bps).

---

## 3. Per-result summaries

### e08-lean-a: lean tell replaces the tca-path tell (reference and Solidity)

These items share the tell definition: buy-grid bounded `sell_one_division` / `buy_grid`, budget 4. Positive label: π → π/(π+(1−π)L), with L = 15/13131 (sell) and 16/12889 (buy), capped at 1−1e-4, keeping the mixture. Negative label: π = 0. Over budget or unsupported: π unchanged. Nothing tuned.

**la-4** (b26-la-4). Status: Q, T, F, G pass; **E FAIL on gas**; P pass.
- Preimages are found by binary search, with a walk of at most 64 steps.
- Q debug 64000..64015 (n=16): +2.901 (se 0.210).
- Q report 10000..10539 (n=540): +3.115 (se 0.044), min +0.258. vs TwoComp: +2.682 (se 0.041). qt1 vs TwoComp: −0.433.
- T on 74200..74249: 351,787 first trades, 0 mismatches. F: max error 1.96e-6 bps.
- G on 9973000..9973007: +3.619, peak 244,484, 24,108 bytes.
- E: peak 249,025 and 1 out-of-gas. Pooled over 64 completed seeds: +3.062 (se 0.130), min −0.237.
- Three chunks (9973100..9973155) were consumed with no paired figures.

**la-5** (b26-la-5). Status: "pass" on all gates. See §2: E window 1 peaked at 249,087.
- Walk of at most 16 bit-steps. 0 mismatches against buy-grid on 27,289 first trades.
- Q debug 64000..64063: +3.060 (se 0.110).
- Q report 10000..12047 (n=2048): +3.1599 (se 0.0222), min −1.360. vs TwoComp: +2.735. Mean edges: lean 536.423, qt1 533.263, TwoComp 533.688.
- T: 350,657 first trades, 0 mismatches. F: 4.83e-7 bps.
- Tell gas alone: peak 26,895, mean 15,973.
- G: the first attempt (9974000..9974007) had 1 out-of-gas call. After a gas trim, 9974008..9974015 passed: peak 224,063, +2.907, 24,504 bytes (72 bytes margin).
- E: 9974100..9974355 +3.163 (peak 249,087), 9974400..9974655 +3.203 (peak 243,441). Pooled n=512: +3.183 (se 0.043), min −0.700.

### e08-lean-b: the same lean tell, independent implementations

**lb-1** (b27-lb-1). Status: complete, with repaired gas failures.
- Q is identical to la-5 (debug +3.060; report n=2048 +3.1599).
- T: 0 mismatches; tell gas 23,102. F: 4.83e-7.
- G took 4 revisions: 9975000..9975007 failed (peak 248,297), then passes at 232,003, 240,277 and 229,654. 24,283 bytes.
- E: the v1 block 9975100..9975355 failed (peak 245,210; +3.215). The final revision on 9975400..9975655 (n=256): +3.263 (se 0.062), min +0.844, peak 232,871.

**lb-2** (b27-lb-2). Status: P, Q, T, F, G pass; E partial.
- Q report 10000..10511 (n=512): +3.127 (se 0.045), min +0.258. Levels: lean 540.117, qt1 536.990.
- First contract failed G (peak 246,022). The final contract packs both reserves into one storage slot: 24,076 bytes, G 9976008..9976015 at +3.120, peak 234,591.
- E on the final contract, 9976164..9976227 (n=64): +3.172 (se 0.117), peak 244,313 (687 gas margin). 192 seeds not run.

**lb-3** (b27-lb-3). Status: P, Q, T, F, G pass; E partial.
- Q report 10000..11023 (n=1024): +3.143 (se 0.031), min +0.226.
- G on 9977008..9977015: +3.467, peak 237,626, 24,202 bytes. First G failed (246,376).
- E (n=448, 64 excluded): +3.185 (se 0.044), min −0.053. Peaks 240,384 and 238,583, 0 out-of-gas.
- Tell gas: 27,567.

**lb-4** (b27-lb-4). Status: complete, all gates pass. This is the contract later confirmed by cf-1..cf-4.
- 22,946 bytes; runtime `dab7d69d…`.
- Fidelity against buy-grid's bounded() on 64000..64031: 0 disagreements. Positive labels on true retail trades: 83 buy, 54 sell.
- Q report 10000..12047 (n=2048): +3.1599 (se 0.0222), min −1.360. TwoComp − qt1: +0.425 (se 0.012). 1 of 14,362,615 tell updates was unsupported.
- T: 0 mismatches on 350,657 first trades. F: 4.83e-7 bps.
- G on 9978000..9978007: +3.286, peak 208,548.
- E, both windows: +3.226 (se 0.062) and +3.100 (se 0.058). Pooled n=512: +3.163 (se 0.043), min +0.573, peak 224,481. Mean edges vs Vanilla: candidate 533.836, qt1 530.673.
- Tell gas alone: peak 9,800, mean 6,196 (see §2). tca-path's tell probe peaked at 183,516.

**lb-5** (b27-lb-5). Status: all gates pass.
- Q report 10000..11279 (n=1280): +3.155 (se 0.028), min −1.360.
- G passed on the 4th revision (9979024..9979031): peak 217,608, **24,574 bytes (2 bytes margin)**. Earlier: 9979000..9979007 had peak 248,619 and 3 out-of-gas calls.
- E on the final contract (n=352): +3.217 (se 0.060), min −1.774 (seed 9979498), peak 240,264, 0 out-of-gas. Earlier gas-only revisions on 9979100..9979259 peaked at 245,179 and 246,960.
- Independent oracle check: 56,174 first trades, 0 mismatches.

### e08-same-label: tca-path tell rewritten in Yul, same labels

Q is not re-run in these items. They inherit tca-path's replica Q: +3.1335 (se 0.0223), min −1.396, on 10000..12047.

**sl-1** (b28-sl-1). Status: **incomplete**; G fails on size.
- P and T pass. T: 0 mismatches; labels retail_only 79,344, buy_pass 96,692, buy_fail 79,488, arb_only 20,473, both 70,976, cap 3,684.
- F deployment was rejected (CreateContractSizeLimit). **26,016 bytes, 1,440 over the limit.** E not run.
- Tell probe median gas went from 69,629 to 53,323 (worst 191,040 to 131,187).

**sl-2** (b28-sl-2). Status: P, T, F, G pass; E window 2 not run.
- 24,479 bytes. G on 9981000..9981007: +3.730, peak 216,573.
- E 9981100..9981355 (n=256): +3.128 (se 0.058), min −0.681, peak 232,387.
- F replay peak: 201,859 (the tca-path contract was 298,073). Tell worst case: 41,221.

**sl-3** (b28-sl-3). Status: **all gates pass**.
- 24,521 bytes. G on 9982000..9982007: peak 214,759, +3.121.
- E: +3.111 (se 0.059) on 9982100..9982355 and +3.085 (se 0.060) on 9982400..9982655. Pooled n=512: +3.098 (se 0.042), peak 227,577, 0 out-of-gas in 5,665,776 callbacks.
- Yul tell: median 12,208 gas, worst 25,859. The tca-path tell was median 45,734, worst 159,472.
- Fuzz: 500,000 cases, 0 mismatches.

**sl-4** (b28-sl-4). Status: P, T, F, G pass; primary E incomplete.
- **24,572 bytes (4 bytes margin).** G pilot on 9983016..9983023: peak 224,276.
- Superseded pilots: 248,939 with 1 out-of-gas; then 239,196.
- Secondary E 9983400..9983655 (n=256): +3.205 (se 0.066), min −0.314, peak 235,732.
- Final-source peak over all returned gas: 242,332.

### e08-lattice-tell: Taylor's lattice belief with the wad tell (replica only)

**lat-a** (b30-lat-a). Report 10000..10511 (n=512); choose window 64000..64255, with nothing chosen.
- LatticeTell − TellPolicy: +0.107 (se 0.013).
- LatticeTell − qt1: +3.207 (se 0.046).
- TellPolicy − qt1: +3.100 (se 0.045).
- TellFull − TellPolicy: +0.099 (se 0.013).
- LatticeTell − TellFull: +0.008 (se 0.008).
- LatticePort (no tell) − qt1: +0.542 (se 0.028).
- LatticeFlag − LatticeTell: +0.034 (se 0.006).
- The choose window agrees: LatticeTell − TellFull +0.005 (se 0.011); TellFull − TellPolicy +0.116.
- Gas, estimated from operation counts (nothing compiled): the lattice alone averages 158,598 per first-of-step callback (low-cost assumptions: 91,442). 5.4% of callbacks are over 245,000 (low: 0.75%), and the worst is over 1M. Verdict: no.

**lat-b** (b30-lat-b), **flagged source**. Choose on 64000..64063 only (mix chosen). Report 10512..10831 (n=320).
- LatticeTell − TellPolicy: +0.123 (se 0.017).
- LatticeTell − qt1: +3.267 (se 0.055).
- TellPolicy − qt1: +3.144 (se 0.055).
- LatticeFlag − LatticeTell: +0.033 (se 0.0095).
- First-trade misclassification for LatticeTell: 0.19%.
- Gas estimate: about 100–250k, not measured.

### e09-confirm: independent confirmation of the lb-4 contract (`a243bb35…`, unchanged)

All four confirm identity, P, T (0 mismatches) and F (≤ 4.82e-7 bps) on fresh seeds. Q is inherited from lb-4.

| Item | T seeds (first trades) | Tell gas peak / mean | E seeds (n) | vs qt1 (se), min | Peak (qt1) |
|---|---|---|---|---|---|
| cf-1 | 74300..74349 (348,387) | 12,811 / 6,196 | 9990000..9990511 (512) | +3.213 (0.043), +0.405 | 225,355 (209,246) |
| cf-2 | 74350..74399 (346,821) | 12,737 / 6,208 | 9990512..9991023 (512) | +3.195 (0.040), +0.524 | 223,146 (209,366) |
| cf-3 | 74400..74449 (350,166) | 12,592 / 6,208 | 9991024..9991343 (320 of 512) | +3.130 (0.054), −0.387 | 222,652 (209,262) |
| cf-4 | 74450..74499 (351,118) | 12,579 / 6,209 | 9991536..9992047 (512) | +3.223 (0.044), −0.552 | 224,693 (209,272) |

- All four runs had 0 out-of-gas.
- cf-3 did not run 9991344..9991535 (time). It puts its difference from lb-4 at −0.47 combined se.

### e09-refit-port: R = lb-4 contract with only the QMS1 coefficient words replaced by the REFIT blob

All three items share these facts:
- 1,599 of 4,896 int16 coefficients differ, across 242 source lines.
- Extracting the blob from StrategyR reproduces `ca5a606d…`.
- StrategyR is 22,953 bytes.
- T on the REFIT-blob stream: 350,950 first trades, 0 mismatches. F: max 4.84e-7 bps.

| Item | Replica Q seeds | R−qt1 | R−LEAN | LEAN−qt1 | Engine E seeds | R−qt1 | R−LEAN | LEAN−qt1 | Peak R / LEAN / qt1 |
|---|---|---|---|---|---|---|---|---|---|
| rp-1 | 10000..10255 | +3.201 (0.064) | +0.041 (0.009) | +3.160 | 9993100..9993355 | +3.129 (0.059) | +0.052 (0.010) | +3.077 | 221,453 / 223,925 / 209,137 |
| rp-2 | 10256..10511 | +3.146 (0.066) | +0.049 (0.010) | +3.097 | 9994100..9994355 | +3.226 (0.062) | +0.048 (0.010) | +3.178 | 222,476 / 222,152 / 209,173 |
| rp-3 | 10512..10767 | +3.216 (0.060) | +0.042 (0.009) | +3.174 | 9995100..9995355 | +3.128 (0.063) | +0.049 (0.011) | +3.079 | 222,787 / 224,354 / 209,287 |

- rp-1's R − LEAN on the engine is positive in all four 64-seed blocks.
- rp-3 ran a negative control: lb-4's Strategy.sol against the R reference fails F (4.23 bps, 151,715 errors). So F tells the two blobs apart.
- rp-3 carries a quote from the REFIT input itself: C − BASE +0.049 (se 0.0037, n=2048), and full-table BASE +0.108 (se 0.013) over BASE on 64512..65023. On that reading, the refit recovers about half of the compression loss.

### e09-refit-q: R vs LEAN on the replica, choose block then report block (replica only)

Rule in every item: pick R if mean(R−LEAN) > 2 se on the choose block. Every item picked R before opening its report block.

| Item | Choose (R−LEAN) | Report seeds | R−LEAN (se), min | R−qt1 (se) | LEAN−qt1 (se) |
|---|---|---|---|---|---|
| rq-1 | 64000..64255: +0.0524 (0.0105) | 10000..10511 | +0.0448 (0.0067), −0.659 | +3.172 (0.046) | +3.127 (0.045) |
| rq-2 | 64256..64511: +0.0369 (0.0096) | 10512..11023 | +0.0417 (0.0076), −1.588 | +3.200 (0.044) | +3.158 (0.044) |
| rq-3 | 64512..64767: +0.0598 (0.0101) | 11024..11535 | +0.0416 (0.0070), −0.542 | +3.174 (0.043) | +3.132 (0.043) |
| rq-4 | 64768..65023: +0.0615 (0.0097) | 11536..12047 | +0.0592 (0.0075), −0.822 | +3.281 (0.046) | +3.222 (0.046) |

- No seed is under −2 vs qt1 for either arm in any block. rq-3's worst R − qt1 seed is 11062 at −1.312.
- Pooled by this merge over all 2048 report seeds: R−LEAN +0.0468 (se 0.0036); R−qt1 +3.2067 (se 0.0224); LEAN−qt1 +3.1599 (se 0.0222).

### e09-gap-oracles: hidden-truth diagnostics on LEAN (replica, 64000..64511, n=512, nothing chosen)

**go-1** (b34-go-1). Arms, each against A0:

| Arm | What it replaces | vs A0 (se) | vs qt1 |
|---|---|---|---|
| A0 | control: LEAN, logging only | 0 | +3.089 (0.044) |
| A1 | true first-trade flag | +0.0066 (0.0056) | +3.096 |
| A2 | callback-time rival state | −7.513 (0.083) | −4.423 |
| A3 | A2 plus band | −8.658 (0.089) | −5.568 |
| A4 | true price | **+1.183 (0.030)** | +4.273 |
| A5 | true price plus rival | −5.279 (0.071) | −2.189 |

- Contrasts: A4 − A1 = +1.177. A3 − A2 = −1.145.
- Flag mismatches on first trades: A0 993 of 3,590,733. A1: 0.
- Attribution over 64000..64127 is in finding 5.
- Its reading: the gain left is mostly price inference between tell pins. A2, A3 and A5 do not bound what rival tracking is worth (see §2).

---

## 4. Gaps and what was not found

- **No result reaches +3.5 over qt1.** The best paired figures are R on the replica, +3.21 (merge-derived), and the lean tell on the engine, +3.19 (merge-derived).
- No result maps replica or engine diffs onto the board, and none submitted. Whether +3.2 over qt1 locally means about 528.1 on the board (524.94 + 3.2) is **not established** by any result here. Treat that number as arithmetic only.
- Not tried in this group:
  - full pol_mid/qm tables in a contract (lat-a's +0.10 lead);
  - better price inference between pins (go-1's +1.18 oracle headroom);
  - an oracle aligned to the rival's post-order state;
  - quoting against the whole posterior (lat-a, Taylor's open item 3);
  - a refit fitted on LEAN's own visits (rq-4).
- Not run for time:
  - la-4: 9973220..9973355 and 9973400..9973655
  - lb-2: 9976228..9976355 and 9976400..9976655
  - sl-2: E window 2
  - cf-3: 192 seeds
  - lat-b: 192 report seeds
  - lb-2 replica: 10512..12047
  - lb-3 replica: 11024..12047
  - lb-5 replica: 11280..12047
- Missing inputs: none. All 25 named results were present, non-empty and matched their SHA-256.