# Root merge 1: evidence and findings

**Credit:** Taylor (gtmcknight), `github.com/gtmcknight/amm-sim` at `4812a6382311624e1506aca131ca35c378f930d9`, `research/solved`. The policy, Gaussian filter, posterior/tell research, tables, replica and gate shape used throughout build on Taylor's work. This merges the 25 supplied results; it is not a contract submission.

## Goal baseline and constraints

The brief identifies the network entry as about 528.2 (seat #39) and target #1 as 528.4152, with places 1–7 at 528.10–528.42. The baseline lb-4 is Taylor's solved policy with a two-component filter and exact-arithmetic arbitrage/retail tell; source SHA-256 `a243bb3570545fb614d8995ced61e811db8e075af68e636add20eaf8fbaeebfb`, 22,946 runtime bytes and 49,905 source characters. The brief reports +3.20 over qt1 on about 1,850 fresh engine seeds, peak 225k; bundle: [artifact 93cc1556…](https://api.imd.fun/artifacts/93cc15561f172c49c8bce174143333ede904fdbfcf51276cbbeb514d4f5b614e). b01-exact-lb4 independently records the hash and size, but does not reproduce the historical score or engine run. (Goal brief; b01-exact-lb4.)

The brief's limits are 50,000 source characters, 24,576 deployed runtime bytes, and 245,000 peak `afterSwap` gas with no OOG. Gates are P, Q, T, F, G, E in order. Several results below are replica experiments or bounded smoke/gas screens, not completion of these gates.

## Merged findings

### Baseline, policy and tell

- **Exact baseline restoration (b01-exact-lb4).** Taylor's published P values matched in 12 cases; restored lb-4 fallback parity had maximum edge error 0 and all callback hashes equal. The lb-4/qt1 Q runner was demonstrated but full Q was not run; T/F were smoke only, G was baseline screening, and E had zero fresh simulations. Screening on seeds 9,700,000 and 9,700,007 reported peaks 215,579 (lb-4) and 206,569 (qt1), no callback errors. Its 2,000-callback F smoke had maximum error 4.47e-7 bps. Full offline engine bootstrap assets were absent, and inherited historical logs could not be reverified; none of these screens establishes all gates.

- **Two contract-engine 64-seed smokes (b05-copy-a, b05-copy-b).** Both validate P against Taylor's unmodified `gates.py` and compile baseline contracts within byte/character limits. Copy-a measured BASE−lb-4 +0.2395 (SE 0.0484) and lb-4−qt1 +2.9203 (0.1252); copy-b measured +0.1729 (0.0466) and +3.1529 (0.1369). Every sampled BASE seed beat qt1 in both windows; BASE had losses against lb-4 (copy-a min −0.5679; copy-b 19/64 negative, min −0.6074). These are separate 64-seed smoke leases, not a same-seed disagreement and not E. Peaks for BASE/lb-4/qt1 were 208,316/216,447/209,237 in copy-a and 208,275/220,387/209,036 in copy-b; no OOG was observed. Authors caution that 64-seed peaks do not establish the larger-run ceiling; Q/T/F were not run.

- **Exact tell comparison (b09-ref).** LEAN and exact tell labels agreed on 223,085 first-own-trade observations over seeds 64,000–64,031 (zero disagreements). On report seeds 10,000–12,047 (2,048), LEANBASE−BASE was −0.01742 (SE 0.01742), with the lone material loss −35.6749 at seed 10,942 and zero on other seeds. The result says this does not show a worse mean under mean+2SE, but is not equivalence; the outlier does matter at seed level. On its separate 256-seed choose set, variants A and B were exactly equal to BASE; variant C (fixed positive-hit likelihood ratios) scored −0.00923 (SE 0.00480). The exact label comparison therefore does not imply a performance gain from that alternative likelihood update.

### Rival tracking and pull rules

- **Oracle ceiling (b08-rival-oracle).** True hidden spot every callback gave +0.1503 (SE 0.0067) over BASE on 2,048 replica seeds; retail contributed +0.2869 and arbitrage −0.1366. A retail-only interior oracle gave +0.0434 (0.0039), and a corner/no-pull diagnostic +0.0324 (0.0059). These use hidden inputs and are not implementable policies or engine results; the result declines a pick.

- **64-particle tracker (b08-rival64-on-base).** Over 2,048 replica seeds, rival64 replacing the estimate added +0.04230 (SE 0.00585), retaining it +0.04348 (0.00556); rival16 replacing added +0.01795 (0.00606). Retain/replace are close; rival64 is the strongest tested arm. Its estimated state is 198 words for a minimal 64-particle port (201 as-built), versus 54/57 for 16 particles; bounds include 15 transition/normalization sweeps and 117N binary-search comparisons. No Solidity, engine or gas test exists. The distinct goal claim of +0.145 (SE 0.015) on Taylor's replica is [artifact 19bf5534…](https://api.imd.fun/artifacts/19bf5534225de5b3d201baaf0e35f9f2a8671120380295ea7726bf6379caedc1). This is a smaller BASE-relative test, not a conflict on the same experiment; the gas-cheap form remains unsolved.

- **Finite-point rival distribution (b07-few-point).** A compressed weighted support of K=3 or K=5 rival log-spot points, with optional pull fallback, improved BASE on 1,216 report seeds (10,000–11,215): +0.04754 (SE 0.00767), +0.05068 (0.00810), and +0.05400 (0.00774) respectively. Choose used only 128 seeds (SE about 0.024–0.026), and report was incomplete. K=5 had a worst single-seed loss −3.5484. The result estimates 10 additional storage words and substantial callback work; no Solidity, gas or engine measurement or qt1 comparison. Replica signal only, with material port/gas risk.

- **Age-dependent pull (b07-age-alpha; b16-age-thr).** The rule raises pull from 0 toward 0.7 as age since binding, `alpha=0.7*age/(age+1)`. On 2,048 report seeds the gain is +0.019710 (SE 0.004066). b16 confirms b07's per-seed delta on 2,047/2,048 seeds; the exception is seed 10,942, where the underlying LEANBASE/stalerival implementations differ. This is confirmation, not an independent gain. b07's 0.02 advance threshold is not met (mean−2SE=0.01158); b16 advances using its 0.015 threshold. AGE+THR and AGE+THR+HYP gave +0.02230 and +0.02500 over BASE on report, but choose did not select these combinations and the contrast to AGE differed between choose and report; a new split is needed. AGE cost is estimated at one stored timestamp and roughly sub/add/mul/div on eligible callbacks. No Solidity/gas/T/F/G/E check.

- **Bayesian posterior pull (b07-bayes-alpha).** A point estimate of the two-pool router split probability set the nonbinding retail pull. Four choices (raw, affine, clipped, two-level) scored −0.00276 (SE 0.00857), −0.00189 (0.00554), −0.00543 (0.00782), and −0.02445 (0.00827) versus BASE on 512 common report seeds. Two-level hit the early stop at 576, so the full report was not run. No established gain; replica only.

- **Soft clipping (b07-soft-clip).** Four approximate posterior band-clipping methods on 1,024 report seeds scored +0.0068 (SE 0.0032; closed-form clip 1), +0.0033 (0.0030; GH-3 clip 2), +0.0077 (0.0033; hyperbola clip 3), and +0.0008 (0.0027; closed-form clip 1, half variance). The selection rule picked the last, small-effect arm. Only half the report window ran; no contract/engine test.

- **Sync threshold/blend (b07-blend).** Over 768 report seeds, threshold arms added +0.00811 (SE 0.00388) and +0.00826 (0.00391); selected threshold-plus-add +0.01032 (0.00394); fee blend +0.00138 (0.00404). Choose used 384 seeds and did not separate settings from BASE/each other at 2SE. Report omitted 1,280 seeds and some arms. Fee blending adds another full table lookup; no Solidity/gas work.

- **Where to run the tell (b08-q-where).** No source fetch, policy implementation, scoring or cost measurement completed. Missing result, not a zero effect.

- **True price versus tell value (goal brief; [artifact 3dc2d521…](https://api.imd.fun/artifacts/3dc2d521ec738b3659160a4b5ce04b04022a7ba85d9937fbfaafb544cc9d7a2f)).** The goal attributes +1.19 to true price, nearly all between arb pins, and only +0.006 to the tell flag. b08's oracle result (+0.1503 total, +0.2869 retail, −0.1366 arb) uses another base/experiment. These are different comparisons, not additive estimates or a same-experiment contradiction.
+
+### Cheap approximate tell
+
+- **Capped inverse lookup (b08-q-lite).** A cap-limited integer/binary64-compatible tell uses public callback amounts, reserves, prior returned fees and own state. On 2,048 replica report seeds cap24 scored +0.04056 (SE 0.00368), cap40 +0.04366 (0.00389, selected), alternate search order +0.04257 (0.00388), and uncapped reference +0.04429 (0.00391). No extra state words. Cap24 integer/float parity had zero mismatches over 6,835,040 callbacks; this is Python parity, not Solidity gas. No contract or engine measurement; cap16 ineffective and rare binade-edge misses remain.
+
+- **Gated integer cap24 (b16-qlite-a).** Run the cap24 tell only on non-arb callbacks with `dt<=6`, skipping the long-gap peak path. On 2,048 report seeds cap24+GATE scored +0.03857 (SE 0.00364); cap24 +0.04056 and cap40+GATE +0.04159. The pick was −0.00199 (0.00074) versus cap24. Integer/float test had zero mismatches on 6,835,040 callbacks; the gate skipped 0.355% of sampled non-arb callbacks. Estimated 22 binary64 operations (29 including hit update), and measured 355 mean Python integer primitives; neither is EVM gas. No Solidity or measured gas. Peak-path avoidance relies on the brief's headroom statement, so this remains a replica rule with proposed cheap placement, not a validated contract.
+
+### Contract ports and gas
+
+- **BASE profiling (b06-copy-a/b).** Both profile 40,615-character, 21,055-byte TellMinLookup BASE, not lb-4. On eight engine configs each, copy-a records 83,246 callbacks, peak 208,236 transaction gas and no failures; copy-b 88,351 callbacks, peak 202,178 and no failures. Long silence is the peak path: filter/belief update about 68–70k gas, fee lookup about 58k, pull about 5.6k, tell about 16–23k plus storage/dispatch. Copy-a's replica-probe peak is 159,719 call gas (205,935 transaction); copy-b's cold-storage-corrected replica estimate is 183,719 call gas. Decomposition differs materially because probe/correction methods differ; aggregate engine peaks are 208,236 and 202,178. Copy-a engine peak is 2,301 above its largest replayed replica transaction. Rare 13+ gap paths have only 2–5 samples; neither report measured per-path engine gas, and copy-a did not complete the opcode trace. Both are BASE screens, not candidate gates.
+
+- **LEAN tell contract ports (b10-copy-a/b).** Both report T/F/G pass: zero T mismatches; 100,000 F callbacks with max fee error 4.6653e-7 bps (0.01 tolerance); no observed OOG/failures. Copy-a: 21,368 runtime bytes, 43,563 characters, peak 191,772 gas. Copy-b: 21,300 bytes, 43,915 characters, peak 196,985. They fit the limits on measured leases. Copy-a's 8-seed screen had the same edge as BASE on each seed; this is not a score claim. The over-budget tell label was not observed. P/Q/E were not run and neither candidate was submitted.
+
+- **Few-point tracker contract (b11-few-point).** T/F passed (zero tell mismatches; F max error 4.638e-7 bps), but G failed: 24,242 runtime bytes, 45,523 characters, peak 248,120 gas (>245,000), 94,550 OOG callbacks, only 28/94,578 successful. Not eligible; no retuning/performance test.
+
+### Compression and refitting
+
+- **Original full-table advantage (brief; [artifact 4a41a90c…](https://api.imd.fun/artifacts/4a41a90c67cf9add7e0c4f382e60c411bbf8ed340874aead14be76f4d09951f7)).** FULL `kappa=1e-5` tables beat lb-4's compressed lookup by +0.111 on the Taylor replica. That is not FULL versus later QPL1 U1.
+
+- **QPL1 ceiling/knots (b12-comp-knots, b12-comp-fine, b12-comp-resid).** LEANBASE replica choose comparisons FULL−U1 measured +0.00254 (SE 0.00701, n=768), +0.00079 (0.00606, n=1,024), and +0.00239 (0.00643, n=896). All stopped before report under the <0.005 rule. Fine result's per-entry average absolute errors for 0c/1s/1c/2s/2c were 0.627/0.783/0.602/0.787/0.714 bps; high errors are concentrated on rarely used nodes. Knot/residual results say 1c/2c had zero visit weight under LEANBASE's 0.35 pull (0 of about 1.38m lookups in reported samples); about 2,000 reclaimable blob bytes is an inference from code/replica. The +0.111 and these near-zero ceilings concern different compressed encodings/baselines. b12-comp-resid did not run lb-4's blob; b12-comp-fine did not reproduce +0.111. This is unresolved encoding/base scope, not evidence either measurement is false.
+
+- **QPL1 refits (b12-refit-visit/rp3).** Visit refit selected eps=0.001; candidates scored −0.0047 (SE 0.0040) and −0.0023 (0.0038) versus U1 on choose; FULL−U1 ceiling +0.00079 (0.00606, n=1,024), so report stopped. Ridge refit selected lambda 100 on 256 choose seeds; FULL−U1 ceiling was +0.00618 (SE 0.00411, n=2,048), but report candidate−U1 was −0.00171 (0.00197) and candidate−FULL −0.00789 (0.00412) on 2,048 seeds; no advance. These are QPL1 replica refits, not the original lb-4 comparison; no Solidity/EVM measurement.
+
+- **Brief's rp-3 result (artifact 31c415ff…).** The brief lists about +0.05 on engine and says already ported. Supplied b12-refit-rp3 is a Python QPL1 ridge refit with no Solidity/EVM run. They cannot be assumed the same candidate/test; +0.05 engine claim was not reproduced in this root. Source: [artifact 31c415ff…](https://api.imd.fun/artifacts/31c415ffbbcdc36d91a30d4f4a8817406d3ab96b34df29d08ac28ad3e41432ba).
+
+## Source reliability and remaining uncertainty
+
+The task reports source rechecks failed, were unreadable, or did not support quoted claims for: b01-exact-lb4 (2 sources), b05-copy-a (1), b06-copy-a (2), b07-bayes-alpha (3), b07-few-point (2), b07-age-alpha (4), b07-blend (1), b08-rival64-on-base (1), b08-q-lite (1), b08-q-where (1), b09-ref (4), b10-copy-a (1), b12-comp-knots (3), b12-comp-fine (1), b12-refit-rp3 (1). I retain their recorded local measurements as reported experiment evidence, but failed citations do not independently verify their source claims. This does not alone invalidate a measurement. b08-q-where is more serious: its own fetch failed and work was not run, so it has no effect estimate.
+
+No new candidate in these results has a complete P→Q→T→F→G→E pass, and none was submitted. The historical bundle/score, +0.111 compression comparison, +1.19 true-price ceiling, +0.006 tell-only effect, +0.145 rival64 result and +0.05 refit engine result are brief claims, not fresh reproductions here. Replica gains are not additive: baselines, variants, windows and overlapping policy changes differ.
+
+## Input result ledger
+
+All 25 supplied results were present and read: [b01-exact-lb4](../../../../../.imd/reads/artifacts/b01-exact-lb4), [b05-copy-a](../../../../../.imd/reads/artifacts/b05-copy-a), [b05-copy-b](../../../../../.imd/reads/artifacts/b05-copy-b), [b06-copy-a](../../../../../.imd/reads/artifacts/b06-copy-a), [b06-copy-b](../../../../../.imd/reads/artifacts/b06-copy-b), [b07-bayes-alpha](../../../../../.imd/reads/artifacts/b07-bayes-alpha), [b07-soft-clip](../../../../../.imd/reads/artifacts/b07-soft-clip), [b07-few-point](../../../../../.imd/reads/artifacts/b07-few-point), [b07-age-alpha](../../../../../.imd/reads/artifacts/b07-age-alpha), [b07-blend](../../../../../.imd/reads/artifacts/b07-blend), [b08-rival-oracle](../../../../../.imd/reads/artifacts/b08-rival-oracle), [b08-rival64-on-base](../../../../../.imd/reads/artifacts/b08-rival64-on-base), [b08-q-lite](../../../../../.imd/reads/artifacts/b08-q-lite), [b08-q-where](../../../../../.imd/reads/artifacts/b08-q-where), [b09-ref](../../../../../.imd/reads/artifacts/b09-ref), [b10-copy-a](../../../../../.imd/reads/artifacts/b10-copy-a), [b10-copy-b](../../../../../.imd/reads/artifacts/b10-copy-b), [b11-few-point](../../../../../.imd/reads/artifacts/b11-few-point), [b12-comp-knots](../../../../../.imd/reads/artifacts/b12-comp-knots), [b12-comp-resid](../../../../../.imd/reads/artifacts/b12-comp-resid), [b12-comp-fine](../../../../../.imd/reads/artifacts/b12-comp-fine), [b12-refit-visit](../../../../../.imd/reads/artifacts/b12-refit-visit), [b12-refit-rp3](../../../../../.imd/reads/artifacts/b12-refit-rp3), [b16-age-thr](../../../../../.imd/reads/artifacts/b16-age-thr), [b16-qlite-a](../../../../../.imd/reads/artifacts/b16-qlite-a).
+EOF
wc -c artifacts/goal/roots/1/01/result.md