# Root merge 1: integer tell, contract integration, engine evidence, and replica experiments

The strongest carry-forward candidate in these inputs is **min-lookup with the frozen QPL1 u1 tables** (`b11-lookup-u1`). Two subsequent three-arm engine studies find it improves on min-lookup by **0.10466573123944156, se 0.012105858020343573**, pooled over 512 distinct seeds, while improving on C0 by **3.2087870597090564, se 0.04432900158143203** on those same seeds. These are merge calculations from `b13-p1` and `b13-p2`, not leaderboard results. The candidate has reported vector, validation, size, integer-shadow/engine-clamped fee, and measured engine gas passes, subject to the reference-domain and source-quality qualifications below. No input supplies a 4,096-seed extension or a submission. The goal enters nothing.

The assignment's starting figures are **8th, 524.94**, seat **#1268**'s Gaussian + qm C0; **5th 528.10 (C0 + 3.16)** and **1st 528.42 (C0 + 3.48)** at [the AMM puzzle](https://paradigm.xyz/puzzles/amm). Its replica premise is **+6.98 over HA**, **+3.21 se 0.02** over C0's policy, with about **0.24** lost to table compression and **3,971 bytes** free; **1.73** remains between pins and true price. Those are brief-supplied context, not newly verified board or engine measurements. The inputs now contain real-engine evidence, but adding any local mean improvement to 524.94 would still be a projection, not proof of a board rank.

All 25 named inputs were present and parsed. Every input is accounted for below; source labels are the supplied `b…` filenames. Their exact content-addressed URLs appear in the source register at the end. Measurements are attributed to those results, rather than presented as independently rerun simulations. This merge independently decoded embedded code/bundles, checked their claimed SHA-256 values, and recomputed the six completed engine studies' aggregate statistics from their embedded per-seed rows. It did not compile or rerun contracts, fetch external pages, or recover unavailable source quotations. Full numerical summaries retained below distinguish observations, estimates, failed gates, setup blocks, and unperformed work.

**Evidence qualifications that affect the conclusion.**

The requester flags failed source rereads for `b07-retail-quotient-signal` (**7 sources**), `b08-min-lookup` (**2**), and `b11-lookup-u1` (**3**): a source was unreadable, changed, or did not support its quotation. The identities/passages of the individual failures are not supplied. None of these three inputs embeds the `sources.json` it cites in its available bundle (min-lookup has no bundle field at all). Consequently this merge cannot identify or rehabilitate the individual citations. Algorithm provenance and external quotations from those sources remain unverified, and are not treated as corroboration. Their numerical/code evidence is retained as worker-reported local evidence with that qualification. The code hashes do match their embedded source, and later independent scoring items identify and score the same min-lookup/u1 source and runtime hashes. That strengthens the engine-performance evidence without certifying the missing quotations or independently proving all gate assertions. (`b07-retail-quotient-signal`, `b08-min-lookup`, `b11-lookup-u1`, `b10-*`, `b13-*`; requester warning.)

There are three distinct fee comparisons: (a) contract versus the original floating-observation TellPolicy, (b) contract versus an integer-observation shadow over the candidate's own decoded tables, and (c) compressed tables versus full qm. A failure of (a) is preserved even when (b) passes. Approximation error in (c) is not a port-parity failure against the candidate's own reference. Finally, raw shadow fees above the engine's 10% cap differ from executable clamped fees. Treating these comparisons as interchangeable would change the reported outcome. (`b03-*`, `b08-*`, `b11-lookup-u1`.)

**Track A: two exact integer classifiers, with different domains and gas accounting.**

Both detector ports match the corpus's **last-field expected answer on 11,856/11,856 vectors**, with zero mismatches. Expected answers include **4,670 hits**, comprising **4,661 arbitrage** and **9 retail** hits; a hit is therefore not an oracle for trade truth. (`b01-bounded-bitmath`, `b01-literal-rational`, `b06-probe-reference`.)

`b01-literal-rational` directly translates rational arithmetic with auditable normalization loops and checked shifts. Its `TellMath.isArb(bool,uint256 × 8)` is internal pure, exposed through a harness; no storage, assembly, or challenge imports. It reconstructs fee-to-double, division by WAD, and subtraction from one as separately rounded operations; uses nearest/ties-even with significand carry; uses half-up for n0; tests positive n0−1,n0,n0+1; and forward-rounds through the handed WAD conversion. Its stated domain is both amounts in [0,2^120), all reserves in [1,2^120); out-of-domain amount/reserve inputs revert `Bounds`. Fees above 1e17 are clamped; equivalence to the reference is claimed for already-clamped fees. The result includes arithmetic bounds reasoning, **31,378 synthetic classifier cases**, **1,032 rounding cases**, **3,000 retail-chance rational checks**, **7 explicit exponent boundaries**, **6 rejection calls**, and **6 passing Forge tests**. The zero-paid exponent helper handles subnormal ulp; its rational helper rejects zero because the denominator exceeds uint256. Source **6,938 bytes**, harness runtime **3,092**, creation **3,120**. Warm-harness STATICCALL gas, including encoding/decoding but excluding the meter's outer call: **min 25,837; mean 31,421.193741565454; p95 34,736; max 36,904**. Its original corpus is an explicit, nonembedded input; clean decoded-bundle replay is reported identical. No whole-strategy/engine performance is claimed.

`b01-bounded-bitmath` uses an eight-step bit-length normalization, exponent estimation and at most one corrective division, with exact rounded rational forward checks. It returns false rather than reverting when paid amount or paid-side before/after reserves are outside [1,2^128), or the side's fee is outside [0,1e17]; it does not clamp internally. Zero reserves return false, whereas the reference is reported to loop. This is a different out-of-domain extension from the literal port, not contradictory vector evidence. It reports **6,892 extra edge vectors**, **2,271 true**, zero mismatches; **1,262** helper boundary checks also pass. `ulpOverGridWad` returns the capped power-of-two chance in WAD, truncating to zero beyond its supported shift/domain. Source **5,670 bytes**, harness runtime **2,949**, initcode **2,977**. Inline vector gas: **min 14,316; mean 17,163.9; p95 18,998; max 20,193**; all **18,748** corpus-plus-edge calls: **min 11,152; mean 17,343.6; p95 19,507; max 20,859**. External-wrapper vector gas: **min 32,280; mean 37,295.0; p95 40,750; max 42,375**. The inline and external measurements are not directly comparable to the literal port's warm STATICCALL measurement. Neither detector item establishes whole-strategy gas or edge.

Both preserve per-vector gas payloads in their source results. Subsequent integrations also retain vector-gas payloads under their own wrappers and compiler contexts. Detector-only harness bytes and gas must not be added mechanically to strategy measurements: optimization and call overhead differ. Both detector results use solc 0.8.24, optimizer 200, viaIR, Paris. (`b01-*`, `b08-*`, `b11-lookup-u1`.)

**C0 lookup headroom is measured without an edge claim.**

`b04-lookup-headroom` replaces C0's 306-leaf coefficient-dispatch tree with loading the selected table's 24–84 words once per callback into a shared 84-word memory array, then reading it for both surfaces. It also starts each x+64 knot-span search at the previous basis span instead of repeating binary search. Knots, coefficients, spline arithmetic, weights, clamps, filter, fees, slots 0–2, name and initialization are unchanged. There is no assembly. Runtime falls **20,605 → 20,128 bytes**, initcode **20,633 → 20,156**, saving **477 bytes** and leaving **4,448** under 24,576.

It reports exact bid/ask equality for **23,166 fee cases**, **132,369 surface cases**, and **218,129 ordered callback replays** on seeds **61000..61019**. Fee-function max gas **100,110 → 89,244**, mean **80,101 → 73,354**. Warm Forge callback peak **176,065 → 164,365**, mean **107,239 → 97,349**, largest single-call saving **14,507**. These are like-for-like harness savings, not engine gas. Its quoted C0 engine peak **208,775** and pyrevm **194,051** are contextual figures, not the replay's absolute peak. No edge gain is asserted; validation, engine scoring, and integration were pending in this item. Reusing bases across mirrored surfaces and fusing sd weights into coefficient lanes were considered but not implemented. (`b04-lookup-headroom`.)

**Minimal tell integration: implemented, with an initially failed literal gate.**

The completed `b08-min-1`, `b08-min-3`, and `b08-min-lookup` candidates keep exact prior callback reserves in slots 3 and 4, prior returned integer fees in packed slot 2, and guard shifts in slot 5, within the inherited 32-slot allowance. Only the first own trade of a new step runs isArb. Off-grid sets arbitrage probability to zero; on-grid multiplies retail likelihood by ulp/grid before the existing soft=1 posterior. A hit alone never pins. Tables and the remaining Gaussian/filter logic are unchanged; min-lookup starts from the lookup-optimized C0. All three report exact vectors, validation, size, no assembly, storage compliance and measured engine-gas passes, but **all three retain `gates_failed` for the originally requested literal floating TellPolicy comparison**. (`b08-min-1`, `b08-min-3`, `b08-min-lookup`.)

| Source | Source SHA-256 prefix | Runtime bytes | Reported engine gas scope | afterSwap peak |
|---|---|---:|---|---:|
| b08-min-1 | 644bdfad1ffd9203 | 23,337 | Candidate-only smoke, seed 60000, 10,657 calls | 224,063 |
| b08-min-3 | c522fcfa78d170fe | 23,519 | Candidate-only, seed 14000528, 9,239 calls | 228,387 |
| b08-min-lookup | 3a799de034a2482f | 22,499 | Eight calibration seeds 60000..60007, 86,129 calls | 222,798 |

Each table entry comes from that row's source, with zero reported OOG/reverts in those runs; min-lookup also explicitly reports zero other halt, transaction error and bad return. None is a paired score study. Min-3's pyrevm peak is **213,463**, min-1's **213,278**. All used the same compiler family/settings above. Min-1's embedded source is **49,733 bytes**, min-3's **49,293**, min-lookup's **44,571** (decoded/hash-checked by this merge).

All three literal-shadow tests drove **90,554 callbacks**, seeds **60000..60007**, synchronized shadow fb/fa to contract-returned fees, and compared against TellPolicy using decoded C0 tables. Engine-clamped max bid/ask discrepancies were **25.961658883156016 / 15.324825506245277 bps**; seeds **60001, 60004, 60006** failed the **0.01 bps** gate. Min-lookup additionally reports raw bid discrepancy **458.62902019074807 bps**. There were **14 first-trade classifier disagreements**, all retail one-ulp collisions. Replacing only the diagnostic shadow's observation test/chance by integer tellref restores observed max errors to **4.831604213939578e-7 / 4.83988439603511e-7 bps**, but those workers expressly did not count this diagnostic as passing the original gate. (`b08-min-1`, `b08-min-3`, `b08-min-lookup`.)

The concrete information-loss example is paid **9.557781723314566** (native float off-grid) versus adjacent **9.557781723314564** (on-grid), both handing **9557781723314565120** after WAD conversion at seed **60001**, timestamp **4596**. The integer contract cannot distinguish those doubles. Min-1 supplies a second collision at seed **60006**, timestamp **4707**: **0.05575503756659037** versus **0.05575503756659038**, both handing **55755037566590376**. Thus exact equality to the native-float decision is not generally implementable using only handed integers. This is evidence of a reference-domain mismatch, not evidence that the integer vector port is wrong. (`b08-min-lookup`, `b08-min-3`, `b08-min-1`.)

The gamma guard excludes integer fees **2999999999999948..3000000000000057**, inclusive, which round to Vanilla's gamma **0.997**; nearest allowed neighbors are **2999999999999947** and **3000000000000058**, lower on a tie. Min-1 reports **2,110** guard checks with no mismatches; min-lookup reports **2,113 cases, 110 shifts**, an exact 110 counter, covering forbidden values, neighbors, zero and cap. Closed-loop guard-shift counts were zero; engine guard counts are **unavailable**, because run_batch does not return storage. A zero count must not be inferred from sparse output fees. (`b08-min-1`, `b08-min-3`, `b08-min-lookup`.)

No paired blocks were run by these three b08 items after their gate failures; paired n=0 and empty rows are **absence of evidence, not a zero gain**. Min-3 consumed **14000528** for gas, leaving **14000529..14000783** in that allocation unrun; min-lookup and min-1 left their assigned paired allocations unrun. The subsequent `b10-*` results report that a requester correction accepted integer-shadow checking (lookup-fresh dates it **04:17Z**) and explicitly used the frozen candidate bytes without rebuilding or rerunning tell gates. This merge records that later reported correction; it neither erases the earlier literal failure nor invents a new primary-gate run. (`b08-*`, `b10-*`.)

**Track P: real engine confirms the signal, but not universal specificity or perfect recall.**

`b06-probe-reference` runs the unpatched engine against Vanilla with tiny fee telemetry, no hidden truth in the contract. It stores previous handed reserves/returned fees, runs the classifier on every callback, and encodes step/callback/hit counters in returned fee integers. External decoding reconstructs arbitrage opportunities from price and prior pool spot/fees, treating arbitrage as the first callback. It reports **4,096 distinct representable telemetry codes, no collisions**, maximum perturbation **4,095 wei = 4.095e-11 bps**, and no saturation, stale aliases, missing arbitrage callbacks, ambiguous boundaries or unreadable steps. This is a telemetry inference, not direct access to hidden trade amounts. Validation passed; runtime **3,699 bytes**; vectors matched exactly.

At **30 bps**, seeds **14000000..14000007**, the pooled result is **29,091 / 29,091 arbitrage trades read**, zero false negatives, but **2,015 / 70,503 retail trades read as arbitrage (2.8580344098832675%)**. Among first callbacks, TP/FN/FP/TN are **29,091 / 0 / 861 / 28,868**, first-trade error **0.014637878272696362**. afterSwap **99,594 successful calls**, peak **99,374 gas**, total **7,749,619,451**, zero OOG/reverts and other recorded failures. This contradicts using the brief/README's roughly **0.21%** mirror false-positive figure as an engine-wide guarantee.

The worker hypothesizes that matching Vanilla's 30-bps gamma, with equal constant products, makes the router's split ratio near one and retail payments resemble the same grid. The **35-bps control reuses those eight seeds** and supports fee sensitivity: **24,806 / 24,807 arbitrage** read and **75 / 60,502 retail** read as arbitrage (**0.1239628442034974%**). It also exposes **one false negative**, seed **14000001**, step **7561**, relative arbitrage margin about **1.3e-8**. Its root cause was not established; amounts were not visible. afterSwap **85,309 calls**, peak **100,064**, total **6,650,400,915**, zero recorded execution failures. The control is diagnostic reuse, not eight more fresh runs. Never claim all arbitrage is always detected, or that the engine retail hit rate is universally one in 500. The evidence motivates both the posterior weighting and gamma guard, without proving they remove every failure mode. (`b06-probe-reference`.)

**Table recovery: retain both methods, prefer u1 for carry-forward.**

`b03-sparse-spline-residual` adds quantized corrections to selected C0 spline grid nodes while preserving its QMS1 decoder, phase/sync/sd structure, and ask/bid mirror. Nodes are ranked using tuning occupancy times squared full-qm error. Frozen **SRS1**, **576 corrections**, quantization denominator **4** (0.25 bps), occupancy exponent **1**; payload **2,055 bytes**, **64 words**, nine packed 28-bit entries per word, one int8 correction clipped. Tuning uses **60000..60255**, with deterministic rebuild. Replica holdout **10000..12047**, n=2048, gains **0.050943 se 0.004653** over local C0-compressed TellPolicy, but remains **−0.061103 se 0.005125** versus shipped tell_qm, or **−0.059079 se 0.005131** versus the local full-qm rerun. It recovers approximately **45%** of that experiment's C0 compression loss. Tuning gain was **0.075806 se 0.012770**; candidate versus full **−0.047111 se 0.013710**.

Its visited-table RMS falls **0.8412 → 0.5378 bps**; all-node RMS changes only **4.8283 → 4.8169**, maximum remains **204.7921 bps**. Shared-callback mean fee difference to full qm falls **0.2609114813725296 → 0.14483882120132113 bps**, but maximum is **36.8207604387738 bps** (C0 **36.14763050610925**). These are table approximation errors. The candidate-specific 0.01-bps Solidity fee gate was not tested. A standalone Forge lookup matches Python on **465 windows**. Estimated integrated cost is unfavorable for simultaneous detector integration: measured standalone net **about 2,980 runtime bytes**, leaving **about 990** of C0's original free bytes; table build about **1,750 gas**, four-window lookup worst **20,271**, estimated C0 total about **231,000**, leaving about **14,000 gas** for the detector. These last integrated totals are estimates, not contract/engine measurements. Occupancy is regenerated, not shipped. (`b03-sparse-spline-residual`.)

`b03-adaptive-linear-grid` instead replaces the spline representation with **QPL1 u1**, an ask-only adaptive trilinear surface of F=A−w, mirrored for bid. It retains all five table identities, the sd axis, phase/sync categories and clamps. Frozen settings **qe=9 auto, power=1, floor=1e-3, sweeps=8, budget=10,167**; payload **10,160 bytes**, **448 records**, at most **31 bytes** per record, deterministic refit. Level/row/column knot layouts are retained in the numerical evidence below. At n=2048 on **10000..12047**, it gains **0.101708 se 0.006165** over C0-compressed TellPolicy and is **−0.010338 se 0.004251** versus tell_qm, **−0.008314 se 0.004216** versus local full qm. Tuning gain over C0 compression was **0.103098 se 0.016409**; settings u1..u5 were within noise and u1 was frozen as a default, not selected for the best tuning score. Reported replica edges versus HA: **u1 +6.964 se 0.044**, C0-compressed **+6.863 se 0.044**, local full **+6.973 se 0.044**.

u1's visited-table RMS is **0.3494 bps** versus C0 **0.8342**, max **61.833** versus **204.792**. Shared tuning-callback fee errors versus full qm: max/RMS **22.6175 / 0.2304 bps**, C0 **36.1476 / 0.6775**. The Python contract-style lookup agreed with decoded-file interpolation to **4.8e-7 bps** on **20,000 random points**. At this stage there was no Solidity/engine gate. Its **16–24k gas per two-side lookup**, **45–60k possible peak saving**, and contiguous blob layout were engineering estimates, not measured evidence. The later b11 port supersedes these estimates for that specific implementation; it does not turn them into prior measurements. (`b03-adaptive-linear-grid`.)

Both table experiments measured local full-qm TellPolicy versus published tell_qm at **−0.002024 se 0.001199**, while local compressed C0 TellPolicy was **−0.112046 se 0.006275**. The brief's historical **about 0.24** compression loss is therefore not the same comparison. The local TellPolicy gate outputs **446.798260 / 574.326680 / 529.637987** differ from the README **446.752500 / 574.326680 / 529.609154** on seeds **10000..10002**. The workers attribute this to float/libm grid sensitivity; the small local full-qm control is retained so that approximation gains are not mistaken for drift. These are TellPolicy replica studies, not direct engine gains over unmodified C0. (`b03-*`, also `b09-give-away`.)

**u1 Solidity port: strong executable parity, explicit raw-cap exception.**

`b11-lookup-u1` takes frozen min-lookup and changes only the tables/decoder and lookup call sites to frozen u1, with no refit. It preserves the integer classifier, odds, soft=1, timestamp behavior and original gamma guard. Source SHA-256 **69c361efb59a346f908ffe30c3197d9d08903bc2305d0ccd79f23e6535daed40**; runtime SHA-256 **4ee7c49f03f8117c15798c45ebbfaa54a2289d62d5d5447d02b45fc287d41919**; runtime **20,977 bytes**. Vector gate **11,856 matches**, zero mismatches. Decoder **65,632 boundary + 20,000 random points**, max error **5.000000271593308e-7 bps** versus frozen q_u1.json, below its **2e-6 bps** decoder tolerance.

On **90,448 closed-loop callbacks**, replica seeds **60000..60007**, integer tellref/chance shadow, synchronized fees, engine-clamped max bid/ask differences are **4.569313677427189e-7 / 4.580097065498556e-7 bps**, within **0.01**. Raw shadow comparison **fails**: on seed **60006**, callback **10755**, timestamp **9989**, raw bid is **0.14588627140291133**, while contract/engine clamp to **0.1**, producing raw discrepancy **458.8627140291132 bps**. Status is consequently `engine_clamped_gates_pass; raw_shadow_cap_exception_reported`, not an unconditional raw-output pass.

Validation, slots 0..5, no assembly and runtime limit pass. Engine gas uses **14001552..14001559**, **88,699 callbacks**, peak **202,190**, zero OOG/revert/other halt/transaction error/bad return. Those same eight gas seeds were run **twice** because the first harness tried to call gas_stats on the result object instead of the module. This is declared reuse, not fresh scoring. Replica gate was also repeated after adding clamped comparison and preserving the raw exception; verification additionally repeated seed 60000. No holdout scores or paired seeds were used in b11. Its shared-callback discrepancy versus full qm, a different reference, was max bid/ask **7.075686619928412 / 16.490430895781394 bps**, RMS **0.22104611559099704 / 0.23408680122874304**, across **180,896 fees**. (`b11-lookup-u1`, with the source-reread warning above.)

**Completed paired engine evidence.**

The six studies below use frozen bytecode, each strategy **alone against VanillaStrategy**, identical configs within each seed, the unpatched engine at **6b6921f8d463314aa7c96234e1be25a25245f704**, `amm_sim_rs.run_batch(X, VanillaStrategy, configs, 8)`, **10,000 steps**, and four saved **64-seed blocks** per study. Variance draws use `numpy.random.default_rng(actual_seed)` in order: retail mean size U[19,21], arrival U[0.6,1], sigma U[0.000882,0.001008]. Initial price/X/Y **100/100/10000**, GBM mu **0**, dt **1**, retail buy probability **0.5**, size sigma **1.2**. Candidate and C0 are not competing pools in the same match. d is candidate edge minus C0 edge; se is sqrt((sumsq−sum²/n)/(n−1)/n). Each completed study reports validation and no missing seeds or submission execution failures. (`b10-*`, `b13-*`; full statistics below.)

| Source | Candidate | Fresh paired seeds, inclusive | n | Mean d | se | Candidate afterSwap peak |
|---|---|---|---:|---:|---:|---:|
| b10-min-1-reserved | min-1 | 14000016..14000271 | 256 | 3.1313189811776008 | 0.06168039206584464 | 237415 |
| b10-lookup-reserved | min-lookup | 14000784..14001039 | 256 | 3.21882618328908 | 0.05837298386396219 | 228504 |
| b10-min-1-fresh | min-1 | 14001040..14001295 | 256 | 3.27081791145147 | 0.062401826979037525 | 237653 |
| b10-lookup-fresh | min-lookup | 14001296..14001551 | 256 | 3.3271287255250126 | 0.0653324668554422 | 228346 |
| b13-p1 | u1 | 14001560..14001815 | 256 | 3.175539473292165 | 0.05989757684666979 | 204898 |
| b13-p2 | u1 | 14001816..14002071 | 256 | 3.2420346461259473 | 0.06541608541773083 | 204879 |

The first four do not isolate min-lookup versus min-1: their seed sets differ. Likewise u1's raw mean versus C0 cannot be ranked against earlier min-lookup means from different seeds. The two b13 studies add a third isolated arm `ref` = min-lookup on the **same configs**, giving a direct table comparison: **p1 u1−ref 0.10695046560810839 se 0.016850758026285193**, **p2 0.10238099687077473 se 0.017417451942822116**. On those same studies ref−C0 is **3.068589007684057 se 0.06053249610939766** and **3.1396536492551723 se 0.06401793561354752**, respectively. This is the sound basis for preferring u1. (`b13-p1`, `b13-p2`.)

Pooling only disjoint seeds for each frozen candidate gives min-1 **n=512, +3.2010684463145354 se 0.043935963047439235** from its two b10 studies, min-lookup **n=512, +3.2729774544070462 se 0.043828271000292594** from its two b10 studies, and u1 **n=512, +3.2087870597090564 se 0.04432900158143203** from b13. The b13 matched u1−ref gain pooled is **+0.10466573123944156 se 0.012105858020343573**. These merge-derived pools sum each input's n, sum and sumsq; they are not new engine runs. Do not combine different candidates into a single strategy score. Although b13 also supplies more min-lookup observations, the direct matched comparison is kept separate from the original b10 min-lookup pool.

All observed afterSwap peaks are below **245,000**, but are sample maxima, not universal bounds. In p1 the top-level `gas_gate.submission_afterSwap_peak` is **227,885**, the maximum across arms: u1 itself is **204,898**, C0 **209,039**, ref **227,885**. Reporting 227,885 as u1's cost would misread the aggregate. In p2 u1/C0/ref peaks are **204,879 / 208,923 / 228,604**. The p2 design says cand,C0,ref execution order while its completed-arm listing puts C0 before cand; this is an internal reporting inconsistency, with no effect shown on the same-config paired rows. All per-block checkpoint statistics and role-separated gas totals are supplied by the source items; the compact ledger below preserves the aggregate audit evidence. (`b13-p1`, `b13-p2`.)

The verified paired seed intervals above are disjoint. Other intervals are not automatically fresh just because absent here: **14000000..14000007** were used by the probe (and its control reused them), **14000528** by min-3's gas test, **14001552..14001559** twice by u1's gas gate. Allocations/unrun gaps are not completed pairs. There is no 4,096-seed carry-forward in these 25 inputs, and no basis here to assert that first place has been reached. (`b06-probe-reference`, `b08-min-3`, `b10-*`, `b11-lookup-u1`, `b13-*`.)

**Track C: promising information, but no new idea reaches the +0.2 promotion bar.**

`b07-retail-quotient-signal` tests a WAD-visible grid of the retail router quotient, only on predicted-retail callbacks, to distinguish likely interior split fills from full orders. It reconstructs compatible previous reserve doubles and gamma from exact handed state, enumerates a ±2-ulp ratio interval and nearest numerator ±1, and accepts by forward WAD equality. On a hit it uses the marginal-price equality to update rival log spot and sets synced; otherwise the original one-sided bound remains. It does not decode an independent rival price or reveal true price. ±2 ulps is an empirical interval, not an all-states rounding proof; full orders can hit by chance. No truth flag, rival hidden state or seed is claimed as a decision input. (`b07-retail-quotient-signal`; source-reread warning applies.)

Frozen weight **1**, ratio radius **2**, soft **1**, full qm; tuning **60000..60255** gives **+0.12323001572156955 se 0.0166118832389228**. Once-only holdout **10000..12047** versus shipped tell_qm gives **+0.12285540499524492 se 0.006284515958726821**, below **0.2**. Candidate mean **536.6550630464546**, reference **536.5322076414594**. Price RMS **7.115711815695286** versus **7.149446150401305 bps**, first-trade misread **3,597 / 14,388,583** versus **3,420 / 14,350,251**. Among **14,567,245 predicted-retail callbacks**, **13,022,844 hits** (~89.40%), **310,025 actual estimate changes** (~2.13%), maximum correction **114.38619342510825 bps**. This hit rate concerns likely split-fill detection, not the arbitrage classifier's false-positive rate.

Its synthetic arithmetic test has **30,000 draws**, **2,086 / 2,086 interior hits**, but **831 / 13,823 full-order hits** (~6.01% false hits). Two unit tests pass. A pre-freeze repair avoids enumerating paid-double preimages; moving evaluation to the retail branch preserved all 256 tuning edge rows exactly. No Solidity or engine score exists. The estimate **60,000..220,000 extra gas per predicted-retail callback** is explicitly unmeasured and could be expensive; typical denominator candidates **3.4939051962124617**. Persistent state can reuse tell's prior reserves and fees. Missing source quotations, empirical rounding limits, and no real-engine validation keep this a qualified research result, not an A integration lead. (`b07-retail-quotient-signal`.)

`b09-give-away` investigates the same marginal-price identity without claiming an exact split classifier. An interior own retail fill implies rival post-trade spot `cand=s*(1-fb)/G2` when the pool buys X, or `s*G2/(1-fa)` when it sells X; a corner fill gives only a bound. On diagnostic seeds **60000..60003**, **27,216 / 30,361** own retail legs are interior and match within **1e-9 log error**. But of **3,867** cases where cand would move the rival estimate against the existing bound, only **744** are interior; candidate RMS **7.96 bps** versus estimate **5.83**. There is still an unknown order size/rival reserve pair, so this does not give an exact true-price read or establish that no future float signature could exist.

Its practical policy softly pulls rival log spot toward cand on the nonbinding side, alpha=alpha2=**0.35**, with no new state. Tuning **60000..60255** tried alpha **0.1/0.25/0.35/0.5/0.75**, gains **0.046/0.081/0.089/0.088/0.063** (respective se **0.012/0.017/0.019/0.022/0.025**); alpha=0.25, alpha2=0 gives **0.076 se 0.015**. Holdout n=2048 yields **+0.091 se 0.0071** versus tell_qm and **+0.093 se 0.007** versus local TellPolicy, below 0.2. HA gains are **+6.998 se 0.064** on **10000..11023** and **+7.134 se 0.059** on **11024..12047**, versus local baseline **+6.900 / +7.045**. Estimated fused port cost **60..120 bytes**, **3k..6k gas** on affected calls (less if rival state stays in logs), is unmeasured; no Solidity/engine work was done. Its failure to find an exact fill test is not in conflict with b07's probabilistic quotient signal. (`b09-give-away`.)

`b12-conditional-rival-pull` follows that idea with `alpha_eff=alpha*size/(size+0.002)/(1+(gap/0.0006)^2)`, gap=log(cand/s2h), size=paid/prior paid-side reserve. It only moves against the nonbinding retail bound and retains Gaussian/tables/soft=1. It uses a corrected WAD observation wrapper and an explicit gamma-equality guard, adding 128 wei while gamma equals Vanilla's. Among alpha **0.35/0.65/1.0**, tuning **61300..61555**, n=256 each, gains versus the identical alpha=0 wrapper are **0.0003275272420744102 se 0.007364533130175156**, **0.008161423546229951 se 0.007906215823267917**, and **0.008822967432809747 se 0.00877603042217026**. Alpha=1 is frozen before holdout. Blindness checks report exact vectors, **2,048** fee/gamma cases, equal state for colliding floats with identical WADs, and true-flag independence.

Its holdout n=2048 yields **−0.0016943641890520833 se 0.003159986467373076** versus shipped tell_qm, first-trade errors **4,202 / 14,355,034** (**1,089 FN, 3,113 FP**), price RMS **7.157145000676935 bps**. This total includes WAD-wrapper/fee/gamma changes, and there is **no corrected alpha=0 holdout arm**, so it does not isolate the pull. It cannot directly refute b09's +0.093 under another observation/reference setup. All holdout seeds completed, with no retuning. Estimated **200..600 bytes**, **4k..12k gas** on affected calls, no new persistent pull state; no compiled/engine evidence. Verdict: below promotion threshold. (`b12-conditional-rival-pull`.)

`b12-pin-volatility` estimates between-pin variance from squared changes in hard-pin log price divided by elapsed steps, with prior shrinkage and bounds. Frozen **C=1, K0=500, S0=9.45 bps, LO=8.5, HI=10.5, DMAX=50**; hard pins are first trades classified arb with posterior≥**0.995**, variance zero. Only **61000..61063** of allowed **61000..61255** were used for completed variant tuning. Corrected WAD-wrapper baseline is TellInt. The selected estimator correlates **0.901** with true sigma in tuning, bias **0.014 bps**, but tuning edge **−0.007 se 0.0293**; C=0.7,K0=3000 gives **+0.0227 se 0.0311**, correlation **0.577**, bias **−0.935 bps**. A 256-seed baseline-only run exists, but its variant timed out and is not paired evidence.

Full holdout **10000..12047** is **−0.005432120005715468 se 0.0033253578320732707** versus shipped float tell_qm; again no corrected TellInt holdout arm isolates the feature. Misreads **13,371 / 14,351,237** versus **3,420 / 14,350,251**, price RMS **7.168313269872027** versus **7.149446150401305 bps**. The much higher misread rate remains visible; the worker's gamma guard was an interpretation, not separately tested. It reports sigma's narrow replica range **8.82..10.08 bps** and little edge sensitivity. Estimated **250..400 bytes**, **5k..10k gas** on hard pins, about two packable storage slots: do not promote absent gain. `tune.py` and `fin.py` were omitted from its bundle; tuning rows are inline. (`b12-pin-volatility`.)

Price-error-by-pin-age diagnostics are retained below. They show residual error between pins, but do not establish a policy that recovers the brief's remaining 1.73. The C studies' shared holdout interval is intentional comparison to shipped rows; it is not a source of additional independent engine seeds. No experiment here crosses the +0.2 replica bar, and their gains should not be added to one another or to the contract's engine gain without a combined frozen-policy study. (`b07-retail-quotient-signal`, `b09-give-away`, `b12-*`.)

**Five blocked items, with no invented results.**

| Input | Reported failed step/error | Evidence retained |
|---|---|---|
| b02-c0-tell-soft1 | Fetch of pinned `contracts/AMMStrategyBase.sol` returned HTTP 404, curl 22 | Block only; no integration, gates or scores. Later items use imports under `contracts/src/`, so this is not proof that integration is impossible. |
| b05-gate-and-pair-runner | setup exited 133 after wheel checksum verification: Rosetta could not open the x86-64 ELF loader | Block only; no completed validation harness or pairs. Later scoring results contain their own runners. |
| b06-probe-independent | Temporary vector harness imported missing `Crypto.Hash.keccak`; a failed replacement write used the wrong checkout-relative path | No vector-gate completion or engine seeds. The reference probe therefore has no completed independent replicate in this group. |
| b07-between-pin-filter | Diagnostic file creation used a duplicate relative path; subsequent Python open failed with exit 2; active holdout interrupted | No holdout, operation-count diagnostic or gain. This is a command/path error, not missing requester input. |
| b08-min-2 | Fetch failed with curl 56, proxy CONNECT aborted; GitHub/raw content unreachable | Setup block only; no candidate or simulation evidence. |

These blocks neither cancel later successful items nor supply corroborating measurements. Min-3's failed literal gate is a measured failure, distinct from these setup blocks. (`b02-c0-tell-soft1`, `b05-gate-and-pair-runner`, `b06-probe-independent`, `b07-between-pin-filter`, `b08-min-2`, `b08-min-3`.)

**Carry-forward and unresolved work.**

Carry frozen u1 forward because the matched b13 comparison isolates a repeatable gain over min-lookup, with substantially lower measured gas and a smaller runtime. Preserve its exact source/runtime identities and the engine-clamped integer-shadow gate definition. The raw-output cap exception, source-reread warnings, gas-seed reuse, probe false negative and fee-sensitive false positives remain open evidence limits. Complete the goal's fresh 4,096-seed study before asserting first-place readiness; no result in this root supplies it. A future engine study must reserve genuinely unused seeds across all roots, rather than assume gaps here are free. No C research result in this group qualifies for automatic integration at +0.2, and no entry/submission is authorized by the goal. (Synthesis from `b11-lookup-u1`, `b13-p1`, `b13-p2`, `b06-probe-reference`, `b07-retail-quotient-signal`, `b09-give-away`, `b12-*`, and the assignment.)

**Numerical evidence ledger.** The following compact records preserve exact aggregate n/mean_diff/se/sum/sumsq/worst5 rather than only rounded headline means. Source keys name the originating result; `merge_pool` records are explicitly calculated here. Gas is role-separated: Submission is the candidate being scored, Baseline is its Vanilla normalizer. Counts, totals, maxima and failure counters must retain that distinction. Detailed fixtures, code, per-vector gas arrays, checkpoints, hashes and per-seed rows remain in the content-addressed source results; they are not silently treated as new measurements or copied as executable deliverables into this Markdown merge.

**Exact paired engine statistics.** Source aggregates, preserving all six requested fields.

`b10-min-1-reserved`

```json
{"paired":{"n":256,"mean_diff":3.1313189811776008,"se":0.06168039206584464,"sum":801.6176591814658,"sumsq":2758.4764434071517,"worst5":[{"seed":14000114,"diff":-2.3787629249890188},{"seed":14000084,"diff":0.7189374211384347},{"seed":14000069,"diff":0.9055512243188559},{"seed":14000019,"diff":1.338760148605047},{"seed":14000071,"diff":1.4566868209443555}]}}
```

`b10-lookup-reserved`

```json
{"paired":{"n":256,"mean_diff":3.21882618328908,"se":0.05837298386396219,"sum":824.0195029220044,"sumsq":2874.8109659517067,"worst5":[{"seed":14001017,"d":0.589986137530218,"edge_candidate":820.976521320085,"edge_C0":820.3865351825548},{"seed":14000843,"d":1.076915949637737,"edge_candidate":451.5118490334342,"edge_C0":450.43493308379647},{"seed":14000971,"d":1.1361548401470145,"edge_candidate":541.8127001499527,"edge_C0":540.6765453098056},{"seed":14000822,"d":1.1662192478856355,"edge_candidate":458.1399007791507,"edge_C0":456.9736815312651},{"seed":14000879,"d":1.2603990099104294,"edge_candidate":617.5436011376445,"edge_C0":616.2832021277341}]}}
```

`b10-min-1-fresh`

```json
{"paired":{"n":256,"mean_diff":3.27081791145147,"se":0.062401826979037525,"sum":837.3293853315763,"sumsq":2992.9514886409725,"worst5":[[14001129,558.6251315913573,557.8839829913287,0.7411486000286232],[14001199,639.5067161786636,638.5803542916577,0.9263618870058963],[14001122,401.9564952641598,400.97666994923884,0.9798253149209586],[14001171,769.1797012589833,768.1924896469919,0.9872116119913699],[14001098,438.31298389361785,437.3082776918042,1.004706201813633]]}}
```

`b10-lookup-fresh`

```json
{"paired_total":{"n":256,"mean_diff":3.3271287255250126,"se":0.0653324668554422,"sum":851.7449537344032,"sumsq":3112.501764785957,"worst5":[0.7816116499219561,1.3244502086272405,1.3898549302174388,1.402472198957355,1.4518406537681585]}}
```

`b13-p1`

```json
{"paired":{"n":256,"mean_diff":3.175539473292165,"se":0.05989757684666979,"sum":812.9381051627943,"sumsq":2815.7233850938555,"worst5":[[14001758,0.6440149167666505],[14001784,1.12880293408557],[14001710,1.1450462174784661],[14001723,1.2050016365991496],[14001685,1.3087353631033238]]},"paired_ref":{"n":256,"mean_diff":0.10695046560810839,"se":0.016850758026285193,"sum":27.37931919567575,"sumsq":21.46435938283442,"worst5":[[14001667,-0.515988051643717],[14001613,-0.5032430003514037],[14001644,-0.4572018689018478],[14001580,-0.4537598108469183],[14001624,-0.4531798091468886]]},"paired_ref_c0":{"n":256,"mean_diff":3.068589007684057,"se":0.06053249610939766,"sum":785.5587859671186,"sumsq":2649.7549273124246,"worst5":[[14001758,0.5010692642778167],[14001723,1.02078793464932],[14001696,1.0731045615646622],[14001784,1.148068649325296],[14001643,1.2179133994652602]]}}
```

`b13-p2`

```json
{"paired":{"n":256,"mean_diff":3.2420346461259473,"se":0.06541608541773083,"sum":829.9608694082425,"sumsq":2970.112262574812,"worst5":[{"seed":14001943,"d":0.32236150733490376},{"seed":14001828,"d":0.96856920096468},{"seed":14001893,"d":0.9912383591444041},{"seed":14002018,"d":1.252879351612762},{"seed":14001853,"d":1.3239107799801104}]},"paired_ref":{"n":256,"mean_diff":0.10238099687077473,"se":0.017417451942822116,"sum":26.20953519891833,"sumsq":22.487197369929124,"worst5":[{"seed":14001871,"d":-0.73781148004241},{"seed":14001889,"d":-0.6025122449309492},{"seed":14001988,"d":-0.4968782036388575},{"seed":14001893,"d":-0.4684221722558277},{"seed":14001935,"d":-0.46347782787262304}]},"paired_ref_c0":{"n":256,"mean_diff":3.1396536492551723,"se":0.06401793561354752,"sum":803.7513342093241,"sumsq":2791.0375776608003,"worst5":[{"seed":14001943,"d":0.23160270167772978},{"seed":14001828,"d":0.8364897543571033},{"seed":14002018,"d":1.0994626902984805},{"seed":14002021,"d":1.1598770200326953},{"seed":14001852,"d":1.309341164899024}]}}
```

`b10-lookup-fresh` omits seed IDs from aggregate worst5. Its embedded rows recover these seed/difference pairs (merge calculation): **14001440: 0.7816116499219561; 14001326: 1.3244502086272405; 14001465: 1.3898549302174388; 14001457: 1.402472198957355; 14001379: 1.4518406537681585**.

**Engine afterSwap gas ledger.** Each row copies aggregate gas_stats. B=Baseline (Vanilla), U=Submission. Every aggregate callback row, including initialization and name calls, has calls=ok and all five failure counters (oog/revert/other_halt/tx_error/bad_return) zero, checked during merge. Maxima are maxima across blocks; sums/counts are summed. Initialization and name counters are routine metadata, omitted here; afterSwap evidence is retained for both roles.

| Source / arm | Role | calls=ok | max_ok_gas | sum_ok_gas |
|---|---|---:|---:|---:|
| b10-min-1-reserved / candidate | B | 2765728 | 22592 | 62402543000 |
| b10-min-1-reserved / candidate | U | 2806459 | 237415 | 445826477188 |
| b10-min-1-reserved / c0 | B | 2794883 | 22592 | 63060281380 |
| b10-min-1-reserved / c0 | U | 2818310 | 208989 | 388610278534 |
| b10-lookup-reserved / candidate | B | 2741971 | 22592 | 61866390152 |
| b10-lookup-reserved / candidate | U | 2782794 | 228504 | 423699598444 |
| b10-lookup-reserved / c0 | B | 2771743 | 22592 | 62538101672 |
| b10-lookup-reserved / c0 | U | 2796864 | 209319 | 385935606305 |
| b10-min-1-fresh / candidate | B | 2747247 | 22592 | 61985462652 |
| b10-min-1-fresh / candidate | U | 2789365 | 237653 | 443303910707 |
| b10-min-1-fresh / c0 | B | 2776665 | 22592 | 62649143304 |
| b10-min-1-fresh / c0 | U | 2802487 | 208962 | 386584691451 |
| b10-lookup-fresh / candidate | B | 2758947 | 22592 | 62249518956 |
| b10-lookup-fresh / candidate | U | 2800420 | 228346 | 426040821658 |
| b10-lookup-fresh / c0 | B | 2788584 | 22592 | 62918100840 |
| b10-lookup-fresh / c0 | U | 2813549 | 208883 | 387976602465 |
| b13-p1 / cand | B | 2742075 | 22592 | 61868724744 |
| b13-p1 / cand | U | 2777107 | 204898 | 360560564609 |
| b13-p1 / C0 | B | 2768714 | 22592 | 62469702064 |
| b13-p1 / C0 | U | 2794281 | 209039 | 385554826157 |
| b13-p1 / ref | B | 2739091 | 22592 | 61801394960 |
| b13-p1 / ref | U | 2780628 | 227885 | 423366290308 |
| b13-p2 / cand | B | 2758253 | 22592 | 62233802308 |
| b13-p2 / cand | U | 2791112 | 204879 | 362147538295 |
| b13-p2 / C0 | B | 2784809 | 22592 | 62832910732 |
| b13-p2 / C0 | U | 2807335 | 208923 | 387176966557 |
| b13-p2 / ref | B | 2755259 | 22592 | 62166264664 |
| b13-p2 / ref | U | 2794829 | 228604 | 425253398987 |

**Probe counts by run**, source `b06-probe-reference`. 35-bps rows reuse the 30-bps seeds.

| Seed | 30bps arb read/total | 30bps retail hits/total | 35bps arb read/total | 35bps retail hits/total |
|---:|---:|---:|---:|---:|
| 14000000 | 3616/3616 | 337/8688 | 3083/3083 | 6/7406 |
| 14000001 | 3362/3362 | 148/6991 | 2896/2897 | 7/6081 |
| 14000002 | 3606/3606 | 362/8203 | 3062/3062 | 7/6995 |
| 14000003 | 3754/3754 | 47/9793 | 3238/3238 | 12/8404 |
| 14000004 | 3705/3705 | 579/9793 | 3137/3137 | 15/8317 |
| 14000005 | 3586/3586 | 115/8909 | 3034/3034 | 11/7672 |
| 14000006 | 3686/3686 | 235/9438 | 3134/3134 | 10/8050 |
| 14000007 | 3776/3776 | 192/8688 | 3222/3222 | 7/7577 |

**Replica paired statistics.** All holdouts use 10000..12047; references are part of each record.

`b03-sparse-spline-residual.holdout_once`

```json
{"paired_vs_tell_qm":{"n":2048,"mean_diff":-0.061103,"se":0.005125,"sum":-125.13975,"sumsq":117.765587,"worst5":[[10522,-1.008008],[11821,-0.936868],[10596,-0.914203],[11025,-0.827782],[11511,-0.782915]]},"paired_vs_C0_compressed_TellPolicy_same_machine":{"n":2048,"mean_diff":0.050943,"se":0.004653,"sum":104.331057,"sumsq":96.07915,"worst5":[[11607,-0.792487],[10543,-0.790498],[11981,-0.712822],[10357,-0.702706],[11613,-0.701917]]},"C0_compressed_vs_tell_qm":{"n":2048,"mean_diff":-0.112046,"se":0.006275,"sum":-229.470807,"sumsq":190.75906,"worst5":[[10843,-1.8952],[11025,-1.389354],[11113,-1.126072],[10460,-1.09048],[10322,-1.074865]]},"local_full_vs_tell_qm":{"n":2048,"mean_diff":-0.002024,"se":0.001199,"sum":-4.145598,"sumsq":6.030799,"worst5":[[11413,-0.465065],[11714,-0.398294],[10852,-0.337024],[11528,-0.318679],[11770,-0.30056]]},"cand_vs_local_full":{"n":2048,"mean_diff":-0.059079,"se":0.005131,"sum":-120.994153,"sumsq":117.514207,"worst5":[[10522,-1.026035],[11821,-0.936868],[10596,-0.90869],[11448,-0.818477],[11025,-0.810814]]},"first_trade_misread_and_price_rms":{"hold_cand":{"first_trades":14353188,"misread":3416,"misread_rate":0.000238,"price_rms_bps":7.1438,"mean_edge":536.471104},"hold_c0":{"first_trades":14364734,"misread":3393,"misread_rate":0.000236,"price_rms_bps":7.1337,"mean_edge":536.420161},"tellqm":{"first_trades":14350251,"misread":3420,"misread_rate":0.000238,"price_rms_bps":7.1494,"mean_edge":536.532208}}}
```

`b03-adaptive-linear-grid.holdout`

```json
{"paired_vs_tell_qm":{"n":2048,"mean_diff":-0.010338,"se":0.004251,"sum":-21.173086,"sumsq":75.977602,"worst5":[[10843,-1.464078],[11659,-1.003288],[11821,-0.95033],[11013,-0.785937],[11206,-0.703885]]},"paired_vs_C0_compressed_TellPolicy_same_machine":{"n":2048,"mean_diff":0.101708,"se":0.006165,"sum":208.297721,"sumsq":180.528534,"worst5":[[12032,-1.256225],[10357,-0.829887],[11613,-0.829853],[10567,-0.820859],[10973,-0.818213]]},"paired_vs_full_qm_same_machine":{"n":2048,"mean_diff":-0.008314,"se":0.004216,"sum":-17.027489,"sumsq":74.64639,"worst5":[[10843,-1.426137],[11659,-0.990834],[11821,-0.95033],[11013,-0.730259],[11206,-0.703885]]},"u1":{"first_trade_misread":0.000255,"price_rms_bps":7.15,"mean_edge":536.521869},"C0_compressed":{"first_trade_misread":0.000236,"price_rms_bps":7.134,"mean_edge":536.420161},"full_qm_local":{"first_trade_misread":0.000249,"price_rms_bps":7.153,"mean_edge":536.530183}}
```

`b07-retail-quotient-signal.holdout.paired`

```json
{"n":2048,"mean_diff":0.12285540499524492,"se":0.006284515958726821,"sum":251.6078694302616,"sumsq":196.48512783728222,"worst5":[[11696,-1.875730951060632],[11701,-1.69652171052212],[11413,-1.1451048876382401],[11022,-1.0567118168170282],[11763,-1.005355664072681]]}
```

`b09-give-away`

```json
{"holdout_paired_vs_tell_qm":{"n":2048,"mean_diff":0.091,"se":0.0071,"sum":186.3655,"sumsq":226.4262,"worst5":[[11696,-2.1039],[10822,-1.6081],[11022,-1.5135],[11277,-1.326],[11413,-1.2409]]},"holdout_paired_vs_local_tellpol_rerun":{"n":2048,"mean_diff":0.093,"se":0.007,"sum":190.511,"sumsq":225.6556,"worst5":[[11696,-2.0865],[11022,-1.5345],[10822,-1.5252],[11277,-1.3462],[10676,-1.1806]]}}
```

`b12-pin-volatility.holdout.paired`

```json
{"n":2048,"mean_diff":-0.005432120005715468,"se":0.0033253578320732707,"sum":-11.12498177170528,"sumsq":46.41841883515113,"worst5":[[10403,-0.7195629244230304],[10423,-0.7111558168908232],[11332,-0.7071503650873865],[11796,-0.686853596593437],[11746,-0.5920471237346874]]}
```

`b12-conditional-rival-pull.holdout.paired`

```json
{"mean_diff":-0.0016943641890520833,"n":2048,"se":0.003159986467373076,"sum":-3.4700578591786666,"sumsq":41.867712508404104,"worst5":[[10676,-1.0688260980772384],[11022,-0.8106807464167787],[11191,-0.7842332726808081],[10746,-0.5901324669192718],[11436,-0.5356792189842849]]}
```

**Additional table tuning.** These are tuning comparisons, not further holdout selection.

`b03-sparse-spline-residual.tuning`

```json
{"improvement_over_C0_compressed_TellPolicy":{"n":256,"mean_diff":0.075806,"se":0.01277,"sum":19.406376,"sumsq":12.116791,"worst5":[[60132,-0.76628],[60213,-0.495623],[60044,-0.490871],[60231,-0.484898],[60034,-0.463587]]},"cand_vs_full":{"n":256,"mean_diff":-0.047111,"se":0.01371,"sum":-12.060416,"sumsq":12.83922,"worst5":[[60182,-0.845665],[60111,-0.808965],[60020,-0.681772],[60122,-0.623303],[60238,-0.546837]]},"C0_vs_full":{"n":256,"mean_diff":-0.122917,"se":0.016396,"sum":-31.466792,"sumsq":21.417689,"worst5":[[60020,-1.142346],[60122,-0.867211],[60210,-0.82389],[60165,-0.778983],[60182,-0.761183]]},"misread_price":{"tune_cand":{"first_trades":1788021,"misread":432,"misread_rate":0.000242,"price_rms_bps":7.1465,"mean_edge":529.648061},"tune_c0":{"first_trades":1789555,"misread":439,"misread_rate":0.000245,"price_rms_bps":7.1374,"mean_edge":529.572255},"tune_full":{"first_trades":1787620,"misread":406,"misread_rate":0.000227,"price_rms_bps":7.1522,"mean_edge":529.695172}},"sweep":[{"cfg":"K128_q8_a1","bytes":519,"vs_c0":0.0292,"se":0.0098,"fee_max_bps":36.404,"visit_rms_bps":0.702,"fmt":"u32 12-bit"},{"cfg":"K256_q8_a1","bytes":1031,"vs_c0":0.0219,"se":0.0108,"fee_max_bps":36.405,"visit_rms_bps":0.639,"fmt":"u32 12-bit"},{"cfg":"K512_q8_a1","bytes":2055,"vs_c0":0.0695,"se":0.0124,"fee_max_bps":36.77,"visit_rms_bps":0.554,"fmt":"u32 12-bit"},{"cfg":"K512_q8_a0.5","bytes":2055,"vs_c0":0.0306,"se":0.0107,"fee_max_bps":26.727,"visit_rms_bps":0.659,"fmt":"u32 12-bit"},{"cfg":"K1024_q8_a1","bytes":4103,"vs_c0":0.0905,"se":0.0134,"fee_max_bps":30.178,"visit_rms_bps":0.451,"fmt":"u32 12-bit"},{"cfg":"K512_q8_a1.5","bytes":2055,"vs_c0":0.0625,"se":0.0122,"fee_max_bps":40.451,"visit_rms_bps":0.599,"fmt":"u32 12-bit"},{"cfg":"K512_q8_a2","bytes":2055,"vs_c0":0.067,"se":0.0118,"fee_max_bps":40.453,"visit_rms_bps":0.654,"fmt":"u32 12-bit"},{"cfg":"K512_q4_a1","bytes":2055,"vs_c0":0.0641,"se":0.0124,"fee_max_bps":36.821,"visit_rms_bps":0.555,"fmt":"u32 12-bit"},{"cfg":"K384_q8_a1","bytes":1543,"vs_c0":0.0491,"se":0.0114,"fee_max_bps":36.771,"visit_rms_bps":0.592,"fmt":"u32 12-bit"},{"cfg":"K768_q8_a1","bytes":3079,"vs_c0":0.0761,"se":0.0131,"fee_max_bps":36.764,"visit_rms_bps":0.494,"fmt":"u32 12-bit"},{"cfg":"K576_q4_a1","bytes":2055,"vs_c0":0.0758,"se":0.0128,"fee_max_bps":36.821,"visit_rms_bps":0.538,"fmt":"28-bit int8"},{"cfg":"K448_q4_a1","bytes":1607,"vs_c0":0.0571,"se":0.0118,"fee_max_bps":36.821,"visit_rms_bps":0.572,"fmt":"28-bit int8"},{"cfg":"K576_q8_a1","bytes":2055,"vs_c0":0.0679,"se":0.0122,"fee_max_bps":36.77,"visit_rms_bps":0.539,"fmt":"28-bit int8"}],"sweep_note":"Each config is one run.py pass on 60000..60255 (se about 0.012), so differences of about 0.02 between configs are noise. Selection is a top-K prefix by score, so a lighter K can be rebuilt with the same generator (K448: 1,607 B, +0.057)."}
```

`b03-adaptive-linear-grid.frozen_knots`

```json
{"0c":"levels [0,7], 24 row knots, 11 col knots, qe -2","1s":"levels [0,3,7], 43 rows, 30 cols, qe -1","1c":"levels [0,2,3,7], 28 rows, 13 cols, qe -1","2s":"levels [0,3,7], 36 rows, 26 cols, qe 0","2c":"levels [0,3,7], 17 rows, 10 cols, qe -1"}
```

`b03-adaptive-linear-grid.tuning_variants`

```json
[{"name":"t1","args":"qe=-2 (old allocator, no lookahead)","bytes":10134,"tune_vs_full":-0.0191,"se":0.0147},{"name":"t2","args":"qe=-1","bytes":10134,"tune_vs_full":-0.0222,"se":0.0149},{"name":"t3","args":"qe=-2 power=0.5","bytes":10156,"tune_vs_full":-0.0248,"se":0.0129},{"name":"t4","args":"qe=-2 floor=0.01 (allocator starved 1s columns: 7)","bytes":10154,"tune_vs_full":-0.1645,"se":0.0194},{"name":"t5","args":"qe=-2 sweeps=20","bytes":10134,"tune_vs_full":-0.0216,"se":0.0145},{"name":"t6","args":"qe=-1 power=0.5","bytes":10156,"tune_vs_full":-0.011,"se":0.0126},{"name":"t7","args":"power=0.75 sweeps=20 (columns starved: 7)","bytes":10143,"tune_vs_full":-0.2392,"se":0.0202},{"name":"u1 (frozen)","args":"lookahead allocator, qe auto","bytes":10160,"tune_vs_full":-0.0198,"se":0.0126},{"name":"u2","args":"qe auto power=0.5","bytes":10144,"tune_vs_full":-0.0315,"se":0.0131},{"name":"u3","args":"qe auto power=0.75","bytes":10158,"tune_vs_full":-0.0299,"se":0.0122},{"name":"u4","args":"qe auto floor=0.01","bytes":10162,"tune_vs_full":-0.0229,"se":0.0119},{"name":"u5","args":"qe auto power=0.5 floor=1e-4","bytes":10150,"tune_vs_full":-0.0302,"se":0.0129},{"name":"b11","args":"qe auto budget=11500 (info: extra bytes buy nothing measurable)","bytes":11475,"tune_vs_full":-0.0307,"se":0.0119},{"name":"C0 QMS1 spline","args":"baseline","bytes":10167,"tune_vs_full":-0.1229,"se":0.0164}]
```

`b03-adaptive-linear-grid.table_error`

```json
{"u1":{"max_abs":61.833,"visit_weighted_rms_all":0.3494,"per_table_A":{"0c":[23.893,1.3008,0.2452],"1s":[61.833,1.9217,0.3496],"1c":[21.7,1.281,0.44],"2s":[48.917,1.9297,0.4387],"2c":[34.966,1.4895,1.0444]}},"C0":{"max_abs":204.792,"visit_weighted_rms_all":0.8342,"per_table_A":{"0c":[37.215,1.2894,0.6091],"1s":[204.792,5.6035,0.8721],"1c":[47.094,2.2495,1.3936],"2s":[160.895,4.5858,0.7963],"2c":[82.95,6.4426,2.3907]}},"columns":"[max, unweighted rms over all nodes, visit-weighted rms]; B identical by mirror (u1 mirror exact; full qm differs from its mirror in 1 cell of 1c by 0.71 bps per qm-spline)","visits":"TellPolicy+full qm lookups on 60000..60255, bid mirrored to ask coords"}
```

**Pin-age diagnostics**, bps RMS; diagnostic truth never enters policy decisions. Pin-volatility tuning bins: ["0", "1", "2-3", "4-7", "8-15", "16-31", ">=32"].

`b12-pin-volatility.tuning`

```json
{"seeds":"61000..61063 (64 of the allowed 61000..61255; machine ran ~1 effective core, ~2 s/seed, so a full 256-seed grid did not fit)","baseline":"pinvol:TellInt = TellPolicy behind the identical WAD observation wrapper (integer tellref.is_arb, chance from integer binades, fees round-tripped through WAD)","rows":[{"cls":"TellInt","opt":{},"mean_diff":0.0,"se":0.0,"rms_bps":7.195,"rms_by_since_pin":[0.387,6.972,10.415,12.468,12.945,12.867,12.634],"misread":439,"first":444999,"sighat_true_corr":null,"sighat_bias_bps":null},{"cls":"PinVol","opt":{"C":0.7,"K0":3000},"mean_diff":0.0227,"se":0.0311,"rms_bps":7.224,"rms_by_since_pin":[0.416,6.949,10.43,12.506,12.911,12.84,12.674],"misread":449,"first":444867,"sighat_true_corr":0.577,"sighat_bias_bps":-0.935},{"cls":"PinVol","opt":{"C":1.0,"K0":500},"mean_diff":-0.007,"se":0.0293,"rms_bps":7.193,"rms_by_since_pin":[0.363,6.974,10.401,12.489,12.958,12.78,12.381],"misread":395,"first":445047,"sighat_true_corr":0.901,"sighat_bias_bps":0.014}],"note":"mean_diff/se are paired vs TellInt on the same seeds. sighat_* compare the end-of-run estimate to the true sigma (harness-only diagnostic). A 256-seed baseline-only run (61000..61255) gave misread 1634/1780475 and p rms 7.187 bps; its variant arm timed out and is not reported."}
```

`b12-conditional-rival-pull.holdout_pin_age`

```json
{"0":{"n":12830012,"bias_bps":-0.0007596449510743768,"rms_bps":0.41318754129661733},"1":{"n":2106990,"bias_bps":0.010164536429371079,"rms_bps":6.974760877294546},"16+":{"n":330189,"bias_bps":-0.019928071784309595,"rms_bps":12.927526102800877},"2-4":{"n":3611833,"bias_bps":-0.0030854600289496287,"rms_bps":10.861767733842088},"5-15":{"n":3403799,"bias_bps":0.016603407388380453,"rms_bps":12.765141206851114},"never":{"n":8645,"bias_bps":0.3742352034330379,"rms_bps":11.98215676291106}}
```

`b12-conditional-rival-pull.tuning_pin_age`

```json
{"corrected_baseline_diagnostics":{"rms":7.141604741605662,"by_age":{"0":{"n":1614437,"bias_bps":-0.0004052910904826331,"rms_bps":0.37515272128615984},"1":{"n":265185,"bias_bps":-0.011794985220034611,"rms_bps":6.99192990522666},"16+":{"n":40531,"bias_bps":-0.1614983573595447,"rms_bps":12.829648797638914},"2-4":{"n":454826,"bias_bps":0.041295396345999595,"rms_bps":10.846712832430935},"5-15":{"n":426840,"bias_bps":0.027444866654635882,"rms_bps":12.752760279011865},"never":{"n":1153,"bias_bps":-0.32106664215776964,"rms_bps":12.02974356125509}}},"selected_diagnostics":{"rms":7.141117250426252,"by_age":{"0":{"n":1615839,"bias_bps":-0.0003339772301784501,"rms_bps":0.43190518628837427},"1":{"n":265431,"bias_bps":-0.013878409088811768,"rms_bps":6.991706281450462},"16+":{"n":40515,"bias_bps":-0.10356476126675379,"rms_bps":12.860835346613984},"2-4":{"n":454990,"bias_bps":0.04207407134147718,"rms_bps":10.844068343753325},"5-15":{"n":426303,"bias_bps":0.010695283056938221,"rms_bps":12.7549278705595},"never":{"n":1153,"bias_bps":-0.3237933326643024,"rms_bps":12.030629187770606}}}}
```

**Source register.** Each row identifies a supplied result via the SHA-256 of its exact input bytes. These URLs identify evidence, not new web verification; all 25 inputs are present.

| Input / citation label | Source |
|---|---|
| b01-bounded-bitmath | [result](https://api.imd.fun/artifacts/22122152083d7c876b3475c321fd3c85be79de48419965491d117f095e3d1905) |
| b01-literal-rational | [result](https://api.imd.fun/artifacts/122533c069dcbd6787c736a7578ab603ca092c90409e9bd6a344bddf94863a38) |
| b02-c0-tell-soft1 | [result](https://api.imd.fun/artifacts/11877d485ec9bb42c093ed5c26d3ca308613653d73a413e71722ef70b7079cce) |
| b03-adaptive-linear-grid | [result](https://api.imd.fun/artifacts/ce5b4e6f21a08070df1df5e784c374eaf555f1540405c1c33864a710683fe8d8) |
| b03-sparse-spline-residual | [result](https://api.imd.fun/artifacts/cc3998563369642f4867cdc5780ca2a7bcdbee80e66fc17e8cf3fbfa8afee701) |
| b04-lookup-headroom | [result](https://api.imd.fun/artifacts/9093159ef6d83b4f6f8c0368355cec5771548c9e9ab3cb9608885007afa43741) |
| b05-gate-and-pair-runner | [result](https://api.imd.fun/artifacts/0d53cbee8155cbc8a9f3a883c82e37d062a192d44c592c218a99cdfff0319372) |
| b06-probe-independent | [result](https://api.imd.fun/artifacts/33387414b6e2db18644650819ee2a6f0ef9cbbf14b920154cfa6d3e05b80438c) |
| b06-probe-reference | [result](https://api.imd.fun/artifacts/b0cb4b28e101ad902ec383c2d4142b6e9a9dd10d229f482b47ca81b273933495) |
| b07-between-pin-filter | [result](https://api.imd.fun/artifacts/e152f3423137fb3ced679022b504685c2fe8ad8a3d81ce5b6f35235d6f33886a) |
| b07-retail-quotient-signal | [result](https://api.imd.fun/artifacts/bb1b85910e7628d6c716ee1328da911b4da42c0903cb6c96309cfda82a379abd) |
| b08-min-1 | [result](https://api.imd.fun/artifacts/6a27a64088c1f95bd06f5b7b2bb6570ecbaf96ea7323c8718b32e79224dc3a16) |
| b08-min-2 | [result](https://api.imd.fun/artifacts/2cb8d01c19c4b6b52605f9aa8f2d0036a2a784f5f3ab9a14ad305be3e268e62b) |
| b08-min-3 | [result](https://api.imd.fun/artifacts/4486cd24cc4728ae80c6c62be6afbd08ca1702f5ff38896911848f19fd43e849) |
| b08-min-lookup | [result](https://api.imd.fun/artifacts/755f4fc0a7b028497ad9ddf23ea568071192341e192335cb7f31174d066d4df0) |
| b09-give-away | [result](https://api.imd.fun/artifacts/e931451c8e4b3ace70dbcde4910728e086fb292489bccaab0bf9c5c3be72fe14) |
| b10-lookup-fresh | [result](https://api.imd.fun/artifacts/b004ccfb25ba0d0af23b57f516797468d6f8584304215f760591425e6f794881) |
| b10-lookup-reserved | [result](https://api.imd.fun/artifacts/9c183672160ba4d6e6d48446d2aedf98c0a83489d74bd2477b3c54ba97a423aa) |
| b10-min-1-fresh | [result](https://api.imd.fun/artifacts/3c91e0bc16a55d5acc8d9a576edac6b440173399e64cd17915f7692fb783d12a) |
| b10-min-1-reserved | [result](https://api.imd.fun/artifacts/a1a6b95c9eccd2814c051236476321c57b30533b1d50bbd7a7beb38d68001565) |
| b11-lookup-u1 | [result](https://api.imd.fun/artifacts/fd38823c16c850438759b77387cecd713241ff3f0b6d5280ef161c6717375ed8) |
| b12-conditional-rival-pull | [result](https://api.imd.fun/artifacts/631a50b4823943d5614ffb901519d34f9dbbb3a6fdce025594edeb70f4abc663) |
| b12-pin-volatility | [result](https://api.imd.fun/artifacts/751a83dfca0c3871042a18f326de6b6a7b21afd63fe40c74d705576c7837c809) |
| b13-p1 | [result](https://api.imd.fun/artifacts/8d5fd22104964207ac8a9306780ca9fb301e44886dd0f91cf13d30c14dfbb19e) |
| b13-p2 | [result](https://api.imd.fun/artifacts/5b6e3d625bcc67607a452d3edf88ced4f5d25129ae0ef02486d67ace491cef74) |

Upstream context: [C0](https://api.imd.fun/artifacts/8a6e303b662e1a5ea9bb47f31acedd3988ef65b3ddb66d074517aa59ad41ca40); [pinned tell README](https://raw.githubusercontent.com/gtmcknight/amm-sim/66604b3426d8e97a73e2c39940b9b4dece51cc73/research/tell/README.md); [integer reference](https://raw.githubusercontent.com/gtmcknight/amm-sim/66604b3426d8e97a73e2c39940b9b4dece51cc73/research/tell/tellref.py); [TellPolicy](https://raw.githubusercontent.com/gtmcknight/amm-sim/66604b3426d8e97a73e2c39940b9b4dece51cc73/research/tell/tellpol.py); [vectors](https://raw.githubusercontent.com/gtmcknight/amm-sim/66604b3426d8e97a73e2c39940b9b4dece51cc73/research/tell/vectors.json.gz); [engine](https://github.com/benedictbrady/amm-challenge/tree/6b6921f8d463314aa7c96234e1be25a25245f704). These are reported dependencies, not independently checked quotations in this merge.

Reproducibility SHA-256 identities: vector gzip `7483623d551bd6334547b6b1fcd621b4d721dd2082011b6c113f083421396947`; engine wheel `aedb68280aca34c110968f00148387c95885207913fb2cf19a1ab4c5cfd6887a`; C0 Solidity `c68887cff61180e12ba2b1ceb333edf76a830f91f63b5d775a8806fb9ec08aca`; min-1 Solidity `644bdfad1ffd92038887faf5453538b412fc4bd42797c887e1a5f9c5d25ad55a`; min-lookup Solidity `3a799de034a2482ff960dc0d89316a18a70ccff80b1d80af2e3b2d110977ec40`; u1 blob `830868f9b3e5ad162c4f2070e6faed0782c7b4cc308ab69044b2cf7306f68099`; decoded u1 qm `d5645b6dd4ed8f1e33cc712d56d9eb916a50db7d5014c285b0f388cd114f96f9`; shipped tell_qm `ad382c07e6c2b3a5a8055ea767e140b7461105f29dafee69b7c1766c90d0634f`. These differ from result-body hashes. (`b01-*`, `b03-adaptive-linear-grid`, `b08-min-1`, `b08-min-lookup`, `b10-*`, `b11-lookup-u1`, `b13-*`.)

**Merge verification limits.** All 25 inputs parsed. All 14 code payloads and 11 available bundles decoded and matched their claimed hashes. Each completed engine study had 256 embedded seed rows, reproducing all reported paired means and standard errors (including both extra b13 comparisons) within 1e-10. This verifies arithmetic consistency and payload identity, not contract execution or external-source validity. Executable sources, corpus, dependencies, detailed per-vector gas arrays and checkpoints remain in the cited results; this bounded delivery is Markdown only. No board movement is claimed.