# Root merge 4: public mechanisms, anchoring, lean diagnostics, replicas, RS2 ports and Vanilla quotes

All 25 supplied JSON results were present. This merge performs no new simulator run, page verification or board submission. Measurement citations name reporting inputs; public links name claimed underlying sources. Code/reproduction strings, raw arrays and trial logs are summarized rather than copied; negative, incomplete and blocked findings remain explicit.

The group does not establish the top-ten objective. Its only fresh STACK confirmation is [b35-b]: +0.5514277421227615,SE .013811303616272655,n2000,OOG0. Other candidates mostly compare with RS2 and cannot be added or translated into STACK gains. Searches recovered no reproducible current top-ten policy; replicas/ports are research tools, not score improvements. [b29-entrants], [b35-b].

Goal figures supplied by the requester: STACK board 519.71 (29th), tenth 524.66, first 528.40; the previous transfer was 0.65 of local, and the brief targets about +5.0 paired local edge. These are task context, not newly measured board facts or a guaranteed transfer law. STACK code: [artifact](https://api.imd.fun/artifacts/c33720874aa1285e9dc766540b8a90410118a8e8b840d949ea0dcc211bdb27c1), SHA-256 `2eaafc7960e520b8a7fd322ec8afaff8fa677c730228a961efb509cc30b25719`; the brief reports 0 OOG and 214k peak afterSwap against 250,000. It also reports prior within-family tuning capped near +1.2 and scratch fee rules losing 18–83, mostly to arbitrage. None of those historical claims is newly tested here.

RS2 is a different baseline: [artifact](https://api.imd.fun/artifacts/19f2ec857df536e8ab62ab1da89ec6623332521ce46849f15bccff402c63e1e5), code SHA-256 `f24b6ca198b744c380842c3a17964a6dc21f311bb04984b26733afa3fee8eaf2`, getName censored_10. CH calibration is [pinned Strategy.sol](https://raw.githubusercontent.com/ChengHua926/amm-challenge/d34a5199c59a4c44d5336a25f1436b4ae1f21104/contracts/src/Strategy.sol), code SHA-256 `6dd68f77a70900319460215374143dbd5d924198450a46d9f5f91f6b1e3d35c3`. CH seeds 0..999 have required mean 525.5258821780834. These identities must not be conflated. [b29-writeups]; [b34-a].

## Evidence qualification and coverage

Assignment flags below count source records that were unreadable or did not support quotations. Specific failed URLs/reasons were not supplied, so all source-dependent claims in those items remain attributed rather than independently verified. Flags do not by themselves disprove embedded measurements, but these also lack independent certification. Reuse of a source is not independent corroboration.

| Input | Source recheck flags (assignment) | Disposition |
| --- | --- | --- |
| [b29-repos] | 2 | Blocked,n=0 |
| [b29-code] | 3 | Retained below |
| [b29-writeups] | 2 | Retained below |
| [b29-entrants] | 1 | Retained below |
| [b30-sigma-a] | none listed | Blocked,n=0 |
| [b30-sigma-b] | 2 | Retained below |
| [b30-act-a] | 2 | Retained below |
| [b30-act-b] | none listed | Incomplete experiment |
| [b30-tox-a] | 2 | Retained below |
| [b30-tox-b] | 2 | Retained below |
| [b31-a] | 4 | Retained below |
| [b31-b] | 2 | Retained below |
| [b32-a] | 2 | Retained below |
| [b32-b] | 2 | Retained below |
| [b33-a] | 3 | Retained below |
| [b33-b] | 1 | Retained below |
| [b33-c] | 2 | Retained below |
| [b33-d] | 1 | Retained below |
| [b33-e] | 1 | Retained below |
| [b34-a] | 1 | Retained below |
| [b34-b] | none listed | Retained below |
| [b34-c] | none listed | Retained below |
| [b34-d] | none listed | Retained below |
| [b35-a] | none listed | Blocked,n=0 |
| [b35-b] | 1 | Retained below |

No flags listed for an item does not establish verification. Source-side setup failures in b29-repos and b35-a leave n=0; machine details are unnecessary to interpret those outcomes and are omitted. b30-sigma-a reports pinned-repository clone and archive requests failed with connection reset after retry, n=0. These failures do not refute completed sibling experiments. [b29-repos]; [b30-sigma-a]; [b35-a].

Common reported real-engine method: pinned [amm-challenge 6b6921f8](https://github.com/benedictbrady/amm-challenge/tree/6b6921f8d463314aa7c96234e1be25a25245f704); wheel digest `aedb68280aca34c110968f00148387c95885207913fb2cf19a1ab4c5cfd6887a`; each candidate and reference separately against Vanilla via run_batch(...,8), never both in one market. Configurations draw default_rng(seed): size U(19,21), arrival U(.6,1), sigma U(.000882,.001008), in that order; price seed=s, retail=s+1, 10,000 steps, initial X=100,Y=10000, price=100, drift=0, dt=1, retail log-sigma=1.2, buy probability=.5. Paired SE is sample SD of seed differences / sqrt(n). Gas maxima refer to successful afterSwap unless stated otherwise, and finite observed maxima are not universal bounds. The usual retail/arb split is retrospective closed-form arb-profit reconstruction from stored fair prices, previous spot/fees, with retail=edge−arb; reconciliation is an arithmetic check, not independently labeled trade evidence. Source: [b30-sigma-b], [b30-act-a], [b30-tox-b], [b35-b] and their [supplied harness](https://api.imd.fun/artifacts/33f54e81f3372088e9eced52c0174f310ac348af98ef5727b73785c088679194).

## Public search: useful rules, no recovered top-ten implementation

b29-repos reports seven repositories with strategy code, dominated by the YQ estimator architecture; its 11 downloaded files received a compile-only check, not challenge validation, simulation or gas validation. It reports n=0, d32/oog unknown, empty measured top3 and no selected code. Other b29 items subsequently benchmark several identical hashes; those measurements supplement rather than retrospectively change b29-repos’s status. Search exclusions included the separate prop-AMM challenge, unrelated name matches and fork enumeration outside that item’s angle. Unauthenticated code search was unavailable; negative search results are bounded by inspected material. [b29-repos].

The following mechanisms are retained as source-attributed descriptions. Board/ablation claims in this catalogue are author claims, not local reproduction; HEAD references are mutable. The b29 source flags apply.

The YQ family (source [b29-repos], [pinned code](https://raw.githubusercontent.com/jiayaoqijia/amm-challenge-yq/3e9dc7d5a6192c88b562a0f8d9c172ca566ec94d/contracts/src/Strategy.sol)) uses 11 slots: fees, timestamp, direction, activity, pHat, sigmaHat, lambdaHat, sizeHat, toxicity and step count. Its reported equations are:

- Implied price = spot·(1−used fee) on AMM buy, otherwise spot/(1−fee). Update pHat only if relative return ≤max(10σ,.03), with first/later alpha .26/.05. First-in-step σ EMA decay .824, capped return .10, initial σ .00095.
- flow=lambda·size. Base=3bps+.20σ+12bps·lambda+4842bps·flow. Mid adds 250bps·tox+11700bps·tox²+91843bps·activity+500bps·σ·tox+15000bps·tox³. tox=.051·old+.949·min(abs(spot−pHat)/pHat,.20). New-step lambda=.99·old+.01·min(count/elapsed,5). Significant trades exceed ratio .002; size/activity blend .818/.985, decay .70^elapsed, elapsed capped 8.
- Direction centered at 1, push=min(2·ratio,.25), decay .80^elapsed. Skew=20bps·abs(direction−1)+100bps·abs(direction−1)·tox, added/subtracted by pressure direction.
- Stale shift=6850bps·tox, attracting discount=1.124·shift. Spot≥pHat raises bid/lowers ask, otherwise mirrored. Aligned trades add 2500bps·ratio on the traded side. Above 500bps compress with slope .93 protective/.955 attracting, then clamp.

[b29-repos] attributes official 523.21 and cross-seed 523.21 versus 522.13 (+1.08) to YQ’s README; ablation “improved pHat removed” costs .42, asymmetric tail removed gives 522.48 (−.01, neutral). These source claims were not reproduced and remain qualified by two unspecified recheck flags. Mutable HEAD references are weaker than pinned hashes.

Variants reported by [b29-repos]: lumen night_7 changes base to 3bps if σ>.0011 else 1bps; retunes cubic=13662bps, aligned boost=2530bps, flow=4779bps, linear tox=315bps, quadratic=12228bps, activity=94855bps, stale=6666bps. House category.xyz retunes threshold=1/650, direction decay .75, activity/size decay .53, sigma decay .69, size blend .828, pHat alphas .27/.06, impact 4, gate 7.2, cubic 20000bps, boost 3500bps, attract multiplier 1.05, return cap 1/35, lambda cap 1.82, base 4bps, linear/quadratic tox 300/15000bps, knee 600bps, attract slope .85. 0xniki L9 and ylintern taMole are additional constant variants; no local simulation here. File URLs and identities follow.

Happybigmtn’s distinct family [b29-repos], [source](https://raw.githubusercontent.com/happybigmtn/ammchallenge-lab/HEAD/amm_submissions/Strategy.sol): once/timestamp compare spot to pHat/gamma on buy, pHat·gamma on sell (gamma=1−used fee); within 55bps implies arb, invert that boundary into pHat; otherwise pHat=(6·old+spot)/7. A 414/415 volatility EMA is unused. Mispricing excess=max(abs(spot−pHat)/pHat in bps−18,0). Mid=23bps+.18·tradeRatioBps; skew=min(.6·excess,500bps), toxic premium=.19·excess. High spot raises bid by skew+premium, lowers ask by skew; mirror below pHat; toxic floor 32bps. Source claims 507.27, W/L/D 1000/0/0, inverted-skew reversal about 340; records historical leader v351 527.0346 (2026-02-11), deficit 19.77. Its telemetry claims top entries ~36bps with average bid/ask differences .04–.26bps and arb volume 23.5k–24.0k Y, own spread ~2.93bps/arb 27.5k, deficit correlation with own arb volume +.609 and growing with arrival rate. These are observations/author claims, not disclosed leader policies or controlled replicated causes. Other files’ URLs follow.

Dipankar WinningV5 [b29-repos], [source](https://raw.githubusercontent.com/dipankar/amm-challenge/HEAD/contracts/src/WinningV5Strategy.sol): ratio=amountY/reserveY, EWMA=(5old+ratio)/6; ratio>2% or >5EWMA classified arb gives 65bps both sides plus 15bps traded side; ratio<.4% gives 20bps; otherwise decay 7bps/step toward 24bps; reserveX·100/reserveY outside [.7,1.3] adds 15bps. README claims local WinningV5 295.57, MaxEdgeFinal 410.58, SigmaAdaptive 526.54 on 500 sims and warns server seeds differ. Not a fresh STACK comparison.

YQ’s research notes [b29-repos], [ideas](https://raw.githubusercontent.com/jiayaoqijia/amm-challenge-yq/HEAD/research/papers.md) list inventory reserve-ratio deviation premiums, hard sigma regimes, decayed cumulative signed-flow imbalance, adaptive shock gates and cubic approximations to exponential fees. Last two were reportedly adopted; remaining ideas are hypotheses, not tested gains.

b29-repos reports downloading, without compiling, 13 further dipankar classification-family contracts (AsymmetricV2, Best78bps, GreedyEdge, GridSearch, Hybrid, MaxEdgeV2, Optimal, Optimized, RegimeV2, SmartAsymmetric, Static80bps, WinningV3, WinningV4), and four older happybigmtn variants (PHatSkewBandInv_manual, Strategy_best_450, Strategy_best_494_60, Strategy_oracle_direct_skew_best418). It reports those older families below the later author scores, but provides no paired measurements for them. [b29-repos].

Compile-only inventory from [b29-repos] (all report compile success; valid, d32 and oog remain null):

| Source file | Code SHA-256 | Deployed bytes |
| --- | --- | --- |
| [yq](https://raw.githubusercontent.com/jiayaoqijia/amm-challenge-yq/HEAD/contracts/src/Strategy.sol) | `00fae418c49cd681ad0879c6f96ebed0163fab5a660b38030f11e6947a39afd4` | 4379 |
| [category.xyz](https://raw.githubusercontent.com/houseofjiao/amm-challenge/HEAD/contracts/src/Strategy.sol) | `07d5510da1972193d7cf20623de5693d54c123ce035ed158e2a7c1dee529bde0` | 4381 |
| [L9](https://raw.githubusercontent.com/0xniki/amm-challenge/HEAD/my_strategy.sol) | `74229c6535524db0bccc1116edd36e0952eb1ddb2acb4a25ec3da3f15e4806d9` | 4379 |
| [night_7](https://raw.githubusercontent.com/lumen-dev-a11y/amm-challenge-lab/HEAD/amm-challenge/my_strategy.sol) | `cc30bc7bceaf5afff5371f81bb4bcac1a8e50706a19eccd21ffff94642f1fcde` | 4414 |
| [SimpleFixed55](https://raw.githubusercontent.com/lumen-dev-a11y/amm-challenge-lab/HEAD/amm-challenge/contracts/src/Strategy.sol) | `9af0bc4976773e86c0b5e2970d3fe32c98a2a30075535bf5c7857555605c266a` | 598 |
| [taMole_Reverso_milli](https://raw.githubusercontent.com/ylintern/ammchallenge/HEAD/Strategy.sol) | `d6e7ab50ede8f5b8aadbfd69a8f966fb6a7bc50dbb57194c081a3233488d1ae7` | 4420 |
| [SigmaAdaptive](https://raw.githubusercontent.com/dipankar/amm-challenge/HEAD/contracts/src/SigmaAdaptiveStrategy.sol) | `84da373d4ecc47b5ecaa96adfcc432ad62825a0c608e7529404fa8a0184cdf90` | 3735 |
| [WinningV5](https://raw.githubusercontent.com/dipankar/amm-challenge/HEAD/contracts/src/WinningV5Strategy.sol) | `dc8dff6827ecc6aadecfe9936edd4fa8b48fc402dc2fa5257503f0feb822bd05` | 1479 |
| [MaxEdgeFinal](https://raw.githubusercontent.com/dipankar/amm-challenge/HEAD/contracts/src/MaxEdgeFinalStrategy.sol) | `0a54f608fdcbd980077c0b552bb850db0ac2cbee5e730fd96b8e15ef0f3b674b` | 1388 |
| [PHatSkewPostSpotToxOnlyV4](https://raw.githubusercontent.com/happybigmtn/ammchallenge-lab/HEAD/amm_submissions/Strategy.sol) | `536d17d72770abfc256708571d34c44919f19215916c0f4a21865c1df7e7011b` | 2446 |
| [happybigmtn best_494](https://raw.githubusercontent.com/happybigmtn/ammchallenge-lab/HEAD/amm_submissions/Strategy_best_494.sol) | `3336170920c2b452df304e76fb945421c77bd72e4c406fb14cbb4d590f61da17` | 2272 |

b29-code located only one qualifying entrant-style non-fork Solidity file: Noise Volatility Plus, [pinned gist](https://gist.githubusercontent.com/dicethedev/0ef000b2e9d7624621a95ab11753a3bc/raw/cb7cf1c21bf14233e5afb3faaebc6ef6ec4f08c3/NoiseAMMStrategy.sol), SHA-256 `9f7abe2656f2a04fec61f3191cb817fc06c1c444511017d9ea646134859000c3`. It found no score, rank or evidence of board submission, and no additional qualifying GitLab/Codeberg/Hugging Face policy in its searches. Codeberg was robots-blocked. Its top3 therefore has one entry. [b29-code].

Noise rule as reported: Exact integer arithmetic, all fee quantities in bps. R=floor(X*1e18/Y); R0 uses initial reserves. I=min(10000,floor(abs(R-R0)*10000/R0)), or 0 if either initial or current reserve is zero. M=min(10000,floor(abs(R-Rprev)*10000/Rprev)), or 0 if either ratio is zero. V=min(10000,floor((floor(amountX*10000/X)+floor(amountY*10000/Y))/2)), treating a zero-reserve component as 0. E=floor((5*Eprev+M)/6). S=1 on direction change, otherwise min(12,Sprev+1). G=timestamp-lastTimestamp when positive, else 1. D=35+floor(122*I/10000)+floor(9*E/100)+floor(7*V/100)+8*(S-1)+[G>5]*2*min(G,25)+[V>145 or M>125]*21+[V>330 or M>270]*23. If D<Dprev, replace D by floor((2*Dprev+D)/3); then cap at 122. K=floor(52*I/10000). If R>R0, bid=D+K and ask=discount(D,13+K); if R<R0, ask=D+K and bid=discount(D,13+K); otherwise both=D. discount(f,d)=16 if d>=f, otherwise f-d. Floor both sides at 16 and convert via bpsToWad/clampFee. Initial fees 35/35. Slots 0,1 initial X,Y; 2,3 previous X,Y (written); 4 Dprev; 5 timestamp; 6 direction bit and streak; 7 Rprev; 8 Eprev. Initialization sets previous reserves equal to initial reserves, Dprev=35, timestamp=0, streak=0, Rprev=R0, Eprev=0. No explicit arb/retail label or external fair-price estimator occurs in this source. [b29-code].

Algebra’s [LinkedIn](https://www.linkedin.com/pulse/amm-fee-challenge-notes-from-our-run-optimization-arena-qe3ff)/[Medium](https://medium.com/@crypto_algebra/amm-fee-challenge-notes-from-our-run-on-optimization-arena-4e980dbbd699) prose reportedly estimates volatility, retail/arb probabilities and normalizer behavior, responds immediately to directional displacement, protects toward external price and models block evolution probabilistically. Claimed peak9/654,rank12 at publication2026-03-27; no equations/constants/code. Medium was readable via one method and403 via another; unspecified source recheck failures further qualify the claims. [b29-code], [b29-writeups], [b29-entrants].

[Brady’s organizer article](https://www.benedict.dev/optimization-arena-learnings) reportedly describes then-top-eight diversity: two neural networks, compact math, many constants and competitor models; common arb probabilities/skew, volatility widths and outlier suppression. No entrant mapping, network weights or exact policies. [Slides](https://www.benedict.dev/optimization-arena-learnings/slides) were linked, no entrant transcript recovered. No verified mechanism disclosure by0xMai/Ponxter, entrant podcast/Reddit/Farcaster, or adopted primary-X formula; score-only/mirror speculation excluded. Bruno I. profile authwall prevented verification. [b29-writeups].

[HackMD](https://hackmd.io/6i1LNsRGRJ27YqTHjfO04A) proposes asymmetric gamma±=1−fee± best responses via first-order conditions under a mispricing distribution or DQN/PPO fee-pair actions rewarded by edge. Unattributed theory, no implemented/evaluated policy or rank: retained as theory by [b29-code], excluded as entrant disclosure by [b29-writeups], compatible scopes.

[Dipankar post-mortem](https://raw.githubusercontent.com/dipankar/amm-challenge/c588ae6c47fc9af2063c9bb1f2efbeb0dd276dab/ANALYSIS.md) repeats the YQ state-estimation/cubic/aligned-protection rules and −.42 pHat ablation; not rerun as ablations. CH uses first/later alpha .27/.06,gate=max(7.2σ,.03),initial fee4bps,σ.00095,lambda.8,size.002; quadratic but no cubic toxicity. [b29-writeups].

### Public code measurements

All public comparisons below are candidate minus RS2, with each arm separately versus Vanilla. Screen seeds 900000..900031, follow-up 901000..901255; these overlap across public-search items and must not be counted as independent fresh replications. No STACK confirmation or seeds ≥5,000,000. b29-writeups forwards all three located files rather than selecting a positive candidate; b29-entrants forwards its best three, including an upstream starter explicitly unrelated to the entrant’s actual ranked code. [b29-code]; [b29-writeups]; [b29-entrants].

| Screen source / file | n=32 Δ | SE | Swap max gas | OOG |
| --- | --- | --- | --- | --- |
| [b29-code] NoiseAMMStrategy.sol | -147.17996286976586 | 6.324947049325078 | 117425 | 0 |
| [b29-writeups] SigmaAdaptiveStrategy.sol | -8.01644894093358 | 0.515870965236206 | 148213 | 0 |
| [b29-writeups] Strategy.sol | -1.9468584042492232 | 0.20503310917898884 | 128929 | 0 |
| [b29-writeups] Strategy.sol | -2.8743337699932106 | 0.24043747036278731 | 127893 | 0 |
| [b29-entrants] category.xyz current public head | -1.951428057157056 | 0.20751625212846006 | 129233 | 0 |
| [b29-entrants] category.xyz historical, subsequently reverted toxicity coefficients | -2.063244829508971 | 0.21255145293519231 | 129243 | 0 |
| [b29-entrants] Unmodified upstream StarterStrategy; not floors.finance | -162.48527364261344 | 7.843403715376201 | 22592 | 0 |
| [b29-entrants] Visualizer builtin baseline30; not zenned.xyz | -189.78043012830778 | 9.546290310013571 | 22587 | 0 |
| [b29-entrants] Visualizer builtin starter50; not zenned.xyz | -162.48527364261344 | 7.843403715376201 | 22592 | 0 |
| [b29-entrants] Visualizer builtin widenBigTrades; not zenned.xyz | -189.4645467586236 | 9.492692413985504 | 27820 | 0 |

Follow-up records, source [b29-code]. Each record retains the code hash, paired n/mean/SE/five worst, component deltas and gas. In b29-entrants max_ok includes initialization; afterSwap_max_ok is the relevant swap maximum.

Code `9f7abe2656f2a04fec61f3191cb817fc06c1c444511017d9ea646134859000c3`; Noise Volatility Plus: inventory-skewed trade/flow/volatility fee; n=256, Δ=-142.66111552699903, SE=2.1642875468927034; worst seed 901169:-294.8720385305972; retail=-53.72315855290897, arb=-88.93795697409006; swap max=117507, OOG=0.

Follow-up records, source [b29-writeups]. Each record retains the code hash, paired n/mean/SE/five worst, component deltas and gas. In b29-entrants max_ok includes initialization; afterSwap_max_ok is the relevant swap maximum.

Code `6dd68f77a70900319460215374143dbd5d924198450a46d9f5f91f6b1e3d35c3`; CH reference: gated implied-price tracking; n=256, Δ=-1.8404066162914532, SE=0.06979100904354843; worst seed 901156:-8.517896528998108; retail=-0.008515070775243494, arb=-1.831891545516214; swap max=151576, OOG=0.

Code `00fae418c49cd681ad0879c6f96ebed0163fab5a660b38030f11e6947a39afd4`; YQ: adaptive shock gate and asymmetric toxicity; n=256, Δ=-2.730905464885787, SE=0.07757919730518127; worst seed 901156:-9.29795016706089; retail=-1.8372431375745026, arb=-0.8936623273112868; swap max=147039, OOG=0.

Code `84da373d4ecc47b5ecaa96adfcc432ad62825a0c608e7529404fa8a0184cdf90`; SigmaAdaptive post-mortem: estimate state rather than classify trades; n=256, Δ=-7.964970098691098, SE=0.2045763429268462; worst seed 901180:-43.041805616406464; retail=-0.7191316719923646, arb=-7.245838426698733; swap max=172035, OOG=0.

Follow-up records, source [b29-entrants]. Each record retains the code hash, paired n/mean/SE/five worst, component deltas and gas. In b29-entrants max_ok includes initialization; afterSwap_max_ok is the relevant swap maximum.

Code `07d5510da1972193d7cf20623de5693d54c123ce035ed158e2a7c1dee529bde0`; category.xyz current public head; n=256, Δ=-1.83816534909646, SE=0.07563375355850031; worst seed 901156:-9.517196614890622; retail=-0.16670318632373737, arb=-1.6714621627727224; swap max=151880, OOG=0.

Code `308ae0dc4343184ab795e1678726345242c6f4287fc88394b6b5c5cfc28f239e`; category.xyz historical, subsequently reverted toxicity coefficients; n=256, Δ=-1.9208984407159286, SE=0.0917561875733872; worst seed 901133:-13.876464995062406; retail=-0.6178726798298795, arb=-1.303025760886053; swap max=151890, OOG=0.

Code `8f2cea337f6736105f58c6758da6c3ebf002951d34492bcd5b7101bef2d1e7f3`; Unmodified upstream StarterStrategy; not floors.finance; n=256, Δ=-158.33909605929554, SE=2.5978760984045217; worst seed 901169:-334.28667476723746; retail=-28.218002710880228, arb=-130.12109334841531; swap max=22592, OOG=0.

No measured public file beats RS2. Noise’s 256-seed loss is −142.66111552699903 (retail −53.72315855290897, arb −88.93795697409006). CH is the best b29-writeups measured file at −1.8404066162914532; house-main is best b29-entrants at −1.83816534909646. Near-equal means do not establish identity. Visualizer builtins are examples, not recovered zenned.xyz code; the demirelo fork contains only the fixed50 starter, not floors.finance. House-main’s ranked byte identity is unestablished. [b29-code]; [b29-writeups]; [b29-entrants].

### Entrant coverage and board snapshot

b29-entrants reports a 2026-11-09 top-30 survey from the [leaderboard API](https://www.paradigm.xyz/puzzles/api/v1/leaderboard?limit=100), public X responses, same-handle GitHub probes and profile-linked blogs. It does not claim full authenticated social archives. A 404 or no match is not proof no code exists; in particular @heswithme_eth was followed to github.com/heswithme. The flagged source record is unspecified, so this is an attributed snapshot, not a newly verified current leaderboard. The network name/rank differs from the task’s STACK snapshot; no ranked byte identity or replacement of the task baseline follows. [b29-entrants].

| Rank | Author / entry | Reported avgEdge | Search outcome |
| --- | --- | --- | --- |
| 1 | @0xMai / Curvance.com | 528.3992637207801 | None found |
| 2 | @Ponxter / Tide v9 | 528.3616108587111 | None found |
| 3 | @KaihuaQIN / MixZ11 | 528.2575935240054 | None found |
| 4 | @pxmwxd_eth / BranchedReturn | 528.2060777235199 | None found |
| 5 | @aaaapsouuu / OpalG5W6I0 | 528.0990216289588 | None found |
| 6 | @cybergenesis621 / Morphogenetically Mogged | 526.7765462820532 | None found |
| 7 | @ujiuifs / v5 | 525.3769622854322 | None found |
| 8 | @cktbot / call me bot | 524.8989933796349 | None found |
| 9 | @onblueroses / lvw | 524.8101934238463 | None found |
| 10 | @frok_ai / mevmogger | 524.6579809037315 | None found |
| 11 | @bdesnos / pz | 523.8150642449694 | None found |
| 12 | @0xFanZhang / Conditional Risk Fees | 522.8168949855759 | None found |
| 13 | @kiteliudingyue / Uniswap Research | 522.4069038854279 | None found |
| 14 | @houseofjiao / — permanent underclass below this line — | 522.399991474802 | House code found; ranked identity unknown |
| 15 | @adrianleb / hmmmm | 522.384956327733 | None found |
| 16 | @yfjolne / v17 | 522.2581092187538 | None found |
| 17 | @unhedged21 / EQX_Labs_v111 | 522.2340584608704 | None found |
| 18 | @AAlex29797 / Routing Fees v19 2deaf4 | 522.2065998119917 | None found |
| 19 | @artemis_onchain / hehe | 522.0510142742021 | None found |
| 20 | @afinkek / CONTRO.APP - waitlist open now | 521.9777433209541 | None found |
| 21 | @cameronspirals / hAMM Sandwich | 521.7988337007108 | None found |
| 22 | @josusanmartin / try_init28 | 521.4814565492002 | None found |
| 23 | @basedfk / New CLIZA.ai Soon! | 521.3533229946398 | None found |
| 24 | @0xseiryu / v22 | 520.9978281489941 | None found |
| 25 | @demirelo / floors.finance | 520.4680740778977 | Starter only; floors.finance code absent |
| 26 | @jynxbt / zenned.xyz | 520.2784679499714 | Examples only; zenned.xyz code unestablished |
| 27 | @heswithme_eth / curve | 519.9165587517682 | No mechanism at linked github.com/heswithme |
| 28 | @builtbyimd / imd.fun swarm (seat #1477) | 519.8458339874795 | Requester supplied RS2 measured as reference; no independently identified new strategy publication added for our own entrant. |
| 29 | @realTomBayes / BayesArbFilter | 519.7210984985201 | None found |
| 30 | @CryptoAlgebra / Algebra Fee | 519.667107869242 | Challenge write-up found; qualitative rules only, no code or coefficients. |

## Anchoring and fee-family experiments

The completed anchoring/vol-flow/lean runs below use RS2, not STACK. Their below-5,000,000 512-seed held-outs do not satisfy the goal’s fresh ≥2,000-seed STACK confirmation. Except b30-act-b’s incomplete protocol, reported selection is best valid search candidates rechecked on separate 256-seed blocks, then frozen before held-out. A positive RS2 estimate is a research lead only. No aggregation of means across different policies is justified.

Mechanisms: sigma-b observes newly updated sigmaHat only on first-in-step; packs raw sigma, mean and capped count into slot 6; downstream gate/sigma/sigma-tox use g·blend(raw,mean,w), with the prior mean for the pre-update gate and updated mean for fees. Raw EMA remains separate. act-a observes actEma and corrected lambdaHat·sizeHat every swap, using mean+k(value−mean), flooring negative extrapolation, packing two means/count above the existing step count in slot 10. tox-a/b similarly sample post-update toxEma every swap, pack mean/count in slot 16, independently blend linear/sigma-tox versus quadratic inputs, keep DIR_TOX, price, stale shift and posterior unchanged. All capped counts continue 1/N updates after N, rather than freezing the mean. Sources: [b30-sigma-b]; [b30-act-a]; [b30-tox-a]; [b30-tox-b].

vol-flow-a/b modify only fMid: multiply sigma contributions by 1+a, flow by 1−b, then subtract c bps with a saturating zero floor; initial quotes/state writes are unchanged. The broader search did not yield a useful held-out candidate. [b31-a]; [b31-b].

| Source | Held-out seeds | n | Δ vs RS2 | SE | Retail Δ | Arb Δ | Swap/init gas/OOG |
| --- | --- | --- | --- | --- | --- | --- | --- |
| [b30-sigma-b] | [919000, 919511] | 512 | 0.16319410920826705 | 0.025062152047006243 | 0.346646167820856 | -0.183452058612589 | 201962/243121/0 |
| [b30-act-a] | 924000..924511 | 512 | 0.11057163065549047 | 0.014084312952773478 | -0.47915168153549403 | 0.5897233121909824 | 204413/243118/0 |
| [b30-act-b] | 929000..929047 (48 of 512 requested) | 48 | -0.12974358337203165 | 0.06757948322549719 | 0.8075704615545133 | -0.9373140449265459 | 220085/243103/0 |
| [b30-tox-a] | [954000, 954511] | 512 | 0.23348546171278806 | 0.03730861769844101 | -0.7774245705147632 | 1.0109100322275493 | 225483/243115/0 |
| [b30-tox-b] | 959000..959511 | 512 | 0.22743129815066498 | 0.029138446294552398 | -0.21262643685636973 | 0.44005773500703543 | 225559/243115/0 |
| [b31-a] | [934000, 934511] | 512 | -0.03716374129388622 | 0.017536324390119 | -0.39612494948503507 | 0.358961208191148 | 202910/243099/0 |
| [b31-b] | 939000..939511 | 512 | -5.35039590164935 | 0.06744925771245823 | -4.437391966873645 | -0.913003934775702 | 204316/243099/0 |
| [b32-a] | 944000..944511 | 512 | 0.009675396187513896 | 0.011377800721184739 | -0.4482334507402661 | 0.4579088469277811 | 224964/243090/0 |
| [b32-b] | 949000..949511 | 512 | 0.010712281250115807 | 0.005927620017292112 | 0.013451958676175324 | -0.0027396774260580875 | 225888/243093/0 |

Component SEs and worst paired seed minima are retained below; five-entry worst lists are compressed to their minima. Gas is reported scope, not an all-input bound. All experiments here lack fresh STACK confirmation.

**[b30-sigma-b]** code SHA-256 `014ad7bd0e6f412183ab5c0ee1560bbe30182b35b10f18d62464f1df0909cfca`; parameters `{"w":0.6827948634397843,"g":1.047182309813441,"N":5377}`.

Worst paired seed (five-entry lists compressed to minimum): 919221:-2.005485129100464. Retail/arb SE: 0.025506667215843336/0.012875661804605565.

29 disjoint 64-seed trials from 915000; recheck 918000..918255; held-out 919000..919511; neutral w=0,g=1 matched full fee/spot trajectories on 919600..919631. Recorded search-arm swap maximum 204249 exceeds the frozen-candidate maximum 201962; both report zero OOG. [b30-sigma-b].

256-seed recheck finalists, Δ (SE): [0.7890799628431452, 0.9419280256499287, 2305]: 0.07403803140111287 (SE 0.03705830021340896); [0.6827948634397843, 1.047182309813441, 5377]: 0.07701590031082128 (SE 0.03434809320168381); [0.848595387417918, 0.9009855182861374, 3553]: -0.002423336990244662 (SE 0.03920402588354445).

**[b30-act-a]** code SHA-256 `0c3836cd5bb7c39acec190a40c574bc02b4a2a302bb1a1fc6696178cecce2484`; parameters `{"act_k":1.3323924421892905,"flow_k":0.216073432653406,"N":4646}`.

Worst paired seed (five-entry lists compressed to minimum): 924119:-1.1281715588015686. Retail/arb SE: 0.014732455377969432/0.005426146630986634.

28 completed search evaluations were checkpointed before external interruption; incomplete work was unscored. Forced mean/count updates at neutral k=1 reproduced RS2 rows on all 32 parity seeds 924600..924631. Frozen held-out positive mean exchanges retail edge for less arb loss. [b30-act-a].

256-seed recheck finalists, Δ (SE): [1.2592823735501313, 0.46767504677057864, 9979]: 0.054519722272040605 (SE 0.019448540235420163); [1.3323924421892905, 0.216073432653406, 4646]: 0.0669062810166785 (SE 0.02124980976697438); [1.117729161432312, 0.7034444324465684, 6128]: 0.050633574016155425 (SE 0.011343636863044366).

**[b30-act-b]** code SHA-256 `b19f349bfee1d1428baae23da917e6a061ce2df0547ee3b39a7bfc212733787a`; parameters `{"kA":0.6,"kF":1.3,"N":800}`.

Worst paired seed (five-entry lists compressed to minimum): 929008:-1.2741603335009586. Retail/arb SE: 0.05984693759694296/0.03352774321596159.

Protocol failure: an initial three-write overlay produced OOG and was invalid. Packing into slot 16 repaired the reported final version, but the CMA state had already been corrupted by counting those earlier halts. Later points were hand-picked, not valid CMA continuation. Only 48/512 held-out seeds and 8/32 parity seeds ran; no 256-seed recheck. The reported final zero OOG does not rehabilitate the invalid earlier result. Not a submission candidate. [b30-act-b].

**[b30-tox-a]** code SHA-256 `ebd9de9bf6af6e55d5e308fd15dbb88edec11fd684891d02a30aec185acd19b3`; parameters `{"k_linear":0.7126960148076509,"k_quadratic":1.2952407538263107,"N":674}`.

Worst paired seed (five-entry lists compressed to minimum): 954369:-8.724713458962242. Retail/arb SE: 0.04220457015290185/0.022803666884412516.

Search random seed 45, population 6; fresh shared 64-seed blocks within each generation, fresh between generations; recheck 953000..953255, held-out 954000..954511. Neutral/off and enabled k=1 parity on 954600..954631 matched edge/components. [b30-tox-a].

256-seed recheck finalists, Δ (SE): [0.7126960148076509, 1.2952407538263107, 674]: 0.270224707720107 (SE 0.05149140371036169); [1.3490720224364616, 1.1781129419149794, 1507]: 0.15912170121785385 (SE 0.04351964221428467); [1.1044031555428824, 1.1706773560174795, 2715]: 0.19160517369881847 (SE 0.033901278835413).

**[b30-tox-b]** code SHA-256 `c7df70f20f8914d4d6f2893959d5eb710c0dd64a318b480a53b15ca3b0c58cd3`; parameters `{"k_linear":0.4729723318203064,"k_quadratic":1.2657629391345844,"N":403}`.

Worst paired seed (five-entry lists compressed to minimum): 959312:-5.207447317714809. Retail/arb SE: 0.03273157722748534/0.016655862486365237.

Search random seed 46, population 6; fresh 64-seed block per candidate from 955000; recheck 958000..958255, held-out 959000..959511. Off returns literal RS2; 32-seed parity 959600..959631 matched edge/components. An interrupted initial calibration was repaired before the complete reported run. [b30-tox-b].

256-seed recheck finalists, Δ (SE): [0.30485889878569955, 1.3053002959080733, 702]: 0.29879506576398174 (SE 0.04132650051849246); [1.0944054702214498, 1.3167995835204296, 406]: 0.09149979702423505 (SE 0.06384964187878969); [0.4729723318203064, 1.2657629391345844, 403]: 0.30283712994011647 (SE 0.036816584325614195).

**[b31-a]** code SHA-256 `9faa436b667bb9308ff9330df82dbc5dcf53e369d86ffd43f16f594f9e46f66c`; params `[-0.16383571745273284,-0.17364509271895479,1.5173936325324675]`.

Worst paired seed (five-entry lists compressed to minimum): 934172:-2.1076599411775305. Retail/arb SE: 0.018484935885295366/0.010429564792701192.

29 evaluations, search random seed 51, population 7; recheck 933000..933255, held-out 934000..934511. Neutral source/bytecode/edge/step-trace equality on 934600..934631. Frozen candidate underperforms; source recommends retaining RS2. [b31-a].

256-seed recheck finalists, Δ (SE): [-0.16383571745273284, -0.17364509271895479, 1.5173936325324675]: -0.0009811337255314356 (SE 0.021435651630418332); [-0.4986562284648844, -0.05511661212581609, -1.9306974783104287]: -0.08932599925136397 (SE 0.031281245540167806); [-0.3405139702622635, -0.11906759853651061, 0.48015797686512274]: -0.17777297413400062 (SE 0.030774509874993583).

**[b31-b]** code SHA-256 `84fc2d2a024b29b779e1b62a636d7b986bfbd0389b4a0750e3f97c2d8c7e6b60`; parameters `{"a":1.8314359716343138,"b":0.8298681871907697,"c":0.7039925637587545}`.

Worst paired seed (five-entry lists compressed to minimum): 939349:-9.717350305287937. Retail/arb SE: 0.06488647365890143/0.0559017750921356.

Five logged evaluations in a time-limited resumed search, random seed 52; only one complete generation, population reduced from 7 to 4. Recheck 938000..938255, held-out 939000..939511. Neutral source/bytecode/full equality on 939600..939631. Interrupted unscored block 935192..935255 was rerun only for gas (199136 swap, 243099 initialization, 0 OOG), excluded from selection/edge results. The strong loss is not an independently located optimum for the family. [b31-b].

256-seed recheck finalists, Δ (SE): {'a': 1.8314359716343138, 'b': 0.8298681871907697, 'c': 0.7039925637587545}: -5.443956090147252 (SE 0.09242955944247651); {'a': 0.47742766933130965, 'b': 0.508672049813459, 'c': 1.2563645354794175}: -7.059508706949509 (SE 0.08648192574931299); {'a': 1.1642270739494998, 'b': 0.8553547246115492, 'c': 0.4099685487184759}: -10.190704458918168 (SE 0.11874972662514016).

**[b32-a]** code SHA-256 `9887279d59be0dcd00fa33029940ef287959b98143f662743ffd345b5cfab06e`; parameters `{"lean_ema_decay_per_print":0.9995,"L_bps":1,"r":0.02}`.

Worst paired seed (five-entry lists compressed to minimum): 944174:-0.8883. Retail/arb SE: 0.012365632677903863/0.0057048934485681.

[b32-a] scan940000..941999,n=2000: RS2 edge526.21; mean bid−ask lean+1.18bps,SD3.34,p1/p99 −6.68/+8.68. Tail20:18 positive(+9.1..12.6),2 negative(−9.7,−10.2), mean edge564.1 vs526.2 overall. Lean correlations: size−.004,rate+.026,sigma+.038,log final return+.022,edge+.065; return-decile mean lean .95..1.57bps. Mean lean vs spot/fair mispricing correlation .98; tails average8–12bps offsets with persistent quarter signs, not one stuck episode; per-step >10bps bid lean ~52% versus ask ~40%. Shrinking staleShift loses−11.8..−18.6, amplification−6.9, pulling pHat→fastHat−.03..−1.08 except weakest K. Screen average lean rises1.00→1.09–1.53; tail20 8.05→8.4–9.5. K tail20 Δ+.0635,SE.0568,n20. Weakest held-out K is indistinguishable from zero. Calibration not rerun; no STACK confirmation. Screen942000..942255,recheck943000..943255,held-out944000..944511; frozen swap224964/init243090/OOG0, same-run RS2 swap202491. Evidence supports protective skew, not a demonstrated stuck estimate.

256-seed recheck finalists, Δ (SE): K: 0.0487 (SE 0.0178); F: -0.0048 (SE 0.0229).

Additional screen settings are summarized below; selected tail data are diagnostic, not independently held out. For b32-a, mode1 pulls pHat toward fastHat, mode2 scales staleShift by 1−r, mode3 pulls fastHat toward pHat, mode4 scales staleShift by 1+r. Slot16 stores a WAD-centered bid−ask EMA, updated each swap before the pull. A very large threshold reproduces RS2 on40 seeds, max edge difference0.

| Screen | Parameters (mode,decay,L,r for a) | Δ | SE | Tail20 Δ |
| --- | --- | --- | --- | --- |
| A | 1,0.999,3,0.1 | -0.167 | 0.0323 | -0.2104 |
| B | 1,0.999,3,0.3 | -1.0837 | 0.0572 | -0.9596 |
| C | 1,0.999,6,0.1 | -0.0912 | 0.0266 | -0.1298 |
| D | 1,0.999,6,0.3 | -0.6742 | 0.048 | -0.8286 |
| E | 1,0.995,5,0.2 | -0.6611 | 0.0483 | -0.6438 |
| F | 1,0.9995,2,0.05 | -0.0345 | 0.0238 | 0.0256 |
| G | 2,0.999,4,0.5 | -18.5768 | 0.3862 | -24.8794 |
| H | 2,0.999,6,0.5 | -11.8155 | 0.3202 | -17.9158 |
| I | 3,0.999,3,0.1 | -0.1451 | 0.0204 | -0.1114 |
| J | 4,0.999,4,0.2 | -6.9012 | 0.2935 | -10.8693 |
| K | 1,0.9995,1,0.02 | 0.0177 | 0.018 | 0.0635 |

**[b32-b]** code SHA-256 `06e440a366489e1296dbc2ff8b42a22c9043e2fa078a6b216f7442ecc22440ca`; parameters `{"alpha":0.001,"L_bps":5,"r":0.3,"near_fast_bps":5}`.

Worst paired seed (five-entry lists compressed to minimum): 949312:-0.5694856441441516. Retail/arb SE: 0.005849669569584211/0.002316812848603645.

[b32-b] scan945000..946999: tail20 mean abs lean9.846838646954248bps vs2.757316632466507 overall;17 positive,all20 same sign both halves,17 same sign all quarters. Tail/all means: rate .8383702367957838/.7973991298737482; sigma .0009445879085119173/.0009445248925498939; size20.009488189585703/19.994131496606904; edge573.0423823054196/524.4849892405938. Final price up12/20, lean/return signs match11/20. Lean vs average spot/fair gap correlation .9959774665335165,mean abs difference .5277346457935114bps,sign matches20/20. Internal pHat/fastHat not recorded, so stuck-estimate diagnosis unproven. Slot16 centered lean EMA alpha=.001; above L, blend pHat→fastHat by r only when correcting lean and spot/fast gap below near_fast. Frozen j2 L5bps,r.3,near_fast5bps; tail20 Δ.01208746795180673. Screen947000..947255,recheck948000..948255,held-out949000..949511. Incorrect empty-EMA preliminary probes discarded; reported settings initialize neutral WAD.

Gas scopes: [b30-act-a] includes completed search/recheck/held-out/parity/probe arms; [b30-sigma-b] frozen201962 versus all recorded204249; [b30-tox-a] all tested225483; [b30-tox-b] all candidate calls225559 versus frozen held-out223339; [b31-a] frozen202910 versus all tested203015; [b31-b] frozen204316. Frozen lean-a224964/lean-b225888 cover their screen/tail/recheck/held-out arms, not every hypothetical governor. All these scoped records report OOG0; invalid preliminary activity-b halts are excluded from its repaired final-arm claim.

The two activity anchors disagree in point sign (+0.1106 versus −0.1297), but act-b changed parameters, reduced samples and broke the planned optimizer protocol; this is not a controlled replication failure. The two toxicity anchors agree on modest positive RS2 gains (~0.23) while sacrificing retail for arb protection, with materially different worst-seed losses. The two vol-flow searches both reject their selected candidates; different search coverage explains the disparate loss magnitudes. Both lean studies agree that large persistent splits track pool-versus-fair mispricing and are not simply bad runs. Their positive-lean counts (18 versus 17 of 20), scan means (526.21 versus 524.4849892405938), correlations and small governor gains come from different scan blocks, not inconsistent measurements on the same seeds. Neither logged internal pHat/fastHat enough to prove a stuck estimator. The explanation “lean is protective” is supported by diagnostics and interventions, not a universal theorem. Sources: the corresponding nine records above.

256-seed recheck finalists, Δ (SE): j3: 0.00946135405180093 (SE 0.006633649844862757); j2: 0.014121991254743893 (SE 0.00891258759820923).

Additional screen settings are summarized below; selected tail data are diagnostic, not independently held out.

| Screen | Parameters (mode,decay,L,r for a) | Δ | SE | Tail20 Δ |
| --- | --- | --- | --- | --- |
| j1 | {'family': 'lag_only_pull', 'alpha': 0.001, 'L_bps': 5, 'r': 0.3, 'near_fast_bps': 3} | -0.00024341293004126463 | 0.007764082265900538 | 0.00799683414193737 |
| j2 | {'family': 'lag_only_pull', 'alpha': 0.001, 'L_bps': 5, 'r': 0.3, 'near_fast_bps': 5} | 0.005064897874317076 | 0.009285735371589911 | 0.01208746795180673 |
| j3 | {'family': 'lag_only_pull', 'alpha': 0.001, 'L_bps': 8, 'r': 0.3, 'near_fast_bps': 5} | 0.009163615857135765 | 0.006678079300249908 | -0.008537005891824379 |
| j4 | {'family': 'lag_only_pull', 'alpha': 0.001, 'L_bps': 8, 'r': 0.3, 'near_fast_bps': 10} | -0.000593303376015264 | 0.007306143298991314 | -0.02691149283070331 |
| j5 | {'family': 'lag_only_pull', 'alpha': 0.001, 'L_bps': 5, 'r': 0.6, 'near_fast_bps': 3} | 0.002325826304309997 | 0.009973782318902008 | 0.01294313724133076 |
| j6 | {'family': 'lag_only_pull', 'alpha': 0.001, 'L_bps': 8, 'r': 0.3, 'near_fast_bps': 3} | 0.0034837006669465875 | 0.005797522219230901 | -0.007155447073651544 |

## Market replicas: useful for family screening, not exact engines

All five b33 items build CH-versus-Vanilla market replicas, not STACK replacements. Outputs are seed-ordered [edge,retail_edge,arb_edge,retail_volume] in real units. They model fee-on-input constant-product execution with fees outside reserves, GBM price evolution, arb before Poisson retail and two-pool routing. Float64 replaces WAD integer floors; none simulates EVM gas, uint overflow, revert behavior or OOG fallback. Same numeric seed across engines is not the same market path. Means therefore use two-sample SE, while perturbations use within-engine paired differences. Baseline/perturbation agreement licenses coarse screening only; every selected strategy still needs exact real-engine confirmation and gas counters. [b33-a], [b33-b], [b33-c], [b33-d], [b33-e].

Path/dependency differences: a uses independent xoshiro128** price/retail streams and bundled exact configuration-draw fallback; c/e use separate MT19937 streams (c’s stdlib fallback uses random.Random and bundled SeedSequence/PCG64 for configurations); d uses independent xorshift64* with SplitMix64; b uses a single legacy MT19937 stream for price and retail. Thus b departs from the required independent-stream structure even though individual marginal distributions match. a/c have standard-library-only fallbacks; d requires NumPy, Numba optional; b/e require NumPy and Numba. Optional binary dependencies were not embedded by the source results, so do not mistake “no runtime network” for bundled offline dependencies. [b33-a], [b33-b], [b33-c], [b33-d], [b33-e].

### b33-a — [b33-a]

Replica-source SHA-256 `25a8eb8af92964ce7171daf6df48f4c4b8dbcbd913de8d0a33054e0ed204f7a8`.

Validation (CH 0..999, flat30 0..255):

| Validation | Real mean | Replica mean | Replica−real | Two-sample SE |
| --- | --- | --- | --- | --- |
| CH | 525.5258821780834 | 526.6481241447553 | 1.122241966671936 | 3.983886406108961 |
| flat30 | 347.9224335871958 | 347.09377738416623 | -0.8286562030295954 | 4.435551180095908 |

Transfer (each intervention is separate; all3 only where explicitly shown):

| Perturbation | Real Δ (SE) | Replica Δ (SE) | Replica retail / arb Δ |
| --- | --- | --- | --- |
| base_plus3 | -1.0552259184310975 (0.08048985801417369) | -0.9222213214113749 (0.01509991812430501) | -3.9340595076476705 / 3.0118381862362806 |
| stale_x08 | -6.858314321978259 (0.17948026265614378) | -6.754375511814141 (0.03468420109446881) | 9.354721880042248 / -16.10909739185641 |
| lambda_x15 | -4.242972174634329 (0.15237986188242605) | -3.924723006182335 (0.029044758228203082) | -9.808124009794632 / 5.883401003612254 |

Transfer real 676100..676227 (128), replica 676100..680195 (4096). Base +3 bps: 4→7; stale ×.8: .685→.548, including derived attract shift; lambda ×1.5: .0012→.0018. Lambda transfer discrepancy is 2.051589199817798 combined SE, a caution for sub-unit gains. Synthetic replay: 3000 callbacks per variant, maximum fractional fee error 8.951173136040325e-16; pure/JIT eight-market outputs equal, 5099 config draws equal; stdlib smoke completed. Reported warmed 4096-market throughput 712.7425188498913 markets/s including process startup/config generation. [b33-a].

### b33-b — [b33-b]

Validation (CH 0..999, flat30 0..255):

| Validation | Real mean | Replica mean | Replica−real | Two-sample SE |
| --- | --- | --- | --- | --- |
| CH | 525.5258821780834 | 526.9153715025097 | 1.3894893244263358 | not provided; replica-only 2.7713799632176648 |
| flat30_vs_vanilla | 347.9224335871958 | 347.7082543503285 | -0.21417923686732365 | 4.420454193246556 |

Transfer (each intervention is separate; all3 only where explicitly shown):

| Perturbation | Real Δ (SE) | Replica Δ (SE) | Replica retail / arb Δ |
| --- | --- | --- | --- |
| base+3 | -0.952649835538776 (0.09576679252215414) | -0.9244567262250536 (0.015302396707790341) | -3.9399607361140676 / 3.0155040098890136 |
| stale_x0.8 | -7.063215576897394 (0.2248496847366739) | -6.786955515142919 (0.03481309849498028) | 9.433848479959815 / -16.220803995102735 |
| lambda_x1.5 | -4.057650802713077 (0.21952925302213738) | -3.9550119797582335 (0.02830731628274585) | -9.85385001430532 / 5.898838034547085 |
| all3 | -12.68530434394319 (0.23565258948232612) | -12.582353409648718 (0.04115884292516971) | -7.809118121726103 / -4.773235287922615 |

CH real mean was copied from the brief, not rerun: its CH uncertainty is replica-only 2.7713799632176648, with only an approximate two-sample estimate. Flat30 and transfer real measurements were run. Transfer real 686100..686227, replica 686100..690195; all3 changes all three constants together, distinct from single-parameter tests. Reported throughput 164.39586703729447 markets/s (8 processes), a separate run about 175/s; no universal relative speed claim is warranted. Requires NumPy/Numba and uses one RNG stream. [b33-b].

### b33-c — [b33-c]

Replica-source SHA-256 `c74286f9b01dd6e8b9e1536959a79097210db3d5e028a347775b540deb91132f`.

Validation (CH 0..999, flat30 0..255):

| Validation | Real mean | Replica mean | Replica−real | Two-sample SE |
| --- | --- | --- | --- | --- |
| CH | 525.5258821780834 | 526.3471407960195 | 0.8212586179361097 | 3.9954526851088 |
| flat30 | 347.9224335871958 | 347.2573107018811 | -0.6651228853147018 | 4.458877189030649 |

Transfer (each intervention is separate; all3 only where explicitly shown):

| Perturbation | Real Δ (SE) | Replica Δ (SE) | Replica retail / arb Δ |
| --- | --- | --- | --- |
| base_plus_3bps | -0.9091767092307963 (0.08221275544689513) | -0.9285434384639791 (0.014947682193452553) | -3.9541006815202286 / 3.02555724305625 |
| stale_x0.8 | -6.793725127595652 (0.20570002352326555) | -6.785175291732687 (0.0351377314267081) | 9.434515962079143 / -16.21969125381183 |
| lambda_x1.5 | -3.9569044733461776 (0.1650826227703827) | -3.9675144112848915 (0.027984493901788646) | -9.878456407317628 / 5.910941996032735 |

Transfer real 696100..696227, replica 696100..700195. 5000 direct callbacks for each of CH/three variants had max fee error <1e-15 away from artificial ties; an exact-threshold test first diverged at callback 594, max fractional fee difference 0.0003153743526118774. This is a real stated limitation, not silently covered by the favorable market means. Stdlib fallback: 256 markets, mean edge 535.4177967793777, SE 5.7845873160884675, 10.905375469077345 markets/s. Warmed accelerated 4096-market trials: 765.7127067249304, 778.6044556686319, 755.8698429609366 markets/s, median 765.7127067249304. [b33-c].

### b33-d — [b33-d]

Replica-source SHA-256 `1e4c44b4bffbdeed65872ee15d46dbde209bf5aa11014329d13d100507b4040c`.

Validation (CH 0..999, flat30 0..255):

| Validation | Real mean | Replica mean | Replica−real | Two-sample SE |
| --- | --- | --- | --- | --- |
| CH | 525.5258821780834 | 526.6263740034892 | 1.1004918254058111 | 4.007958854995302 |
| flat | 347.9224335871958 | 348.27948443948867 | 0.3570508522928435 | 4.417125810915255 |

Transfer (each intervention is separate; all3 only where explicitly shown):

| Perturbation | Real Δ (SE) | Replica Δ (SE) | Replica retail / arb Δ |
| --- | --- | --- | --- |
| base_plus_3bps | -0.8949458610045338 (0.07657846719616337) | -0.9585254169128314 (0.015113137802125498) | not reported / not reported |
| stale_x0.8 | -6.764372082761492 (0.18239242275149145) | -6.851756075894003 (0.034233800614338956) | not reported / not reported |
| lambda_x1.5 | -4.114213852795671 (0.1358366480253364) | -4.000539724171688 (0.028400049828551124) | not reported / not reported |

Transfer real 706100..706227, replica 706100..710195. 5000 callbacks per CH/variant, largest fractional fee error 8.465450562766819e-16; 256 config draws exact; 16-market serial/parallel equality, flat analytic split/band checks, 64-step plain Python/NumPy equality. Reported warmed 4096-market throughput 3721.1054638422524 markets/s, startup/config included; earlier concurrent batches were slower. No market gain or STACK comparison. [b33-d].

### b33-e — [b33-e]

Replica-source SHA-256 `b2904402ddda43e4740d950c7bfe277f7262640b5506608e288e7e2a885a4b91`.

Validation (CH 0..999, flat30 0..255):

| Validation | Real mean | Replica mean | Replica−real | Two-sample SE |
| --- | --- | --- | --- | --- |
| CH | 525.5258821780834 | 526.3471654389 | 0.8212832608165854 | 3.9954519001014526 |
| flat_30bps | 347.9224335871958 | 347.25731070116933 | -0.665122886026495 | 4.458877189092782 |

Transfer (each intervention is separate; all3 only where explicitly shown):

| Perturbation | Real Δ (SE) | Replica Δ (SE) | Replica retail / arb Δ |
| --- | --- | --- | --- |
| base_fee_plus_3bps | -0.9058536543617239 (0.08199528053565687) | -0.9011643071935824 (0.014761166454869619) | -3.917312878454588 / 3.016148571261006 |
| stale_shift_x0.8 | -6.897337567611605 (0.19503060979126158) | -6.799350669820447 (0.03590243698523202) | 9.367730796568674 / -16.16708146638912 |
| lambda_coefficient_x1.5 | -3.854866626656657 (0.1646415375101408) | -3.9271277472953194 (0.028623301058450474) | -9.80710898421332 / 5.879981236918001 |

Transfer real 716100..716227, replica 716100..720195. 2000 callback replay max fractional fee error 7.389922007661198e-16; invariant/positive-trade/decomposition/parallel-determinism checks reported passed. Warmed 4096-market throughput 1409.6884851319262 markets/s, startup/config included. Real aggregate swap gas max 151647, OOG 0 across CH/flat/transfer; no arbitrary future strategy safety follows. [b33-e].

The five replicas agree on the sign and rough size of these three CH perturbations: base +3 bps loses roughly one edge, stale protection ×.8 loses roughly seven, lambda ×1.5 loses roughly four. Components, where reported, show stale reduction buys retail at larger arb cost and wider base/lambda fees lose retail while saving arb. Real component deltas are explicitly unavailable in a/c; replica components are not substitutes for measured real event labels. CH real calibration was reproduced in a/c/d/e, but not b. Their different replica means and timings reflect different streams, workloads and implementations; they are not pathwise equality or a common throughput contest. All reported real validation/transfer arms with gas evidence had zero OOG. Source claims remain subject to the assignment’s b33 recheck flags.

## RS2 float ports: tested callbacks, not scoring improvements

[b34-a], [b34-b], [b34-c], [b34-d] target the same RS2 hash. API: strat_init(S,TH,x0,y0), then strat_after(S,TH,is_buy,amount_x,amount_y,timestamp,reserve_x,reserve_y), returning fee fractions and updating 40-element float state. Inputs are real-unit gross amounts/post-trade reserves; timestamp is unscaled integral steps. is_buy means AMM buys X. Fees price the next fill. TH/state layouts differ: do not interchange arrays.

All omit WAD floors, integer sqrt, packing truncation/overflow and checked-arithmetic reverts; thresholds and moment subtraction can amplify rounding. No finite differential suite proves all-input or arbitrary-retuning equivalence. All report compiled execution, no >.01-bps divergence and no suppressed EVM failure. Synthetic single-pool tests do not establish two-pool scores, gas safety or board gains. a has one unspecified external-source recheck flag; other port items have none listed, which is not independent certification.

| Source | Compared callbacks | Max fee error bps | Mean fee error bps | Fraction >.01bps |
| --- | --- | --- | --- | --- |
| [b34-a] | 440220 | 3.841996165654393e-09 | 7.788136290840319e-12 | 0 |
| [b34-b] | 400000 | 2.966168977103223e-09 | 6.86e-12 | 0 |
| [b34-c] | 800534 | 0.0003545963610240843 | 9.038573310404743e-09 | 0 |
| [b34-d] | 400200 | 3.7855135692765884e-09 | 5.515070219688841e-12 | 0 |

[b34-a] port SHA-256 `c348f81163e1d3c5dc4a9cb8572f8994994eac2f0e678d2f27a591fd95b729c9`.

[b34-b] port SHA-256 `383166d96744f5aad83a4af6b60954f0d35d5b2f4531051c3881d1a8a7dc700b` (merge-computed from embedded source).

[b34-c] port SHA-256 `ae9a5d4802a1d5981c175d43ad4196ceec2a41d63e83461f36c7247384f0d3b2` (merge-computed from embedded source).

[b34-d] port SHA-256 `9eac3553357528b06eeae3ed8d18283d83401e1968145ceba16be356a147e271`.

Ports have differing synthetic distributions, counts, input quantization, fee feedback and benchmark overhead; maxima/timings cannot rank them on a common workload. Their evidence supports research integration only; selected Solidity still needs real-engine score and gas validation.

## Vanilla quote mechanism and the only direct fresh STACK confirmation here

b35-a is blocked at setup, with no implementation, code hash, parameters, evaluations, held-out sample or gas evidence. Its proposed mechanism was to model Vanilla virtual reserves and adjust the attracting fee toward the model quote, but n=0 is not an implementation or negative test. [b35-a].

b35-b implements: Two lazily populated slots track constant-product virtual reserves for the 30 bps Vanilla pool; each own callback projects its spot into the RS2 price estimate's arbitrage band and inferred retail fills update it toward the router's equal-marginal-price condition. The attracting fee moves by g times the difference from the fee matching Vanilla's modelled marginal quote minus m, with the adjustment clipped to plus or minus c bps and the resulting fee clamped to the strategy's allowed range. Source [b35-b].

Code SHA-256 `f61c0f28d8a55c3030e811777cf451549a075ddf23e1de453edd10309d4a1452`; frozen parameters `{"g":0.15,"c_bps":8.0,"m_bps":4.0}`. The estimate is existing RS2 70% slow/30% fast; the target is infinitesimal marginal quote, not finite-order average execution. Positive margin undercuts that fee-equivalent target; negative gain repels it. Later same-step prints are classified retail, first prints retail only if posterior arb probability <.5; competitor-only retail is unobservable, so the virtual pool is approximate. On corner routes it moves in the inferred retail direction only. Virtual constant product is recovered from own invariant; first own callback writes X, next recovers/stores Y, avoiding new initialization writes. [b35-b].

Search comprised 55 reported parameter trials on fresh small blocks, followed by shared 256-seed recheck 968000..968255. Recheck selected g=.15,c=8bps,m=4bps: +0.21750591046678536, SE .02739007609650152; alternatives .15/8/0 gave +.16320545601025316, SE .027488230030163742, and .15/2/0 gave +.08437273939788059, SE .020824744761921102. Negative/large-gain or broad adjustments often lost materially; one g=2,c=24,m=0 trial lost −13.644551427468635 (n=64). These are tuning evidence, not held-out certification. A preliminary unstaggered-slot version reached 248547 swap gas and was rejected under the item’s stricter <235000 rule; search restarted after repair. [b35-b].

held_out:

RS2 held-out 969000..969511: n=512, Δ=0.22302213597420917, SE=0.018347855427829837; worst 969388:-2.5931706138052846, 969456:-1.272216527805199, 969487:-1.0385307588909427, 969495:-1.0157713943274302, 969105:-0.6869833850482223; candidate/RS2 means 528.6040810191898/528.3810588832155.

retail_edge_delta:

Mean 0.1792315797774614, SE 0.018748483322800748.

arb_edge_delta:

Mean 0.04379055619674558, SE 0.0060582486649508206.

gas:

Aggregate gas: swap max 231403, init 243118, OOG 0, other errors 0.

stack_confirmation:

STACK confirmation: n=2000, Δ=0.5514277421227615, SE=0.013811303616272655; five worst seed:Δ 5820440:-2.7035756105987048, 5820200:-2.121250971171662, 5821076:-1.4619161492168473, 5820236:-1.3331411452205657, 5820229:-1.25186424229463. Component SEs retail=0.013698115720490553, arb=0.006235123968165564.

Neutral g=0 on 969600..969631 had exactly zero edge/retail/arb differences versus RS2 (n=32), max swap 199748, init 243099, OOG=0. CH calibration reproduced 525.5258821780834 exactly, swap max 151647, init 185532, OOG=0. Frozen aggregate gas maximum across relevant search/recheck/held-out/STACK runs is 231403, initialization 243118, OOG=0 and no other errors; the fresh STACK block alone peaked 230790. These scopes differ and are not contradictory. [b35-b].

The source records abandoning an initial STACK-baseline launch on 5000000..5001999 before return because the harness had already used that block; no candidate was evaluated there and no result inspected. Completed confirmation instead uses fresh 5820000..5821999, n=2000, candidate mean 529.0510425830435 versus STACK 528.4996148409207, delta +0.5514277421227615, SE .013811303616272655, mostly retail (+.5417309461804739) rather than arb (+.009696795942287522). Worst paired seed 5820440 is −2.7035756105987048. This meets the described sample-size/range/OOG requirements as reported, but external-source provenance has one unspecified recheck flag and this merge did not rerun it. The +.2230 RS2 held-out and +.5514 STACK confirmation concern different comparators and blocks; no constant RS2-minus-STACK offset is established. [b35-b].

## What carries forward

[b35-b] is a modest reported STACK improvement, not a top-ten solution. Sigma/activity/tox anchoring gives small RS2 leads; activity-b is incomplete and selected vol-flow policies lose. Lean governors largely trade retail for arb protection without material net gains. Public searches supply hypotheses, not recovered leader code. Replicas and ports can accelerate whole-family searches but cannot replace exact-engine score/gas checks. Time-limited searches do not establish global optima or rule out every related mechanism. No additive gains, new combined policy, board submission or guaranteed transfer is established.

## Input provenance

All 25 input names are linked to their original result artifacts below. Raw code/reproduction strings, per-seed arrays and redundant trial counters are not reproduced. Measured outcomes, negative/incomplete results and limitations are retained above.

[b29-repos]: ../../../batches/e07-public-search/items/repos/result.json
[b29-code]: ../../../batches/e07-public-search/items/code/result.json
[b29-writeups]: ../../../batches/e07-public-search/items/writeups/result.json
[b29-entrants]: ../../../batches/e07-public-search/items/entrants/result.json
[b30-sigma-a]: ../../../batches/e07-run-anchor/items/sigma-a/result.json
[b30-sigma-b]: ../../../batches/e07-run-anchor/items/sigma-b/result.json
[b30-act-a]: ../../../batches/e07-run-anchor/items/act-a/result.json
[b30-act-b]: ../../../batches/e07-run-anchor/items/act-b/result.json
[b30-tox-a]: ../../../batches/e07-run-anchor/items/tox-a/result.json
[b30-tox-b]: ../../../batches/e07-run-anchor/items/tox-b/result.json
[b31-a]: ../../../batches/e07-vol-flow/items/a/result.json
[b31-b]: ../../../batches/e07-vol-flow/items/b/result.json
[b32-a]: ../../../batches/e07-lean-tail/items/a/result.json
[b32-b]: ../../../batches/e07-lean-tail/items/b/result.json
[b33-a]: ../../../batches/e08-replica/items/a/result.json
[b33-b]: ../../../batches/e08-replica/items/b/result.json
[b33-c]: ../../../batches/e08-replica/items/c/result.json
[b33-d]: ../../../batches/e08-replica/items/d/result.json
[b33-e]: ../../../batches/e08-replica/items/e/result.json
[b34-a]: ../../../batches/e08-rs2-port/items/a/result.json
[b34-b]: ../../../batches/e08-rs2-port/items/b/result.json
[b34-c]: ../../../batches/e08-rs2-port/items/c/result.json
[b34-d]: ../../../batches/e08-rs2-port/items/d/result.json
[b35-a]: ../../../batches/e08-vanilla-quote/items/a/result.json
[b35-b]: ../../../batches/e08-vanilla-quote/items/b/result.json