## table

Snapshot: ranks from the fetched [leaderboard](https://www.paradigm.xyz/puzzles/api/v1/leaderboard?limit=100). Each linked ID supplies that row and its derived statistics below. Fees are basis points (raw API fraction ×10,000); volume and edge retain API units. d is entry minus NP2 **by array position**; SE = sample SD(d)/√1000, worst = min(d), lost = count(d<0). Rounding is display-only.

**Alignment warning:** all 21 files contain exactly 1,000 complete numeric runs. Every top-20 baselineEdge sequence differs from NP2 at all 1,000 positions; no top-20 sequence equals another. Thus the brief’s identical-baseline premise fails. Positional differences, SEs, losses, cross-entry correlations and regressions below are requested descriptive calculations, not certified paired gains or causal evidence. Different baselines alone cannot establish whether seeds differ or the baseline responds to the competing strategy. No reordering or baseline adjustment was applied.

|Rank|ID|Board score|Mean d|SE|Worst d|Lost|Retail|Arb|Bid bp|Ask bp|
|---:|---|---:|---:|---:|---:|---:|---:|---:|---:|---:|
|1|[52df1e42-4219-4931-b014-586d91720298](https://www.paradigm.xyz/puzzles/api/v1/submissions/52df1e42-4219-4931-b014-586d91720298)|528.399264|9.57013|0.06334|3.59266|0|77878.13|23665.16|35.3501|35.4814|
|2|[c38c9e1f-f458-4d13-963c-9294c3b91c62](https://www.paradigm.xyz/puzzles/api/v1/submissions/c38c9e1f-f458-4d13-963c-9294c3b91c62)|528.361611|9.53248|0.06291|3.44452|0|77893.81|23709.31|35.3612|35.3832|
|3|[e9362d90-f6b7-4497-835c-dd538d030160](https://www.paradigm.xyz/puzzles/api/v1/submissions/e9362d90-f6b7-4497-835c-dd538d030160)|528.257594|9.42846|0.06332|3.97376|0|77912.30|23789.31|35.3627|35.4511|
|4|[4aad6b12-aa93-4593-98cc-642e0b9fd006](https://www.paradigm.xyz/puzzles/api/v1/submissions/4aad6b12-aa93-4593-98cc-642e0b9fd006)|528.206078|9.37694|0.06238|3.59615|0|77493.97|23494.60|35.5022|35.5567|
|5|[88bbb4b5-6f95-45a4-8fd0-d1d8ba43ca52](https://www.paradigm.xyz/puzzles/api/v1/submissions/88bbb4b5-6f95-45a4-8fd0-d1d8ba43ca52)|528.099022|9.26989|0.06195|-5.73011|1|78056.72|23717.15|35.2186|35.2718|
|6|[8cdc1896-049f-4ae0-8e54-022d4866e4a1](https://www.paradigm.xyz/puzzles/api/v1/submissions/8cdc1896-049f-4ae0-8e54-022d4866e4a1)|526.776546|7.94741|0.05341|2.32508|0|78341.55|23750.87|34.8902|35.0253|
|7|[4f22492b-9643-47d2-82a2-bddb09edaccc](https://www.paradigm.xyz/puzzles/api/v1/submissions/4f22492b-9643-47d2-82a2-bddb09edaccc)|525.376962|6.54783|0.05595|-0.78832|1|78302.42|24416.69|35.5598|35.5794|
|8|[ff0c41ee-376c-4869-90e4-52b937a2fb61](https://www.paradigm.xyz/puzzles/api/v1/submissions/ff0c41ee-376c-4869-90e4-52b937a2fb61)|524.898993|6.06986|0.05124|0.13871|0|78935.08|24822.82|34.4677|35.0391|
|9|[2c1b6306-9e54-4f26-9c03-8c2f009ee6db](https://www.paradigm.xyz/puzzles/api/v1/submissions/2c1b6306-9e54-4f26-9c03-8c2f009ee6db)|524.810193|5.98106|0.05247|-4.96953|3|78259.92|24328.70|35.3246|35.5535|
|10|[65573db6-d287-47b1-928a-bd65eaa4b7a9](https://www.paradigm.xyz/puzzles/api/v1/submissions/65573db6-d287-47b1-928a-bd65eaa4b7a9)|524.657981|5.82885|0.04884|1.41924|0|77928.13|24488.85|35.1915|35.3983|
|11|[4aa20eb3-f72a-4908-b684-dbdf67717700](https://www.paradigm.xyz/puzzles/api/v1/submissions/4aa20eb3-f72a-4908-b684-dbdf67717700)|523.815064|4.98593|0.04455|-1.16346|1|77836.03|24238.13|35.7913|35.0449|
|12|[3828a970-8124-4566-87c7-66f33fc36435](https://www.paradigm.xyz/puzzles/api/v1/submissions/3828a970-8124-4566-87c7-66f33fc36435)|522.816895|3.98776|0.03970|-3.97146|4|77376.69|24117.74|35.5883|35.4913|
|13|[4fce1f40-19bd-4778-8d99-ff67456c1a02](https://www.paradigm.xyz/puzzles/api/v1/submissions/4fce1f40-19bd-4778-8d99-ff67456c1a02)|522.406904|3.57777|0.03643|-2.24369|1|77087.56|23646.64|36.1898|35.5349|
|14|[c221b6dc-dfbf-41cf-97fd-dfe893e02aec](https://www.paradigm.xyz/puzzles/api/v1/submissions/c221b6dc-dfbf-41cf-97fd-dfe893e02aec)|522.399991|3.57086|0.03832|-0.35742|2|77136.39|24114.62|35.4104|36.0443|
|15|[35de50ab-b1e1-4d2e-b304-d7dec57cbaec](https://www.paradigm.xyz/puzzles/api/v1/submissions/35de50ab-b1e1-4d2e-b304-d7dec57cbaec)|522.384956|3.55582|0.04096|-0.77320|3|77138.87|24246.71|35.8377|35.5099|
|16|[8e8bbcb9-94e3-4c17-bac7-588d826c708f](https://www.paradigm.xyz/puzzles/api/v1/submissions/8e8bbcb9-94e3-4c17-bac7-588d826c708f)|522.258109|3.42897|0.04890|-2.42927|7|77807.67|24978.47|34.8791|35.0429|
|17|[029e616b-4005-4b07-ad1f-bcc5bad09d83](https://www.paradigm.xyz/puzzles/api/v1/submissions/029e616b-4005-4b07-ad1f-bcc5bad09d83)|522.234058|3.40492|0.04077|-2.78076|3|77836.20|24572.28|35.1806|35.2816|
|18|[daeb2f71-8a69-46cc-a63c-35e4b75d2302](https://www.paradigm.xyz/puzzles/api/v1/submissions/daeb2f71-8a69-46cc-a63c-35e4b75d2302)|522.206600|3.37746|0.04437|-1.31835|7|76995.61|23280.50|36.2245|36.7808|
|19|[c99f1bc3-d8a7-496a-a7f9-af2145111aa3](https://www.paradigm.xyz/puzzles/api/v1/submissions/c99f1bc3-d8a7-496a-a7f9-af2145111aa3)|522.051014|3.22188|0.04720|-17.36563|6|77997.51|25066.99|34.9780|35.0877|
|20|[a1731836-9dbc-4c10-8290-6631285030c6](https://www.paradigm.xyz/puzzles/api/v1/submissions/a1731836-9dbc-4c10-8290-6631285030c6)|521.977743|3.14861|0.04727|-3.54112|11|79262.05|25782.66|34.2793|33.7079|
|39 (NP2)|[d5c8f6a9-febd-4cee-898e-3d81bc88038d](https://www.paradigm.xyz/puzzles/api/v1/submissions/d5c8f6a9-febd-4cee-898e-3d81bc88038d)|518.829135|0.00000|0.00000|0.00000|0|76497.61|24049.14|36.2591|35.2359|

## analysis

All statistics in this section are calculated from the row-linked submission files. Index means array position, not a verified seed identifier. As a concrete alignment counterexample, position 1 baselineEdge is 339.88607570648344 for rank 1 versus 347.58579804754498 for NP2.

OLS: outcomes are rank-1 positional d and the equal-weight mean of ranks 1–5 positional d. Regressors are NP2’s five run features, centered and divided by their sample SD; intercept included. Each coefficient is edge units per one feature SD. Conventional homoskedastic t = coefficient / OLS SE, residual df=994; these are descriptive, with no multiple-testing adjustment. No feature is a directly available on-chain baseline oracle.

|Term|Leader coefficient|t|Top-5 coefficient|t|
|---|---:|---:|---:|---:|
|Intercept|9.57013|202.646|9.43558|203.797|
|baselineEdge|-2.94063|-5.125|-2.80764|-4.991|
|retailVolumeY|2.97370|6.243|2.87627|6.159|
|arbVolumeY|-0.19591|-2.196|-0.16621|-1.901|
|averageBidFee|1.04180|9.732|0.96170|9.164|
|averageAskFee|0.96905|8.480|0.91048|8.127|

R²: leader 0.446887; top-5 0.439883. n=1,000 each. Standardized design condition number 30.78: correlated predictors make individual coefficients sensitive. NP2 feature sample SDs (baseline, retail, arb, bid fraction, ask fraction): 61.331222, 9938.3903, 1680.8315, 0.0002784303, 0.00023942065.

Fee diagnostics: mean fee = (bid+ask)/2; asymmetry = bid−ask. SDs use ddof=1. rBid = Pearson correlation of the entry’s bid with NP2 bid at the same index. rBase = correlation of its mean fee with **its own file’s** baselineEdge; rNPbase uses NP2 baselineEdge instead (important given the mismatch). Positive rBase is association with higher-baseline runs, not proof of a pressure-detection mechanism. All fee quantities below are bp.

|Rank|rBid|rBase|rNPbase|Mean fee|SD mean fee|Mean asym|SD asym|Family|
|---:|---:|---:|---:|---:|---:|---:|---:|---|
|1|0.83750|0.76095|0.73261|35.4158|1.6107|-0.1313|3.3848|F2|
|2|0.83601|0.74028|0.71668|35.3722|1.4340|-0.0220|3.3223|F2|
|3|0.85096|0.77205|0.76224|35.4069|1.4308|-0.0884|3.4559|F2|
|4|0.84254|0.77305|0.76219|35.5295|1.2923|-0.0546|3.3164|F2|
|5|0.86517|0.78897|0.77903|35.2452|1.4302|-0.0533|3.3751|F2|
|6|0.86456|0.80901|0.79160|34.9577|1.5358|-0.1351|3.2570|F2|
|7|0.85735|0.74294|0.72931|35.5696|1.5504|-0.0197|3.7197|F2|
|8|0.87576|0.79725|0.78769|34.7534|1.4146|-0.5714|3.3752|F2|
|9|0.87250|0.71918|0.70536|35.4391|1.6628|-0.2288|3.7650|F2|
|10|0.85698|0.80070|0.79064|35.2949|1.3281|-0.2068|3.3324|F2|
|11|0.88628|0.83030|0.82354|35.4181|1.6005|+0.7464|3.5085|F2|
|12|0.94144|0.91681|0.91520|35.5398|2.0966|+0.0970|3.4061|F1|
|13|0.83525|0.78576|0.75169|35.8623|1.7663|+0.6548|3.5886|F2|
|14|0.87820|0.81767|0.80880|35.7273|1.4454|-0.6339|3.5337|F2|
|15|0.89322|0.85298|0.84799|35.6738|1.4775|+0.3278|3.4817|F2|
|16|0.85875|0.78665|0.77975|34.9610|1.3181|-0.1638|3.1974|F2|
|17|0.85499|0.75962|0.74931|35.2311|1.4260|-0.1010|3.5086|F2|
|18|0.89248|0.85669|0.84871|36.5027|1.6760|-0.5563|3.5666|F2|
|19|0.78846|0.56279|0.54252|35.0329|1.8471|-0.1097|4.3463|F3|
|20|0.84361|0.78589|0.75440|33.9936|1.4835|+0.5713|3.3120|F2|
|NP2|1.00000|0.92207|0.92207|35.7475|1.9650|+1.0232|3.3948|F1|

Clustering: exploratory Ward agglomeration with Euclidean distance on six equally weighted z-scored features across 21 entries: mean fee, SD mean fee, mean asymmetry, SD asymmetry, rBid, rBase. Cut at three clusters for a compact descriptive taxonomy; this does not identify source-code mechanisms. NP2 is included in normalization and clustering. Family means average each member’s mean positional d (NP2 contributes zero).

|Family / descriptive name|Members by rank|Mean d vs NP2|
|---|---|---:|
|F1: higher baseline coupling|12, NP2|1.99388|
|F2: main lower-variability group|1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 20|6.03351|
|F3: high asymmetry dispersion|19|3.22188|

F2 leads by family mean positional d (+6.03351) and contains rank 1. This broad group is heterogeneous; it is not 18 independent confirmations of one mechanism. Leader mean-fee/baseline correlation is **less** than NP2: 0.76095 vs 0.92207 using each file’s baseline. Using NP2 baseline for both gives 0.73261 vs 0.92207. Leader mean-fee SD is 1.6107 vs NP2 1.9650 bp; mean asymmetry -0.1313 vs +1.0232 bp. These are cross-run averages, not within-run fee response paths.

## implications

These are hypotheses to test in the simulator on genuinely matched seeds; API aggregates cannot reveal their implementation. Each uses only local swaps/reserves/time and stored state.

1. **Damp the pressure response.** Maintain a timestamp-decayed EWMA of absolute reserve-implied price changes; apply a saturating fee response. Compare matched-seed edge and fee dispersion against NP2: leader SD 1.6107 vs 1.9650 bp and rBase 0.76095 vs 0.92207 motivate less aggressive tracking, not a fixed-fee retune.
2. **Remove persistent directional bias.** Track signed trade/reserve imbalance with decay and apply zero-centered opposite bid/ask adjustments. Test whether shrinking long-run bid−ask bias toward zero helps: leader -0.1313 bp versus NP2 +1.0232, while asymmetry SD remains 3.3848 versus 3.3948 bp. Preserve transient skew rather than eliminating it.
3. **Separate flow intensity from price displacement.** Use distinct decayed counters for traded notional per timestamp interval and reserve-price innovation, then gate fee response on their interaction. Leader OLS retail coefficient +2.97370 (t=6.243) alongside baseline -2.94063 (t=-5.125) motivates testing separate local flow/price channels; neither API feature is observable directly during a swap.
4. **Cap directional fee overshoot.** Bound skew by a decayed absolute-price-change scale and relax it after reversals. Rank 19 asymmetry SD is 4.3463 bp versus leader 3.3848; its mean positional gain is 3.22188 versus leader 9.57013. Test the cap against an uncapped ablation; this singleton correlation does not establish benefit.

## fetch

Endpoints: [leaderboard](https://www.paradigm.xyz/puzzles/api/v1/leaderboard?limit=100), then `https://www.paradigm.xyz/puzzles/api/v1/submissions/<id>` for each of the 21 IDs linked in the table. Files were saved one JSON per ID in temporary research scratch. Every ID: 1,000 runs fetched; failed IDs: none. No simulator, external strategy code, or estimated missing data used. User-Agent: `Mozilla/5.0 (compatible; AMMBoardResearch/1.0)`. Requests succeeded without rate-limit retries. The table is a fetch snapshot, not a claim about future ranks. Sources registry is capped at 20: the board plus NP2 and ranks 1–18 have exact raw-JSON excerpts there; rank 19–20 endpoints remain cited directly in their rows.