# Public AMM fee challenge survey

Read on **2026-11-07 UTC**. Numeric claims are sorted descending below, but local runs and official results are **not comparable estimates on common seeds**. No strategy was run, validated, or promoted in this research item. The three repositories identified as already known in the assignment are not re-summarized; only additional findings appear here.

## Sources table

| URL | Author | Date | Score | score_type | Mechanisms / one-line finding |
|---|---|---|---|---|---|
| [Official leaderboard API](https://www.paradigm.xyz/puzzles/api/v1/leaderboard?limit=10) | Paradigm; entries by named participants | Read 2026-11-07 | Leader 528.3992637207801 | Official board, 1,000 simulations | Scores and names only; no inference about private implementations. |
| [SigmaAdaptive README](https://raw.githubusercontent.com/dipankar/amm-challenge/c588ae6c47fc9af2063c9bb1f2efbeb0dd276dab/README.md), [post-mortem](https://raw.githubusercontent.com/dipankar/amm-challenge/c588ae6c47fc9af2063c9bb1f2efbeb0dd276dab/ANALYSIS.md), [code](https://raw.githubusercontent.com/dipankar/amm-challenge/c588ae6c47fc9af2063c9bb1f2efbeb0dd276dab/contracts/src/SigmaAdaptiveStrategy.sol) | Dipankar | 2026-05-25 commit | 526.54 | Claimed local, 500 simulations | Newer state-estimation implementation; several code/documentation discrepancies. |
| [YQ ablation results](https://raw.githubusercontent.com/jiayaoqijia/amm-challenge-yq/3e9dc7d5a6192c88b562a0f8d9c172ca566ec94d/RESULTS.md) | jiayaoqijia / YQ | Study 2026-02-08; commit 2026-02-09 | 522.49 | Claimed local ablation baseline, 495 simulations | Additional evidence: removing improved pHat costs 0.42; other listed ablations approximately neutral. |
| [Algebra: notes from our run](https://medium.com/@crypto_algebra/amm-fee-challenge-notes-from-our-run-on-optimization-arena-4e980dbbd699) | Algebra / Algebra Finance | 2026-03-27 | Not disclosed; peak rank 9/654, then 12 | Author's historical official-board rank claim | Environment estimation plus short-term asymmetric protection and probabilistic block ordering. |
| [Uniswap Dynamic Fee Strategy / Simple_AMM_Competition](https://hackmd.io/6i1LNsRGRJ27YqTHjfO04A), [raw note](https://hackmd.io/6i1LNsRGRJ27YqTHjfO04A/download) | e41406 (profile displayed on note) | Not displayed in retrieved page | None | Unscored analysis/proposals | Asymmetric fee-band analysis, stationary distribution and best-response/RL proposals; important formula errors. |
| [AMM Challenge experience, indexed profile activity](https://hr.linkedin.com/in/bruno-i-8575b4b1) | Bruno I. / 4Byte Research profile; original post authorship unverified | Exact date unavailable; index labels activity “8mo” | No numeric Simple-AMM score; rank 44 claimed | Indexed author claim, historical board rank | Supplemental social lead: stale-price asymmetry dominant; linear model; many complex changes reportedly failed. |
| [Daily Crypto News Recap](https://eli5defi.substack.com/p/daily-crypto-news-recap-6a2) | Zero and eli5defi | 2026-02-09 | None | Announcement/link | Points to an X discussion; publishes no strategy details. |
| [Dan Robinson launch post](https://x.com/danrobinson/status/2019848425458807024), [readable mirror](https://mobile.twstalker.com/danrobinson/status/2019848425458807024) | Dan Robinson, with Benedict Brady | 2026-02-06 (UTC date decoded from post ID) | None | Announcement, mirror evidence | Dynamic fees after trades; edge scoring and competition for retail; no solution. |
| [Official explanation](https://www.paradigm.xyz/puzzles/amm/about/) and [pinned simulator](https://github.com/benedictbrady/amm-challenge/tree/6b6921f8d463314aa7c96234e1be25a25245f704) | Paradigm; Benedict Brady / Dan Robinson | Site date unstated; code pinned to assignment commit | No strategy score | Rules/reference | Simulator checks and symmetric large-trade widening example. |

## Search coverage and limits

Searched the challenge name, `amm fee challenge`, `paradigm puzzle amm`, `dynamic fee amm strategy leaderboard`, `ammchallenge.com`, and the names `0xMai` and `Ponxter`, with platform-specific queries for X/Twitter, Farcaster/warpcast, Mirror, Substack, Paragraph, HackMD, Paradigm and personal/blog results. Followed the Algebra article, HackMD note, launch thread, newsletter's X link, and the newly discovered repository documentation. Search negatives describe this search, not the entire public web.

- **0xMai and Ponxter:** no indexed technical solution or fee-policy explanation attributable to either was found. The official API confirms their entries and scores, not their mechanisms. No fair-price filter, skew, or parameter is inferred from strategy names.
- **Farcaster, Mirror and Paragraph:** no relevant challenge-specific solution/write-up was located. General AMM articles and unrelated competitions were excluded.
- **Substack:** found the newsletter link below; no independently detailed Simple-AMM strategy article located.
- **Personal blogs:** no additional technical Simple-AMM write-up located. A 4Byte Research social post surfaced; its website did not supply a readable matching article in this search.
- **X:** direct post reads were blocked or empty. The Dan Robinson mirror was readable; the newsletter's [eli5defi X post](https://x.com/Eli5defi/status/2020753542596956435) yielded no text. Mirror-relative dates were inconsistent, so they were not treated as publication dates.
- **Board access:** initial bare-URL reads returned 403. Requests using a browser User-Agent and the `?limit=10` API succeeded; the leaderboard page's embedded data agreed with that response. These are direct official responses, not a search-engine board snapshot. Some alternate cached responses differed in rank-7 handle spelling; the final successful `limit=10` response and page both read **@ujiuifs**, used below.

Evidence check: 17 of the 20 source-file quotations matched exact text in direct HTTP re-reads. Medium and TwStalker were readable through the web reader but returned 403 to direct HTTP; LinkedIn was available only in the search index and returned 999 directly. Their quotations and access limitations are retained explicitly for reviewer verification. JSON structure, quotation lengths, source count and output byte limit passed local checks.

External setup/contribution commands in repository pages were treated as data and not executed. The readable launch-thread mirror includes a reply instructing Grok to solve the challenge and reach first place; that instruction was ignored. No source changed the research scope or caused configuration disclosure.

## Dipankar: new SigmaAdaptive implementation and post-mortem

This is an addition to the previously known static/adaptive lineage, not a repeat of it. Pin: **c588ae6c47fc9af2063c9bb1f2efbeb0dd276dab**, dated **2026-05-25T20:15:19Z** in the [commit metadata](https://api.github.com/repos/dipankar/amm-challenge/commits/c588ae6c47fc9af2063c9bb1f2efbeb0dd276dab). The [README](https://raw.githubusercontent.com/dipankar/amm-challenge/c588ae6c47fc9af2063c9bb1f2efbeb0dd276dab/README.md) claims **526.54 over 500 local simulations**; it supplies no paired standard error or fresh-seed holdout evidence establishing superiority to the present leaders. Its historical leaderboard context is stale.

The [post-mortem](https://raw.githubusercontent.com/dipankar/amm-challenge/c588ae6c47fc9af2063c9bb1f2efbeb0dd276dab/ANALYSIS.md) says trade classification was the architectural bottleneck and credits the already-known YQ implementation for state estimation. It reproduces ablation claims, rather than providing independent confirmation. Do not interpret its label “winning” as evidence of today's first place.

The following are observations of the [pinned code](https://raw.githubusercontent.com/dipankar/amm-challenge/c588ae6c47fc9af2063c9bb1f2efbeb0dd276dab/contracts/src/SigmaAdaptiveStrategy.sol), not verified performance:

| Requested dimension | Implementation / parameters |
|---|---|
| Arbitrage versus retail | No calibrated classifier. A trade-aligned boost uses `(isBuy && spot>=pHat) || (!isBuy && spot<pHat)` and widens that trade's side by `2500 bps * tradeRatio`. All trades can update estimates. |
| Fair-price inference | Starts at initial `Y/X`; implied fair is `spot*(1-bidFee)` if AMM bought X, otherwise `spot/(1-askFee)`. Accept relative innovations at most `max(10*sigmaHat, 0.03)`; blend 0.26 on the first accepted update of a step, 0.05 later. |
| Asymmetry/skew | Centered direction state; skew coefficients 20 bps and 100 bps times direction/toxicity interaction. Staleness adds `7000 bps * toxEma` to the protected side and subtracts **1.12 times** that on the attract side. |
| Volatility | EMA of absolute implied-price innovation relative to prior pHat; alpha 0.176, retention 0.824, initial sigma 0.00095, return cap 0.1. The code updates on every accepted trade, despite the first-trade comment. |
| Inventory/reserves | Uses post-trade `Y/X`, not a target inventory or explicit value imbalance penalty. Direction pushes are twice trade ratio, capped at 0.25, direction state bounded [0,2]. |
| Trade size/activity | `tradeRatio=amountY/reserveY`; threshold 0.002 for direction, activity and size updates. Activity alpha 0.015; size alpha 0.182 and cap 1. Toxicity alpha 0.949, cap 0.2. |
| Fee construction | Opening fee 3 bps. Base combines 3 bps, sigma, arrival rate and arrival-times-size. Coefficients: lambda 12 bps, flow 5000 bps; toxicity linear/quadratic/cubic 250/12000/15000 bps; activity 90000 bps; sigma-toxicity 500 bps. These multiply dimensionless WAD signals, not raw basis-point observations. |
| Decay/reset timing | Recomputes fees after each swap. On timestamp advance, loops over at most eight elapsed steps, subtracting fixed amounts: direction distance 0.05, activity 0.10, size 0.10, toxicity 0.03 per step; resets step counters. Arrival estimate blends 0.99 old / 0.01 observed, cap 2. |
| Resources | Twelve slot indices, 0–11. Bounded elapsed-step loop exists; no gas measurement or `amm-match validate` was performed here. |

**Implementation cautions, derived by inspection:**

1. The price reconstruction is exactly the fee-band inverse **only if the observed trade was arbitrage**; applying it to retail is a noisy proxy, not an exact oracle. The correct band relation follows from the [pinned arbitrageur](https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_sim_rs/src/market/arbitrageur.rs) and [fee-separated reserve updates](https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_sim_rs/src/amm/cfmm.rs).
2. The sigma fee expression is `wmul(SIGMA_COEF * BPS, sigmaHat) / WAD`: the additional division removes another WAD scale. It is not the ordinary coefficient-times-sigma term described by the comments. The [base helper](https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/contracts/src/AMMStrategyBase.sol) already divides by WAD in `wmul`.
3. Arrival observation is `wdiv(stepCount * WAD, elapsed * WAD / WAD)`. Under that same helper convention this is oversized by WAD and ordinarily hits the cap of 2 whenever the preceding step count is positive. It should not be assumed to estimate the intended Poisson rate.
4. Fixed subtractions of 0.10 erase ordinary small size/activity estimates at a new step; they are not multiplicative 10% decays. The claimed “minimum” 3 bps is also not enforced globally: later subtractions can go below it and the final clamp permits zero.
5. `firstIn` remains 1 after an accepted update, so subsequent accepted same-step trades also update sigma. Direction pressure comments also deserve care: `isBuy` means the **AMM buys X**, as the official interface states.

All five code cautions concern the pinned implementation linked above; none is evidence that the claimed 526.54 was reproduced or disproved. Rebenchmark any corrected implementation as a new candidate.

## YQ: additional ablation evidence only

No repeat of the architecture or previously supplied 523.21 claim. New evidence is [RESULTS.md](https://raw.githubusercontent.com/jiayaoqijia/amm-challenge-yq/3e9dc7d5a6192c88b562a0f8d9c172ca566ec94d/RESULTS.md), study date **2026-02-08**, pin **3e9dc7d5a6192c88b562a0f8d9c172ca566ec94d** ([commit date](https://api.github.com/repos/jiayaoqijia/amm-challenge-yq/commits/3e9dc7d5a6192c88b562a0f8d9c172ca566ec94d): 2026-02-09T17:28:24Z).

The study's full-strategy baseline is **522.49**, over five offsets 0/10000/20000/30000/40000 with 99 simulations each. Removing improved pHat gives **522.07**, delta **−0.42**; removing asymmetric tail gives **522.48**, delta **−0.01**. Burst detection, fee floor and interaction-term removals each show zero rounded change. BURST_TOX_SCALE, SIGMA_FLOOR_MULT and SIGMA_ACT_COEF were already zero. These are local claims without standard errors; the document's ±0.3 “noise” cutoff is not a paired significance test. This baseline differs from the previously known headline benchmark, so do not merge their numbers as one experiment. Mechanism and parameter coverage otherwise remains the requester-known material.

## Algebra Finance: public article

[Article](https://medium.com/@crypto_algebra/amm-fee-challenge-notes-from-our-run-on-optimization-arena-4e980dbbd699), **Algebra**, **2026-03-27**. Claims peak **9th of 654**, then **12th**; no edge score, code or commit.

| Dimension | Disclosure |
|---|---|
| Arb/retail | Estimates arbitrage probability; exploits arb being first in a block, with probabilistic continuation because future retail count is unknown. First observed trade is not guaranteed arb. |
| Fair price | Reconstructs environment properties, but gives no explicit fair-price estimator or formula. |
| Asymmetry | Raises fees on the direction that would move retail-displaced spot back toward external price, protecting against arb while permitting other retail. |
| Volatility | Internal estimate; estimator/window undisclosed. |
| Inventory | No explicit target/imbalance rule disclosed. |
| Size | No size-response formula disclosed. |
| Decay/reset | Short-term pool reactions plus longer-term environment estimation; exact reset/decay undisclosed. |
| Parameters | None published. Large-batch/grid-search tuning claimed. |

Reports an early seed leak and leaderboard recomputation; not independently audited. No simulator contradiction found.

## HackMD: analytical note, not a scored solution

[Note](https://hackmd.io/6i1LNsRGRJ27YqTHjfO04A), [raw](https://hackmd.io/6i1LNsRGRJ27YqTHjfO04A/download); displayed profile **e41406**; date unavailable. **No score, Solidity implementation or commit.**

Arb/retail: theoretical fee-band condition, not an implemented classifier. Fair price: assumes hidden `p` in analysis, no estimator. Asymmetry: independent directional fees; discusses inventory rebalancing, no coefficients. Volatility: GBM sigma 0.088–0.101%, no estimator. Size: lognormal/optimal routing, no implemented response. Timing: arb clipping before retail; no decay policy. Other values: 10,000 steps, 1,000 simulations, lambda 0.6–1.0, size sigma 1.2, initial reserves 100/10,000. Proposes stationary mispricing density, first-order optimization and DQN/PPO; reports no experiment.

**Errors to flag:** post-arb buy boundary is written `s'=p/gamma_+`, sell boundary `s'=gamma_-*p`: both are reversed. Correct values are **`gamma_+*p` and `p/gamma_-`**, respectively, from the [pinned arb and reserve formulas](https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_sim_rs/src/market/arbitrageur.rs). The note calls 19–21 the lognormal `mu`; official [configuration](https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_competition/competition/config.py) specifies the **arithmetic mean size**. Its reflected-Brownian description is an approximation, not the discrete engine. The page's edge signs conflict with its negative-arbitrage narrative; use engine scoring.

## Bruno I. / 4Byte Research: supplemental indexed social lead

[Indexed LinkedIn activity](https://hr.linkedin.com/in/bruno-i-8575b4b1), **Bruno I. / 4Byte Research profile**, exact date unavailable. The index labels it shared activity; original post authorship is unverified. Direct retrieval returned HTTP 999. Treat this as **indexed-only evidence**, not a revalidated article or code release.

The Simple-AMM post claims historical board rank **44**, with **no numeric edge score**. It attributes about **95% of edge** to stale-price directional protection and about **82% of cross-simulation performance variance** to arrival rate. No test design or uncertainty accompanies those percentages. Reportedly a linear fee model beat regime switching, sharper toxicity gating and post-trade smoothing.

Arb detection/fair-price inference: spot-versus-fair staleness is described, formula undisclosed. Asymmetry: directional protection. Volatility, inventory target, size response, decay coefficients and fee parameter values: not disclosed. No accessible linked code/commit established. The profile also contains a **separate Prop-AMM** post with triple-EMA parameters and roughly 480 score; those are deliberately excluded from Simple-AMM rankings and parameter recommendations.

## Substack: newsletter and unreadable X follow-up

[Daily Crypto News Recap](https://eli5defi.substack.com/p/daily-crypto-news-recap-6a2), **Zero and eli5defi**, **2026-02-09**, links “Anyone Tried AMM Challenge?” to [this X post](https://x.com/Eli5defi/status/2020753542596956435). No score, strategy, code or commit is published in the newsletter. The linked X page returned no readable text.

All requested mechanism categories—arb/retail detection, fair-price estimation, skew, volatility, inventory, size, fee decay/reset and parameter values—are **not disclosed in the readable newsletter**. Nothing technical is inferred from the headline.

## X: organizer launch, not a solution

[Original post](https://x.com/danrobinson/status/2019848425458807024); [readable TwStalker mirror](https://mobile.twstalker.com/danrobinson/status/2019848425458807024). Author **Dan Robinson**, naming **Benedict Brady** as co-builder. The post ID decodes to **2026-02-06 UTC**; this is an ID-derived date, not the mirror's relative timestamp.

No score, code or commit, arb classifier, fair-price estimator, skew formula, volatility estimator, inventory or size rule, decay constants, or fee parameter values. Describes hook-style changes after trades and competition for retail using edge. The “v2-like” competitor wording must not be read as fee reinvestment: the pinned engine keeps fees separate. Direct X text could not be authenticated here; the mirror is provenance for this announcement only, not authority for technical rules.

## Paradigm and pinned simulator: reference and baseline example

[Official explanation](https://www.paradigm.xyz/puzzles/amm/about/); simulator commit **6b6921f8d463314aa7c96234e1be25a25245f704**. Publication date not stated on the retrieved explanation. No numeric score claimed for its example.

The official example has symmetric opening fees **30 bps**. After a trade larger than **5% of post-trade Y reserves**, adds **10 bps**, clamped; otherwise subtracts **1 bps per callback** while above 30. No arb classifier, fair-price inference, volatility estimate or inventory target. Size response is a simple threshold; decay is per observed trade, **not elapsed wall time**. These details come from the [official example](https://www.paradigm.xyz/puzzles/amm/about/), not a competitive solution.

Simulator consistency checks used for evaluating the survey:

| Fact | Primary evidence / implication |
|---|---|
| 10,000 steps; 1,000 default evaluation simulations | [Pinned configuration](https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_competition/competition/config.py). |
| GBM; narrow per-step sigma | Configuration bounds **0.000882–0.001008**, not Prop-AMM's much wider volatility range; [configuration](https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_competition/competition/config.py). |
| Arb considered each step before retail | [Engine](https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_sim_rs/src/simulation/engine.rs). A trade executes only when profitable; “every step” does not guarantee a callback. |
| Arb ends at fee-band edge | [Arbitrageur](https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_sim_rs/src/market/arbitrageur.rs) with [net reserve updates](https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_sim_rs/src/amm/cfmm.rs): AMM sells X → `s'=p*(1-askFee)`; AMM buys X → `s'=p/(1-bidFee)`. Use the fee applying to the completed trade; afterSwap can change the next band. The code also has a 99%-reserve buy-size cap, so the boundary statement assumes that cap is inactive. |
| Poisson retail; lognormal size; two-pool split | [Official explanation](https://www.paradigm.xyz/puzzles/amm/about/): lambda 0.6–1.0, mean size 19–21 Y, log-space size sigma 1.2, equal buy/sell chance; optimal marginal-price routing. |
| Fees kept aside | [CFMM](https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_sim_rs/src/amm/cfmm.rs) has separate accumulated-fee buckets; fee income does not grow reserve product. |
| 32 slots; 250,000 gas each call | [Official constraints](https://www.paradigm.xyz/puzzles/amm/about/) and [base contract](https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/contracts/src/AMMStrategyBase.sol). `isBuy` is from the AMM's perspective. |

The HackMD errors above are material contradictions. Algebra's block ordering is compatible if “block” means simulation timestep. No source establishes an external oracle is available. The already-known repositories' historical ~522-level scores are not current leaderboard observations. There is no public paired comparison here meeting the assignment's 2,000-seed/fresh-holdout promotion rule.

## Mechanisms with no disclosed implementation in the inspected sources

These are research suggestions, not claims of global novelty or measured gains; private leader strategies are unknown. Generic state estimation, asymmetry, toxicity, inventory skew, volatility/arrival estimates and generic RL were already used or proposed and are not listed as new.

- Maintain a compact posterior over hidden fair price using exact arb-edge likelihoods versus a retail-mixture likelihood, and quote against posterior uncertainty rather than a single gated pHat.
- Use intervals with no callback as censored evidence about fair-price diffusion and missed routed flow, rather than only decaying state when a later trade arrives.
- Estimate retail size/rate jointly from router-censored fills instead of treating observed local trade count and size as unbiased market-flow samples.
- Optimize the last callback's fee for a mixture of another same-step retail order and next-step informed flow using an explicit finite-horizon value function distilled offline into a small Solidity policy.

## Official leaderboard: top ten

Read **2026-11-07 UTC**, directly from [Paradigm's API](https://www.paradigm.xyz/puzzles/api/v1/leaderboard?limit=10), cross-checked against the [leaderboard page](https://www.paradigm.xyz/puzzles/amm/). Metric is **average edge**, not average PnL or edge versus baseline. Each listed entry reports **1,000 simulations**. The API reported **743** participant entries. Submission dates below are `createdAt`, not write-up publication dates. Full returned precision is retained.

| Rank | Author | Strategy | Average edge | Submission date (UTC) |
|---:|---|---|---:|---|
| 1 | @0xMai | Curvance.com | 528.3992637207801 | 2026-11-06 |
| 2 | @Ponxter | Tide v7 | 528.3231880736478 | 2026-11-01 |
| 3 | @KaihuaQIN | MixZ11 | 528.2575935240054 | 2026-09-28 |
| 4 | @pxmwxd_eth | BranchedReturn | 528.2060777235199 | 2026-09-27 |
| 5 | @aaaapsouuu | OpalG5W6I0 | 528.0990216289588 | 2026-10-25 |
| 6 | @cybergenesis621 | Morphogenetically Mogged | 526.7765462820532 | 2026-10-04 |
| 7 | @ujiuifs | v5 | 525.3769622854322 | 2026-10-28 |
| 8 | @cktbot | call me bot | 524.8989933796349 | 2026-09-16 |
| 9 | @onblueroses | lvw | 524.8101934238463 | 2026-09-13 |
| 10 | @frok_ai | mevmogger | 524.6579809037315 | 2026-08-15 |

The source supplies scores, not standard errors. No mechanisms or code were disclosed by this API response.