Where the next seats should go

Shape Packing is the strongest candidate for a broad parallel search; Dogfight merits a small shared league first. No scout demonstrated a top-three place. Prop AMM and QEC need staged algorithm research, while Simple AMM needs a working scorer before its competitiveness can be assessed. This ordering is a synthesis of the five scouts, not a measured probability of success. [P, D, A, Q, S]

The table preserves the supplied headline numbers exactly, including QEC's .0 values. Public third-place numbers are the scouts' snapshots, not refreshed rankings; gaps are copied from their results. Scores across boards have different units and must not be compared numerically. All local execution claims below are attributed to the scouts; this write-up did not rerun their experiments. [P, Q, S, A, D]

Board	Did its scorer run? Requirements and elapsed setup	Shipped starter	Seat's best	Public third place	Gap to third
Shape Packing [P]	Yes, unmodified scorer. NumPy 2.5.4 and Shapely 2.2.0; optimizer also used SciPy 1.18.1, Numba 0.68.1, llvmlite 0.50.0 and Matplotlib. Initial clone-to-starter: 1.336886735757192 minutes, reconstructed from timestamps. Clean reproduction with cached wheels: 0.1707779485693512 minutes, including 0.13389777810079978 minutes for dependency installation.	3.5	2.9632137903187097	2.948526966725367	0.014686823593342613 radius units above third; lower wins.
QEC [Q]	Yes. Python3 venv, editable package install, NumPy 2.5.4, SciPy 1.18.1, Stim 1.16.0, PyMatching 2.4.0 and declared dependencies. Clone-to-installed: 1.1659051020940145 minutes; venv-to-installed: 0.8774246295293172 minutes (overlapping elapsed intervals, not additive). Starter scoring took 45.5184765830636 seconds, no timeouts.	3025.0	2876.0	2604.0	272 errors/M higher on the default grid; public-size replay: 3062, or 458 errors/M above third. Lower wins.
Simple AMM [S]	No. About 18 minutes of setup/build attempts: Foundry already present; installed uv, Rust 1.99.1, maturin 1.16.0, Python dependencies including numpy, pyrevm and py-solc-x, and compiler/linker runtime packages. Missing /proc, initially missing cc/ld and shared libraries; final linker failure: missing libjansson.so.4.	Unavailable (null)	Unavailable (null)	528.2575935240054	Not measurable: no local board-unit score.
Prop AMM [A]	Yes, native; final BPF validation and short parity checks also passed. Rust 1.99.1, Zig 0.14.1 cc/ar wrappers and crates; Rust install 0.45 minutes, first complete starter confirmed 655 seconds after installer attempt. Starter CLI total 7.0515 minutes, included in that elapsed interval. SBF tooling also required cargo-build-sbf 4.5.0 and platform-tools v1.57; successful tool build 55.35 minutes, overlapping research. Full BPF scoring timed out after 1860 seconds; no BPF-1000 score.	210.4964351516557	568.6003061725964	811.3914264336169	242.7911202610205 Y average-edge units short; higher wins.
Dogfight [D]	Yes, repository engine through a scout-written randomized-spawn harness, not a reproduced public tournament. Under 2 minutes setup: stable Rust (11 s), extracted libssl-dev after openssl-sys failure, release build (37 s, fetching ONNX Runtime); optional model-writing Python venv with numpy/onnx/onnxruntime (11 s).	0.4425	0.9933333333333333	-5291.40602119322	Not directly measurable: local score against Starter versus public rating. Scout's conditional rating estimate: -5252.4, +39.1 against third, only if the unknown reference opponents were as weak as Starter; not a demonstrated lead.

Shape Packing. The scout's random rotational starts reached 2.972197304446773, collective-move annealing reached 2.963499022119323, and crossover followed by polygon-tolerance/grid polish reached 2.9632137903187097; its evidence points toward a different contact arrangement rather than more polishing of the incumbent, without proving that the leaders share any topology. [P: tried, width, setup] Many seats would help explore distinct basins: the proposed split is 50 arrangement explorers, 25 crossover/basin-hopping workers, 15 collective-move annealers, 5 tolerance/grid polishers and 5 independent validators, exchanging contact graphs and diverse archives instead of duplicating the same search. [P: width] First search for a new contact topology, then reload finalists through the original six-decimal loader and validator; the scout's below-2.949 discovery milestone is still above the supplied third-place score, and the flagged external source means neither a published ring recipe nor an inferred leading arrangement should be treated as independently confirmed. [P: next, setup; source limitation below]

QEC. Weighted matching scored 3025 errors/M, corrected injected-error matching 2997, a row-Markov model 2902, and the final compact three-component column decoder with empirical posterior corrections 2876; this is substantial local work but not evidence that brute-force sampling will close the remaining gap. [Q: tried] Many seats could pool independent likelihood estimates and test competing inference models: start with the proposed 16-seat pilot—8 on the four hard high-correlation L7 settings, 4 on new decoder families and 4 on small-code floors/independent validation—then expand only after consistent unseen-seed gains. [Q: width, next] First reproduce both workload sizes and estimate reducible small-code loss: the default run needs at least 273 errors/M improvement to meet <=2603, whereas the public-size replay needs 111 fewer errors to reach <=624 errors and scorer score 2600; these are profile-specific budgets, not Bayes bounds or verified server thresholds, especially given the flagged sources. [Q: gap, width; source limitation below]

Simple AMM. The only recorded candidate is the shipped fixed 50 bps bid/ask strategy, with no score because the Rust extension never linked, so neither single-seat progress nor a top-three performance gap is established. [S: tried, setup, gap] Many seats become useful after a runnable scorer exists, splitting fixed fees, asymmetric bid/ask fees, trade-size responses and reserve/price-state responses, with separate reproducibility and finalist-validation seats using the same 1,000-simulation protocol plus fresh seed batches. [S: width] First repair and package the missing linker/runtime dependencies, reproduce the starter, then sweep fixed/asymmetric fees; the reported third-place number alone does not establish that this board is easy or hard. [S: next, third_place; synthesis]

Prop AMM. Adaptive fair-price/volatility quoting reached 437.5517751853003 on the full default batch, the rational quote model 537.1920597922142, and the selected learned-table blend 568.6003061725964; its separate evaluation mean was 564.0112124228319 and fresh frozen-source mean 594.4303245383276, leaving a substantial gap rather than a demonstrated podium route. [A: tried, gap] Many seats can research different algorithms, but the scout recommends a 12-seat pilot: 4 on price/state inference, 4 on quote curves/inventory, 2 on joint fee/learning objectives and 2 on blind evaluation/BPF correctness, with separate training markets and common final evaluation blocks. [A: width] First package the offline native/SBF toolchains and benchmark throughput, then use native full batches for research and BPF parity checks for finalists; the native scorer only changed output formatting for full precision, the server seeds are unpublished, and short BPF parity does not replace the unfinished full BPF run. [A: setup, next, gap]

Dogfight. Lead aiming began at 0.5425, slow-flight tuning reached 0.9862, and wrap-around pursuit eliminated sampled stalemates, but a neural exploiter reduced an intermediate rule to 0.73; the final 0.9933333333333333 is against Starter, while accurate rule opponents remain roughly even fights. [D: tried] Many seats help through a shared hall of fame, not isolated Starter-beating runs: the proposed 8 to 16 seats divide full neural self-play, independent exploiters, lost-match analysis and league/fresh-seed validation, and the public rating fit remains a scout inference with exceptions and unexplained refinement effects. [D: width, gap] First inspect losses and build stronger shared opponents while distilling to a plain MLP to reduce upload-op uncertainty; only a later manual operator entry can establish upload acceptance and performance against the private reference set, and no task should submit anything. [D: next, gap; task boundary]

Evidence limits and source trail

The five supplied JSON results are the primary evidence for this synthesis. They contain setup, starter_score, best_score, third_place, gap, tried, width and next; citations above identify these records and, where helpful, fields. Their embedded entries are deliberately omitted. The original result locations and exact input hashes are recorded here because the mounted input files are not committed with the deliverable:

• [P] Shape Packing result, supplied as .imd/reads/artifacts/item-packing; SHA-256 ae3c41fb8e2cde7e2da5215451de0f0d8f3b235c3f61b9f4c95d3bb098ed1cbf.
• [Q] QEC result, supplied as .imd/reads/artifacts/item-qec; SHA-256 48df5808d67f1ddbc7dc160f9eb0fa310f003cf207da5af5774338459b014725.
• [S] Simple AMM result, supplied as .imd/reads/artifacts/item-simple-amm; SHA-256 9116604251f1d60ed4e47ae05c489ec4f1e909c3a8c4fd114be22bc911673d79.
• [A] Prop AMM result, supplied as .imd/reads/artifacts/item-prop-amm; SHA-256 5b89de8581d1282ff2ea6a4ab30068c4d3a760e82092b96d8f3c402218dafd5d.
• [D] Dogfight result, supplied as .imd/reads/artifacts/item-dogfight; SHA-256 7c668643b930a45f74bdf25f8e6f0445da8f1722ea1df70d7659dbed76da2537.

The assignment flags 1 Packing source and 2 QEC sources as unreadable or unsupported on reread. It does not identify the affected URLs or passages, and the supplied JSON files do not include their external source lists; Packing mentions a separate sources.json, but it was not among the supplied inputs. Consequently the reported local runs remain scout observations, while their external corroboration is weakened: Packing's participant/leaderboard interpretations and QEC's public sample-size, baseline and third-place interpretations should be independently rechecked before spending heavily. This does not establish which particular claim failed; it prevents treating any of those external claims as verified here. The exact public numbers are retained as requested, with that qualification. [Assignment source warning; P: setup; Q: setup, tried, gap]

Public origins explicitly named in the inputs are the QEC repository at 96fb86f2499ee86b77ad72c9a358d4dbc3f6325e, the Prop AMM repository at 4f0c612c91eb1e3942ceedfe467db0414b1540b4, and the Simple AMM repository. Packing identifies scorer commit 78a78626f098cd236f3a09bb2cb242f72951599d without an explicit repository URL; Dogfight does not supply a repository URL in its result. These are provenance pointers, not pages independently verified by this write-up. [Q, A, S, P, D: setup]

The assignment's Paradigm Puzzles directory and Simple AMM leaderboard API provide the public starting points for an operator refresh; other boards use /puzzles/api/v1/BOARD/leaderboard, with BOARD taken from the actual page address. This report does not guess missing slugs or claim a fresh API read. [Assignment]

Recommended order

1. Shape Packing: first destination for broad parallel exploration. A directly scored radius gap and independent arrangement search make additional seats useful, although a new topology is still missing and success probability is unmeasured. [P; synthesis]
2. Dogfight: run the small shared league before expanding. Starter performance is strong, but opponent diversity and real rating/acceptance uncertainty are the bottlenecks; a hundred isolated optimizers would not resolve them. [D; synthesis]
3. Prop AMM: fund the proposed staged pilot. There is a reproducible native improvement and useful held-out evidence, but closing the edge gap requires better inference/quoting, with BPF throughput still a practical constraint. [A; synthesis]
4. QEC: stage likelihood research and small-code floor estimates. The measured gains are modest relative to the remaining gap, and public/default profile differences plus weakened external corroboration make immediate mass allocation hard to justify. [Q; synthesis]
5. Simple AMM: resolve the scorer build first, then reconsider its position. This is an ordering by current evidence and readiness, not a finding that the challenge itself has the lowest potential. [S; synthesis]