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Find where the 0.12 between this network's paradigm.xyz/puzzles/amm entry (QLX5, 528.3333, 4th) and #1 (528.452) could come from, and measure each source's ceiling before anyone builds anything.

Base: QLX5, Taylor (gtmcknight)'s solved policy (github.com/gtmcknight/amm-sim at 4812a6382311624e1506aca131ca35c378f930d9 research/solved) plus network extensions; source sha256 e183e5bc3fb794b7067703b10a7da9920267aa5f4caa968e16ca101b02338f40 in https://api.imd.fun/artifacts/1ef80bfb6d6791b877b1f4048a5e63cf2ae54153e6e8763ae3f8ab13132dfb15 (code_zb64.QLX5). Credit Taylor in every file.

Tools: the engine-faithful replica (equal to the engine within its printed precision on 512 seeds): https://api.imd.fun/artifacts/a1eef2f3dbbcbc7a1de9d15a2b22d1d25ac6d316a72efde67275b5d5a16ab16b, core https://api.imd.fun/artifacts/2ad2abf45223c729557e83e77d22de54c5db7da2be0599658144906b91dbf0f7, faster build https://api.imd.fun/artifacts/72b58a1407966f0223f06ab7c6ddd979a24fb4593f1a9b3dc43508a7f133d00b; table harness https://api.imd.fun/artifacts/9ad960e6c7e11509b81f2852f7f34d395425adc226141b0bc828ed6f5f344663; oracle-probe examples https://api.imd.fun/artifacts/6c23d23d4a21a37a502bf47a69d9f87b4c7ac84f614f2097e2488c6d5e6dd164 and https://api.imd.fun/artifacts/9d06411b9d249e074a426b33b08474edac375f300111ace5bb34928f853531e6.

Settled, do not repeat: perfect arb/retail labels +0.011 (se 0.007); perfect router split truth +0.004 (se 0.006); every QLX5 scalar constant at a local optimum; about 45 rule ideas and combinations (best +0.026); Taylor's tables (joint 1,393-node correction +0.011 on 2,048 report seeds; small gains overlap and do not stack); residual heads; price-belief variants; rival trackers; kappa.

Round 1, ceilings: one item each, on the replica, QLX5 given perfect knowledge of one hidden quantity at each own callback, all else unchanged: (a) the true fair price; (b) each run's true volatility; (c) each run's true retail arrival rate and size distribution; (d) the next trade's side and size; (e) everything the engine knows, with the best fee policy for that information searched or solved, not just QLX5 fed it (the full-information bound). Also one item that reads the engine source (amm_sim_rs) for any scoring or routing behaviour QLX5 does not use, and states each with a quick ceiling.

Round 2, only for sources whose ceiling advances: a realisable estimator or rule that captures part of it, on the replica, reporting the fraction captured.

Seeds: choose 64000..65023, report 10000..12047. result.json carries gain_vs_base, se, n, seeds, source_sha256 and advance (true only when the ceiling's mean − 2 se ≥ +0.08). Early-stop with score.py when mean + 2 se < +0.08. Batches of at most 5; every item requires {platform [linux-x64], minCpus 8}; caches under test/scratch/; full 64-character hashes in every brief.

No Solidity, no engine runs and no submissions in this goal.

The answer

Rank by measured mean	Headroom source and evidence	Measured “ceiling” gain	SE	n	Actual report seeds, inclusive	`advance`	Best realisable capture measured here
1	Next retail order's side and size — future-order oracle; restricted fee adapter	+55.741962	0.239707	2,048	10000..12047	true numerically	None measured. Foresight is unavailable to a strategy; requester excluded this from round two.
2	Full callback-time engine information — achieved search lower bound, optimum unresolved	+23.838254	0.275076	2,048	10000..12047	true numerically	None measured. Winning policy needs private price, rival state and the already-generated order queue.
3	True current fair price — fixed-QLX5 posterior replacement	+1.456614	0.013306	2,048	10000..12047	true	Particle filter, arm A: +0.021165, SE 0.016351, n=128, seeds 10000..10127; 1.4530% of this reference. Approximate, stopped; exact inferable fraction unresolved.
4	True run volatility — process-variance substitution	+0.028547	0.012706	128	10000..10127	false; early stop	Not commissioned: this substitution did not advance.
5	Engine behaviours: terminal fee oracle — one decision on the final step	+0.003894	0.001105	128	10000..10127	false; early stop	Not commissioned. Broader terminal relaxation: +0.026440 cap, SE 0.006966, same n/seeds; scope below.
6	True retail arrival/size law — selected likelihood-parameter mapping	+0.000569	0.007191	128	10000..10127	false; early stop	Not commissioned: this mapping did not advance.

All gains are paired changes in own-pool quote-asset edge per complete 10,000-step replica run. The ranking orders the reported means; the information sets, policy searches and kinds of bound differ. In particular, these six numbers are neither universal ceilings nor an additive explanation of the standings gap. “Realisable” here means using callback-visible information; contract cost has not been established.

Is 528.45 reachable from QLX5? There is no demonstrated route in these results, and no justified contract design to build next. Reachability remains unresolved. The supplied standings imply +0.1167 to reach 528.45, or +0.1187 to match #1 at 528.452 from 528.3333. The best measured callback-only candidate here is approximately +0.0212 with SE 0.0164 and a two-SE range spanning zero. It does not support a +0.12 forecast. These paired replica gains cannot be added to the supplied leaderboard score as a prediction.

Fair-price truth is the only advancing source pursued for realisable capture. It offers a large sensitivity, but both follow-up implementations explicitly failed to establish the requested exact posterior. Their small gains therefore do not prove that the remaining information is irreducible. The conditional contract sketch was not run because its gate failed. This closes the allocation with partial scientific findings, not an impossibility result. Fair-price result, particle result, grid result.

Credit: Taylor (gtmcknight), whose solved policy in gtmcknight/amm-sim at commit 4812a6382311624e1506aca131ca35c378f930d9 underlies QLX5. QLX5's network extensions and the supplied replica retain their contributors' credits. The baseline is the supplied code_zb64.QLX5, source SHA-256 e183e5bc3fb794b7067703b10a7da9920267aa5f4caa968e16ca101b02338f40, from the pinned baseline artifact. This report concerns the supplied standings and pinned research, not a fresh leaderboard check.

What the measurements establish

For seed i, the measured delta is candidate edge minus unchanged QLX5 edge on the same exogenous path. Reported SE is the sample standard deviation of those deltas divided by sqrt(n), with the n−1 sample-variance denominator. The rival remains the fixed 30-bps policy. A policy can change routing, inventories and subsequent callback opportunities; preservation of exogenous draws does not imply preservation of fills.

The prescribed report bank was 10000..12047, with score.py checks at n=128, 256, 512, 1,024 and 2,048. Workers stopped when mean + 2 SE < +0.08. A positive advance required the lower endpoint to reach +0.08; the recorded protocol also required all 2,048 report seeds and passing execution controls. The completed advancing results have lower endpoints +55.262548 for next retail order, +23.288101 for full information, and +1.430001 for fair price. The stopped round-one probes have upper endpoints +0.053960 for volatility, +0.014951 for retail law and +0.006104 for the terminal fee oracle. All stopping figures were recomputed from the supplied deltas for this write-up.

These repeated two-SE checks implement the requested screening rule. They are not an anytime-valid confidence sequence or a guarantee against selection error. SE across seeds also does not measure approximation bias in a filter. Unrun report seeds have no results assigned to them.

Selection remained inside the permitted choose bank, but several items used only prefixes:

Item	Actual choose/diagnostic use	Selection scope
Fair price	64000..65023, n=1,024	One prescribed posterior replacement; no fitted fee parameters. Choose gain +1.492901, SE 0.019280.
Volatility	64000..65023, n=1,024	One sigma-squared substitution. Choose gain −0.001319, SE 0.003926.
Retail law	64000..65023, n=1,024	Three fixed parameter mappings; selected the highest choose mean.
Next retail order	Screening 64000..64127; final comparison 64000..65023	55 arm evaluations, including repeats/controls, in groups of at most five; final selected mean +55.923961, SE 0.342372.
Full information	Search 64000..64031, refined to 64000..64063; off-controls through 64127	Three policy families; selected mean +22.590409, SE 1.178813 on 64 seeds.
Engine behaviours	Terminal probe/cap 64000..65023; rounding/dust diagnostics 64000..64127	One primary terminal mechanism. Diagnostic caps use unchanged choose trajectories.
Particle	64000..64031, n=32	Compared 512 and 2,048 particles; used 2,048 on report.
Grid	Four complete runs, 64000..64003; refinements on seed 64000 for 2,000 steps	Selected 8-bps spacing and eight joint parameter nodes; fine-resolution checks were short traces.

Sources: FP, VOL, LAW, NT, FI, AUDIT, PF, GRID. Each reports freezing its implementation before report evaluation. The prefixes and short refinement traces are limitations, particularly for posterior convergence; they are not the full planned choose bank.

Fair price: large truth sensitivity, small approximate capture

The fair-price intervention resets QLX5's log-price posterior mean to ln(current true price) and its current posterior variance to zero at each successful own callback, before the existing rival-price clipping and fee selection. It occurs after the triggering fill, so it cannot change that fill. Initialization and the fixed process variance remain unchanged; no callbacks are added during silent intervals. No true event label, run parameter, rival reserve or future order is supplied. The measured effect therefore includes the coupled mean-and-uncertainty reset and its later consequences. It is not the effect of changing the mean alone. FP

Its gain is +1.4566139111071181, SE 0.013306207949579568, n=2,048. The baseline and oracle means on this bank are 533.2560040516776 and 534.7126179627846. Those sample means also illustrate why this result is not a direct forecast from the leaderboard's 528.3333. It is a sensitivity of the existing QLX5 policy to truth; the optimal price-informed policy was not solved. FP

The requester's later note narrowed round two to a single deciding question: how much of that reference can be recovered by an exact posterior using everything available at own callbacks? Particle and grid methods were commissioned as two attempts at that measurement. Arm A infers run parameters from their laws and callback history; arm B additionally receives the actual run volatility and retail parameters as an oracle sensitivity. Arm B is not a callback-only capture.

Filter and arm	Gain vs QLX5	SE	n / report seeds	Mean + 2 SE	Fraction of +1.4566139111071181	Outcome
Particle A: callback-only inputs	+0.021165036359	0.016351362073	128 / 10000..10127	+0.053867760504	1.453030%	First-look stop; `advance=false`; sketch gate failed.
Grid A: callback-only inputs	+0.020141961941	0.015283153832	128 / 10000..10127	+0.050708269605	1.382793%	First-look stop; `advance=false`; sketch gate failed.
Particle B: true run parameters added	+0.021280721692	0.015620277501	128 / 10000..10127	+0.052521276695	1.460972%	First-look stop; parameter-truth sensitivity only.
Grid B: true run parameters added	+0.017761660423	0.014961759813	128 / 10000..10127	+0.047685180050	1.219380%	First-look stop; parameter-truth sensitivity only.

Sources: particle, grid. Percentages divide each reported point estimate by the full-bank fair-price reference. The denominator uses 2,048 seeds while the numerators use 128; these are descriptive capture ratios, without a joint ratio-confidence claim. As a scale comparison only, +0.1187 is 8.1490% of the truth reference, whereas the best measured A-arm point estimate captures 1.4530%. Neither percentage predicts leaderboard movement.

The A arms used callback side/amounts, own reserves, timestamps, own fees and the known process laws; they report excluding seed IDs, market RNG state, true prices, true labels, true rival reserves, drawn run parameters and future orders. The particle filter uses its own independent random stream. The grid tracks price, rival state, parameter uncertainty and hidden retail counts, with analytic inversion of continuous router relations. Both replace QLX5's belief through the supplied hook, preserving its other policy equations and tables. PF, GRID

The two A-arm outcomes agree on these seeds: particle minus grid is +0.001023074418, paired SE 0.012656452720, n=128, recomputed from their common-seed deltas. They must not be pooled as independent evidence or added together. Agreement also does not exclude shared approximation bias.

Both report recovering the same fair-price control on seeds 10000..10127: +1.472416081754699, SE 0.05109604665169002. This exactly matches the first 128 deltas of the original fair-price result. Hook-off/passive parity and exogenous-stream checks support the mechanics of the experiment, but do not establish the likelihood's exactness. Those execution claims were not rerun during this write-up. FP, PF, GRID

Where the filters improve price error

The following are passive measurements on unchanged QLX5 trajectories. They compare both beliefs against true contemporaneous price at the same callbacks. True prices and event labels are used for diagnostics after inference, not as A-arm inputs.

Method and callback class	QLX5 RMSE, bps	Approximate posterior RMSE, bps	Callbacks	Passive seeds
Particle: all	7.086835	7.054083	1,386,726	10000..10127, n=128
Particle: arbitrage	0.602288	0.305614	486,154	Same 128 seeds
Particle: retail	8.782899	8.750518	900,572	Same 128 seeds
Grid: all	7.111594	7.088328	348,145	10000..10031, n=32
Grid: arbitrage	0.503472	0.130631	121,537	Same 32 seeds
Grid: retail	8.807023	8.785379	226,608	Same 32 seeds

Particle error is 10,000 × RMS log-price error. Grid error is RMS of 10,000 × (estimated price / true price − 1), where estimated price is the exponential of the filter's log-price mean. Different definitions and samples prevent a direct cross-method RMSE ranking. The grid scoring experiment still used 128 seeds; only its passive audit used 32. PF, GRID

Within each method, arbitrage error falls substantially, while retail error changes little and remains much larger. This is consistent with the small measured fee-score gains. It does not quantify how much of the remaining retail error is fundamentally unobservable. Passive nominal-95% interval coverage was 97.8574% for particle and 98.4969% for grid; conservative coverage and posterior atoms do not certify an exact posterior. PF, GRID

The exact-posterior requirement remains open for specific reasons:

Both methods use continuous observation densities and Taylor's tell/lattice approximations instead of integrating the complete binary64/WAD rounding preimages of the joint callback observation. Some available low-bit router evidence is omitted, and the extreme 99%-reserve arbitrage cap is not separately integrated in the likelihood.
The particle result uses 2,048 particles, resampling, finite path histories and parameter rejuvenation. Its 512-versus-2,048 comparison on 32 choose seeds supplies no convergence certificate or bias bound.
The grid result uses 8-bps price/rival grids, two prior quadrature nodes per run parameter, eight joint parameter states, truncated hidden-order integration and an idealized constant-product rival. Finer grids and three-node parameter checks cover only one 2,000-step choose trace, not complete-run score convergence.

The particle result explicitly records exact_posterior_established=false; its controls.passed=true applies to mechanical controls. The grid records controls.passed=false, execution_controls_passed=true and exact_posterior_requirement_passed=false. Administrative acceptance of these reports does not change those scientific qualifications. Consequently, the requester's “otherwise irreducible” conclusion cannot be supported by these approximate measurements. PF, GRID

What the other oracle sources mean

The next-trade item actually reveals the next distinct retail order, before routing, rather than the next own fill or an arbitrage-inclusive next event. Its size is quote notional; a future sell's native-X size is not supplied. The next order may be in a later timestamp, with unobserved arbitrage in between. The replica copies the retail RNG to peek without consuming the live stream. The intervention also changes the fee returned at initialization, in addition to own swap callbacks. This initialization exposure and narrower event definition should be retained as differences from a strict swap-callback-only reading of the requested probe. NT

The selected adapter computes z = clamp(next size / (0.002 × own Y reserve) − 1, −1, 4), adds 5 + 17z bps on the predicted side and subtracts 11 bps on the opposite side, preserving the fee cap and gamma guard. Its +55.741962 is an achieved gain from a restricted three-coefficient search with future knowledge. It is neither a universal upper bound nor evidence that order prediction from callback history is possible. No estimator or capture fraction was measured for this source; an absent measurement is not zero. NT

The full-information item searched fee policies, rather than only injecting truth into QLX5. Its winning rule acts at a retail callback with another already-generated order in the same timestamp. It accounts for the pending rival fill, searches the next order's fee over 0..1,000 bps in 50-bps coarse steps, then applies 15 golden-search refinements around the best point. It keeps the other QLX5 fee and falls back to QLX5 when no eligible next order exists. Current true price, rival state and the private queue are used; no next-timestamp draws are used. FI

This achieves +23.838253663028897, SE 0.27507639991996496, over 2,048 report seeds. It is a lower bound on the value attainable with that engine-private information. The local one-order optimization ignores later value and has no global optimality guarantee across routing discontinuities. The smaller gain than the next-retail oracle is not a certified optimization gap: the latter sees across timestamps and acts at initialization, and the searched policy families differ. FI, NT

The full-information report also supplies a very loose pathwise upper envelope: each retail order's positive own edge is at most its quote-notional input, arbitrage contributes nonpositive edge, so total edge is bounded by the sum of retail notionals, with a 0.001 numerical allowance per run. On report paths, its mean bound minus QLX5 is +159,185.816529, SE 523.669587, n=2,048, seeds 10000..12047; the reported mean upper-minus-achieved gap is 159,161.978275. The report calls this bound certified, but this write-up has not independently certified its numerical allowance. Even taken at face value, it does not locate the full-information ceiling anywhere near the precision needed here. FI

The volatility probe replaces only QLX5's process-variance slot with the true run sigma squared after each own fill. It leaves initialization, tables, posterior state and the silent-step handling unchanged. Its first-look upper endpoint +0.053960 fails the +0.08 continuation screen. This closes that substitution, not every possible volatility-conditioned policy. VOL

The retail-law probe supplies the exact Poisson rate and full-order lognormal parameters, but QLX5's fitted likelihood concerns the first own fill after routing and selection. The worker compared three midpoint-preserving maps on choose seeds; the selected map scales QLX5's rate weight by lambda/0.8, shifts its log-mean by the change in the true full-order log-mean, and preserves the existing shape because the run's log standard deviation is fixed at 1.2. Its +0.000569, upper endpoint +0.014951, closes this approximate transport. It does not bound a freshly solved routing-conditioned likelihood or reoptimized tables. LAW

Engine scoring and routing audit: quick ceilings and exclusions

The audit read amm_sim_rs and the competition caller in benedictbrady/amm-challenge at commit 6b6921f8d463314aa7c96234e1be25a25245f704. It reports checking formula/order alignment with the supplied replica and the core's pinned provenance. This is a separate engine-source pin from Taylor's strategy repository. The supplied 512-seed printed-precision parity was inherited, not rerun. Neither public source nor inherited parity independently proves the live leaderboard binary/configuration. All entries below are from the engine-behaviours result. File/line references are at that engine pin.

Behaviour and source locus	Quick ceiling or exclusion	Scope and decision
Final-step fee opportunity; `simulation/engine.rs:136–180`, `market/router.rs:181–249`	Fee oracle +0.003893548970, SE 0.001105287207, n=128, 10000..10127. Broader relaxed cap +0.026439950457, SE 0.006966149108, same seeds; upper two-SE +0.040372248673.	At first own callback of t=9999, search 43×43 fee pairs using true price, rival reserves and remaining orders. Later fees follow QLX5. The cap allows arbitrary later fee choices from that callback but uses ideal CFMM arithmetic plus a numerical allowance. It excludes earlier anticipatory policies and is not interval-certified. No advance.
Terminal inventory/PnL; `simulation/engine.rs:141–164,183–216`, `competition/match.py:168–188`	Exactly 0 direct score improvement from changing terminal valuation alone.	The competition sums trade edges; terminal mark-to-market PnL is separate. Holding fills fixed, there is no liquidation or final-price scoring bonus to recover.
Retail output WAD roundtrip; `types/wad.rs:30–40`, `market/router.rs:198–244`	Mean direct-error cap 7.03789336238333e−11, SE 8.757230069646189e−13, n=128, choose 64000..64127.	Bound sums conservative rounding envelopes on unchanged baseline fills. It excludes routing/classification/path changes and assumes finite nonsaturating arithmetic. Too small as a direct scoring effect.
Side-asymmetric router dust; `market/router.rs:188–244`	Mean gross-input cap 0.004508218487429125, SE 0.0004440842175567628, n=128, choose 64000..64127.	Legs execute only for input >0.0001, in the input token, and dropped allocations are not reassigned. Cap covers positive baseline own allocations that were skipped, valued even with free output. A fee-changing policy's dynamic dust ceiling is unmeasured.
Continuous splitting and fee aliases; `market/router.rs:40–118`, `amm/cfmm.rs:119–196`	0 extra pricing action from aliases mapping to the same binary64 fee/gamma.	Routing continuously splits; ties do not award the entire order to the first pool. QLX5 already uses split arithmetic and guards the vanilla-gamma preimage. This is not a zero bound on all floating-point path effects.
Own-first callbacks and frozen allocations; `simulation/engine.rs:120,136–163`, `market/router.rs:196–280`	0 ability to reprice the triggering fill or its already-computed rival allocation.	Callback fees affect subsequent orders. There is one arbitrage attempt per pool per step and no second arbitrage pass after retail. Subsequent-order benefits belong to other probes.
Separate fee buckets, reserve arithmetic and arb cap; `amm/cfmm.rs:119–284`, `market/arbitrageur.rs:54–138`	0 direct gain from counting/compounding fee buckets again for fixed fills.	Existing QLX5 tells already use these operations. The 99%-X-output arb cap is outside ordinary near-price states; no universal extreme-state dynamic cap is established.
Revert fallback, legal-fee decoding and gas; `amm/cfmm.rs:293–298`, `types/trade_info.rs:116–134`, `evm/strategy.rs:31–34,179–188`	0 extra fee action from deliberately reverting; 0 direct edge from gas savings with fixed fills.	A failed callback retains prior fees, an action already available by returning them. Malformed or >10% fees are rejected. Replica omits EVM gas/rollback behaviour, so no engine-exploit conclusion is claimed.
Configuration and RNG paths; `competition/config.py:26–47`, `competition/match.py:99–138`, `simulation/engine.rs:51–70`	No separate measured ceiling.	Active Python configuration sampling matches the replica; a different Rust helper is not on that caller path. Price and retail streams are separate. Hidden-law and next-order effects are delegated to their round-one probes.

The terminal oracle, its relaxation, dust and rounding figures must not be summed. They are overlapping mechanisms measured under different restrictions. No engine behaviour supplied a qualifying new lead; dynamic dust and extreme-state policy effects remain unmeasured rather than ruled out globally.

Build decision and remaining evidence

Keep QLX5 as the implementation baseline. No contract change in this allocation has a supported expected gain sufficient to reach 528.45. The best measured callback-only point estimate is the finite particle filter's +0.021165, with substantial sampling uncertainty, unresolved numerical bias and no contract-cost validation. The grid offers essentially the same measured scale. True-parameter arm B does not improve that conclusion.

If the question is reopened, the deciding research remains the one the requester specified: complete the exact observation likelihood, including rounding preimages and hidden rival/arrival state; establish full-run numerical convergence; then evaluate the frozen posterior-to-QLX5 replacement with the stated seed split and controls. Only a validated posterior result of at least +0.15 on the full report bank would justify the conditional cheapest-approximation sketch. That sketch would need a measured capture and evidence for ≤50,000 source characters and ≤245,000 peak afterSwap gas. No such capture, size or gas estimate exists in these results, so none is invented here.

Two scientific deliverables remain unresolved: the exact callback-inferable price fraction, and a tight optimized full-information ceiling. The next-retail measurement also differs from a literal next-event, swap-callback-only experiment as disclosed above. These gaps prevent declaring 528.45 impossible, declaring fair-price headroom irreducible, or claiming that every source has been tightly bounded. They do support withholding a new build recommendation.

The objective's settled scalar, rule/table, label/split, residual-head, prior belief, rival-tracker and kappa work was treated as prior evidence and not rerun. No joint estimator/rule combination was measured in this allocation; earlier small gains cannot be stacked with these figures.

Batch and closeout record

The goal record shows eight accepted research results across the first three batches, and one conditional sketch item cancelled as not_run. All four batches specify requires={"platform":["linux-x64"],"minCpus":8} and have at most five items. The notes/brief previews require caches under test/scratch/, Taylor credit, replica-only work, no Solidity, no engine runs and no submissions. Full original briefs are not present: goal.json contains shortened previews. The following records the per-item work and expected evidence from the objective, notes and results; it does not invent missing verbatim briefs or launch another batch.

Batch	One item's piece of work	Required result content	Recorded outcome
`r1-oracle-ceilings`, 5 items	Each item handles exactly one of fair price, run volatility, retail law, next trade, or full information. The full-information item searches/solves a fee policy.	`result.json` with gain, SE, n, seeds, source hash, advance, exposure/timing, selection, controls, stop history and scope of ceiling.	Five accepted reports. Three numerical advances; substantial bound limitations disclosed above.
`r1-routing-audit`, 1 item	One item reads engine scoring/routing behaviour and assigns each finding a quick ceiling, with a primary replica probe.	Same numerical fields for the primary probe; source loci, per-behaviour caps/exclusions, assumptions and unmeasured effects.	Accepted; primary probe stopped at 128 report seeds.
`r2-exact-posterior`, 2 items	Each item attempts one posterior method, particle or grid, with A/B arms and passive error diagnostics.	Standard numerical fields, fraction of the fair-price reference, RMSE by callback type, information isolation, truth/off controls, approximation/convergence disclosure and `gates.posterior_ge_015`.	Both reports accepted as measurements; neither established exactness; both gates failed.
`r2-contract-sketch`, 1 conditional item	One item, paired to particle, sketches the cheapest contract-feasible approximation only after `gates.posterior_ge_015 == "pass"`.	Capture vs posterior and truth reference, size/gas estimates with estimation method and limit assessment.	Gate-cancelled, `not_run`; no sketch evidence exists.

All batches are settled. trunk is null in the supplied goal record: this research goal has no produced code repository or merged wave commit to name. Taylor's repository/commit and the audit's engine repository/commit above are source provenance, not a new goal build. Worker research implementations are carried in their result artifacts. This deliverable is only report.md.

For the closeout record, the decision is one JSON object in the reference's shape, embedded here to preserve the requested single-file output:

{
  "notes": "Credit Taylor (gtmcknight), amm-sim research/solved at 4812a6382311624e1506aca131ca35c378f930d9, and QLX5 network extensions. Close this allocation with eight research results. No measured callback-only route to the supplied 0.1187 gap; exact posterior inferability and a tight full-information ceiling remain unresolved. The conditional contract sketch did not run. No new batches or build recommendation.",
  "spawn": [],
  "finish": true
}

Evidence identity and checks on this write-up

Every supplied result's raw bytes were checked against the requester-pinned SHA-256. The embedded paired data were decoded as data, their supplied payload hashes verified, and all eight headline means, SEs and n values recomputed. Both B arms, all five checkpoints of each full-bank oracle, the A-arm paired comparison and the capture ratios were also checked. Reproduction source/patch bundle hashes were verified in memory; no embedded commands, simulation, engine, Solidity build or submission were executed for this write-up. These checks establish internal consistency, not independent experimental replication.

The plane flags sources for fair price, volatility, retail law and engine behaviours without giving reasons. Those flags are disclosed, not explained away. The unflagged results are not independent method certification either. Mechanical controls, source alignment and inherited engine parity remain worker-reported evidence except for the artifact/statistical checks just described.

Result hashes identify the input JSON bytes. source_sha256 identifies each worker's measured implementation under its declared hash scope; it is distinct from both the result hash and the common QLX5 baseline hash.

Input / citation	Result JSON SHA-256	Measured `source_sha256` and scope
`b01-fair-price` / FP	`c9ac833b4a6837bf0bd56fc2c4b931ef58d34dc98a000278ee4cec091fb216ee`	`bd90489648c1112a14767bd0befbefc9687cd32f68ae647860cf8929ed5f966d`; sorted runtime filenames and bytes with NUL separators.
`b01-run-volatility` / VOL	`9f16f7d816edaff1d23de863f4f2149b1823b2842856cb8a0b41f986442226b0`	`2092df4f2801811a7c17a658ca0a601ae4416b0ffd212fdc40f6333faf9c9310`; measured `core.hpp`.
`b01-retail-law` / LAW	`ef182bcb6b8d517b486b508ecf6969451bc7fa7da9ccced5fb76033d19f2117a`	`c72de3145ffb1d049dc254397533c72efe8ceb01bbf82c1c0a44f3535c7babcc`; probe `policy.hpp`.
`b01-next-trade` / NT	`19a9830766394638451d952df2f20e3a66d25059305d112fe0dd0ec47b7701f1`	`7adb2807e9e6e48ac41d449c5840016a761f96f73e79374c7598297b5b65ee0c`; probe `core.hpp`.
`b01-full-information` / FI	`7aef6cf758ba6716bcfcbfa89a011cfc40a1bcadaae5fd3548e572ff96f1e50a`	`56cde84d17fef731c3608ba3a564ddbc0074060247c27b4f51418add6b173e80`; `oracle/oraclepolicy.py`.
`b02-engine-behaviours` / AUDIT	`5b2315dfcf16f8f0040df6f5db14b27f68e24ebae38b6b15350ee85425d016c0`	`498b799e13b2543f9117420ccc2a37f94c418bdc6657257d2ef7280b0c8742ce`; decoded compact JSON source map.
`b03-particle` / PF	`3310b67bbc4b909c06e9623fe6e0fdc7d4d8fac21093abe25467f5400d61c5a9`	`eb43f176d444c38407937639655ed965e67386c15d48889e68e61fb1eb79575c`; sorted compiled runtime filenames and bytes with NUL separators.
`b03-grid` / GRID	`d9475f9a38366c72168c33423e2fbe84754883cb7312d9a47d22887c151511e7`	`8110ed30d87ab08fa381b58cf35fb218f61d1d7162dcb52ca2c6d66edb963165`; sorted runtime filenames and bytes with NUL separators.

The source corpus is the baseline, engine-faithful replica, core, faster-build metadata, table/scoring harness, and the two oracle-probe examples. The exact scoring script hash recorded by the results is 38856d193fa9f8e8a7ca0e43b62778f5d9f7b8a6bc7bf67168843ca1e03c6958. The result links below retain the full 64-character artifact identities, so the findings and their limitations remain traceable after temporary read inputs are removed.

report.md

The swarm

finishedran 1 h 42 minItems, page by page →

Round 1r1-oracle-ceilings5 of 5 backr1-routing-audit1 of 1 back
Agent #1342 planned it. Started 7 min after the job was posted.
what r1-oracle-ceilings was asked
Credit Taylor (gtmcknight), github.com/gtmcknight/amm-sim@4812a6382311624e1506aca131ca35c378f930d9 research/solved, in every file. One research item, under 1h; caches test/scratch/. No Solidity, engine builds/runs, submissions or realisable estimators. Fetch JSONs via https://api.imd.fun/artifacts/ + full ID: base 1ef80bfb6d6791b877b1f4048a5e63cf2ae54153e6e8763ae3f8ab13132dfb15 replica a1eef2f3dbbcbc7a1de9d15a2b22d1d25ac6d316a72efde67275b5d5a16ab16b core 2ad2abf45223c729557e83e77d22de54c5db7da2be0599658144906b91dbf0f7 fast 72b58a1407966f0223f06ab7c6ddd979a24fb4593f1a9b3dc43508a7f133d00b harness 9ad960e6c7e11509b81f2852f7f34d395425adc226141b0bc828ed6f5f344663 probes 6c23d23d4a21a37a502bf47a69d9f87b4c7ac84f614f2097e2488c6d5e6dd164 probe2 9d06411b9d249e074a426b33b08474edac375f300111ace5bb34928f853531e6 Decode base.code_zb64.QLX5; verify SHA256 e183e5bc3fb794b7067703b10a7da9920267aa5f4caa968e16ca101b02338f40. Verify fetched artifact IDs. Use replica; fast links its build_result_url; harness supplies score.py. Task {{source}}: {{task}} Expose only assigned truth at each own callback. For single sources keep all other QLX5 logic/constants/tables fixed. Oracle-off must equal QLX5; preserve event order, RNG draws and callback opportunities. Distinguish QLX5 sensitivity from a universal upper bound. Choose only 64000..65023; freeze before report 10000..12047. Pair complete runs against unchanged QLX5 with identical exogenous RNG, rival and scoring. At report n=128,256,512,1024,2048 run score.py --base base.csv --candidate probe.csv --bar 0.08; stop when mean+2*se<0.08. Report actual n/seeds; no report tuning. advance=true only after all 2048 report seeds if mean-2*se>=0.08 and controls pass. Do not repeat settled labels, router-split truth, scalar tuning, 45 rules, tables, residual heads, price-belief variants, rival trackers or kappa. Write result.json: credit, source, gain_vs_base (mean paired edge delta), se (sample SD/sqrt(n)), n, seeds {choose,report}, source_sha256 (measured probe), base_source_sha256, advance, stop/history, info/timing/units, controls, ceiling_kind/limitations, search details, hashes/hash_scope, reproducible patch/commands and compressed per-seed deltas. Keep it <=64000 bytes; unknowns null with reason, never invented gains.
what r1-routing-audit was asked
Credit Taylor (gtmcknight), github.com/gtmcknight/amm-sim@4812a6382311624e1506aca131ca35c378f930d9 research/solved, in every file. One static-source audit plus quick replica ceilings, under 1h; caches test/scratch/. No Solidity, engine builds/runs, submissions or realisable estimators. Fetch JSONs via https://api.imd.fun/artifacts/ + full ID: base 1ef80bfb6d6791b877b1f4048a5e63cf2ae54153e6e8763ae3f8ab13132dfb15 replica a1eef2f3dbbcbc7a1de9d15a2b22d1d25ac6d316a72efde67275b5d5a16ab16b core 2ad2abf45223c729557e83e77d22de54c5db7da2be0599658144906b91dbf0f7 fast 72b58a1407966f0223f06ab7c6ddd979a24fb4593f1a9b3dc43508a7f133d00b harness 9ad960e6c7e11509b81f2852f7f34d395425adc226141b0bc828ed6f5f344663 probes 6c23d23d4a21a37a502bf47a69d9f87b4c7ac84f614f2097e2488c6d5e6dd164 probe2 9d06411b9d249e074a426b33b08474edac375f300111ace5bb34928f853531e6 Decode base.code_zb64.QLX5; verify SHA256 e183e5bc3fb794b7067703b10a7da9920267aa5f4caa968e16ca101b02338f40. Verify fetched artifact IDs. Use replica; fast links its build_result_url; harness supplies score.py. Read github.com/benedictbrady/amm-challenge@6b6921f8d463314aa7c96234e1be25a25245f704/amm_sim_rs statically; verify provenance against replica. Find scoring/routing behaviours QLX5 does not use: trace engine scoring/terminal valuation, router/CFMM rounding/ties, callback timing and config. For EACH new behaviour cite pinned file:lines, compare QLX5 use, and estimate an analytic ceiling or isolated replica oracle gain with assumptions and overlap. Preserve legal fees, event order, RNG and rival. Oracle-off must equal QLX5. Pick one primary mechanism using choose seeds before report; never cherry-pick report winners or sum overlapping gains. Choose only 64000..65023; freeze before report 10000..12047. Pair complete runs against unchanged QLX5 with identical exogenous RNG, rival and scoring. At report n=128,256,512,1024,2048 run score.py --base base.csv --candidate probe.csv --bar 0.08; stop when mean+2*se<0.08. Report actual n/seeds; no report tuning. advance=true only after all 2048 report seeds if mean-2*se>=0.08 and controls pass. Do not repeat settled labels, router-split truth, scalar tuning, 45 rules, tables, residual heads, price-belief variants, rival trackers or kappa. Write result.json with credit, source, gain_vs_base, se, n, seeds, source_sha256, base_source_sha256, advance for the primary; behaviours[] with citations, QLX5 comparison, ceiling_kind, numerical ceiling/units, assumptions and the same statistics for each measured mechanism; controls, stop/history, limitations, hashes/hash_scope and compact reproducible patch/commands plus compressed per-seed deltas. Analytic caps alone cannot set advance. If none new, show inspected coverage and reasons, null gain/se, n=0, advance=false; unmeasured is not zero. <=64000 bytes.
the whole memo
Credit Taylor (gtmcknight), github.com/gtmcknight/amm-sim@4812a6382311624e1506aca131ca35c378f930d9 research/solved, in every file. Episode 1/3: goal.json has 0/24 items used, no batches, results, requester notes or refusals. Schedule exactly six round-one research items: five oracle ceilings and one static engine scoring/routing audit, in batches of five and one. All require linux-x64 and minCpus 8. This reserves 18 items and two episodes for evidence-led follow-up. No round-two estimators are commissioned yet; no Solidity, engine execution or submissions anywhere. QLX5 source SHA256 e183e5bc3fb794b7067703b10a7da9920267aa5f4caa968e16ca101b02338f40; goal's supplied standings gap is 528.452-528.3333=0.1187. That leaderboard gap is context, not a paired-seed gain. Credit Taylor and his pinned solved policy in every file; network extensions remain in the baseline. The public artifact JSONs were readable with curl. Base has code_zb64.QLX5; replica/core contain code_zb64 archives. Fast artifact is verification metadata linking build_result_url, not a standalone bundle. Harness implementation_zb64 decodes to a JSON source map containing score.py, whose CSVs require seed,edge and explicit --bar 0.08. Its score is the mean of paired candidate-base edges and sample SD/sqrt(n); its stop is strict upper_2se<bar. Historical example advance fields and 0.03 stop lines are irrelevant to this goal. No artifact code or simulations were executed here. The Taylor fork's amm_sim_rs path at the supplied commit returned HTTP 404. Verified the static engine directory at https://github.com/benedictbrady/amm-challenge/tree/6b6921f8d463314aa7c96234e1be25a25245f704/amm_sim_rs via GitHub API; audit must check alignment with replica provenance, cite file lines/hashes and disclose mismatch. This does not change QLX5's pinned baseline or authorize running the engine. On episode 2, read all six individual JSONs (requested below); check full hashes, actual report seeds, oracle-off equality, legal callback timing, RNG preservation, uncertainty and info-set isolation. Selection is 64000..65023 only, held-out report 10000..12047 with prescribed score.py early stops. advance requires complete 2048 report seeds, controls and mean-2se>=0.08. Stopped probes retain actual n/range; do not label insufficient or unmeasured evidence a zero ceiling. A low QLX5 truth-injection gain bounds that adapter, not all possible uses of the information. A searched full-information policy is an achieved lower bound unless supported by a certified upper bound or gap; full information must optimize fees, not merely replace QLX5 inputs. Treat future-path relaxations separately from information available at callbacks. Round 2 ONLY for validated advancing sources: assign one realisable estimator/rule per source using callback-visible history alone, on the same replica and seed split; carry parent result URL and exact ceiling, report paired gain/se and fraction captured=gain_vs_base/parent ceiling gain. Full-info advances require a justified observable approximation, not latent truth, seed IDs or future draws. Audit behaviours need their own qualifying measured ceiling; a positive analytic cap alone does not authorize round two. Reserve episode 3 to assess results, audit overlap and finish a research account with limits. Repair genuinely failed/invalid ceiling work within remaining budget if needed; never rerun the settled topics. Do not add source gains without measuring joint overlap. If nothing qualifies and ceilings are adequate, finish without building estimators. Wake when both batches settle; no periodic wake is set because only two decision episodes remain. If an external wake arrives early, preserve running work and wait for it. Do not relax the requester's linux-x64/minCpus 8 requirement. No cancellations now.
1 step
r1-oracle-ceilings, item by item r1-routing-audit, item by item
Round 2r2-exact-posterior2 of 2 backr2-contract-sketch0 of 1 back, 1 cancelled
Agent #1299 planned it.
what r2-exact-posterior was asked
Credit Taylor (gtmcknight), github.com/gtmcknight/amm-sim@4812a6382311624e1506aca131ca35c378f930d9 research/solved, in every file. One research item, under 1h, replica only, caches under test/scratch/. No Solidity, engine runs or submissions; no gas or size limit. Artifacts, https://api.imd.fun/artifacts/<id>: base 1ef80bfb6d6791b877b1f4048a5e63cf2ae54153e6e8763ae3f8ab13132dfb15 (code_zb64.QLX5, sha256 e183e5bc3fb794b7067703b10a7da9920267aa5f4caa968e16ca101b02338f40); replica a1eef2f3dbbcbc7a1de9d15a2b22d1d25ac6d316a72efde67275b5d5a16ab16b; harness (score.py) 9ad960e6c7e11509b81f2852f7f34d395425adc226141b0bc828ed6f5f344663; ceiling c9ac833b4a6837bf0bd56fc2c4b931ef58d34dc98a000278ee4cec091fb216ee (QLX5 fed the true fair price at each own callback: +1.4566139111071181, se 0.0133, n 2048; its reproduce.source_lzma_b85 is the replica with a hook setting QLX5's belief m, v). Do: measure how much of that gain a strategy can infer. Compute the exact Bayesian posterior of the fair price at each own callback, as {{method}}. Inputs: only what QLX5's callbacks receive (side, amounts, own reserves, timestamps, own fees) and the engine's laws as the replica codes them: the price process and the law of its parameters, exact arbitrage sizing (an arb fill pins the price, a step without one bounds it), the retail law, the router split, the 30 bps rival. Never the seed, RNG state, true price, true labels, rival reserves, the run's drawn parameters or the future. Arms, paired by seed with unchanged QLX5. A: QLX5 with m := posterior mean of ln price and v := posterior variance replacing its Gaussian filter, all else unchanged. B: A with the run's true volatility and retail parameters given to the filter. Filter gap, on unchanged QLX5's trajectory with the posterior run passively: RMSE in bps against the true price of QLX5's m and of the posterior mean, over all, arb and retail own callbacks. Seeds: tune on 64000..65023, freeze; report 10000..12047 with score.py --bar 0.08 at n = 128, 256, 512, 1024, 2048, stopping when mean + 2 se < 0.08. Controls: hook off equals QLX5 exactly; true price with v = 0 through your hook gives the ceiling's 1.472416081754699 on 10000..10127; exogenous draws unchanged; posterior coverage of the true price. Result: one JSON object: gain_vs_base, se, n, seeds, source_sha256, base_source_sha256, advance (true only when n = 2048 and mean - 2 se >= 0.08), fraction_of_ceiling (gain_vs_base / 1.4566139111071181), arm_b {gain_vs_base, se, n}, filter_gap {qlx5_rmse_bps, posterior_rmse_bps, each {all, arb, retail}}, gates {posterior_ge_015: "pass" only when arm A ran all 2,048 report seeds, controls pass and gain_vs_base >= 0.15, else "fail"}, approximations, stop history, controls, limitations, per-seed deltas, source to reproduce offline.
what r2-contract-sketch was asked
Credit Taylor (gtmcknight), github.com/gtmcknight/amm-sim@4812a6382311624e1506aca131ca35c378f930d9 research/solved, in every file. One research item, under 1h, replica only, caches under test/scratch/. No Solidity, engine runs or submissions. Artifacts, https://api.imd.fun/artifacts/<id>: base 1ef80bfb6d6791b877b1f4048a5e63cf2ae54153e6e8763ae3f8ab13132dfb15 (code_zb64.QLX5, sha256 e183e5bc3fb794b7067703b10a7da9920267aa5f4caa968e16ca101b02338f40); replica a1eef2f3dbbcbc7a1de9d15a2b22d1d25ac6d316a72efde67275b5d5a16ab16b; harness (score.py) 9ad960e6c7e11509b81f2852f7f34d395425adc226141b0bc828ed6f5f344663; ceiling c9ac833b4a6837bf0bd56fc2c4b931ef58d34dc98a000278ee4cec091fb216ee (QLX5 fed the true fair price at each own callback: +1.4566139111071181, se 0.0133, n 2048). Parent: {{after.result}} (item {{after.key}} of {{after.batch}}): the exact posterior of the fair price from callback-visible data, fed to QLX5 in place of its Gaussian filter, gained at least +0.15 over QLX5 on the report seeds. Read its gain_vs_base, filter_gap, approximations and source. Do: sketch the cheapest approximation of that posterior a contract could run, and estimate how much of the parent's gain it keeps. Contract limits: source at most 50,000 characters (QLX5 is 47,230: say what the sketch replaces), afterSwap peak gas at most 245,000. Write it as replica policy code in QLX5's integer WAD arithmetic, fixed-size state, callback-visible inputs only (no seed, true price, true labels, rival reserves, run parameters or future draws). Estimate gas from operation counts (storage reads and writes, mul/div, ln/exp calls, loop lengths) with the unit costs you assume, and characters from the code's size. Measure, paired by seed with unchanged QLX5: tune on 64000..65023, freeze; report 10000..12047 with score.py --bar 0.08 at n = 128, 256, 512, 1024, 2048, stopping when mean + 2 se < 0.08. Controls: sketch off equals QLX5 exactly; exogenous draws unchanged. Result: one JSON object: gain_vs_base, se, n, seeds, source_sha256, base_source_sha256, advance (true only when n = 2048 and mean - 2 se >= 0.08), parent {url, gain_vs_base, se}, fraction_of_exact_posterior (gain_vs_base / parent gain), fraction_of_ceiling (gain_vs_base / 1.4566139111071181), sketch_rmse_bps {all, arb, retail}, estimated_gas {afterSwap_peak, operation counts, unit costs}, estimated_characters, fits_limits (true, false or "unknown", and why), the approximation described so a builder could implement it, what of the parent it drops, stop history, controls, limitations, per-seed deltas, source to reproduce offline.
the whole memo
Credit Taylor (gtmcknight), github.com/gtmcknight/amm-sim@4812a6382311624e1506aca131ca35c378f930d9 research/solved, in every file. EPISODE 2 of 3. Episode 3 is the last: read, judge, set finish true. Items: 6 used + 3 spawned now = 9 of 24. ROUND 1 AS READ (4 of 6 results; own edge per 10,000-step run, paired by seed with QLX5 e183e5bc3fb794b7067703b10a7da9920267aa5f4caa968e16ca101b02338f40, replica only, no engine runs): - fair-price (r1-oracle-ceilings/fair-price; also served at https://api.imd.fun/artifacts/c9ac833b4a6837bf0bd56fc2c4b931ef58d34dc98a000278ee4cec091fb216ee, fetched, sha256 equal): true current price at every own callback (m := ln P, v := 0 before the rival clipping): +1.4566139111 se 0.0133062, n 2048 (10000..12047), mean - 2 se 1.4300, advance TRUE. Choose 64000..65023: +1.4929 se 0.0193. It reports oracle-off bit-equal on 3,072 runs and exogenous draws unchanged. I did not recompute its per-seed deltas myself. It is a fixed-QLX5 sensitivity, not a universal bound: the best policy given the price is unknown and could be higher. - next-trade: next retail order's side and size, searched 3-coefficient fee adapter (+5+17z bps on the predicted side, -11 bps opposite): +55.742 se 0.240, n 2048, advance true by the gate. It is foresight of a future draw; the requester rules it not usable. No round 2 for it. - retail-law: true lambda, mu, tau put in QLX5's retail likelihood: +0.00057 se 0.00719, n 128 (10000..10127), early stop (mean + 2 se 0.0150 < 0.08), advance false. Closed: excludes this substitution, not every use of the law. - engine-behaviours (r1-routing-audit; engine source read at github.com/benedictbrady/amm-challenge@6b6921f8d463314aa7c96234e1be25a25245f704 amm_sim_rs): terminal-step fee oracle +0.003894 se 0.001105, n 128, early stop; relaxed analytic cap on any terminal-step policy 0.0264 (se 0.0070, upper 0.040); terminal pnl is not scored (0); rounding and fixed-path dust small, a dynamic dust policy unmeasured. advance false. Closed. - NOT YET IN: two items of r1-oracle-ceilings were still running (true run volatility; the full-information bound). Their results are handed when accepted. Report them in the write-up; spawn nothing for them (requester's note). A full-information number is an achieved lower bound of a future-knowing policy, not usable headroom, unless its information is callback-visible. If either never lands, say unmeasured, not zero. - goal.json flags the sources of fair-price, retail-law and engine-behaviours (sources.flagged) and does not say why. Their figures are local replica runs with self-reported passing controls, not cited claims; round 2 reproduces the fair-price ceiling as a control. Say this in the write-up. - The 0.1187 standings gap (528.452 - 528.3333) is context, not a paired-seed gain: no item's gain is an estimate of leaderboard gain; do not add sources. REQUESTER NOTE 1 (2026-11-11, followed): the lead is the fair price. One deciding measurement, nothing else until it lands: how much of +1.4566 is inferable from what a strategy observes, by an exact posterior (particle filter or exact grid) fed to QLX5 in place of its Gaussian filter, plus the filter gap (RMSE in bps of QLX5's estimate and of the posterior against the true price, at arb and retail callbacks). Only if the exact posterior gains >= +0.15 on report seeds: one item sketching the cheapest approximation within the contract limits (<= 50,000 characters, afterSwap peak gas <= 245,000) with its capture. Otherwise state that the fair-price headroom is irreducible and close the goal. DECIDED THIS EPISODE: 1. r2-exact-posterior, 2 items, the one deciding measurement made twice, by the two methods the requester named (keys particle, grid). Twice because episode 3 is the last and a single failed item would leave the goal's question open; two methods also check each other. Each reports arm A (headline: the filter knows only the engine's laws and infers the run's parameters), arm B (sensitivity: the run's true volatility and retail parameters given to the filter; this covers the other reading of the requester's words 'the true price process and its parameters as the engine draws them'), the filter gap, fraction_of_ceiling = gain / 1.4566139111071181, and gates.posterior_ge_015 ('pass' only with all 2,048 report seeds, controls passing and gain >= 0.15). 2. r2-contract-sketch, 1 item (key particle), staged after r2-exact-posterior by item with check gates.posterior_ge_015 == 'pass'. It runs only if the particle item is accepted and passes; otherwise it is cancelled not_run and costs nothing. This is the requester's step 3, staged because no episode remains between the measurement and the end. If the plane refused the stage, the sketch was never run: say so. No Solidity, no engine runs, no submissions anywhere. All items require linux-x64, minCpus 8 (in each batch's requires). To fit 3,000 characters the briefs name base, replica, harness and the fair-price ceiling by full hash and leave out core, the faster build and the two older probe examples: the ceiling result embeds the whole replica with the belief hook. EPISODE 3, IN ORDER: a. Validate each r2-exact-posterior result before believing it: hook-off equals QLX5 exactly; the truth-fed control reproduces the ceiling (mean 1.472416081754699 on 10000..10127, 1.4566139111 on all 2,048); the filter used no seed, RNG state, true price, true labels, rival reserves or drawn parameters in arm A; calibration reported; tuned on 64000..65023 only; n and stop history honest (an early stop at mean + 2 se < 0.08 is a valid 'below 0.15' answer with its actual n). Compare particle and grid: they should agree within about 2 se; if not, the one with the weaker approximation of the rival state or of the arb inversion is the less exact, and the disagreement is a finding. b. If the valid exact-posterior gain is < 0.15: conclude as the requester asks: the fair-price headroom is irreducible for a strategy (the +1.46 is price information its callbacks do not carry), give the fraction captured, the filter gap by callback type, and arm B to show whether knowing the run's parameters would change that. Close. c. If >= 0.15 and the sketch landed: report its gain, fraction of the exact posterior and of the ceiling, estimated gas and characters, fits_limits, as the candidate to build in a later goal; an estimate from operation counts is not a measured gas figure. d. If >= 0.15 on grid only, or the sketch failed or was not run: report the measurement, say the sketch is missing and why; recommend it as the next step, without guessing its capture. e. If both r2 items failed: the question is unanswered; say so plainly, report round 1, do not call the headroom zero or irreducible. Then finish true. The write-up ranks the sources of the gap with their ceilings: fair price (+1.4566 with truth; the inferable part from round 2), next trade (+55.7, foresight, unusable), volatility and full information (as landed), retail law (+0.0006, closed), engine behaviours (+0.004, closed), with n, se and the limits of each (replica sensitivities, restricted adapters, early-stopped n, mean +/- 2 se is a screen and not a sequential confidence interval). Settled topics in the objective are not repeated.
1 step
r2-exact-posterior, item by item r2-contract-sketch, item by item
Round 3Credit Taylor (gtmcknight), github.com/gtmcknight/amm-sim@4812a6382311624e1506aca131ca35c378f930d9 research/solved; retain QLX5 network-extension credits.
Agent #65 planned it.
the whole memo
Credit Taylor (gtmcknight), github.com/gtmcknight/amm-sim@4812a6382311624e1506aca131ca35c378f930d9 research/solved; retain QLX5 network-extension credits. Baseline source SHA256 e183e5bc3fb794b7067703b10a7da9920267aa5f4caa968e16ca101b02338f40. Episode 3/3: finish this allocation with partial scientific findings; spawn nothing. All batches settled; no effects pending or refusals; eight items used of 24. r2-contract-sketch/particle was gate-cancelled (not_run), not a measured failure. No qualifying exact-posterior gain >=0.15 was established. No cancellation or timed wake needed. Request all eight accepted results for final citation. No Solidity, engine runs or submissions. Both round-two workers explicitly did NOT establish the requested exact posterior. Their finite-approximation measurements cannot prove fair-price headroom irreducible. Correct episode 2's proposed irreducibility wording: the exact inferable fraction remains unresolved. A low approximate-filter gain is not an upper bound on all callback-only inference. Finish closes this allocation, not every scientific question. No new work in this last episode: another unvalidated approximation or contract sketch would not establish the missing exact likelihood and convergence. r2-exact-posterior/particle: A gain 0.02116503635869993, se 0.016351362072875866, n=128, report 10000..10127; upper two-SE 0.05386776050445166. First-look score.py stop (<0.08), advance=false, posterior_ge_015=fail. Fraction of supplied full-bank fair-price reference 0.014530299482457347 (1.4530%). B, true run parameters supplied: gain 0.021280721691998572, se 0.015620277501296699, same n/seeds; also stopped. r2-exact-posterior/grid: A gain 0.020141961941068764, se 0.015283153831748475, n=128, report 10000..10127; upper two-SE 0.05070826960456572. First-look score.py stop (<0.08), advance=false, posterior_ge_015=fail. Fraction of supplied full-bank fair-price reference 0.013827934628030298 (1.3828%). B, true run parameters supplied: gain 0.01776166042325178, se 0.014961759813164239, same n/seeds; also stopped. All gains are paired own-pool edge differences over complete 10000-step replica runs. Particle used 2048 particles, choose 64000..64031. Grid used 8-bps spacing, eight parameter nodes, choose full runs 64000..64003 and a 2000-step refinement trace of 64000. From the embedded SAME-seed deltas, particle-minus-grid A = 0.0010230744176311646, se 0.012656452719674978, n=128. No material disagreement; shared approximation bias remains. Do not pool as independent studies or add gains. Passive filter gap, baseline -> posterior RMSE in bps (rounded). Particle: 128 seeds 10000..10127, 1,386,726 callbacks (486,154 arb; 900,572 retail): all 7.086835 -> 7.054083; arb 0.602288 -> 0.305614; retail 8.782899 -> 8.750518. Definition: 10000*RMS log-price error. Grid: ONLY 32 seeds 10000..10031, 348,145 callbacks (121,537 arb; 226,608 retail): all 7.111594 -> 7.088328; arb 0.503472 -> 0.130631; retail 8.807023 -> 8.785379. Definition: RMS of 10000*(estimated price/true price-1). Both improve arb error more than retail error. Different samples/error definitions prevent direct cross-method RMSE ranking. Both report hook-off/passive parity, preserved exogenous draws, callback-only A inputs and truth-fed control gain 1.472416081754699 on the same 128 seeds. True price/labels enter diagnostics only; B also receives run parameters. These execution controls were not independently replayed here. Particle controls.passed=true is mechanical only, exact_posterior_established=false. Grid controls.passed=false, execution_controls_passed=true. Both approximate the binary64/WAD observation likelihood with Taylor's tell/lattice factor and continuous densities, omit some rounding evidence and separate integration of the 99%-reserve arb cap. Particle lacks a convergence/bias bound; grid has sparse fixed parameter quadrature and short refinement traces. Passive nominal-95% coverage: 97.8574% particle, 98.4969% grid, descriptive only. Exact likelihood and full-run numerical convergence remain missing. Seed SE does not measure approximation bias. r1-oracle-ceilings/run-volatility: true sigma squared replaces only QLX5 process variance at own callbacks. Gain 0.028547394601922793, se 0.012706129241827322, n=128, report 10000..10127; upper two-SE 0.05395965308557744; first-look stop, advance=false. Choose 64000..65023 n=1024: -0.0013192673583428682, se 0.003926038841478276. Closes this plug-in, not every volatility-aware policy. r1-oracle-ceilings/full-information: searched policy gain 23.838253663028897, se 0.27507639991996496, n=2048, report 10000..12047; lower two-SE 23.28810086318897, advance=true numerically. Choose 64000..64063. Uses true price, rival/pending-fill state and next already-generated same-timestamp order; optimizes that order's fee and otherwise falls back to QLX5. No next-timestamp draws, but queue knowledge is unavailable to a strategy. An achieved search LOWER bound, not a solved optimum or usable headroom. Worker-reported loose pathwise upper bound: gain 159185.8165286168, se 523.6695874018054, gap at most 159161.97827495376 on report paths. It does not locate the ceiling. No estimator follows under the requester's fair-price-only direction. Earlier round one, carried from episode 2; read originals for citation. fair-price: +1.4566139111071181, se 0.013306207949579568, n=2048, 10000..12047, advance=true; fixed-QLX5 truth sensitivity, not optimized upper bound. Result https://api.imd.fun/artifacts/c9ac833b4a6837bf0bd56fc2c4b931ef58d34dc98a000278ee4cec091fb216ee. next-trade: +55.742, se 0.240, n=2048; future retail side/size, foresight, unusable. Its different information exposure/search prevents interpreting its difference from full-information as a certified optimization gap. retail-law: +0.00057, se 0.00719, n=128, 10000..10127, early-stopped plug-in, advance=false. r1-routing-audit/engine-behaviours: terminal-step probe +0.003894, se 0.001105, n=128, early stop; relaxed terminal cap 0.0264 (se 0.0070; upper about 0.040). Terminal PnL unscored; dynamic dust policy unmeasured; no qualifying lead. Validation: all four input hashes match pins; embedded delta hashes, paired means/SEs and full-information checkpoint statistics recomputed successfully. Reproduction archive hashes checked in memory, plus included volatility/full-information file hashes. No embedded code or simulation executed. Result hashes, distinct from source_sha256: b03-particle: 3310b67bbc4b909c06e9623fe6e0fdc7d4d8fac21093abe25467f5400d61c5a9 b03-grid: d9475f9a38366c72168c33423e2fbe84754883cb7312d9a47d22887c151511e7 b01-run-volatility: 9f16f7d816edaff1d23de863f4f2149b1823b2842856cb8a0b41f986442226b0 b01-full-information: 7aef6cf758ba6716bcfcbfa89a011cfc40a1bcadaae5fd3548e572ff96f1e50a Plane source flags exist for fair-price, volatility, retail-law and engine-behaviours without reasons; disclose without inventing why. Unflagged results do not certify methods. Preserve actual n/seed prefixes; distinguish truth sensitivities, searched lower bounds and approximate realisable gains. Repeated two-SE looks are the requested screen, not an anytime-valid confidence interval. Supplied standings gap 528.452-528.3333=0.1187 is context, not a paired gain or additive decomposition. No demonstrated callback-only route to the gap; exact inferability and a tight full-information ceiling remain unresolved, not zero or irreducible.
1 step
Write-upAgent #973made 1 file
Wrote and checked report.md.

Conclusion: no demonstrated route to 528.45; exact posterior headroom remains unresolved.

All eight results’ hashes and headline statistics verified. Only the requested report was created, left untracked.
ran oncodex · gpt-6-astra · 5 turns · 8m 39s · 77.4K in · 18.7K out · 842.1K cached
submission84cdadfb7492d8ec63bf974b4667ba18e4d2e8f627149a9785619a894e1bbd90
device2c736d2f8963f8a507c1f105407e5ba312f42ab34716c5f81b163e655e340023
started from0243d7da4a4337ae8b16bcdf15bb4ead736fd68f
bundlenone
verifiedrebuilt and matched · verifier 0.1.0 ·
made · 1 file
artifacts/goal/writeup/report.md · 33 KB
may write
artifacts/goal/writeup/**
JudgeAgent #1242found 2 medium
Recorded two medium findings in .imd-findings.json:

Missing Round 2 capture measurements for two advancing sources.

Next-trade oracle measures the next retail order, skipping intervening arbitrage.

Headline calculations matched the supplied data.
ran oncodex · gpt-6-astra · 5 turns · 7m 57s · 110.7K in · 12.9K out · 1.5M cached
submission846aac6f4c997f4d203a448ee83c355c415b62108fc0ab109642cc9d9684a805
device228636b860e0212ca9c796406585cb488ec9eaec0a9c92866812ac7dcce5e03d
started from0243d7da4a4337ae8b16bcdf15bb4ead736fd68f
bundlenone
mediumComplete Round 2 for the two advancing non-price sourcesartifacts/goal/writeup/report.md:3
The opening table and "Fair price" section close Round 2 after measuring only fair-price capture, leaving both next-order and full-information capture unmeasured. The assigned goal requires a realisable estimator or rule, with its fraction captured, for sources that advance. Both omitted sources pass that gate by a wide margin.

The report attributes this exclusion to a later requester note (also mentioned at line 47), but supplies neither that note nor a citation to it; the review assignment contains no such exclusion. Private oracle inputs explain why the oracle itself is not deployable, but do not measure how much a callback-visible rule can capture. The requester therefore cannot compare realisable gains across the three advancing sources.
Read the next-trade result at https://api.imd.fun/artifacts/19a9830766394638451d952df2f20e3a66d25059305d112fe0dd0ec47b7701f1 and full-information result at https://api.imd.fun/artifacts/7aef6cf758ba6716bcfcbfa89a011cfc40a1bcadaae5fd3548e572ff96f1e50a.

Their (gain_vs_base, se, n) are (55.74196209411537, 0.239706933374455, 2048) and (23.838253663028897, 0.27507639991996496, 2048); subtracting twice SE gives 55.262548227366466 and 23.28810086318897, both above 0.08.

Then inspect the Round-2 table at report lines 49-54 and batch record at lines 141-142: all measured capture arms target fair price, and neither omitted source has a replica estimator result or capture fraction.

Expected: those advancing sources receive the requested capture measurements (or a substantiated source-specific non-realisability result).

Actual: both opening-table capture cells say "None measured".
mediumMeasure the requested next-trade oracle, rather than only the next retail orderartifacts/goal/writeup/report.md:91
Round 1(d) asks for the next trade's side and size at each own callback. The +55.741962 result instead reveals the next distinct retail order and skips intervening arbitrage. This is a different information experiment, not merely a different fee adapter: the supplied side can be opposite to that of the next executable own trade.

The report correctly discloses this difference, but never supplies the commissioned next-trade measurement, so this row cannot answer that part of the goal. Keep the retail-only result as a separate diagnostic and provide the requested event definition and measurement.
Decode reproduction.source_map_xzb85 in https://api.imd.fun/artifacts/19a9830766394638451d952df2f20e3a66d25059305d112fe0dd0ec47b7701f1 with base85 then lzma, and inspect probe/core.hpp (also patch.diff).

Next contains only retail buy/size; peek advances a copy of the retail RNG until a nonempty retail batch, and the callback uses that payload even when arbitrage comes first.

Concrete state: after the last own callback of a timestamp, let own reserves be X=100, Y=10000, bid=ask=0.0028; let the next timestamp's fair price be 101 and its first retail order be a sell of quote-notional size 20.

The unchanged replica core.hpp runs own arbitrage before retail.

The next own trade is therefore a trader buy of X=100-sqrt(1000000/(0.9972*101))=0.3566825471656614 (positive profit), whereas this oracle reports the later trader sell with size 20.

Expected: the Round-1(d) payload identifies the next trade; actual: the measured payload identifies a later retail order.

Report lines 91 and 129 acknowledge the mismatch, and no corrected result is linked.
Publishedresearch report
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60 agents at most, judge accepted, 1 note

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