{ "credit": "Taylor (gtmcknight), github.com/gtmcknight/amm-sim@4812a6382311624e1506aca131ca35c378f930d9 research/solved.", "mech": "endgame: callback-timestamp-gated symmetric fee offsets at the beginning or end of a fixed 10,000-step run; tested independently at each end.", "already_present": { "value": false, "where": "Inspected leanbase.py:Policy, stalerival.py:Policy.on_trade, real.py:RealPolicy.on_trade/lookup, and tellpol.py:TellPolicy.on_trade from reference_zb64 at https://api.imd.fun/artifacts/efb8e653f8fd061cecf3e92b186470c9c96c5188523364b60ed101e9672869aa. Their time dependence is elapsed-step filtering and router staleness, not absolute first/last-N windows. fastlean.py likewise had no horizon fee rule. No substitute mechanism was needed." }, "definition": { "formula": "delta_bps(t) = first_delta_bps * 1{0 <= t < first_N} + last_delta_bps * 1{10000-last_N <= t < 10000}; bid = fee_round(base_bid + delta_bps*1e-4), ask = fee_round(base_ask + delta_bps*1e-4). Applied after policy lookup and optional hook, before rounding and storing the returned fees.", "state_kept": "No added persistent state. Uses only the afterSwap timestamp and hard-coded parameters; corrected fees replace the existing stored fees. No actual run parameters, future price, rival state or trade count is read.", "timing": "Replica timestamps are zero-based 0..9999. Initial quotes are unchanged. Windows trigger only on callbacks; the first trade at a boundary still sees the prior callback's quotes, and a first-window quote can persist until the next callback beyond its boundary. No synthetic callback or clock look-ahead is introduced.", "baselines": { "LEAN": { "a0": 0.35, "ainf": 0.35, "tau": 2.0 }, "AGE": { "a0": 0.0, "ainf": 0.7, "tau": 1.0 } }, "design": "Exactly 12 predeclared schedules: N in {10,100,1000}, first-only or last-only, delta in {-2,+2} bps. No simultaneous two-window schedule was searched. Contiguous choose rounds of 128 seeds from 64000 through 65023; cumulative paired differences; drop immediately after a round if mean+3*se<0. A setting crossing the cutoff at the final round is marked dropped_early although n=1024. Choose the largest final mean among survivors; tie by lowest index. Freeze before either report. SE = sample sd(ddof=1)/sqrt(n); seeds_positive counts strictly positive paired differences.", "reproduction": "Unpack the cited replica code_zb64, apply patch_zb64 to fastlean.py, provide pol_mid.json and qm_k1e-5.json from sources.json. tabs=fastlean.load(AMM_DIR,a0=0.35,ainf=0.35,tau=2,endgame=(first_N,first_delta_bps,last_N,last_delta_bps)); fastlean.run_batch(tabs,seeds,n_steps=10000). Omit endgame for LEAN; for AGE use a0=0,ainf=0.7,tau=1, with and without the identical chosen endgame tuple. No weights or feature head used. CPython 3.12 with numpy 2.2.6, numba 0.61.2, llvmlite 0.44.0.", "provenance": { "replica_url": "https://api.imd.fun/artifacts/a88ff982eba7e078bc6ccb1555b90a211c00c9fd76ec90a62ab13a4074f2c3d0", "reference_url": "https://api.imd.fun/artifacts/efb8e653f8fd061cecf3e92b186470c9c96c5188523364b60ed101e9672869aa", "base_fastlean_sha256": "d9c758bb280fe24e09c039496f84ab0804173ff70cec24c332f8683f28efa582", "patched_fastlean_sha256": "ab36b0966fe98dfb8ce4016956661134b589ce42125dde7cd132e568916b7301", "patch_sha256": "7b10049734add44a2abf3b42694ac2c058f4222e61ed831d52a1fc6083b36c1a", "table_sha256": { "pol_mid.json": "efbb5ee102db4d312f64565d9bf7232b6becbe02b624164f744a402bbbf2983b", "qm_k1e-5.json": "5ff53e42ca87390e5f65d1caa3f7a480e67a8212fb0670274dfd562b05ba1afd" }, "policy_sha256": { "leanbase.py": "ba015769f7981d7798acbbc9aff8c0e0c59825bb1541d55bcdef49311d7a04bc", "stalerival.py": "d124a171d35b024daed840e5449d352b2b5e50a68ce98c8a9aaafaf3419d23da", "real.py": "6a4a0f0e7f8b43d38e5eaa9d8b2e847a0771aee7f89551b122fe89bfe7969b5f", "tellpol.py": "7d5961c45bec56292533e65607245ad119b8733c760a5bf28f76a2e07bc3960b" } }, "checks": { "origin": "Local measurements, not independent certification or engine results.", "source_hashes": "Original fastlean.py hash matches its artifact; all ten imported reference modules checked against the reference artifact frozen hashes; all six source downloads re-fetched byte-identically.", "disabled_patch_bit_identical": { "n": 128, "seeds": [ 64000, 64127 ], "versus": "unmodified fastlean.py" }, "boundary_assertions": 192, "python_reference": { "n_full_runs": 24, "seed": 64000, "schedules": "all 12, each on LEAN and AGE", "max_abs_edge_diff": 0.0, "callbacks": 228537, "max_fee_diff_bps": 0.0, "fee_pair_mismatches": 0, "method": "Independent Horizon subclass adds the timestamp shift inside round_fees before stalerival rounding; each Python callback shadows compiled on_trade on identical inputs, then compares full-run edge." }, "tell_labels": { "recorded": 20313, "recorded_mismatch": 0, "perturbed": 25775, "perturbed_mismatch": 0, "seeds": [ 64000, 64001 ] } } }, "settings_tried": [ { "id": 0, "parameters": { "first_N": 10, "first_delta_bps": -2.0, "last_N": 0, "last_delta_bps": 0.0 }, "n": 896, "mean_diff": -0.0020339254873989227, "se": 0.0006276386434104654, "dropped_early": true, "seed_range": [ 64000, 64895 ], "rounds": [ { "seed_end": 64127, "n": 128, "mean_diff": -0.0019103144746850376, "se": 0.0010757092637898268, "seeds_positive": 61 }, { "seed_end": 64255, "n": 256, "mean_diff": -0.0021221177136188096, "se": 0.0011189936191288736, "seeds_positive": 122 }, { "seed_end": 64383, "n": 384, "mean_diff": -0.0014069086310485683, "se": 0.0008211418636181456, "seeds_positive": 192 }, { "seed_end": 64511, "n": 512, "mean_diff": -0.002227313703124789, "se": 0.0009033339928136631, "seeds_positive": 252 }, { "seed_end": 64639, "n": 640, "mean_diff": -0.00215271083629105, "se": 0.0007847402522874583, "seeds_positive": 318 }, { "seed_end": 64767, "n": 768, "mean_diff": -0.002060669059676723, "se": 0.0007028649904390334, "seeds_positive": 381 }, { "seed_end": 64895, "n": 896, "mean_diff": -0.0020339254873989227, "se": 0.0006276386434104654, "seeds_positive": 442 } ] }, { "id": 1, "parameters": { "first_N": 10, "first_delta_bps": 2.0, "last_N": 0, "last_delta_bps": 0.0 }, "n": 1024, "mean_diff": -0.0018263351179785836, "se": 0.0007164780284960467, "dropped_early": false, "seed_range": [ 64000, 65023 ], "rounds": [ { "seed_end": 64127, "n": 128, "mean_diff": 0.0026887396532675467, "se": 0.00272512583652712, "seeds_positive": 51 }, { "seed_end": 64255, "n": 256, "mean_diff": 0.0010255176000741884, "se": 0.0015187680233702107, "seeds_positive": 108 }, { "seed_end": 64383, "n": 384, "mean_diff": -0.00033589793244962846, "se": 0.0012523016521217237, "seeds_positive": 154 }, { "seed_end": 64511, "n": 512, "mean_diff": -0.0011853188780535096, "se": 0.001109893447921264, "seeds_positive": 210 }, { "seed_end": 64639, "n": 640, "mean_diff": -0.0012608058560759972, "se": 0.0009255284299785357, "seeds_positive": 254 }, { "seed_end": 64767, "n": 768, "mean_diff": -0.0015035096808682091, "se": 0.0008497804732944634, "seeds_positive": 307 }, { "seed_end": 64895, "n": 896, "mean_diff": -0.0018897671261204657, "se": 0.0007914824762584543, "seeds_positive": 358 }, { "seed_end": 65023, "n": 1024, "mean_diff": -0.0018263351179785836, "se": 0.0007164780284960467, "seeds_positive": 409 } ] }, { "id": 2, "parameters": { "first_N": 0, "first_delta_bps": 0.0, "last_N": 10, "last_delta_bps": -2.0 }, "n": 384, "mean_diff": -0.002376947121348394, "se": 0.0005331537765993568, "dropped_early": true, "seed_range": [ 64000, 64383 ], "rounds": [ { "seed_end": 64127, "n": 128, "mean_diff": -0.0019589804163335778, "se": 0.0008490691488820648, "seeds_positive": 58 }, { "seed_end": 64255, "n": 256, "mean_diff": -0.0015030423391846348, "se": 0.0005873267638623371, "seeds_positive": 122 }, { "seed_end": 64383, "n": 384, "mean_diff": -0.002376947121348394, "se": 0.0005331537765993568, "seeds_positive": 181 } ] }, { "id": 3, "parameters": { "first_N": 0, "first_delta_bps": 0.0, "last_N": 10, "last_delta_bps": 2.0 }, "n": 1024, "mean_diff": -0.00044629770173748584, "se": 0.0004214170706887863, "dropped_early": false, "seed_range": [ 64000, 65023 ], "rounds": [ { "seed_end": 64127, "n": 128, "mean_diff": -0.0020710695469787765, "se": 0.0011966213314438803, "seeds_positive": 48 }, { "seed_end": 64255, "n": 256, "mean_diff": -0.002339751263077172, "se": 0.0008145151902497939, "seeds_positive": 93 }, { "seed_end": 64383, "n": 384, "mean_diff": -0.0008582633977326873, "se": 0.0007242425004400516, "seeds_positive": 147 }, { "seed_end": 64511, "n": 512, "mean_diff": -0.0008313744878233331, "se": 0.0005887393899645997, "seeds_positive": 197 }, { "seed_end": 64639, "n": 640, "mean_diff": -0.0008358317951706162, "se": 0.0004998230905594645, "seeds_positive": 242 }, { "seed_end": 64767, "n": 768, "mean_diff": -0.0005156373909565026, "se": 0.000446841625008193, "seeds_positive": 304 }, { "seed_end": 64895, "n": 896, "mean_diff": -0.0002772024838693099, "se": 0.00045729639824997157, "seeds_positive": 360 }, { "seed_end": 65023, "n": 1024, "mean_diff": -0.00044629770173748584, "se": 0.0004214170706887863, "seeds_positive": 412 } ] }, { "id": 4, "parameters": { "first_N": 100, "first_delta_bps": -2.0, "last_N": 0, "last_delta_bps": 0.0 }, "n": 1024, "mean_diff": -0.005991086269366064, "se": 0.001648097594086959, "dropped_early": true, "seed_range": [ 64000, 65023 ], "rounds": [ { "seed_end": 64127, "n": 128, "mean_diff": -0.002172856631700526, "se": 0.004720255942140544, "seeds_positive": 68 }, { "seed_end": 64255, "n": 256, "mean_diff": -0.005166012770721373, "se": 0.0030887498896201115, "seeds_positive": 123 }, { "seed_end": 64383, "n": 384, "mean_diff": -0.0032352117725912657, "se": 0.002666062993128134, "seeds_positive": 183 }, { "seed_end": 64511, "n": 512, "mean_diff": -0.0034427900995279703, "se": 0.0023613288644985715, "seeds_positive": 239 }, { "seed_end": 64639, "n": 640, "mean_diff": -0.004956006342765562, "se": 0.002101203634994058, "seeds_positive": 292 }, { "seed_end": 64767, "n": 768, "mean_diff": -0.005733654216335982, "se": 0.0019377607426583376, "seeds_positive": 345 }, { "seed_end": 64895, "n": 896, "mean_diff": -0.005046750305384913, "se": 0.0017676514438440644, "seeds_positive": 410 }, { "seed_end": 65023, "n": 1024, "mean_diff": -0.005991086269366064, "se": 0.001648097594086959, "seeds_positive": 467 } ] }, { "id": 5, "parameters": { "first_N": 100, "first_delta_bps": 2.0, "last_N": 0, "last_delta_bps": 0.0 }, "n": 256, "mean_diff": -0.015943599218445126, "se": 0.0035082752512296056, "dropped_early": true, "seed_range": [ 64000, 64255 ], "rounds": [ { "seed_end": 64127, "n": 128, "mean_diff": -0.012305140540888715, "se": 0.004837626370311706, "seeds_positive": 49 }, { "seed_end": 64255, "n": 256, "mean_diff": -0.015943599218445126, "se": 0.0035082752512296056, "seeds_positive": 90 } ] }, { "id": 6, "parameters": { "first_N": 0, "first_delta_bps": 0.0, "last_N": 100, "last_delta_bps": -2.0 }, "n": 256, "mean_diff": -0.012172596800749558, "se": 0.0026495091062224475, "dropped_early": true, "seed_range": [ 64000, 64255 ], "rounds": [ { "seed_end": 64127, "n": 128, "mean_diff": -0.010183821434840645, "se": 0.0038795989449737518, "seeds_positive": 52 }, { "seed_end": 64255, "n": 256, "mean_diff": -0.012172596800749558, "se": 0.0026495091062224475, "seeds_positive": 97 } ] }, { "id": 7, "parameters": { "first_N": 0, "first_delta_bps": 0.0, "last_N": 100, "last_delta_bps": 2.0 }, "n": 128, "mean_diff": -0.01975976806989843, "se": 0.004562094628715589, "dropped_early": true, "seed_range": [ 64000, 64127 ], "rounds": [ { "seed_end": 64127, "n": 128, "mean_diff": -0.01975976806989843, "se": 0.004562094628715589, "seeds_positive": 40 } ] }, { "id": 8, "parameters": { "first_N": 1000, "first_delta_bps": -2.0, "last_N": 0, "last_delta_bps": 0.0 }, "n": 128, "mean_diff": -0.10753108417354174, "se": 0.015677809941873018, "dropped_early": true, "seed_range": [ 64000, 64127 ], "rounds": [ { "seed_end": 64127, "n": 128, "mean_diff": -0.10753108417354174, "se": 0.015677809941873018, "seeds_positive": 34 } ] }, { "id": 9, "parameters": { "first_N": 1000, "first_delta_bps": 2.0, "last_N": 0, "last_delta_bps": 0.0 }, "n": 128, "mean_diff": -0.16661008681316058, "se": 0.017694668369188475, "dropped_early": true, "seed_range": [ 64000, 64127 ], "rounds": [ { "seed_end": 64127, "n": 128, "mean_diff": -0.16661008681316058, "se": 0.017694668369188475, "seeds_positive": 25 } ] }, { "id": 10, "parameters": { "first_N": 0, "first_delta_bps": 0.0, "last_N": 1000, "last_delta_bps": -2.0 }, "n": 128, "mean_diff": -0.12036920215131053, "se": 0.014696043169319455, "dropped_early": true, "seed_range": [ 64000, 64127 ], "rounds": [ { "seed_end": 64127, "n": 128, "mean_diff": -0.12036920215131053, "se": 0.014696043169319455, "seeds_positive": 32 } ] }, { "id": 11, "parameters": { "first_N": 0, "first_delta_bps": 0.0, "last_N": 1000, "last_delta_bps": 2.0 }, "n": 128, "mean_diff": -0.1853807630005111, "se": 0.018157588114296172, "dropped_early": true, "seed_range": [ 64000, 64127 ], "rounds": [ { "seed_end": 64127, "n": 128, "mean_diff": -0.1853807630005111, "se": 0.018157588114296172, "seeds_positive": 23 } ] } ], "chosen": { "id": 3, "parameters": { "first_N": 0, "first_delta_bps": 0.0, "last_N": 10, "last_delta_bps": 2.0 }, "selection": { "n": 1024, "mean_diff": -0.00044629770173748584, "se": 0.0004214170706887863, "seeds_positive": 412 }, "all_dropped": false, "interpretation": "Best surviving schedule was selected even though its choose mean was negative; it is a required held-out test, not an asserted improvement." }, "report": { "vs_lean": { "n": 2048, "mean_diff": 0.00035885772081734046, "se": 0.0003227178901749649, "seeds_positive": 879, "seed_range": [ 10000, 12047 ], "mean_baseline": 536.603390956178, "mean_candidate": 536.6037498138988, "evaluation_passes": 1 }, "on_age": { "n": 2048, "mean_diff": 3.906800292433066e-05, "se": 0.00032759570186093344, "seeds_positive": 870, "seed_range": [ 10000, 12047 ], "mean_baseline": 536.6231002985178, "mean_candidate": 536.6231393665207, "evaluation_passes": 1 } }, "promote": false, "contract_cost": { "storage_words": 0, "gas": { "additional_peak_estimate_range": [ 30, 200 ], "measured": null }, "characters": { "additional_estimate_range": [ 200, 500 ], "measured": null }, "runtime_bytes": { "additional_estimate_range": [ 40, 200 ], "measured": null }, "basis": "Engineering estimate for hard-coded chosen rule: compare callback timestamp with 9990 and 10000, conditionally add 2e14 wad to each fee before the existing clamp/store. No new SLOAD/SSTORE, table or logarithm. Estimates include a credit comment in source, but depend on compiler and insertion point; no Solidity implementation or gas measurement.", "budget_context": "Requester supplied current peak about 208000/245000 gas, runtime 22440/24576 bytes, source 47230/50000 chars: headroom 37000 gas, 2136 bytes, 2770 chars. The estimated extension is small relative to those margins; compliance is not certified." }, "patch_zb64": "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", "not_done": [ "No QLX5 or qt1 comparison: this bounded item evaluates LEAN and AGE on the supplied replica only.", "No engine-faithfulness repair, Solidity port, engine seeds, gas measurement, deployed-byte measurement, OOG test or leaderboard submission.", "Formal P/G/E pipeline gates were not run; local hash, parity, label and fee checks are described above and do not constitute engine certification.", "Only the fixed 12 schedules were searched. No claims about untuned horizon rules, terminal liquidation, or a gain against QLX5 follow from these results.", "Working downloads and packages remain in test/scratch and are not deliverables; this result delivers the requested patch against the named existing replica, not a standalone vendored simulator." ] }