{ "item": "information-a (batch e03-information): kappa sweep for quoting on COMBO two-component belief, with/without the oracle arb flag", "credit": "Taylor (gtmcknight): replica2.py, real.py filter, dp.py solver, qmdp.py tables, gates.py; github.com/gtmcknight/amm-sim @4812a638 research/solved. qt1 (QMRef), TC (TwoComp), COMBO (Combo) and QMS1 (blob) are IdentityMD items built on Taylor's work and are used unmodified.", "environment": "plain python3 -I (CPython 3.12.3, Linux x86_64, 4 cores) for every replica run; a uv venv (numpy 2.5.4, numba 0.68.1) under scratch/.venv only for dp.py / qmdp.py / tabcheck.py. No engine, no Solidity, no contract: no candidate reached +0.5 over qt1 on the report seeds beyond what COMBO already has, and the only variant that beats COMBO needs the oracle flag.", "hashes": { "amm-sim commit": "4812a6382311624e1506aca131ca35c378f930d9 (git rev-parse HEAD after checkout)", "research/solved files sha256": { "README.md": "02d2b51f17adbb5411a2a67f7a37255143ba381a73ff10abba557d7d23c0cef2", "gates.py": "603280c1f595ca163ffaf2ba1ebdc7945fdb08dabae67fc53c922d39e1cce604", "replica2.py": "6e37b4e61e1ffa5ffb1e43912ddb8659105989aa986eb48fcd1d7608f8dca685", "evalpol.py": "6e67667bfed7798bdd3384652a6efc6ba0b1fce653740d0f9af2bcbcb8e6a27c", "real.py": "1305b5333731c046c3e6736cc2578eff4635c88132a39c22f5780d78aef2c81e", "latt.py": "925c0fe996b19fd51fb79a85d5e4dba4bc2f5453d0a156cc1e480f65a6a00cc8", "dp.py": "ca4e7c378d23c46c7def4716611135c471a831d15234b984fe30d58d9eec5734", "qmdp.py": "63b8c35048718c37eb0a5dae9e70849fa3af257c335e4a2e3a625c833f1dc1eb", "pol_mid.json": "efbb5ee102db4d312f64565d9bf7232b6becbe02b624164f744a402bbbf2983b", "qm_k1e-5.json": "5ff53e42ca87390e5f65d1caa3f7a480e67a8212fb0670274dfd562b05ba1afd" }, "artifacts (sha256 == URL suffix, verified with sha256sum -c)": { "qt1": "8a6e303b662e1a5ea9bb47f31acedd3988ef65b3ddb66d074517aa59ad41ca40", "TC": "d3c849db2ac31e567b57e52b80b86e8c24c842e5b4125b9d75c78e3cb07115b9", "COMBO": "d360bea6c8c982717b7b43a8069a87013169c89ee3e4da25622db4d880b936d4", "QMS1": "17d249ab0c33fc44931d9b105cf3f9e3846a560bd518b67310c2a56defacdecc" }, "extracted (all equal their published sha256)": { "qmref.py (qt1 \"## Python reference\" fence)": "1dfc9b7a3c2237ff7a93dd9f0af54b9bdab16f2ce0a7eb00784cb4432598db92 7739 B", "twocomp.py (TC first python fence after \"## Code\")": "9d3c1833321493fb51bbde4e1b4dabc2f8978bd6d774ee2af8dc8aed13f0f0af 11202 B", "combo.py (COMBO first python fence after \"## Code\")": "c5b711a0b4fb4783e8879a484bf87a427171f4a11aa5eb5ec3513c24ead1a796 5929 B", "blob.bin (QMS1 \"## Data\" base64 decoded)": "3ac7cb8811ecfb6a17f499aa4e9b70dd55f7fb6432b3aec3b904e11a3dece38e 10167 B", "Strategy.sol (qt1 solidity fence)": "c68887cff61180e12ba2b1ceb333edf76a830f91f63b5d775a8806fb9ec08aca 42990 B (== c68887cf... as the brief states)" }, "this item code sha256": { "kpol.py": "f89c6328f6a2c334b930cb6f082236b96f8a7f4e1d110ed800de53c03f1497e0", "run.py": "c9f1469feea0823d84ca5746afc01c7a3450c0ac3f967abd6cc055754f571462", "agg.py": "4c7a95582c19f2dc590da4059d30b5740520e8ad7ff8bb829137121c27c429b7", "tabcheck.py": "66f0c79a184c29ebdd310e7a0f6e60db1dab8fbca639894f1945a3d381f23401", "solve.sh": "28700e45aadde3017763023d85d57fa16742fb6d95b6581bc5e041882fe386db", "qmdp.sh": "c8e7405adf0e6d099a5c55a150c1fd6ce4dc9f43792143e97cdf3ae4ee574cb1", "screen.sh": "781b1c8c2d290f27625ec65ff9def285bd8784cdfc3242f48fd5df7623be10ac", "cmp_tabs.py": "99dec2c442c81b5681790fea58f378d6236e473c2f9166f77326bbfbcf1a45bc" } }, "gate_P": { "command": "python3 -I gates.py (unmodified checkout, before any change), 2.8 s", "output": [ "seed perfect-info gaussian+plain gaussian+qm lattice+qm", "10000 448.261189 443.455598 443.522608 443.663520", "10001 576.779199 571.463409 571.623551 571.977293", "10002 531.886497 525.168028 525.865859 526.411631" ], "matches_README_6dp": true, "qt1 = QMRef(blob.bin), not RealPolicy; replica2.run(seed, QMRef)[edge] on 10000..10002": [ "443.101741", "571.454483", "525.908441" ], "COMBO = Combo(blob.bin) on 10000..10002 (equals the COMBO artifact table)": [ "444.195330", "572.172682", "526.274760" ] }, "controls": { "ComboK(blob) == Combo(blob)": "bit-identical edges on seeds 10000 (444.195330) and 64000 (437.710000); ComboK re-states combo.py on_trade with two inserted diagnostic lines (see patch)", "hidden_input_invariance": { "method": "Scramble wrapper passes arb->not arb, p->1.37p, s2->0.61 s2, j->j+5 to the live policy; edges must be identical", "qt1 and COMBO (blob) seeds 10000, 64000": "identical (443.101741 / 436.408765 and 444.195330 / 437.710000)", "C_k0, C_k1e-5, C_k3e-5, C_k1e-4 seeds 10000, 64000, 11500": "identical for all 12 (edge == scrambled edge exactly)", "flagged variants": "NOT invariant by construction (they read arb); oracle-only diagnostics" }, "VN_regeneration": { "command": "DP_SAVEVN=1 DP_AMINL=-12 DP_NA=43 python dp.py solve 0.8 9.45 20 scratch/vn/pol_mid.json (README command), 425 s wall on 4 cores, 110 sweeps, gain 536.821", "tables vs pol_mid.json": "A0 B0 A1 B1 A2 B2: max |diff| = 0.0 bps, 0 cells differ (of 4173/15729 per table); g 0.05368206098114493 vs 0.05368206098114671 (float noise); regenerated JSON sha256 fafe2c68faec494c434339f78ae688bd281a3fd23f0921d0d63a39d9bd06ff04 differs from efbb5ee1... only through g", "VN sha256 (float32 .npy, 5 bps lattice, NW 321, N2 49, NA 43, AMINL -12)": { "pol_mid_VN0.npy": "dc602095804048829da58040ce5b40dee25b25edaeeba921f45033e9894072b6", "pol_mid_VN1.npy": "871274b7f2ede9ee9f610c7dfaf7fe450d971259aec3cf4b74245d9cb79be0fd", "pol_mid_VN2.npy": "7fa4b401dde383b3a37f2ba3f79edb63702ece1f4c059f8a486850cdbb32c086" } }, "qmdp_regeneration_control": "DP_AMINL=-12 DP_NA=43 python qmdp.py scratch/vn/pol_mid.json scratch/tabs/qm_ig1_k1e-5.json 1e-5 (no IG2, Taylor's igtab): all ten tables A0c..B2c cell-for-cell identical to qm_k1e-5.json (0 of 866,000+ cells differ); file sha256 afeab9ec765609bc466d8631444afb2caa283c2bbf7c24de078e9f97511e33c2 (differs from 5ff53e42... only through g)", "compression_control (choose window)": "C_IG1_k1e-5(control) = COMBO quoting rule on the full regenerated kappa=1e-5 tables minus COMBO on the QMS1 blob: +0.0607 se 0.0104 (n 1024), consistent with QMS1's published compression loss 0.0632 se 0.0072; so COMBO-blob is a faithful stand-in for Taylor's kappa=1e-5 tables", "IG2_vs_IG1_at_kappa_1e-5 (choose)": "C_k1e-5 (igtab2, ambiguity-aware) minus C_IG1_k1e-5(control) (igtab): -0.0894 se 0.0118 (n 1024): the ambiguity-aware term is slightly worse than Taylor's plain term at the same kappa" }, "candidates_predeclared": { "C_k0": "ComboK on qm_ig2_k0.json (kappa 0; value-only QMDP tables; level 0 = pol_mid within 0.005 bps rounding)", "C_k1e-5": "ComboK on qm_ig2_k1e-5.json (kappa 1e-5, IG2=1)", "C_k3e-5": "ComboK on qm_ig2_k3e-5.json (kappa 3e-5, IG2=1)", "C_k1e-4": "ComboK on qm_ig2_k1e-4.json (kappa 1e-4, IG2=1)", "Cflag_k*": "same four tables with the oracle flag intervention; Flag = ComboK(blob, flag=True)", "bases": "qt1 = QMRef(blob.bin); COMBO = Combo(blob.bin) (QMS1 spline of Taylor's kappa=1e-5 igtab tables)", "filter": "TwoComp's, fixed (DUAL_CUTS=2), identical statements in every variant; only the table JSON differs" }, "params": { "kappa_sweep": [ 0, 1e-05, 3e-05, 0.0001 ], "information_term": "qmdp.igtab2 (IG2=1) for kappa>0; kappa=0 ignores it", "qmdp settings": "DP_AMINL=-12 DP_NA=43, SLEV=[0,4,8,12,16,20,26,34] bps, sigma 9.45 bps, lam 0.8, size 20, H 5 bps, IGMAX 60", "phase weights (kappa*(1-h[phase]) as qmdp.py)": { "phase0": 0.449329, "phase1": 0.652773, "phase2": 0.76689 }, "phase_probs h": [ 0.550671, 0.347227, 0.23311 ], "replica": "replica2.run(seed, policy) unmodified defaults, n_steps 10000, no cfg, no qcap", "windows": { "choose": "64000..65023 (n 1024)", "report": "10000..12047 (n 2048)" }, "selection_rule": "live winner = argmax over the four predeclared kappas of mean_diff(C - COMBO) on choose 64000..65023; flagged winner = argmax of mean_diff(Cflag - Flag) on the same window; report window never used for selection", "workers": "2-4 processes (multiprocessing.Pool), each seed run once per policy" }, "selection_on_choose": { "live_winner": "C_k1e-5", "live_choose_C_minus_COMBO": { "C_k0": -0.268082, "C_k1e-5": -0.028718, "C_k3e-5": -1.091368, "C_k1e-4": -16.921044 }, "flag_winner": "Cflag_k1e-5", "flag_choose_Cflag_minus_Flag": { "Cflag_k0": -0.001473, "Cflag_k1e-5": 0.096967, "Cflag_k3e-5": -0.470844, "Cflag_k1e-4": -13.689942 } }, "headline_report_10000_12047": { "live winner C_k1e-5 - COMBO": { "n": 2048, "mean_diff": -0.016225, "se": 0.009022, "worst5": [ [ 11191, -2.095877 ], [ 11370, -1.831229 ], [ 11693, -1.468556 ], [ 10893, -1.268267 ], [ 11911, -1.250677 ] ], "wins": 972 }, "live winner C_k1e-5 - qt1": { "n": 2048, "mean_diff": 0.581166, "se": 0.014402, "worst5": [ [ 10146, -3.460459 ], [ 11062, -2.315958 ], [ 11808, -1.820214 ], [ 10519, -1.779457 ], [ 11164, -1.747538 ] ], "wins": 1707 }, "flag winner Cflag_k1e-5 - Flag": { "n": 2048, "mean_diff": 0.102716, "se": 0.007554, "worst5": [ [ 12006, -2.101913 ], [ 10208, -1.167917 ], [ 10357, -1.031574 ], [ 10726, -0.933981 ], [ 11392, -0.905762 ] ], "wins": 1271 }, "flag winner Cflag_k1e-5 - COMBO": { "n": 2048, "mean_diff": 2.672835, "se": 0.021316, "worst5": [ [ 11701, -1.945788 ], [ 11693, -0.538746 ], [ 11911, -0.389702 ], [ 10731, -0.305428 ], [ 11519, -0.295766 ] ], "wins": 2041 }, "flag winner Cflag_k1e-5 - qt1": { "n": 2048, "mean_diff": 3.270226, "se": 0.022922, "worst5": [ [ 11062, -0.423465 ], [ 11808, -0.042483 ], [ 10731, 0.253017 ], [ 10141, 0.303308 ], [ 11701, 0.413313 ] ], "wins": 2046 }, "reading": "No live gain from the information weight: C_k1e-5 is -0.016 se 0.009 against COMBO (COMBO already carries kappa=1e-5 tables; the regenerated ambiguity-aware ones are no better), kappa=0 costs 0.28, kappa=3e-5 costs 1.04, kappa=1e-4 costs 16.9. With the true flag the same tables are worth +0.10 se 0.008 over Flag at kappa=1e-5 and nothing at kappa=0: buying pins only pays once the arb/retail call is right. The frozen live winner C_k1e-5 is +0.581 se 0.014 over qt1 on the report seeds, i.e. the same as COMBO (+0.597)." }, "windows": { "choose": { "seeds": "64000..65023", "n": 1024, "coverage": { "qt1": "1024/1024", "COMBO": "1024/1024", "Flag": "1024/1024", "C_k0": "1024/1024", "C_k1e-5": "1024/1024", "C_k3e-5": "1024/1024", "C_k1e-4": "1024/1024", "Cflag_k0": "1024/1024", "Cflag_k1e-5": "1024/1024", "Cflag_k3e-5": "1024/1024", "Cflag_k1e-4": "1024/1024", "C_IG1_k1e-5(control)": "1024/1024" }, "row_sha256": { "qt1": "126f9d4216df2d34a8248137ddf967f4e496f3edaf7322130eade9f3133d5bc1", "COMBO": "c987ed04db3c3fd423ee0fc56fca03132af3226eb3c52d7f9ab799482eb6e367", "Flag": "1838202a6ff0db200af3291b94d5f3c93bb476b58f9c376f6512f7de445ce534", "C_k0": "2e7146a59f37d1ff5b0acef0a6076611fb7db74fae384cb1d4eb2f2db6f04fcb", "C_k1e-5": "cdb6aa3ecc98fc193e9093ac7eae8b6e00b1a4c098e173c6e82d36d4b595b517", "C_k3e-5": "591e343ba0fca673a567c9bfb3f87eedc8632e2d82b64aa0ff74539faa4c90e7", "C_k1e-4": "b5bd8e9d491811ebe93480db828706732465291c62fa0630613165a777e0b7f3", "Cflag_k0": "bc81b60f8ffde9004b1d0497e76f3f071130383aebe22fa8dc5639ab40783c3e", "Cflag_k1e-5": "cc4360f5b0170a1920ce7298994389daa42d9b34b5baad3062c42ca1ed9c65d2", "Cflag_k3e-5": "03dc0a45c5bcf230b6c03c7497269c79d8fc640cb1c658f79a06fc845f321e67", "Cflag_k1e-4": "98fe57d545acc99735db93cfdc5081774d2426a70d5de68a2930b1684d4fbf2d", "C_IG1_k1e-5(control)": "6b24a903a9662c2680d173443d5980fd8fd3f311693c3f23901f04f06711af37" }, "mean_edge": { "qt1": 535.720495, "COMBO": 536.3301, "Flag": 538.833479, "C_k0": 536.062018, "C_k1e-5": 536.301382, "C_k3e-5": 535.238732, "C_k1e-4": 519.409056, "Cflag_k0": 538.832005, "Cflag_k1e-5": 538.930445, "Cflag_k3e-5": 538.362635, "Cflag_k1e-4": 525.143537, "C_IG1_k1e-5(control)": 536.39083 }, "first_call_errors": { "qt1": { "wrong": 1239361, "total": 7197347, "rate": 0.1722 }, "COMBO": { "wrong": 1154223, "total": 7201469, "rate": 0.16028 }, "Flag": { "wrong": 847125, "total": 7192654, "rate": 0.11778 }, "C_k0": { "wrong": 1137672, "total": 7057844, "rate": 0.16119 }, "C_k1e-5": { "wrong": 1135476, "total": 7184041, "rate": 0.15806 }, "C_k3e-5": { "wrong": 1109317, "total": 7398167, "rate": 0.14994 }, "C_k1e-4": { "wrong": 839870, "total": 8155564, "rate": 0.10298 }, "Cflag_k0": { "wrong": 816623, "total": 7065340, "rate": 0.11558 }, "Cflag_k1e-5": { "wrong": 827143, "total": 7166996, "rate": 0.11541 }, "Cflag_k3e-5": { "wrong": 835062, "total": 7358548, "rate": 0.11348 }, "Cflag_k1e-4": { "wrong": 707412, "total": 8118812, "rate": 0.08713 }, "C_IG1_k1e-5(control)": { "wrong": 1150113, "total": 7194163, "rate": 0.15987 } }, "new_path_calls_per_run": { "qt1": 0.0, "COMBO": 5876.74, "Flag": 0.0, "C_k0": 5747.06, "C_k1e-5": 5850.36, "C_k3e-5": 6023.59, "C_k1e-4": 6509.02, "Cflag_k0": 0.0, "Cflag_k1e-5": 0.0, "Cflag_k3e-5": 0.0, "Cflag_k1e-4": 0.0, "C_IG1_k1e-5(control)": 5870.18 }, "secs_per_seed": { "qt1": 0.0808, "COMBO": 0.1418, "Flag": 0.1044, "C_k0": 0.2204, "C_k1e-5": 0.2093, "C_k3e-5": 0.2353, "C_k1e-4": 0.2466, "Cflag_k0": 0.162, "Cflag_k1e-5": 0.1597, "Cflag_k3e-5": 0.1119, "Cflag_k1e-4": 0.115, "C_IG1_k1e-5(control)": 0.1453 }, "pairs": { "COMBO-qt1": { "n": 1024, "mean_diff": 0.609605, "se": 0.019401, "worst5": [ [ 64101, -2.776983 ], [ 64845, -1.163868 ], [ 64374, -1.023434 ], [ 64795, -0.983171 ], [ 64555, -0.946189 ] ], "wins": 875 }, "Flag-COMBO": { "n": 1024, "mean_diff": 2.503378, "se": 0.02856, "worst5": [ [ 64901, -1.316929 ], [ 64003, -1.15932 ], [ 64132, -0.028623 ], [ 64778, 0.009376 ], [ 64150, 0.051428 ] ], "wins": 1021 }, "Flag-qt1": { "n": 1024, "mean_diff": 3.112983, "se": 0.030987, "worst5": [ [ 64322, 0.08756 ], [ 64509, 0.148183 ], [ 64593, 0.208364 ], [ 64109, 0.570966 ], [ 64636, 0.581355 ] ], "wins": 1024 }, "C_k0-COMBO": { "n": 1024, "mean_diff": -0.268082, "se": 0.018867, "worst5": [ [ 64454, -2.273499 ], [ 64999, -2.063109 ], [ 64338, -1.947157 ], [ 64603, -1.813771 ], [ 64099, -1.744715 ] ], "wins": 335 }, "C_k0-qt1": { "n": 1024, "mean_diff": 0.341523, "se": 0.023616, "worst5": [ [ 64348, -2.08977 ], [ 64454, -1.857222 ], [ 64022, -1.842969 ], [ 64101, -1.718222 ], [ 64707, -1.542489 ] ], "wins": 692 }, "C_k1e-5-COMBO": { "n": 1024, "mean_diff": -0.028718, "se": 0.013323, "worst5": [ [ 64044, -2.113044 ], [ 64003, -1.773495 ], [ 64682, -1.381315 ], [ 64458, -1.308014 ], [ 64839, -1.27451 ] ], "wins": 484 }, "C_k1e-5-qt1": { "n": 1024, "mean_diff": 0.580887, "se": 0.019876, "worst5": [ [ 64101, -2.119136 ], [ 64458, -1.429545 ], [ 64348, -1.08836 ], [ 64795, -1.064959 ], [ 64698, -1.028516 ] ], "wins": 863 }, "C_k1e-5-C_k0": { "n": 1024, "mean_diff": 0.239364, "se": 0.018215, "worst5": [ [ 64720, -2.907327 ], [ 64044, -2.207874 ], [ 64783, -1.510961 ], [ 64920, -1.439673 ], [ 64447, -1.298489 ] ], "wins": 681 }, "C_k3e-5-COMBO": { "n": 1024, "mean_diff": -1.091368, "se": 0.021064, "worst5": [ [ 64261, -3.554097 ], [ 64326, -3.156092 ], [ 64768, -3.059449 ], [ 64568, -2.954428 ], [ 64697, -2.768348 ] ], "wins": 52 }, "C_k3e-5-qt1": { "n": 1024, "mean_diff": -0.481764, "se": 0.023153, "worst5": [ [ 64712, -2.758392 ], [ 64294, -2.67928 ], [ 64245, -2.668495 ], [ 64190, -2.618038 ], [ 64261, -2.556534 ] ], "wins": 266 }, "C_k3e-5-C_k0": { "n": 1024, "mean_diff": -0.823287, "se": 0.028025, "worst5": [ [ 64656, -3.924404 ], [ 64697, -3.822764 ], [ 64945, -3.655177 ], [ 64261, -3.573141 ], [ 64303, -3.347014 ] ], "wins": 186 }, "C_k1e-4-COMBO": { "n": 1024, "mean_diff": -16.921044, "se": 0.071186, "worst5": [ [ 64689, -24.410074 ], [ 64114, -23.711641 ], [ 64303, -23.194955 ], [ 64549, -22.883591 ], [ 64553, -22.510178 ] ], "wins": 0 }, "C_k1e-4-qt1": { "n": 1024, "mean_diff": -16.311439, "se": 0.070516, "worst5": [ [ 64689, -23.815298 ], [ 64303, -23.277334 ], [ 64761, -22.220008 ], [ 64114, -22.041926 ], [ 64340, -21.945017 ] ], "wins": 0 }, "C_k1e-4-C_k0": { "n": 1024, "mean_diff": -16.652962, "se": 0.074429, "worst5": [ [ 64303, -24.210588 ], [ 64114, -24.175285 ], [ 64689, -24.112925 ], [ 64930, -22.898818 ], [ 64340, -22.802579 ] ], "wins": 0 }, "Cflag_k0-Flag": { "n": 1024, "mean_diff": -0.001473, "se": 0.015617, "worst5": [ [ 64568, -1.8821 ], [ 64353, -1.870606 ], [ 64844, -1.595698 ], [ 64946, -1.590292 ], [ 64454, -1.404513 ] ], "wins": 489 }, "Cflag_k0-COMBO": { "n": 1024, "mean_diff": 2.501905, "se": 0.029262, "worst5": [ [ 64003, -1.253522 ], [ 64778, -0.28105 ], [ 64568, 0.07218 ], [ 64132, 0.140286 ], [ 64103, 0.155977 ] ], "wins": 1022 }, "Cflag_k0-qt1": { "n": 1024, "mean_diff": 3.11151, "se": 0.031877, "worst5": [ [ 64322, 0.171353 ], [ 64103, 0.21074 ], [ 64778, 0.339607 ], [ 64020, 0.353868 ], [ 64101, 0.487044 ] ], "wins": 1024 }, "Cflag_k1e-5-Flag": { "n": 1024, "mean_diff": 0.096967, "se": 0.009706, "worst5": [ [ 64568, -1.490069 ], [ 64865, -0.918804 ], [ 64926, -0.81431 ], [ 64288, -0.790275 ], [ 64353, -0.722705 ] ], "wins": 646 }, "Cflag_k1e-5-COMBO": { "n": 1024, "mean_diff": 2.600345, "se": 0.028427, "worst5": [ [ 64901, 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"2048/2048", "COMBO": "2048/2048", "Flag": "2048/2048", "C_k0": "2048/2048", "C_k1e-5": "2048/2048", "C_k3e-5": "2048/2048", "C_k1e-4": "2048/2048", "Cflag_k0": "2048/2048", "Cflag_k1e-5": "2048/2048", "Cflag_k3e-5": "2048/2048", "Cflag_k1e-4": "2048/2048", "C_IG1_k1e-5(control)": "0/2048" }, "row_sha256": { "qt1": "ac1b4c1342309fedbdf2f2445523e50805bebeded91a994c6460beccbfd6d2eb", "COMBO": "0c929012f1c24b75963757dd3e4462bf49ffb5468fc544cdf00a9d8f83bce21d", "Flag": "d3ad176fbb89b7e354af4c6514983856bb407df6c2a063ae4cf84aadcd54a3fb", "C_k0": "5baada64fe21200e09c1db7bc139869290aa2f430664649d0423f6bb446150c5", "C_k1e-5": "af7a1fc1d8e7ff1ad49acee9c08589dcd9dd86127abe195602c77eb2a5a5240f", "C_k3e-5": "9ff0fb2d0ef525110f4e1241fbd7a988ddca37425c80b215c1384b1073edac43", "C_k1e-4": "43186d6cb53e0bdf6e58e85a4038d9d0871909277dfa094ac1c79c0464f1b261", "Cflag_k0": "674cc05bd4ced6cd434a753b4be68c329d9d847fe26e4025682ee48d00f57c0c", "Cflag_k1e-5": 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"Cflag_k1e-4-Flag": { "n": 2048, "mean_diff": -13.67449, "se": 0.046317, "worst5": [ [ 10942, -29.062869 ], [ 11077, -21.40577 ], [ 11737, -19.882494 ], [ 12005, -19.842114 ], [ 10960, -19.775882 ] ], "wins": 0 }, "Cflag_k1e-4-COMBO": { "n": 2048, "mean_diff": -11.10437, "se": 0.043285, "worst5": [ [ 10942, -24.606611 ], [ 11077, -19.032068 ], [ 11737, -18.238389 ], [ 11770, -17.462256 ], [ 10659, -17.248446 ] ], "wins": 0 }, "Cflag_k1e-4-qt1": { "n": 2048, "mean_diff": -10.506979, "se": 0.043484, "worst5": [ [ 10942, -24.069593 ], [ 11770, -18.150434 ], [ 11737, -18.082487 ], [ 11077, -18.061978 ], [ 10519, -16.945569 ] ], "wins": 0 }, "Cflag_k1e-4-Cflag_k0": { "n": 2048, "mean_diff": -13.675609, "se": 0.049756, "worst5": [ [ 10942, -29.600293 ], [ 11077, -21.862184 ], [ 10401, -21.267231 ], [ 11737, -20.944679 ], [ 10336, -20.57656 ] ], "wins": 0 } } } }, "edge_error_tradeoff": { "definition": "first-call error = live filter pi>0.5 disagrees with the true arb flag on a step's first own trade (truth used for the label only); rate = wrong/total over the window; edge = mean replica edge", "report_window": { "qt1": { "error_rate": 0.17307, "wrong": 2487830, "total": 14374445, "mean_edge": 533.262831, "vs_COMBO": -0.597391 }, "COMBO": { "error_rate": 0.16119, "wrong": 2318251, "total": 14382447, "mean_edge": 533.860222, "vs_COMBO": 0.0 }, "C_k0": { "error_rate": 0.16199, "wrong": 2283603, "total": 14097011, "mean_edge": 533.576901, "vs_COMBO": -0.283321 }, "C_k1e-5": { "error_rate": 0.15903, "wrong": 2281826, "total": 14348095, "mean_edge": 533.843997, "vs_COMBO": -0.016225 }, "C_k3e-5": { "error_rate": 0.15085, "wrong": 2228691, "total": 14774412, "mean_edge": 532.820175, "vs_COMBO": -1.040046 }, "C_k1e-4": { "error_rate": 0.10342, "wrong": 1685154, "total": 16294671, "mean_edge": 516.991031, "vs_COMBO": -16.869191 } }, "reading": "Raising kappa does buy information: the live error falls 16.2% -> 15.9% -> 15.1% -> 10.3% from kappa 0 to 1e-4 (first-call count rises 14.10M -> 16.29M, i.e. more arb pins), but the edge falls -0.28 -> -0.02 -> -1.04 -> -16.87 against COMBO. The error reduction never pays for the fee revenue the tighter quotes give up; the sweet spot stays at Taylor's kappa=1e-5, where the error is only 0.3 points lower than at kappa 0 while the quote change itself is worth +0.27. Under the oracle flag the pattern is the same (+0.10 at 1e-5, -0.47 at 3e-5, -13.7 at 1e-4), so the loss at high kappa is fee revenue, not classification." }, "information_formula": { "objective": "U(w,R,phase,sd; a,b) = sum_e bel(e) V_N[phase](w-e, w2(e), a-e, b+e) + kappa*(1-h[phase]) * IG(a-w clipped, b+w clipped); (a,b)* = argmax, parabola-refined; bel = Gaussian on the 5 bps lattice, 3 sd wide (qmdp.ebel)", "IG_igtab2 (used, IG2=1)": "tau^2 = sd^2 + sigma^2 (bps^2); Z = Phi(a/tau) - Phi(-b/tau); V = truncated-normal variance on (-b, a); amb_side = 0.5 * sum_d dens_arb(d) * ret(d) / (dens_arb(d) + ret(d)) * (x_arb(d) - mu)^2 with ret(d) = Z*RHO*lognormal_pdf(d; ln 11.12, 1.176), x_arb = a+d on the ask, -(b+d) on the bid, d = 0.25..200 bps step 0.5; IG = tau^2 - Z*V - amb_ask - amb_bid = expected drop in belief variance over the next step boundary, net of the arb/retail ambiguity", "IG_igtab (Taylor, control only)": "IG = tau^2 - Z*V: the arb pins p exactly when the move crosses a quote, otherwise the belief is cut to the no-arb interval", "units": "U = sum_e bel(e) V_N[phase] + kappa*(1-h[phase]) * IG(a,b); IG in bps^2, V_N in Y per step; e.g. kappa=1e-5 * IG=89 bps^2 = 8.9e-4 Y per step = 8.9 per run", "between_component_variance": "enters through the belief sd the policy feeds the tables: TwoComp.moments gives v = sum_i w_i (v_i + (m_i - m)^2), so on every callback where the belief is collapsed (all non-ambiguous first trades and all later trades of a step) the sd level includes pi(1-pi)(lp-mt)^2. On the ambiguous first trade COMBO's rule (kept fixed) looks up each branch at its own sd (0 for the point mass, sqrt(vt) for the retail branch) and pi-weights the offsets, so there the between-component part is carried by the weighting, not by the sd level. Measured on seeds 10000/64000 (C_k1e-5): between-component variance averages 140/133 bps^2 of a 215/204 bps^2 mixture variance on ambiguous first trades (65%).", "samples_bps2 (sd level -> igtab vs igtab2 at offsets a,b relative to the estimate)": { "sd0": { "a+30bps_b+30bps": { "igtab": 0.6411, "igtab2": 0.0404 }, "a+50bps_b+50bps": { "igtab": 0.0009, "igtab2": 0.0 }, "a+0bps_b+0bps": { "igtab": 89.3025, "igtab2": 89.3025 }, "a+15bps_b+60bps": { "igtab": 14.9788, "igtab2": 5.9513 }, "a-10bps_b+60bps": { "igtab": 85.4348, "igtab2": 74.545 }, "tau2_total_prior_var_bps2": 89.3025, "max_igtab2": 89.3025, "min_igtab2": -0.0, "any_negative_igtab2": false }, "sd8": { "a+30bps_b+30bps": { "igtab": 11.2311, "igtab2": 1.5982 }, "a+50bps_b+50bps": { "igtab": 0.061, "igtab2": 0.0003 }, "a+0bps_b+0bps": { "igtab": 153.3025, "igtab2": 153.3025 }, "a+15bps_b+60bps": { "igtab": 47.4531, "igtab2": 18.4176 }, "a-10bps_b+60bps": { "igtab": 143.2979, "igtab2": 120.597 }, "tau2_total_prior_var_bps2": 153.3025, "max_igtab2": 153.3025, "min_igtab2": -0.0, "any_negative_igtab2": false }, "sd20": { "a+30bps_b+30bps": { "igtab": 264.2181, "igtab2": 91.6745 }, "a+50bps_b+50bps": { "igtab": 63.6134, "igtab2": 5.628 }, "a+0bps_b+0bps": { "igtab": 489.3025, "igtab2": 489.3025 }, "a+15bps_b+60bps": { "igtab": 280.0085, "igtab2": 133.4509 }, "a-10bps_b+60bps": { "igtab": 441.8467, "igtab2": 358.6712 }, "tau2_total_prior_var_bps2": 489.3025, "max_igtab2": 489.3025, "min_igtab2": -0.0, "any_negative_igtab2": false }, "sd34": { "a+30bps_b+30bps": { "igtab": 1044.0266, "igtab2": 648.3749 }, "a+50bps_b+50bps": { "igtab": 659.0791, "igtab2": 202.6488 }, "a+0bps_b+0bps": { "igtab": 1245.3025, "igtab2": 1245.3025 }, "a+15bps_b+60bps": { "igtab": 974.2925, "igtab2": 598.1035 }, "a-10bps_b+60bps": { "igtab": 1166.425, "igtab2": 968.5889 }, "tau2_total_prior_var_bps2": 1245.3025, "max_igtab2": 1245.3025, "min_igtab2": -0.0, "any_negative_igtab2": false } } }, "point_mass_zero_weight_checks": { "qmdp.ebel(0)": { "nodes": [ 0 ], "weights": [ 1.0 ] }, "qmdp.ebel(4)": { "n_nodes": 7, "weight_sum": 1.0000000000000002, "min_weight": 0.00044074336693235636 }, "igtab2 sign": { "sd0": { "min": -0.0, "max": 89.3025, "any_negative": false, "tau2": 89.3025 }, "sd4": { "min": -0.0, "max": 105.3025, "any_negative": false, "tau2": 105.3025 }, "sd8": { "min": -0.0, "max": 153.3025, "any_negative": false, "tau2": 153.3025 }, "sd12": { "min": -0.0, "max": 233.3025, "any_negative": false, "tau2": 233.3025 }, "sd16": { "min": -0.0, "max": 345.3025, "any_negative": false, "tau2": 345.3025 }, "sd20": { "min": -0.0, "max": 489.3025, "any_negative": false, "tau2": 489.3025 }, "sd26": { "min": -0.0, "max": 765.3025, "any_negative": false, "tau2": 765.3025 }, "sd34": { "min": -0.0, "max": 1245.3025, "any_negative": false, "tau2": 1245.3025 } }, "level0_vs_solved_tables": { "qm_ig2_k0": { "A0c_level0_vs_pol_mid": { "max_bps": 0.005, "cells_over_0.01bps": 0, "cells": 4173 }, "B0c_level0_vs_pol_mid": { "max_bps": 0.005, "cells_over_0.01bps": 0, "cells": 4173 }, "A1s_level0_vs_pol_mid": { "max_bps": 0.005, "cells_over_0.01bps": 0, "cells": 15729 }, "B1s_level0_vs_pol_mid": { "max_bps": 0.005, "cells_over_0.01bps": 0, "cells": 15729 }, "A2s_level0_vs_pol_mid": { "max_bps": 0.005, "cells_over_0.01bps": 0, "cells": 15729 }, "B2s_level0_vs_pol_mid": { "max_bps": 0.005, "cells_over_0.01bps": 0, "cells": 15729 } }, "qm_ig2_k1e-5": { "A0c_level0_vs_pol_mid": { "max_bps": 31.108, "cells_over_0.01bps": 1968, "cells": 4173 }, "B0c_level0_vs_pol_mid": { "max_bps": 31.108, "cells_over_0.01bps": 1968, "cells": 4173 }, "A1s_level0_vs_pol_mid": { "max_bps": 47.53, "cells_over_0.01bps": 5958, "cells": 15729 }, "B1s_level0_vs_pol_mid": { "max_bps": 47.53, "cells_over_0.01bps": 5958, "cells": 15729 }, "A2s_level0_vs_pol_mid": { "max_bps": 52.041, "cells_over_0.01bps": 6311, "cells": 15729 }, "B2s_level0_vs_pol_mid": { "max_bps": 52.041, "cells_over_0.01bps": 6311, "cells": 15729 } }, "qm_ig2_k3e-5": { "A0c_level0_vs_pol_mid": { "max_bps": 33.185, "cells_over_0.01bps": 2030, "cells": 4173 }, "B0c_level0_vs_pol_mid": { "max_bps": 33.185, "cells_over_0.01bps": 2030, "cells": 4173 }, "A1s_level0_vs_pol_mid": { "max_bps": 49.028, "cells_over_0.01bps": 7169, "cells": 15729 }, "B1s_level0_vs_pol_mid": { "max_bps": 49.028, "cells_over_0.01bps": 7169, "cells": 15729 }, "A2s_level0_vs_pol_mid": { "max_bps": 53.138, "cells_over_0.01bps": 7479, "cells": 15729 }, "B2s_level0_vs_pol_mid": { "max_bps": 53.138, "cells_over_0.01bps": 7479, "cells": 15729 } }, "qm_ig2_k1e-4": { "A0c_level0_vs_pol_mid": { "max_bps": 39.044, "cells_over_0.01bps": 2083, "cells": 4173 }, "B0c_level0_vs_pol_mid": { "max_bps": 39.044, "cells_over_0.01bps": 2083, "cells": 4173 }, "A1s_level0_vs_pol_mid": { "max_bps": 53.097, "cells_over_0.01bps": 7442, "cells": 15729 }, "B1s_level0_vs_pol_mid": { "max_bps": 53.097, "cells_over_0.01bps": 7442, "cells": 15729 }, "A2s_level0_vs_pol_mid": { "max_bps": 56.118, "cells_over_0.01bps": 7719, "cells": 15729 }, "B2s_level0_vs_pol_mid": { "max_bps": 56.118, "cells_over_0.01bps": 7719, "cells": 15729 } }, "qm_ig1_k1e-5": { "A0c_level0_vs_pol_mid": { "max_bps": 30.818, "cells_over_0.01bps": 1373, "cells": 4173 }, "B0c_level0_vs_pol_mid": { "max_bps": 30.818, "cells_over_0.01bps": 1373, "cells": 4173 }, "A1s_level0_vs_pol_mid": { "max_bps": 47.41, "cells_over_0.01bps": 2652, "cells": 15729 }, "B1s_level0_vs_pol_mid": { "max_bps": 47.41, "cells_over_0.01bps": 2652, "cells": 15729 }, "A2s_level0_vs_pol_mid": { "max_bps": 51.951, "cells_over_0.01bps": 2044, "cells": 15729 }, "B2s_level0_vs_pol_mid": { "max_bps": 51.951, "cells_over_0.01bps": 2044, "cells": 15729 } } }, "nan_cells": { "qm_ig2_k0": 0, "qm_ig2_k1e-5": 0, "qm_ig2_k3e-5": 0, "qm_ig2_k1e-4": 0, "qm_ig1_k1e-5": 0 }, "in_policy (Diag subclass of ComboK, C_k1e-5, seeds 10000 / 64000)": { "first_calls": [ 6297, 6569 ], "two_component_posteriors": [ 5375, 5587 ], "single_point_mass (pi>=.995, v=0)": [ 273, 314 ], "single_gaussian (pi<=.005)": [ 649, 668 ], "components_with_weight<=1e-300": [ 0, 0 ], "two_component_beliefs_collapsed_to_one_in_propagate (zero-mass fallback or DUAL_CUTS)": [ 391, 362 ], "asserts": "every two-component belief has v_arb == 0, .005 < pi < .995, weights summing to 1; every single component has weight 1.0; trunc(v=0) returns the indicator mass (qmref.trunc) so a point mass propagates without division by zero" } }, "table_regeneration": { "qm_ig2_k0": { "sha256": "7a1ee71ab0a0fabfe21f485fe8ad6d664d4af56c753dff0b1cc9f7e18cf68a96", "bytes": 7887325, "kappa": 0.0, "vs_kappa0_tables": null }, "qm_ig2_k1e-5": { "sha256": "8089dec083acc744e163c657ad4bc4e016f8f8fd172ce99c1318e834803eb168", "bytes": 7899218, "kappa": 1e-05, "vs_kappa0_tables": { "A0c": { "mean_diff_bps": -0.494, "frac_cells_changed": 0.5105 }, "A1s": { "mean_diff_bps": -0.681, "frac_cells_changed": 0.479 }, "A1c": { "mean_diff_bps": -0.706, "frac_cells_changed": 0.5109 }, "A2s": { "mean_diff_bps": -0.768, "frac_cells_changed": 0.4877 }, "A2c": { "mean_diff_bps": -0.771, "frac_cells_changed": 0.5081 } } }, "qm_ig2_k3e-5": { "sha256": "461046701b49bfec634935d51a5d5ab1d8799d262ef976219d7c51312b33c69a", "bytes": 7916108, "kappa": 3e-05, "vs_kappa0_tables": { "A0c": { "mean_diff_bps": -1.459, "frac_cells_changed": 0.5149 }, "A1s": { "mean_diff_bps": -1.977, "frac_cells_changed": 0.4949 }, "A1c": { "mean_diff_bps": -1.984, "frac_cells_changed": 0.5164 }, "A2s": { "mean_diff_bps": -2.085, "frac_cells_changed": 0.5038 }, "A2c": { "mean_diff_bps": -2.111, "frac_cells_changed": 0.5196 } } }, "qm_ig2_k1e-4": { "sha256": "48ece9ad5f1cedf326420ec339732f49179a83fb717f48d8e33a28539ec92894", "bytes": 7949611, "kappa": 0.0001, "vs_kappa0_tables": { "A0c": { "mean_diff_bps": -4.406, "frac_cells_changed": 0.5191 }, "A1s": { "mean_diff_bps": -5.246, "frac_cells_changed": 0.5031 }, "A1c": { "mean_diff_bps": -5.078, "frac_cells_changed": 0.5228 }, "A2s": { "mean_diff_bps": -5.133, "frac_cells_changed": 0.5133 }, "A2c": { "mean_diff_bps": -5.142, "frac_cells_changed": 0.5263 } } }, "qm_ig1_k1e-5": { "sha256": "afeab9ec765609bc466d8631444afb2caa283c2bbf7c24de078e9f97511e33c2", "bytes": 7892018, "kappa": 1e-05, "vs_kappa0_tables": { "A0c": { "mean_diff_bps": -0.331, "frac_cells_changed": 0.4879 }, "A1s": { "mean_diff_bps": -0.472, "frac_cells_changed": 0.43 }, "A1c": { "mean_diff_bps": -0.488, "frac_cells_changed": 0.4577 }, "A2s": { "mean_diff_bps": -0.525, "frac_cells_changed": 0.4251 }, "A2c": { "mean_diff_bps": -0.531, "frac_cells_changed": 0.4443 } } } }, "source_patch": { "kpol.py": "ComboK(Combo): __init__ takes a table path (.json -> JsonTables: A/B tags 0c 1s 1c 2s 2c read straight from the qmdp.py JSON; else qmref.Tables on the blob) and a flag; on_trade is combo.py lines 46-110 verbatim with three lines inserted right after \"pi = la / (la + lr) if la + lr > 0 else 0.\":", "inserted_lines": [ "self.total += 1", "if (pi > .5) != bool(arb): self.wrong += 1", "if self.flag: pi = float(bool(arb))" ], "placement": "immediately after the likelihood, before is_arb, the posterior (self.comp / self.m / self.v), the rival clip, the phase and the quote; other callbacks unchanged", "QMRefCount(QMRef)": "qt1 reference with the same error counter (cnt == 0 after a first call <=> classified as arb)", "Scramble": "hidden-input invariance wrapper", "run.py": "resumable Pool runner, rows [seed, edge, wrong, total, new_path_calls, secs] to scratch/state/MODE.jsonl", "agg.py": "paired stats, coverage, row hashes, selection" }, "regeneration_recipe": [ "git clone https://github.com/gtmcknight/amm-sim; git checkout 4812a6382311624e1506aca131ca35c378f930d9", "uv venv --python 3.12 scratch/.venv; uv pip install numpy numba", "cd research/solved; DP_SAVEVN=1 DP_AMINL=-12 DP_NA=43 python dp.py solve 0.8 9.45 20 scratch/vn/pol_mid.json", "for K in 0 1e-5 3e-5 1e-4: IG2=1 DP_AMINL=-12 DP_NA=43 python qmdp.py scratch/vn/pol_mid.json scratch/tabs/qm_ig2_k$K.json $K", "control: DP_AMINL=-12 DP_NA=43 python qmdp.py scratch/vn/pol_mid.json scratch/tabs/qm_ig1_k1e-5.json 1e-5 (equals qm_k1e-5.json)", "extract qmref.py / twocomp.py / combo.py / blob.bin from the four artifacts (first python fence after \"## Code\" for TC and COMBO; \"## Python reference\" fence for qt1; \"## Data\" base64 for QMS1), check the sha256s above, place beside kpol.py", "python3 -I run.py qt1,combo,flag,c0,c1,c3,c10,f0,f1,f3,f10,cT 64000 65024 4 420 (repeat until todo=0); same for 10000 12048 without cT; python3 -I agg.py" ], "commands_timings": [ "python3 -I gates.py: 2.8 s", "uv install + venv + numpy/numba: ~60 s", "dp.py solve (VN): 425 s", "qmdp.py: 15 s (k0), 15 s (1e-5), 16 s (3e-5), 16 s (1e-4), 13 s (IG1 control)", "run.py qt1,combo,flag choose, 2 workers: 170 s", "run.py kappa+control choose (3 workers) || bases report (1 worker): 430 s each, then 93 s to finish choose", "run.py report, 4 workers: 150 s + 428 s", "agg.py < 2 s; tabcheck.py ~20 s; invariance + Diag checks ~10 s", "no command exceeded 8 minutes; all state under scratch/" ], "limitations": [ "Replica only (Taylor's replica2, different RNG streams from the Rust engine); paired gaps, not board scores. No contract, no engine seeds consumed.", "The live winner is chosen by the rule but does not beat COMBO (-0.016 se 0.009 on report); the item's useful finding is negative for live quoting and positive only under the oracle flag (+0.10 at kappa 1e-5).", "The control C_IG1_k1e-5 was run on the choose window only (1024 seeds), to keep the report window within time; it is a control, not a candidate.", "Between-component variance is included through the collapsed moments the policy feeds the tables; on ambiguous first trades COMBO's per-branch lookups were kept as published (filter and quoting rule fixed by the brief), so the information term is not evaluated at the full mixture sd on those callbacks. A table family indexed by both the within- and the between-component sd was not built.", "kappa was swept at the four predeclared values only; no interpolation between 1e-5 and 3e-5 was tried.", "The flagged error counts report the live filter's disagreement with truth while the policy follows truth; they are lower than the live ones (11.6-11.8%) because oracle quoting changes the trades the filter sees.", "Per-seed timings are from a loaded 4-core box with 2-8 concurrent workers; they are not clean measurements." ] }