{"variant":"rep-b-truncated-gaussian-latent-router","status":"complete_replica_experiment_target_missed","target_gap_max":2.0,"target_met":false,"seeds_configs":{"train":[128,255],"evaluation":[10000,10255],"ablation":[10000,10063],"steps":10000,"n":256,"forbidden_seeds_used":false,"replica_config":"random.Random(10000000+seed): size_mean U[19,21], lambda U[.6,1], sigma U[.000882,.001008], in that order. Overrides none. Hidden from Filter; initial reserves X=100,Y=10000 in each pool; initial fair price100; rival fee .003; policy initial fee .003. Python random streams from unmodified replica.py, not Rust-engine seeds."},"provenance":[{"url":"https://raw.githubusercontent.com/gtmcknight/amm-sim/main/research/filter-brief.md","sha256":"0ef2200226b68aa58de6aad268442ba09ada710c54b3fb0ec35c77b491f78a4b"},{"url":"https://raw.githubusercontent.com/gtmcknight/amm-sim/main/research/oracle_table.json","sha256":"3e9d1fc8874c6d796d4c26948d486b587f2a6b5610b20fba99923a60954cf4b5"},{"url":"https://raw.githubusercontent.com/gtmcknight/amm-sim/main/research/replica.py","sha256":"d079712fa1f4850ad8337e656e7ee8dbdde806cd4762d597fae50f547ef9c7c4"},{"url":"https://raw.githubusercontent.com/gtmcknight/amm-sim/main/research/setup.sh","sha256":"dc7fa6a1e59f5b043d3954cf68d538318b7affaf5c0db3ca69a1822680f300d4"},{"url":"https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_competition/market/router.py","sha256":"6ecb8e68513757b7d3e4a6f327bc47d693c7d923591ebee815621026afeff842"},{"url":"https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_competition/market/arbitrageur.py","sha256":"b0227af3548d74f70f3cc86f731715a64045ee00200a2dbf20a78da66b4ad832"}],"parameters":"{\"sigma0\":0.000945,\"lambda0\":0.4,\"router_strength\":0.15,\"rival_tail\":0.35,\"variance_floor\":1e-12,\"sigma_prior_weight\":200.0,\"order_mean\":20.0,\"order_log_sd\":1.2}","freeze":{"parameters":{"sigma0":0.000945,"lambda0":0.4,"router_strength":0.15,"rival_tail":0.35,"variance_floor":1e-12,"sigma_prior_weight":200.0,"order_mean":20.0,"order_log_sd":1.2},"source_sha256":"c82aaa246c6e86e575dfd3d739674c6f404f4027310107ce07030a03aae16431","unix_time":1794240312.0,"selection":"router04 on training128..255; router-off slightly better on training but retain requested router likelihood"},"method":{"state":"m=E[ln(p/spot)], v=Var[ln(p/spot)], own reserves and last timestamp/returned fees; shrunk sigma estimate and last high-confidence inferred arb pin. No RS2 code or fee overlay.","timing":"Initialize z=0,t=-1. Each fully silent step: GBM log drift -sigma²/2 and variance +sigma², then Gaussian truncation to [ln(1-bid),-ln(1-ask)]. Diffuse once for current new timestamp. First callback mixes arb and no-arb/retail branches. Same-timestamp later callbacks are retail without further diffusion/truncation. Shift both hypothesis means by -ln(spot_after/spot_before).","arb":"First-callback arb density is prior Normal density at the uncapped fee-adjusted price pin, in log reserve-displacement units. Retail branch is current no-arb truncation weighted by effective retail intensity/2 and marginalized fill density. Later callbacks are retail. Table flag is posterior arb probability, never truth.","router":"Inverse router marginalizes a lognormal total-order prior and a 3-node rival band plus 3-node broad tail. Tail weight .35 on first callback, .8 repeated: band is only a post-rival-arb prior. Five-point Gaussian quadrature, likelihood power .15 for moments; raw fill density for branch evidence. Entire-order-to-own endpoint included. Exact formulas are in source.","sigma":"Squared inferred-pin log moves divided by elapsed time, weighted only at arb posterior>.98; winsorized, shrunk with200 pseudo-observations, bounded to generator support. Selection-biased; sigma uncertainty is not propagated. See source for exact constants.","table":"Frozen original 17 ask+17 bid knots at displacement -8..8 in .003 units, plus arb offset .1463. Linear interpolation, endpoint clamp, fees clamp[0,.1]. Uses p_hat=spot*exp(m).","closure":"Callback discarded standardized third central moment and fourth central moment minus3, absolute values averaged by callback. Retail quadrature moments plus arb point mass computed before Gaussian projection. These are local non-Gaussian closure diagnostics, not KL/RMS versus an exact grid posterior; silent-step truncation closure was not separately benchmarked."},"per_seed_columns":["seed","filtered_edge","filtered_retail_edge","filtered_arb_edge","filtered_retail_volume_y","filtered_arb_volume_y","oracle_edge","oracle_retail_edge","oracle_arb_edge","oracle_retail_volume_y","oracle_arb_volume_y","diagnostic_edge","diagnostic_retail_edge","diagnostic_arb_edge","diagnostic_retail_volume_y","diagnostic_arb_volume_y","oracle_minus_filtered","filtered_squared_log_error_sum","filtered_callback_count"],"per_seed":[[10000,43935,46209,-2274,61515,21383,44568,46542,-1974,62676,20750,44572,46544,-1972,62267,20687,6330,21013885,8467],[10001,56650,59599,-2949,87479,26712,57259,59836,-2576,88629,26004,57252,59823,-2571,88079,25898,6096,27899011,11729],[10002,52316,55355,-3039,68412,24887,52797,55546,-2749,69316,23992,52780,55528,-2749,68896,23949,4807,27190407,9691],[10003,56537,59479,-2942,81650,26745,57364,59941,-2577,82804,25936,57355,59928,-2573,82341,25847,8269,30176063,11178],[10004,51790,54369,-2580,72318,24092,52459,54757,-2298,73742,23809,52457,54750,-2292,73298,23740,6691,24362475,9866],[10005,52380,55092,-2712,72595,24106,52773,55098,-2325,73539,23415,52798,55123,-2325,73061,23363,3933,24167667,10002],[10006,48052,50619,-2567,74204,23699,48762,51014,-2251,75296,22988,48722,50969,-2247,74762,22909,7106,22422629,10303],[10007,52029,54774,-2745,76170,24364,52721,55118,-2397,77243,23735,52690,55077,-2387,76742,23622,6921,28998954,10494],[10008,65520,68739,-3219,95029,28317,66411,69207,-2796,96184,27361,66382,69171,-2789,95565,27249,8911,30442976,12030],[10009,64484,67643,-3160,91499,28029,65373,68157,-2783,92586,27195,65380,68154,-2775,92082,27125,8897,30889820,12110],[10010,47270,49812,-2542,74887,23419,47956,50160,-2204,76561,22847,47971,50169,-2199,76142,22777,6859,27390968,10679],[10011,36623,38606,-1983,58032,18840,37152,38893,-1741,58838,18499,37098,38840,-1742,58467,18471,5292,19350862,8300],[10012,45266,47931,-2665,73842,23628,45900,48124,-2224,75283,22751,45850,48066,-2216,74673,22653,6343,31007851,10305],[10013,39766,41823,-2057,56939,19383,40285,42049,-1764,58206,18876,40264,42026,-1762,57816,18827,5192,21229081,8285],[10014,69547,73200,-3653,86771,27274,70286,73525,-3239,87676,26631,70268,73503,-3234,87167,26577,7388,25193593,11257],[10015,62080,65382,-3302,91670,28392,63233,66092,-2859,93499,27734,63213,66068,-2855,92908,27671,11536,33615811,11750],[10016,55889,62841,-6952,70528,24035,56934,63546,-6612,71953,23389,56940,63550,-6609,71506,23321,10450,26780722,9668],[10017,48922,51611,-2689,72000,24271,49451,51884,-2433,73105,23875,49431,51858,-2428,72691,23801,5289,23698063,10094],[10018,47594,50237,-2643,69325,24198,48217,50476,-2259,70469,23390,48210,50470,-2260,70033,23375,6226,24277721,9505],[10019,45132,47400,-2268,60909,21072,45547,47495,-1949,62126,20408,45543,47490,-1947,61754,20358,4145,20309039,8464],[10020,49241,51825,-2584,67485,23872,49815,52105,-2289,68460,23206,49792,52081,-2289,68071,23176,5737,21933901,9357],[10021,40604,42711,-2107,56169,20199,41341,43131,-1790,57696,19503,41260,43059,-1800,57292,19548,7369,22678430,8325],[10022,43490,45807,-2317,60771,20984,44204,46185,-1982,61813,20259,44177,46157,-1980,61393,20207,7141,24765929,8727],[10023,62858,66150,-3291,86420,27193,63530,66430,-2900,87931,26226,63493,66384,-2891,87293,26124,6718,26843288,10957],[10024,47458,50138,-2680,72498,24478,48368,50696,-2329,73875,23743,48319,50641,-2321,73419,23615,9098,28676709,10577],[10025,44222,46581,-2359,61698,21381,44767,46814,-2047,62444,20480,44725,46771,-2046,62030,20465,5456,26594407,9224],[10026,34175,36136,-1961,53302,18809,34739,36463,-1724,54625,18426,34732,36453,-1720,54295,18374,5643,22277621,8330],[10027,54330,57147,-2816,73045,24839,54971,57440,-2469,73914,24197,54993,57454,-2461,73568,24102,6405,26749867,10161],[10028,52180,55191,-3011,67631,23541,52777,55483,-2706,68638,23007,52764,55471,-2707,68254,22971,5965,24231046,9267],[10029,43763,46130,-2367,71827,22215,44458,46482,-2023,72761,21296,44393,46411,-2018,72166,21203,6958,26452783,10316],[10030,58887,62107,-3220,88798,28045,59782,62556,-2774,89760,27047,59751,62516,-2765,89151,26927,8943,32303807,11708],[10031,33568,35736,-2168,56820,20504,34356,36174,-1818,58012,19671,34324,36142,-1818,57634,19662,7878,26049943,8598],[10032,63119,66213,-3095,85886,27046,63794,66471,-2678,86666,26072,63802,66477,-2676,86213,26032,6749,26935570,10999],[10033,53007,55924,-2917,80937,25943,53645,56136,-2491,82156,25100,53645,56134,-2489,81706,25019,6374,27878946,10877],[10034,56008,58831,-2823,83793,25473,56654,59086,-2432,84710,24619,56648,59073,-2425,84124,24513,6459,30353446,11490],[10035,62793,66107,-3314,93791,28530,63615,66460,-2845,95097,27580,63566,66408,-2842,94527,27517,8223,31925665,12214],[10036,54101,56986,-2885,81332,25477,54664,57115,-2451,82299,24462,54623,57070,-2447,81748,24413,5631,30947337,11036],[10037,43923,46372,-2450,66273,22549,44518,46613,-2094,67466,21412,44503,46592,-2089,66972,21367,5959,25637093,9431],[10038,61365,64441,-3076,91194,27882,62061,64759,-2699,92528,2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are integers: multiply each column by its scale. Edge resolution .01Y; volume1Y; gap.001Y; squared log error1e-9. Aggregates use original full precision. Aggregate floats retain10 significant figures.","aggregate":{"filtered":{"edge":528.6008375,"retail":563.6836357,"arb":-35.08279812,"rv":75130.86852,"av":24719.58032,"fb":37.2760993,"fa":36.32369985,"callback_count":2635831,"squared_log_error_sum":6.864977511,"estimator_rms_bps":16.13841127,"estimator_bias_bps":0.05637321185,"coverage_1sd":0.7620405102,"coverage_1_96sd":0.9298088535,"discarded_abs_standardized_third":3.6398581,"discarded_abs_excess_fourth":5487.335739,"arb_brier":0.07588530553,"high_confidence_true_arb":315282,"high_confidence_false_arb":4868,"sigma_final_mean":0.000882,"sigma_final_range":[0.000882,0.000882],"sigma_final_rmse_vs_hidden":7.061281997e-05},"oracle":{"edge":535.2169861,"retail":566.7139983,"arb":-31.49701214,"rv":76276.09986,"av":23965.94175,"fb":36.81822657,"fa":35.84340548,"callback_count":2634811,"squared_log_error_sum":6.711691735,"estimator_rms_bps":15.96030795,"estimator_bias_bps":-0.004270734669,"coverage_1sd":0.763184532,"coverage_1_96sd":0.9105332413,"discarded_abs_standardized_third":4.81400818,"discarded_abs_excess_fourth":18156.1418,"arb_brier":0.07522681224,"high_confidence_true_arb":317052,"high_confidence_false_arb":5115,"sigma_final_mean":0.000882,"sigma_final_range":[0.000882,0.000882],"sigma_final_rmse_vs_hidden":7.061281997e-05},"diagnostic":{"edge":535.0002466,"retail":566.4609466,"arb":-31.46069999,"rv":75810.50624,"av":23902.02368,"fb":37.16580079,"fa":36.20707555,"callback_count":2616580,"squared_log_error_sum":6.847965875,"estimator_rms_bps":16.17758852,"estimator_bias_bps":-0.0118951996,"coverage_1sd":0.76287635,"coverage_1_96sd":0.9091791575,"discarded_abs_standardized_third":4.678432657,"discarded_abs_excess_fourth":15591.75319,"arb_brier":0.07507237379,"high_confidence_true_arb":315054,"high_confidence_false_arb":4897,"sigma_final_mean":0.000882,"sigma_final_range":[0.000882,0.000882],"sigma_final_rmse_vs_hidden":7.061281997e-05}},"paired":{"oracle_minus_filtered":{"n":256,"mean":6.61614861,"se":0.0862074089,"ci95":[6.447182088,6.785115131]},"oracle_minus_diagnostic":{"n":256,"mean":0.2167395737,"se":0.01372342749,"ci95":[0.1898416558,0.2436374915]},"diagnostic_minus_filtered":{"n":256,"mean":6.399409036,"se":0.08641890421,"ci95":[6.230027984,6.568790088]},"ci":"Normal approximation mean +/-1.96 sample-SE, paired across independent seeds; no IID callback CI asserted."},"ablation":{"n":64,"retuned":false,"change":"router=False; remove both router moment likelihood and router evidence in branch classification; use fixed retail displacement density100. All frozen parameters unchanged.","aggregate":{"edge":519.6117744,"retail":565.158698,"arb":-45.54692358,"rv":75064.67434,"av":24550.3861,"fb":36.7385379,"fa":36.33443211,"callback_count":661064,"squared_log_error_sum":2.228018331,"estimator_rms_bps":18.35851828,"estimator_bias_bps":0.03742199139,"coverage_1sd":0.7287312575,"coverage_1_96sd":0.8594765408,"discarded_abs_standardized_third":5.244451947,"discarded_abs_excess_fourth":6810.176087,"arb_brier":0.1028968177,"high_confidence_true_arb":120533,"high_confidence_false_arb":5521,"sigma_final_mean":0.000882,"sigma_final_range":[0.000882,0.000882],"sigma_final_rmse_vs_hidden":6.665610233e-05},"oracle_minus_off":{"n":64,"mean":6.778905206,"se":0.2149034594,"ci95":[6.357694426,7.200115987]},"off_minus_on":{"n":64,"mean":-0.01579416824,"se":0.1549372062,"ci95":[-0.3194710924,0.2878827559]},"per_seed_columns":["seed","off_edge","oracle_minus_off","off_minus_on","squared_log_error_sum","callback_count"],"per_seed":[[10000,44020,5482,848,25152800,8544],[10001,56626,6333,-237,37825714,11778],[10002,52125,6718,-1911,31881289,9725],[10003,56489,8755,-486,40166577,11199],[10004,51833,6254,437,31590605,9910],[10005,52311,4624,-691,31321765,10031],[10006,48066,6963,143,29617450,10364],[10007,51946,7754,-833,37676428,10557],[10008,65402,10088,-1177,38101355,12128],[10009,64530,8439,458,42991794,12145],[10010,47410,5453,1406,36022330,10780],[10011,36631,5215,77,23041166,8389],[10012,45260,6400,-57,41954639,10442],[10013,39865,4202,990,24704481,8372],[10014,69464,8218,-830,33726744,11330],[10015,62124,11094,442,46757383,11886],[10016,56129,8049,2401,36070344,9814],[10017,48927,5244,45,30292123,10166],[10018,47749,4675,1551,29790845,9596],[10019,45075,4716,-571,25982808,8525],[10020,49171,6444,-707,31434069,9500],[10021,40861,4795,2574,27994901,8487],[10022,43620,5838,1303,31222816,8832],[10023,62749,7811,-1092,35502670,10970],[10024,47509,8582,516,37670218,10648],[10025,44300,4666,789,33654284,9290],[10026,34298,4416,1227,26854193,8470],[10027,54480,4906,1498,37411354,10249],[10028,52119,6578,-614,30935654,9341],[10029,43519,9391,-2433,35702335,10323],[10030,58862,9196,-253,41243781,11762],[10031,33796,5597,2281,33958098,8735],[10032,63124,6700,49,34023667,11034],[10033,53024,6201,173,38296197,10936],[10034,55819,8354,-1896,40051877,11509],[10035,62838,7770,452,41173776,12327],[10036,54084,5800,-170,40875960,11088],[10037,43908,6106,-147,33027470,9470],[10038,61164,8965,-2006,44381056,12446],[10039,58393,6660,-578,42173475,10670],[10040,60179,8193,-1609,36801529,12281],[10041,62227,10010,-597,36216864,11319],[10042,70403,7181,-2855,36889745,12191],[10043,62970,9558,-2880,42139527,11594],[10044,41756,4334,1835,23939390,8557],[10045,38189,6220,549,32653022,9125],[10046,42701,7185,-46,34444499,10133],[10047,59071,8928,-250,41796976,12066],[10048,49224,4973,890,41242886,10146],[10049,37937,6534,-122,26537813,8607],[10050,37010,8454,-385,27674513,8858],[10051,41834,6388,-382,29645195,8695],[10052,42532,6226,-204,33744469,10210],[10053,52980,8168,-1527,37102368,10180],[10054,44058,3749,522,38198134,9259],[10055,70439,6350,498,42674940,12458],[10056,57759,5873,-674,35209166,10902],[10057,50323,7609,-1643,31853500,9694],[10058,43612,3951,2597,27397060,8905],[10059,50355,5891,592,34773695,9994],[10060,92262,6158,384,40828244,11758],[10061,55504,7864,-1239,35373989,11218],[10062,60170,9285,1371,37205494,11829],[10063,42402,5314,1193,31418820,9317]],"per_seed_scales":[1,0.01,0.001,0.001,1e-09,1]},"training":{"protocol":"25 candidate combinations screened on128..143: router off with effective arrival factors .15,.4,.8,1.6,3.2; router on same factors crossed likelihood powers0,.15,.5,1. Finalists compared on128..255. Selected weak router at .4/.15 to retain requested observation, despite off variant scoring slightly higher. All frozen before evaluation.","baseline_original_parameters":"lambda0=.8,router_strength=.25, remaining parameters unchanged","baseline_gap":{"n":128,"mean":8.370301881,"se":0.1269872306,"ci95":[8.121406909,8.619196853]},"finalists":[{"variant":"router04","parameters":{"lambda0":0.4,"router_strength":0.15},"router":true,"edge_mean":516.3595076,"oracle_minus_filter":{"n":128,"mean":6.983440888,"se":0.1219395832,"ci95":[6.744439305,7.222442471]}},{"variant":"off04","parameters":{"lambda0":0.4,"router_strength":0.0},"router":false,"edge_mean":516.4572377,"oracle_minus_filter":{"n":128,"mean":6.885710749,"se":0.1428245108,"ci95":[6.605774708,7.16564679]}},{"variant":"router04zero","parameters":{"lambda0":0.4,"router_strength":0.0},"router":true,"edge_mean":516.3697546,"oracle_minus_filter":{"n":128,"mean":6.973193859,"se":0.1217366289,"ci95":[6.734590066,7.211797651]}}]},"tests":{"command":"python tests.py","result":"11 groups passed; assertion-based tests included verbatim in runnable source.","groups":["uncapped arb pin signs under informative prior","repeat timestamp zero arb/no diffusion","fully silent gap recurrence","t0 single diffusion","hidden p/s2/arb/init sigma/lambda/size isolation","truncated Gaussian moments vs20000-bin numerical integration","table knots","control-arm actual fee history","interpolation/endpoint clamp","initial reserves","10000-step gap finite bounded state"],"setup":"Pinned checkout and requested setup.sh succeeded; StarterStrategy compiled and validated. This is setup validation only.","harness":"Unmodified replica.py dynamics, RNG, accounting and router. Arm discards hidden init metadata and passes only own side/amounts/time/post-reserves to Filter. Hidden p/arb used after observe for measurements and the explicitly labeled controls. Control arms store the actual returned fees in Filter. No real-engine strategy test or Solidity port.","source_hashes":{"moments.py":"271d4bb2e160b3e6ee2a582c054d6656be862292b6602e3eff30efb6418c4459","replica.py":"5595300d079e1adb52528ad2f9d11a071f5a00b5404becfc0e15c6369894cb87","oracle_table.json":"3e9d1fc8874c6d796d4c26948d486b587f2a6b5610b20fba99923a60954cf4b5","tests.py":"b10da635f6178a2c21b9122d56f6231706a5403b596fe1f2ff2edb8f35576886"},"embedded_source_replay":"PASS: extracted embedded source; 11 test groups pass on system Python standard library; seed10000 all3 arms/all numeric metrics match original within1e-12.","output_validation":"PASS: JSON parse, <=64000 bytes,256 evaluation rows,64 ablation rows, source hashes, column lengths. Six source quotes matched fresh URL reads."},"runnable_source":{"moments.py":"import math,json,random,time,sys,hashlib\nfrom concurrent.futures import ProcessPoolExecutor\nimport replica\nSQ=math.sqrt(2*math.pi)\nTABLE=json.load(open(__file__.replace('moments.py','oracle_table.json')))\nPARAM=dict(sigma0=.000945,lambda0=.4,router_strength=.15,rival_tail=.35,variance_floor=1e-12,sigma_prior_weight=200.,order_mean=20.,order_log_sd=1.2)\ndef normal(x): return math.exp(-.5*x*x)/SQ\ndef trunc(m,v,lo,hi):\n    sd=math.sqrt(max(v,1e-16));a=(lo-m)/sd;b=(hi-m)/sd\n    Z=.5*(math.erf(b/math.sqrt(2))-math.erf(a/math.sqrt(2)))\n    if Z<1e-12:\n        return min(hi,max(lo,m)),min(v,(hi-lo)**2/12),max(0.,Z)\n    pa=normal(a);pb=normal(b);d=(pa-pb)/Z\n    return m+sd*d,max(1e-14,v*(1+(a*pa-b*pb)/Z-d*d)),Z\ndef fees(z,flag):\n    q=min(16.,max(0.,-z/.003+8));i=min(15,int(q));w=q-i\n    a=TABLE['ask'][i]*(1-w)+TABLE['ask'][i+1]*w+TABLE['arb_flag']*flag\n    b=TABLE['bid'][i]*(1-w)+TABLE['bid'][i+1]*w+TABLE['arb_flag']*flag\n    return replica.clampf(1-math.exp(z-b*.003)),replica.clampf(1-math.exp(-z-a*.003))\nNODES=(-2.8569700139,-1.35562618,0.,1.35562618,2.8569700139)\nWEIGHTS=(.0112574113,.222075922,.5333333333,.222075922,.0112574113)\nclass Filter:\n    def __init__(self,router=True): self.router=router\n    def init(self,x0=100.,y0=10000.):\n        self.m=0.;self.v=0.;self.s=y0/x0;self.x=x0;self.y=y0;self.k=x0*y0;self.t=-1\n        self.fb=self.fa=.003;self.sig2=PARAM['sigma0']**2;self.lastpin=None\n        self.sw=PARAM['sigma_prior_weight'];self.sv=self.sig2*self.sw\n        self.flag=0.;self.closure4=0.;self.closure=0.;self.closure_n=0;self.calls=0;self.mass=0.\n        return self.fb,self.fa\n    def retail_like(self,z,buy,ax,ay,first):\n        p=self.s*math.exp(z);g=1-(self.fb if buy else self.fa);g2=.997;r=math.sqrt(g/g2);d=g+r*g2\n        own=ax if buy else ay; jac=d/(r*g2)\n        mu=math.log(PARAM['order_mean'])-.72\n        out=0.\n        tail=PARAM['rival_tail'] if first else .8\n        for broad,mix in ((False,1-tail),(True,tail)):\n            offsets=(-.012,0.,.012) if broad else (-.002324,0.,.002324)\n            weights=(1/6,2/3,1/6) if broad else (5/18,8/18,5/18)\n            for off,w in zip(offsets,weights):\n                s2=p*math.exp(off); rival=math.sqrt(self.k/s2) if buy else math.sqrt(self.k*s2)\n                ours=self.x if buy else self.y\n                total=(d*own+ours-r*rival)/(r*g2)\n                size=total*p if buy else total\n                density=0.\n                if total>=own and size>0:\n                    density=math.exp(-.5*((math.log(size)-mu)/1.2)**2)/(size*1.2*SQ)*jac*(p if buy else 1)\n                atown=(r*(rival+g2*own)-ours)/d\n                if atown>=own:\n                    sizeown=own*p if buy else own\n                    density+=math.exp(-.5*((math.log(sizeown)-mu)/1.2)**2)/(max(sizeown,1e-15)*1.2*SQ)*(p if buy else 1)\n                out+=mix*w*density\n        post=self.x+g*ax if buy else self.y+g*ay\n        return max(1e-12,out*post/(2*g))\n    def observe(self,buy,ax,ay,t,x,y):\n        first=t!=self.t;lo=math.log1p(-self.fb);hi=-math.log1p(-self.fa)\n        if first:\n            for step in range(self.t+1,t):\n                self.m-=.5*self.sig2;self.v+=self.sig2\n                self.m,self.v,_=trunc(self.m,self.v,lo,hi)\n            self.m-=.5*self.sig2;self.v+=self.sig2\n        pm,pv=self.m,self.v\n        sn=y/x; shift=math.log(sn/self.s)\n        za=shift+(math.log1p(-self.fb) if buy else -math.log1p(-self.fa))\n        valid=first and ((buy and za<lo) or (not buy and za>hi)) and not (not buy and ax>=.989999*self.x)\n        la=normal((za-pm)/math.sqrt(max(pv,1e-16)))/math.sqrt(max(pv,1e-16)) if valid else 0.\n        if first: rm,rv,Z=trunc(pm,pv,lo,hi)\n        else: rm,rv,Z=pm,pv,1.\n        lr=1.;postm=rm;postv=rv;r3=0.;r4=3*rv*rv\n        if self.router:\n            vals=[rm+math.sqrt(rv)*n for n in NODES]\n            ls=[self.retail_like(z,buy,ax,ay,first)**PARAM['router_strength'] for z in vals]\n            lr=sum(w*l for w,l in zip(WEIGHTS,ls));postm=sum(w*l*z for w,l,z in zip(WEIGHTS,ls,vals))/lr\n            postv=max(1e-14,sum(w*l*(z-postm)**2 for w,l,z in zip(WEIGHTS,ls,vals))/lr)\n            r3=sum(w*l*(z-postm)**3 for w,l,z in zip(WEIGHTS,ls,vals))/lr\n            r4=sum(w*l*(z-postm)**4 for w,l,z in zip(WEIGHTS,ls,vals))/lr\n        raw=self.retail_like(rm,buy,ax,ay,first) if self.router else 100.\n        rb=PARAM['lambda0']*.5*Z*raw\n        prob=la/(la+rb+1e-300) if valid else 0.\n        m=prob*za+(1-prob)*postm\n        v=prob*(za-m)**2+(1-prob)*(postv+(postm-m)**2)\n        third=prob*(za-m)**3+(1-prob)*((postm-m)**3+3*(postm-m)*postv+r3)\n        fourth=prob*(za-m)**4+(1-prob)*((postm-m)**4+6*(postm-m)**2*postv+4*(postm-m)*r3+r4)\n        self.closure4+=abs(fourth/max(v,1e-14)**2-3)\n        self.closure+=abs(third)/max(v,1e-14)**1.5;self.closure_n+=1\n        if prob>.98:\n            lp=math.log(self.s)+za\n            if self.lastpin:\n                pt,pp=self.lastpin;dt=t-pt\n                if dt>0:\n                    est=min(1.5e-6,max(3e-7,(lp-pp)**2/dt))\n                    self.sw+=prob;self.sv+=prob*est\n                    self.sig2=min(1.016064e-6,max(7.77924e-7,self.sv/self.sw))\n            self.lastpin=(t,lp)\n        self.m=m-shift;self.v=max(PARAM['variance_floor'],v);self.s=sn;self.x=x;self.y=y;self.t=t;self.flag=prob\n        self.fb,self.fa=fees(self.m,prob);self.calls+=1;self.mass+=prob\n        return self.fb,self.fa\nclass Arm:\n    def __init__(self,mode,router=True): self.mode=mode;self.f=Filter(router)\n    def init(self,*hidden):\n        self.brier=0.;self.false_pin=0;self.true_pin=0;self.ss=0.;self.n=0;self.cover=0;self.cover1=0;self.bias=0.;return self.f.init()\n    def on_trade(self,buy,ax,ay,t,x,y,arb,p,s2):\n        out=self.f.observe(buy,ax,ay,t,x,y)\n        self.brier+=(self.f.flag-float(arb))**2\n        if self.f.flag>.98:\n            self.true_pin+=int(arb);self.false_pin+=int(not arb)\n        err=math.log(y/x)+self.f.m-math.log(p)\n        self.ss+=err*err;self.n+=1;self.bias+=err\n        self.cover+=int(abs(err)<=1.96*math.sqrt(self.f.v));self.cover1+=int(abs(err)<=math.sqrt(self.f.v))\n        if self.mode=='filtered': return out\n        out=fees(math.log(p/(y/x)),arb if self.mode=='oracle' else self.f.flag)\n        self.f.fb,self.f.fa=out\n        return out\ndef one(args):\n    seed,router=args;row=[seed];details=[]\n    for mode in ('filtered','oracle','diagnostic'):\n        a=Arm(mode,router);r=replica.run(seed,a)\n        details.append(dict(mode=mode,**r,ss=a.ss,n=a.n,cover=a.cover,cover1=a.cover1,bias=a.bias,closure=a.f.closure/a.f.closure_n,sigma_est=math.sqrt(a.f.sig2),closure4=a.f.closure4/a.f.closure_n,brier=a.brier,false_pin=a.false_pin,true_pin=a.true_pin))\n    return dict(seed=seed,arms=details)\ndef runbatch(start,n,path,router=True):\n    begin=time.time()\n    with ProcessPoolExecutor(max_workers=8) as pool: rows=list(pool.map(one,[(s,router) for s in range(start,start+n)]))\n    json.dump(dict(rows=rows,seconds=time.time()-begin,parameters=PARAM),open(path,'w'))\nif __name__=='__main__': runbatch(int(sys.argv[1]),int(sys.argv[2]),sys.argv[3],len(sys.argv)<5)\n","replica.py":"import math, random\nK = 100.0 * 10000.0\nMAXF = 0.1\nNF = 0.003\ndef clampf(f):\n    return 0.0 if f < 0.0 else (MAXF if f > MAXF else f)\ndef run(seed, policy, n_steps=10000, cfg=None):\n    cr = random.Random(10_000_000 + seed)\n    size_mean = cr.uniform(19.0, 21.0)\n    lam = cr.uniform(0.6, 1.0)\n    sigma = cr.uniform(0.000882, 0.001008)\n    if cfg:\n        size_mean, lam, sigma = cfg\n    pr = random.Random(seed)\n    rr = random.Random(seed + 1)\n    drift = -0.5 * sigma * sigma\n    mu_ln = math.log(size_mean) - 0.5 * 1.2 * 1.2\n    emlam = math.exp(-lam)\n    p = 100.0\n    x1, y1 = 100.0, 10000.0\n    x2, y2 = 100.0, 10000.0\n    fb, fa = policy.init(sigma, lam, size_mean)\n    fb, fa = clampf(fb), clampf(fa)\n    e1 = e2 = 0.0\n    ret1 = arb1 = 0.0\n    rv1 = av1 = 0.0\n    sum_fb = sum_fa = 0.0\n    g2 = 1.0 - NF\n    sqrt = math.sqrt\n    for t in range(n_steps):\n        p *= math.exp(drift + sigma * pr.gauss(0.0, 1.0))\n        s2 = y2 / x2\n        if s2 < p:\n            nx = sqrt(K / (g2 * p)); ax = x2 - nx\n            if ax > 0:\n                ax = min(ax, x2 * 0.99)\n                nrx = x2 - ax; nry = K / nrx; net_y = nry - y2; ty = net_y / g2\n                prof = ax * p - ty\n                if prof > 0:\n                    x2, y2 = nrx, nry; e2 -= prof\n        elif s2 > p:\n            xv = sqrt(K * g2 / p); ax = (xv - x2) / g2\n            if ax > 0:\n                nrx = x2 + ax * g2; nry = K / nrx; yo = y2 - nry\n                prof = yo - ax * p\n                if yo > 0 and prof > 0:\n                    x2, y2 = nrx, nry; e2 -= prof\n        s1 = y1 / x1\n        if s1 < p:\n            g = 1.0 - fa\n            if g > 0:\n                nx = sqrt(K / (g * p)); ax = x1 - nx\n                if ax > 0:\n                    ax = min(ax, x1 * 0.99)\n                    nrx = x1 - ax; nry = K / nrx; net_y = nry - y1; ty = net_y / g\n                    prof = ax * p - ty\n                    if prof > 0:\n                        x1, y1 = nrx, nry; e1 -= prof; arb1 -= prof; av1 += ty\n                        fb, fa = policy.on_trade(False, ax, ty, t, x1, y1, True, p, y2 / x2)\n                        fb, fa = clampf(fb), clampf(fa)\n        elif s1 > p:\n            g = 1.0 - fb\n            if g > 0:\n                xv = sqrt(K * g / p); ax = (xv - x1) / g\n                if ax > 0:\n                    nrx = x1 + ax * g; nry = K / nrx; yo = y1 - nry\n                    prof = yo - ax * p\n                    if yo > 0 and prof > 0:\n                        x1, y1 = nrx, nry; e1 -= prof; arb1 -= prof; av1 += yo\n                        fb, fa = policy.on_trade(True, ax, yo, t, x1, y1, True, p, y2 / x2)\n                        fb, fa = clampf(fb), clampf(fa)\n        n = 0; q = rr.random()\n        while q > emlam:\n            n += 1; q *= rr.random()\n        for _ in range(n):\n            size = rr.lognormvariate(mu_ln, 1.2)\n            buy = rr.random() < 0.5\n            if buy:\n                ga = 1.0 - fa\n                a1 = sqrt(x1 * ga * y1); a2 = sqrt(x2 * g2 * y2); r = a1 / a2\n                d = ga + r * g2\n                u1 = (r * (y2 + g2 * size) - y1) / d if d != 0 else size / 2\n                u1 = 0.0 if u1 < 0 else (size if u1 > size else u1)\n                u2 = size - u1\n                if u2 > 1e-4:\n                    nry = y2 + u2 * g2; nrx = K / nry; xo = x2 - nrx\n                    if xo > 0:\n                        e2 += u2 - xo * p; x2, y2 = nrx, nry\n                if u1 > 1e-4:\n                    nry = y1 + u1 * ga; nrx = K / nry; xo = x1 - nrx\n                    if xo > 0:\n                        ed = u1 - xo * p; e1 += ed; ret1 += ed; rv1 += u1\n                        x1, y1 = nrx, nry\n                        fb, fa = policy.on_trade(False, xo, u1, t, x1, y1, False, p, y2 / x2)\n                        fb, fa = clampf(fb), clampf(fa)\n            else:\n                tx = size / p\n                gb = 1.0 - fb\n                b1 = sqrt(y1 * gb * x1); b2 = sqrt(y2 * g2 * x2); r = b1 / b2\n                d = gb + r * g2\n                v1 = (r * (x2 + g2 * tx) - x1) / d if d != 0 else tx / 2\n                v1 = 0.0 if v1 < 0 else (tx if v1 > tx else v1)\n                v2 = tx - v1\n                if v2 > 1e-4:\n                    nrx = x2 + v2 * g2; nry = K / nrx; yo = y2 - nry\n                    if yo > 0:\n                        e2 += v2 * p - yo; x2, y2 = nrx, nry\n                if v1 > 1e-4:\n                    nrx = x1 + v1 * gb; nry = K / nrx; yo = y1 - nry\n                    if yo > 0:\n                        ed = v1 * p - yo; e1 += ed; ret1 += ed; rv1 += yo\n                        x1, y1 = nrx, nry\n                        fb, fa = policy.on_trade(True, v1, yo, t, x1, y1, False, p, y2 / x2)\n                        fb, fa = clampf(fb), clampf(fa)\n        sum_fb += fb; sum_fa += fa\n    return dict(edge=e1, norm=e2, retail=ret1, arb=arb1, rv=rv1, av=av1,\n                fb=sum_fb / n_steps * 1e4, fa=sum_fa / n_steps * 1e4,\n                sigma=sigma, lam=lam, size=size_mean)\n","oracle_table.json":"{\n \"units\": \"offset from the true price p in units of 30 bps; ask above p, bid below p; knots at own displacement ln(spot/p) = -8..+8 x 30 bps; add arb_flag to both offsets right after an own arb trade\",\n \"fees\": \"askFee = 1 - exp(ln(spot/p) - ask*0.003); bidFee = 1 - exp(-bid*0.003 - ln(spot/p)); clamp to [0, 0.10]\",\n \"ask\": [\n  -0.8836,\n  -0.9345,\n  -0.8159,\n  -0.7282,\n  -0.6342,\n  -0.5652,\n  -0.2453,\n  0.7252,\n  1.1735,\n  1.4444,\n  1.6154,\n  2.7552,\n  2.9767,\n  3.3159,\n  4.4695,\n  5.071,\n  5.7838\n ],\n \"bid\": [\n  5.6921,\n  5.1279,\n  4.4766,\n  4.0233,\n  3.3293,\n  2.4659,\n  1.7209,\n  1.4329,\n  1.2125,\n  0.7478,\n  -0.2275,\n  -0.5564,\n  -0.6444,\n  -0.7169,\n  -0.7926,\n  -0.8617,\n  -0.8452\n ],\n \"arb_flag\": 0.1463,\n \"replica_score_1000_seeds\": 532.45,\n \"same_table_p_from_own_arbs_only\": 507.61,\n \"retrained_for_p_from_own_arbs\": 519.24\n}","tests.py":"import math,random,json\nfrom moments import Filter,Arm,trunc,fees,PARAM\ndef close(a,b,tol=1e-10): assert abs(a-b)<tol,(a,b)\nfor buy in (False,True):\n f=Filter(False);f.init();p=100.8 if not buy else 99.2;g=.997\n f.m=math.log(p/100)\n s=p*g if not buy else p/g;x=math.sqrt(1e6/s);y=1e6/x\n ax=100-x if not buy else (x-100)/g;ay=(y-10000)/g if not buy else 10000-y\n f.observe(buy,ax,ay,0,x,y)\n assert f.flag>.999\n close(math.log(s)+f.m,math.log(p),1e-7)\nf=Filter(False);f.init();f.observe(False,.01,1.,0,99.99,10001.0001)\nv=f.v;sig=f.sig2\nf.observe(False,.01,1.,0,99.98,10002.0004)\nassert f.flag==0;close(f.v,v)\nf=Filter(False);f.init();m=v=0.\nfor _ in range(3): m,v,_=trunc(m-.5*f.sig2,v+f.sig2,math.log(.997),-math.log(.997))\nm-=.5*f.sig2;v+=f.sig2\nimport moments\norig=moments.trunc;seen=[]\ndef spy(*args): seen.append(args);return orig(*args)\nmoments.trunc=spy\nf.observe(False,.01,1.,3,99.99,10001.0001)\nmoments.trunc=orig\nclose(seen[-1][0],m);close(seen[-1][1],v)\nf=Filter(False);f.init();seen=[];moments.trunc=spy\nf.observe(False,.01,1.,0,99.99,10001.0001);moments.trunc=orig\nassert len(seen)==1;close(seen[0][1],PARAM['sigma0']**2)\na=Arm('filtered');b=Arm('filtered');a.init(.01,999,1);b.init(999,.01,999)\nfor t,buy,ax,ay,x,y in [(0,False,.01,1,99.99,10001.0001),(0,True,.02,2,100.01,9999.0001),(4,False,.03,3,99.98,10002.0004)]:\n assert a.on_trade(buy,ax,ay,t,x,y,True,50,1)==b.on_trade(buy,ax,ay,t,x,y,False,1000,9999)\n assert a.f.__dict__==b.f.__dict__\nfor m,v,lo,hi in [(0,1,-1,2),(.002,1e-6,-.003,.003),(0,1,-.01,.02)]:\n n=20000;h=(hi-lo)/n;xs=[lo+(i+.5)*h for i in range(n)];ws=[math.exp(-.5*(x-m)**2/v) for x in xs];Z=sum(ws)\n mn=sum(x*w for x,w in zip(xs,ws))/Z;vv=sum(w*(x-mn)**2 for x,w in zip(xs,ws))/Z\n tm,tv,_=trunc(m,v,lo,hi);close(tm,mn,1e-8);close(tv,vv,1e-8)\nassert fees(-1,0)==fees(-1,0)\nfor z in (-.024,.024):\n q=-z/.003+8;idx=int(round(q));aoff=moments.TABLE['ask'][idx]*.003;boff=moments.TABLE['bid'][idx]*.003\n close(fees(z,0)[0],max(0,min(.1,1-math.exp(z-boff))))\n close(fees(z,0)[1],max(0,min(.1,1-math.exp(-z-aoff))))\nfor mode in ('oracle','diagnostic'):\n a=Arm(mode);a.init();out=a.on_trade(False,.01,1.,0,99.99,10001.0001,False,100.2,99.)\n assert (a.f.fb,a.f.fa)==out\nfor z in (-.031,-.0135,.0015,.031):\n q=min(16.,max(0.,8-z/.003));i=min(15,int(q));w=q-i\n ao=moments.TABLE['ask'][i]+w*(moments.TABLE['ask'][i+1]-moments.TABLE['ask'][i]);bo=moments.TABLE['bid'][i]+w*(moments.TABLE['bid'][i+1]-moments.TABLE['bid'][i])\n expected=(max(0,min(.1,1-math.exp(z-.003*bo))),max(0,min(.1,1-math.exp(-z-.003*ao))))\n for a,b in zip(fees(z,0),expected):close(a,b)\nf=Filter();f.init(200.,10000.);assert f.s==50 and f.k==2000000\nf=Filter(False);f.init();keys=set(f.__dict__);f.observe(False,.01,1.,9999,99.99,10001.0001)\nassert math.isfinite(f.m+f.v) and f.v>0 and set(f.__dict__)==keys\nprint(json.dumps({'passed':11,'groups':['arb pin signs','repeat no diffusion','silent gap recurrence','t0','hidden input isolation','truncated moments quadrature','table knots','control fee history','interpolation/clamp','initial reserves','10000-step gap bounded state']}))\n"},"run_instructions":"Materialize runnable_source keys as files in one empty directory. Standard library only; Python3.12 used. Run python tests.py. For each32-seed shard run python moments.py START 32 OUTPUT.json (START10000,10032,...10224); source model stays frozen. For off use python moments.py 10000 64 OFF.json off. No network or third-party dependencies. Embedded source removes comments/docstrings and unused replica example policies only; test hashes refer to delivered text. Freeze hash is the original pre-evaluation moments.py, whose semantics are preserved.","runtime":{"training_baseline_seconds":133.7096529,"training_sweep_seconds":114.5375044,"training_finalists_seconds":61.70698142,"evaluation_shard_seconds":[22.727283,24.31353116,23.05455589,22.9104743,22.56266069,24.71113157,23.81702447,22.52675104],"evaluation_seconds":186.6234121,"ablation_seconds":5.105745316,"elapsed_seconds_from_first_saved_brief":834.1304893,"workers":8,"checkpoint":"Every32 evaluation seeds saved independently; every command below480seconds."},"bounded_state_port":{"state":"O(1) persistent state: approximately15 scalar words for live inference, plus35 frozen table numbers as constants; no callback history list. Evaluation accumulators removable.","compute":"Up to36 rival-state quadrature evaluations per router callback (5 normal nodes plus one branch-evidence call, each6 rival nodes), with exp/log/sqrt and erf for truncation. Silent gaps cost O(number_of_silent_steps), bounded by10000 in this evaluation.","gas":"Not ported or gas measured. No defensible <245k claim; quadrature transcendental functions and an arbitrarily long silent-step loop are likely port blockers. Need math approximations, precomputed rival offsets and a validated accelerated silent-gap update."},"dead_ends":[{"name":"baseline moment filter","training_gap":8.370301881,"finding":"Lower effective retail branch intensity helped; still far above2-point target."},{"name":"router weak vs off training","on_edge":516.3595076,"off_edge":516.4572377,"finding":"Router prior/likelihood model does not establish a gain over router-off. It is a nuisance marginal approximation, not an exact rival posterior."}],"limitations":["Target missed; no RS2 gain, board score, or real-engine confirmation claimed. All256 requested evaluation seeds completed.","Gaussian closure loses multimodality/truncated-tail shape; reported discarded moments are local diagnostics, not exact-grid error.","Fixed nuisance order/rival priors; no learned rival trajectory or silent no-retail likelihood. Broad tails approximate unseen rival-only fills.","Selected inferred-arb sigma estimates remain biased; no sigma hyperposterior.","Capped sell arbs cannot pin; dedicated censored-arb likelihood and cap counters absent.","Training filtered/full-oracle edges unaffected by repaired control fee-history bookkeeping; heldout uses repair."],"missing_work":["Exact-grid closure comparison, Solidity port/gas certification, and real-engine confirmation are not performed; these do not change the reported replica gap failure."]}