{"credit":"Taylor (gtmcknight), github.com/gtmcknight/amm-sim@4812a6382311624e1506aca131ca35c378f930d9 research/solved: replica, Gaussian filter, posterior policy, TellPolicy and qm tables (research at 66604b3426d8e97a73e2c39940b9b4dece51cc73). LEANBASE (leanbase.py, A/efb8e653...), qlite.py (A/365a3649...), qbase.py (A/88712dac...) and stalerival.py from IdentityMD network artifacts.","item":"qlite-a","batch":"e03-cheap-ref","rule":{"state_kept":"none beyond LEANBASE: previous own callback timestamp (the replica keeps it for its first-trade test, real.py tlast), previous reserve WADs and the fee WADs returned last","per_callback":{"when":"only on callbacks LEANBASE's lean tell does NOT read as arbitrage, and only if dt = timestamp - timestamp of previous own callback <= 6 (dt<=0: later callbacks of a step; 1<=dt<=6: first callbacks at most 6 steps after the previous own callback). dt >= 7: no test, LEANBASE unchanged. Runs before that callback's table lookup.","gate_cost":"1 subtraction + 1 comparison on every non-arb callback","test_cap24 (binary64, RNE)":["paid = f(paid_w)/1e18 (paid_w = amountX WAD if the pool bought X else amountY WAD)","gamma = 1 - f(clamp(fee_w,0,1e17))/1e18 (fee_w = bid fee WAD returned last if pool bought X else ask)","x0 = f(rx_w)/1e18, y0 = f(ry_w)/1e18 (reserves handed on the previous callback)","grid = ulp(x0 if pool bought X else y0)","a = (y0*gamma)*x0 if pool bought X else (x0*gamma)*y0; r = sqrt(a)/SQK, SQK = binary64 sqrt(1e6*0.997) constant","d = gamma + r*0.997","n = round_half_even(paid*d/grid) (division by grid is an exponent shift)","HIT iff n > 0 and trunc(((n*grid)/d)*1e18) == paid_w; else MISS"],"on_hit":"qbase/qlite update: s = cwy/cwx; g = 1 - fee_w/1e18; cand = s*g/0.997 if pool bought X else s*0.997/g; rival s2h := cand, synced, lookup at it; LEANBASE's 0.35 pull skipped on that callback","on_miss":"LEANBASE unchanged","integer_form":"qlite_int.capped_int(cap=24): every binary64 value as (m, e), m in [2^52, 2^53); exact integer mantissa products/quotients/aligned sums, isqrt with a sticky bit, each rounded half-to-even on 53 bits; nextafter = m+-1 with binade carry; ulp = 2^e; grid division/multiplication = exponent shift"}},"choose":{"seeds":[64000,65023],"n":1024,"pick_rule":"Written before any choose scoring. Arms on LEANBASE (soft=1 qm=qm_k1e-5.json a0=0.35 ainf=0.35, q=1 pull=1 order=b):\n cap24 (gate=-1), cap24+GATE (cap=24 gate=6), cap40+GATE (cap=40 gate=6). Choose seeds 64000..65023.\nPick: among the two gated arms, cap24+GATE unless cap40+GATE's paired mean_diff vs LEANBASE exceeds it by more than 0.005 (then cap40+GATE).","arms":[{"name":"cap24","n":1024,"mean_diff":0.03527,"se":0.0049,"min":-0.595},{"name":"cap24+GATE","n":1024,"mean_diff":0.03412,"se":0.00487,"min":-0.55906},{"name":"cap40+GATE","n":1024,"mean_diff":0.03813,"se":0.00505,"min":-0.58586}],"pick":"cap24+GATE (cap40+GATE leads it by 0.00401, within 0.005)"},"frozen":{"pick":"cap24+GATE","policy":"qlgate:Policy","params":{"q":1,"pull":1,"cap":24,"order":"b","gate":6,"soft":1,"qm":"qm_k1e-5.json","a0":0.35,"ainf":0.35},"code_sha256":"0823f2d25728bf95238fc350a8aabefe8e73143cfaf9859e894a7c2c06984de6","code_sha256_definition":"SHA256 of UTF-8 qlgate.py bytes","dependency_sha256":{"qlgate.py":"0823f2d25728bf95238fc350a8aabefe8e73143cfaf9859e894a7c2c06984de6","qlite_int.py":"b75d7d00d77e5265865ce27ba85ff1ccd7cae4b0789f6cc0ef208ea20cd17197","qlite.py":"2ab8337870a2375b79f1773619e3b11a472bc6d8b4b9085f5047cec645c57535","qbase.py":"1a6dc9fa4bf27891d91701c9b1fce91c19091b7559dfcc282342c5ab47bb306a","stalerival.py":"d124a171d35b024daed840e5449d352b2b5e50a68ce98c8a9aaafaf3419d23da","leanbase.py":"ba015769f7981d7798acbbc9aff8c0e0c59825bb1541d55bcdef49311d7a04bc","lean_tell.py":"b70054f8c0561779e40c4c8df3f41ab08da05b9aef591816ac6c9034beb40a95","tellref.py":"4867a33106ce2597863b8d7c8fb396288954b98f291714801fae8820f1f47aa3","tellpol.py":"7d5961c45bec56292533e65607245ad119b8733c760a5bf28f76a2e07bc3960b","real.py":"6a4a0f0e7f8b43d38e5eaa9d8b2e847a0771aee7f89551b122fe89bfe7969b5f","replica2.py":"54380c8755f4e42e9a0426759e918eacd2c5f915b7f04e5d0501c394c5846b40","run.py":"91133e4ef485626226679d73349b5b4e374d9713ac5d7e9d36a39e1afd75933c","qm_k1e-5.json":"5ff53e42ca87390e5f65d1caa3f7a480e67a8212fb0670274dfd562b05ba1afd"},"frozen_before_report":true},"report":{"seeds":[10000,12047],"n":2048,"blocks_of_64_in_order":32,"base":"LEANBASE (leanbase:Policy, same options), each arm alone vs the replica 30 bps rival, paired by seed","arms":[{"name":"cap24","minus_base":{"mean_diff":0.04056,"se":0.00368,"min":-2.33113}},{"name":"cap24+GATE","minus_base":{"mean_diff":0.03857,"se":0.00364,"min":-2.33902}},{"name":"cap40+GATE","minus_base":{"mean_diff":0.04159,"se":0.00385,"min":-2.3268}}],"pick_minus_cap24":{"mean_diff":-0.00199,"se":0.00074,"min":-0.28944},"block_means":[{"seeds":[10000,10063],"cap24":0.0107,"cap24+GATE":0.0041,"cap40+GATE":0.0072},{"seeds":[10064,10127],"cap24":0.0731,"cap24+GATE":0.0734,"cap40+GATE":0.0786},{"seeds":[10128,10191],"cap24":0.0454,"cap24+GATE":0.0404,"cap40+GATE":0.0449},{"seeds":[10192,10255],"cap24":0.0646,"cap24+GATE":0.0686,"cap40+GATE":0.0768},{"seeds":[10256,10319],"cap24":0.0375,"cap24+GATE":0.0347,"cap40+GATE":0.0293},{"seeds":[10320,10383],"cap24":0.0503,"cap24+GATE":0.0523,"cap40+GATE":0.0557},{"seeds":[10384,10447],"cap24":0.0286,"cap24+GATE":0.0224,"cap40+GATE":0.027},{"seeds":[10448,10511],"cap24":0.044,"cap24+GATE":0.0463,"cap40+GATE":0.0517},{"seeds":[10512,10575],"cap24":0.0273,"cap24+GATE":0.0225,"cap40+GATE":0.0183},{"seeds":[10576,10639],"cap24":0.052,"cap24+GATE":0.0549,"cap40+GATE":0.0631},{"seeds":[10640,10703],"cap24":0.0203,"cap24+GATE":0.014,"cap40+GATE":0.0199},{"seeds":[10704,10767],"cap24":0.0361,"cap24+GATE":0.0359,"cap40+GATE":0.0357},{"seeds":[10768,10831],"cap24":0.0422,"cap24+GATE":0.0409,"cap40+GATE":0.0368},{"seeds":[10832,10895],"cap24":0.0107,"cap24+GATE":0.0121,"cap40+GATE":0.0201},{"seeds":[10896,10959],"cap24":0.045,"cap24+GATE":0.0315,"cap40+GATE":0.0298},{"seeds":[10960,11023],"cap24":0.0399,"cap24+GATE":0.0504,"cap40+GATE":0.0552},{"seeds":[11024,11087],"cap24":0.0632,"cap24+GATE":0.0576,"cap40+GATE":0.0578},{"seeds":[11088,11151],"cap24":0.0551,"cap24+GATE":0.0526,"cap40+GATE":0.0559},{"seeds":[11152,11215],"cap24":0.0338,"cap24+GATE":0.0322,"cap40+GATE":0.0367},{"seeds":[11216,11279],"cap24":0.0712,"cap24+GATE":0.0744,"cap40+GATE":0.0633},{"seeds":[11280,11343],"cap24":0.0422,"cap24+GATE":0.0365,"cap40+GATE":0.042},{"seeds":[11344,11407],"cap24":0.0238,"cap24+GATE":0.0227,"cap40+GATE":0.0334},{"seeds":[11408,11471],"cap24":0.0295,"cap24+GATE":0.0213,"cap40+GATE":0.0272},{"seeds":[11472,11535],"cap24":0.0802,"cap24+GATE":0.0789,"cap40+GATE":0.0818},{"seeds":[11536,11599],"cap24":0.0329,"cap24+GATE":0.0237,"cap40+GATE":0.0321},{"seeds":[11600,11663],"cap24":0.0117,"cap24+GATE":0.0095,"cap40+GATE":0.0126},{"seeds":[11664,11727],"cap24":0.0067,"cap24+GATE":0.0081,"cap40+GATE":0.0192},{"seeds":[11728,11791],"cap24":0.002,"cap24+GATE":-0.0005,"cap40+GATE":0.0038},{"seeds":[11792,11855],"cap24":0.0509,"cap24+GATE":0.0457,"cap40+GATE":0.0414},{"seeds":[11856,11919],"cap24":0.0612,"cap24+GATE":0.0673,"cap40+GATE":0.0746},{"seeds":[11920,11983],"cap24":0.0546,"cap24+GATE":0.0549,"cap40+GATE":0.0509},{"seeds":[11984,12047],"cap24":0.0513,"cap24+GATE":0.0446,"cap40+GATE":0.0482}]},"cost":{"extra_storage_words":0,"worst_ops_per_callback":{"binary64_ops_cap24_test":22,"binary64_ops_with_hit_update":29,"gate_ops":2,"integer_primitives_qlite_int":{"max":397,"mean":354.8,"tested_callbacks":6835040,"unit":"Python integer primitives counted by qlite_int.OPS (+ - * divmod << >> & compare bit_length isqrt), test only, hit update excluded"},"source":"binary64 op counts from the qlite artifact cost table (cap24 order b worst 29 incl. +7 hit update); integer counts measured here"},"runs_on_peak_path":false,"runs_on_peak_path_basis":"by construction the test never runs on a first callback with dt >= 7; the brief states the later/dt<=6 callbacks have 66,000 gas free and the peak call is not among them. No Solidity or gas measured here."},"checks":{"q0_equals_leanbase":"qlgate q=0 gave the same edge as leanbase:Policy on 12 seeds 64000..64011 (525.629 both)","int_vs_float_cap24_gated":{"seeds":[64000,65023],"n_seeds":1024,"tested_callbacks":6835040,"hits":5358479,"mismatches":0},"int_vs_float_cap40_gated":{"seeds":[64064,64127],"n_seeds":64,"tested_callbacks":449025,"hits":398961,"mismatches":0},"int_primitives_unit_test":"200,000 random doubles: mul, div, add, sub, sqrt, i2f (1..127-bit ints), nextafter both ways, round-half-even, trunc, plus 4,999 exact .5 ties: 0 mismatches vs native binary64","check_wrapper_edges_equal_run_py":"check-wrapper edges on 64000..64063 equal run.py cap24+GATE rows: 64/64","gate_share":{"not_arb_callbacks":6859370,"gated_off":24330,"share":0.00355,"seeds":[64000,65023]},"frozen_hashes_rechecked_before_each_report_command":3,"report_blocks_in_order_every_arm_per_block":32,"blind_inputs":"run.Blind passes only (is_buy, ax, ay, t, x, y); qlgate reads self.cur = paid WAD, own fee WAD returned last, reserves now and last, dt from own last timestamp","post_report_code_unchanged":{"files":13,"all_match":true}},"advance":true,"advance_reason":"pick cap24+GATE report mean_diff 0.03857 (>= 0.015: True), mean_diff - 2se = 0.03129 (> 0: True); reads only callback values and own state; int vs float mismatches 0 over 6835040 tested callbacks; frozen code unchanged: True","code_encoding":"base64(zlib(JSON {path: text})): qlgate.py, qlite_int.py, qlite.py, qbase.py, CREDIT.txt; place beside Taylor's research files (66604b34) with LEANBASE's modules","code_zb64":"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","seeds_used":{"timing":[64000,64011],"choose":[64000,65023],"int_check":[64000,65023],"report":[10000,12047],"report_reused_for_selection":false},"not_done":["No Solidity port, no gas or engine measurement: replica only; runs_on_peak_path rests on the brief's statement about where 66,000 gas is free.","Integer op counts are Python-level primitive counts of qlite_int, not EVM opcode or gas counts.","Integer form assumes normal binary64 values (no subnormals, no overflow), which holds for WAD inputs in the replica; not proven for arbitrary uint256 inputs.","cap40 integer form checked on 64 seeds only (not the pick)."]}