{
 "credit": "Taylor (gtmcknight), github.com/gtmcknight/amm-sim@4812a6382311624e1506aca131ca35c378f930d9 research/solved: the solved policy, Gaussian filter, qm tables, exact-arithmetic arb/retail tell and U1 tables that LEAN and QLX5 are built on. QLX5 = LEAN plus the drift-tolerant (tracked-offset) split test, from A/1ef80bfb code_zb64.QLX5, built by mku.py of A/8b18deed on LEAN (A/a79a3606). This map only names constants of that source; all credit for the policy is Taylor's.",
 "qlx5_sha256": "e183e5bc3fb794b7067703b10a7da9920267aa5f4caa968e16ca101b02338f40",
 "qlx5_source": "code_zb64.QLX5 of https://api.imd.fun/artifacts/1ef80bfb6d6791b877b1f4048a5e63cf2ae54153e6e8763ae3f8ab13132dfb15 (decoded: 47230 characters, sha256 checked)",
 "how_to_apply": "Apply one knob at a time: variant = QLX5 source with its single occurrence of find replaced by lo (or hi). Each find occurs exactly once in QLX5 (asserted). Knob pairs whose find strings overlap are listed in overlapping_finds and cannot be stacked by plain replacement.",
 "compile": {
  "compiler": "solc 0.8.24+commit.e11b9ed9 (linux-amd64 binary sha256 fb03a29a517452b9f12bcf459ef37d0a543765bb3bbc911e70a87d6a37c30d5f, as pinned in the kit's bootstrap/manifest.tsv)",
  "settings": "standard JSON as amm-challenge@6b6921f8d463314aa7c96234e1be25a25245f704 amm_competition/evm/compiler.py: optimizer enabled runs 200, viaIR true, evmVersion paris, with that commit's IAMMStrategy.sol and AMMStrategyBase.sol",
  "validator": "each variant also passed that commit's amm_competition/evm/validator.py SolidityValidator",
  "qlx5_runtime_bytes": 22440,
  "qlx5_source_chars": 47230,
  "check": "QLX5 itself compiled here to 22440 runtime bytes, the figure A/1ef80bfb reports for it",
  "variants_compiled": 64,
  "variants_total": 64,
  "max_runtime_bytes": 22493,
  "max_source_chars": 47258,
  "limits": "every variant <= 50,000 source characters and <= 24,576 runtime bytes",
  "replaced": "level_interp (n=24) lo was first 'int256 tt=0;', which failed to compile (YulException: Variable sum_9 is 1 too deep in the stack); it was replaced by the lower-level-unless-at-top form now listed, which compiles."
 },
 "ordering": "n orders knobs by the edge each is expected to move, most first, with families interleaved. The order is judgment from reading the source (how often the constant acts and how directly it sets the fee), not a measurement: no engine or replica run was made.",
 "overlapping_finds": [
  [
   2,
   9
  ],
  [
   4,
   17
  ],
  [
   14,
   20
  ],
  [
   15,
   19
  ]
 ],
 "knobs": [
  {
   "n": 0,
   "id": "sd_scale",
   "family": "table levels",
   "meaning": "Scale from the belief standard deviation sqrt(v) to the bps value that picks and interpolates the sd level of the fee tables (lo reads the belief as 25% calmer, hi as 25% noisier).",
   "value": "10000 (sd in bps)",
   "find": "int256 sd=root(v)*10000;",
   "lo": "int256 sd=root(v)*7500;",
   "hi": "int256 sd=root(v)*12500;",
   "compiled_lo": true,
   "runtime_bytes_lo": 22437,
   "source_chars_lo": 47229,
   "source_sha256_lo": "9bab9600628b76f25eb77fc115c260cfdfe7f645ab3d576c5caebad788fecd98",
   "compiled_hi": true,
   "runtime_bytes_hi": 22437,
   "source_chars_hi": 47230,
   "source_sha256_hi": "12fcb256c5be34483364971c14d9b3537ad923adf1a1a9efff8e3f36bd358457"
  },
  {
   "n": 1,
   "id": "arb_cut",
   "family": "phase thresholds",
   "meaning": "Posterior arbitrage probability above which the first own trade of a step is read as arbitrage, which puts the callback in phase 0 (table 0, rival logic skipped).",
   "value": "U/2 (posterior 0.5)",
   "find": "arb=pi>U/2;",
   "lo": "arb=pi>U/4;",
   "hi": "arb=pi>3*U/4;",
   "compiled_lo": true,
   "runtime_bytes_lo": 22440,
   "source_chars_lo": 47230,
   "source_sha256_lo": "fe570e5a3ded2a903ea164e07f7d7b4f55d42cbbf90032ad7a1efa471f6b4f66",
   "compiled_hi": true,
   "runtime_bytes_hi": 22440,
   "source_chars_hi": 47232,
   "source_sha256_hi": "69a43189b60523b6097fc97686d7198db8606eaf0aaa417858428ba2d91b33fa"
  },
  {
   "n": 2,
   "id": "pull",
   "family": "rival clip and band widths",
   "meaning": "Fraction of the way ln r is pulled toward the fill's rival-bound candidate ln c when the bound does not bind (GivePolicy alpha).",
   "value": "35e16 (alpha 0.35)",
   "find": "r=exp(lr+mul(35e16,ln(c)-lr))",
   "lo": "r=exp(lr+mul(2e17,ln(c)-lr))",
   "hi": "r=exp(lr+mul(5e17,ln(c)-lr))",
   "compiled_lo": true,
   "runtime_bytes_lo": 22440,
   "source_chars_lo": 47229,
   "source_sha256_lo": "4d4e38337f4b18395cb1717be538d1e1a5155d7d906734ea133a02693a3a6d21",
   "compiled_hi": true,
   "runtime_bytes_hi": 22440,
   "source_chars_hi": 47229,
   "source_sha256_hi": "dd5854fd13b2759994f5c367822f7bcb0cdfed7d40321249f492adecec91e1ae"
  },
  {
   "n": 3,
   "id": "syn_tables",
   "family": "synced-table switches",
   "meaning": "Whether the synced flag chooses between the synced and unsynced phase-1/2 tables: lo always uses the synced tables (1, 3), hi always the unsynced ones (2, 4).",
   "value": "+(syn?0:1) (synced flag picks table 1/3 vs 2/4)",
   "find": "+(syn?0:1)",
   "lo": "+0",
   "hi": "+1",
   "compiled_lo": true,
   "runtime_bytes_lo": 22421,
   "source_chars_lo": 47222,
   "source_sha256_lo": "995a217d885d0542daf870df80a3ed160e5e65d4a9fd5e18b3f0657ad73997a5",
   "compiled_hi": true,
   "runtime_bytes_hi": 22425,
   "source_chars_hi": 47222,
   "source_sha256_hi": "08055c9451e824ad852d7ec2e394832401b9b44b92f05d237765ac25a1f396b1"
  },
  {
   "n": 4,
   "id": "window",
   "family": "the split test's window and candidates",
   "meaning": "Largest gap in steps since the previous own callback at which the tracked-offset split test qHitX is tried (lo dt<=3, hi dt<=9).",
   "value": "+7 (split test when dt <= 6)",
   "find": "(s2>>128&M64)+7){int256 m0",
   "lo": "(s2>>128&M64)+4){int256 m0",
   "hi": "(s2>>128&M64)+10){int256 m0",
   "compiled_lo": true,
   "runtime_bytes_lo": 22440,
   "source_chars_lo": 47230,
   "source_sha256_lo": "aab6bbd96c794810f1a7760118ef5a735c96caa3a940a69b13afb845fd5ae352",
   "compiled_hi": true,
   "runtime_bytes_hi": 22440,
   "source_chars_hi": 47231,
   "source_sha256_hi": "95972864a99e12e35e4f610bdc148d4f7c5571e1ba954bb2269b5dd81b282481"
  },
  {
   "n": 5,
   "id": "mix_band",
   "family": "tell floors",
   "meaning": "Floor (and mirror ceiling) on the arbitrage posterior inside which the filter keeps a two-way mixture; outside it the belief snaps to the arbitrage point or the retail truncation.",
   "value": "5e15 / 995e15",
   "find": "if(pi>5e15&&pi<995e15)",
   "lo": "if(pi>25e14&&pi<9975e14)",
   "hi": "if(pi>75e14&&pi<9925e14)",
   "compiled_lo": true,
   "runtime_bytes_lo": 22440,
   "source_chars_lo": 47232,
   "source_sha256_lo": "0a8f64b80c3e339fce7bf23be824e44b0e4083e5b466f218fa37a0c6b0daa7c9",
   "compiled_hi": true,
   "runtime_bytes_hi": 22440,
   "source_chars_hi": 47232,
   "source_sha256_hi": "7d66aef0ed371e1e9fa0c04cc7ebc415e96097d8a526c66d9371cad1efb2af36"
  },
  {
   "n": 6,
   "id": "rival_clip",
   "family": "rival clip and band widths",
   "meaning": "Half-width of the band around the belief price exp(m) into which the rival spot r is clipped at every new step (lo 15 bps, hi 45 bps).",
   "value": "997e15 (rival kept within 30 bps of exp(m))",
   "find": "r=clip(r,mul(pe,997e15),divi(pe,997e15));",
   "lo": "r=clip(r,mul(pe,9985e14),divi(pe,9985e14));",
   "hi": "r=clip(r,mul(pe,9955e14),divi(pe,9955e14));",
   "compiled_lo": true,
   "runtime_bytes_lo": 22440,
   "source_chars_lo": 47232,
   "source_sha256_lo": "f493c67a8961d487cbd1d943ee90c3644a6d837548ce68859201bd0451be414d",
   "compiled_hi": true,
   "runtime_bytes_hi": 22440,
   "source_chars_hi": 47232,
   "source_sha256_hi": "5aaf48527343a5636a5f7e654be848378a1743b0aa263f0df5e57c96101db940"
  },
  {
   "n": 7,
   "id": "phase_cnt",
   "family": "phase thresholds",
   "meaning": "Count of non-arbitrage own callbacks in a step that are quoted from the phase-1 tables before switching to phase 2 (lo none, hi two).",
   "value": "cnt==1 -> phase 1, later -> phase 2",
   "find": "cnt++;ph=cnt==1?1:2;",
   "lo": "cnt++;ph=2;",
   "hi": "cnt++;ph=cnt<=2?1:2;",
   "compiled_lo": true,
   "runtime_bytes_lo": 22416,
   "source_chars_lo": 47221,
   "source_sha256_lo": "a97542f076007b95be31aa0ba448348704852d8880d640d63c2b97c8cb7ac1af",
   "compiled_hi": true,
   "runtime_bytes_hi": 22437,
   "source_chars_hi": 47230,
   "source_sha256_hi": "4ffc4e1eb8338e279eaf31fff2ed5d3d8ffb3765816f9d4f2ce7c4cba6fb74c9"
  },
  {
   "n": 8,
   "id": "pred_var",
   "family": "table levels",
   "meaning": "Variance handed to the table lookup: QLX5 uses the posterior v; lo adds half and hi one step of the filter's diffusion (893025000000) so the level reflects the next step.",
   "value": "v (posterior variance, no step added)",
   "find": "(fb,fa)=fees(w,rr,ph,syn,v);",
   "lo": "(fb,fa)=fees(w,rr,ph,syn,v+446512500000);",
   "hi": "(fb,fa)=fees(w,rr,ph,syn,v+893025000000);",
   "compiled_lo": true,
   "runtime_bytes_lo": 22447,
   "source_chars_lo": 47243,
   "source_sha256_lo": "2fcc1d88a70fbbdbcae525219914d667ff695e45f966ba0150b66b439c5ed186",
   "compiled_hi": true,
   "runtime_bytes_hi": 22447,
   "source_chars_hi": 47243,
   "source_sha256_hi": "a5ce466a646f2498e9dbf739430f0a86e5e59a5d8252f8994ef6cfe3b803ade5"
  },
  {
   "n": 9,
   "id": "pull_syn",
   "family": "synced-table switches",
   "meaning": "Whether a callback whose rival estimate came only from the 0.35 pull is quoted from the synced tables (lo never, hi only on the first non-arbitrage callback of the step).",
   "value": "syn=true after the 0.35 pull",
   "find": "ln(c)-lr));syn=true;}",
   "lo": "ln(c)-lr));syn=false;}",
   "hi": "ln(c)-lr));syn=cnt==0;}",
   "compiled_lo": true,
   "runtime_bytes_lo": 22441,
   "source_chars_lo": 47231,
   "source_sha256_lo": "3cbf4b16bcfc7f4be6fde84c1cf534d2fd2e61a2f5c7ce7ff6b14c31ddcf15a2",
   "compiled_hi": true,
   "runtime_bytes_hi": 22441,
   "source_chars_hi": 47232,
   "source_sha256_hi": "662076420f0fe46453ddb1341ffaca95ebd949f75bcdafd3798e41ad9acb117e"
  },
  {
   "n": 10,
   "id": "track",
   "family": "the split test's window and candidates",
   "meaning": "How the split test's denominator offset m0 is carried: QLX5 keeps the last accepted offset; lo never tracks (always centred at 0), hi resets to 0 after a miss.",
   "value": "offset m0 tracked across hits (slots[6])",
   "find": "if(mm!=m0)slots[6]=uint256(mm);",
   "lo": "",
   "hi": "if(!qx)mm=0;if(mm!=m0)slots[6]=uint256(mm);",
   "compiled_lo": true,
   "runtime_bytes_lo": 22429,
   "source_chars_lo": 47199,
   "source_sha256_lo": "14c1b8f039c87b97a3bbf7b9c2339ee710c34258a4440c63b206d6c380d903db",
   "compiled_hi": true,
   "runtime_bytes_hi": 22456,
   "source_chars_hi": 47242,
   "source_sha256_hi": "acf3f1a16ea41c939ac92f0c8716ef80683dfe57fd2b37b96ddd395bd3406a7a"
  },
  {
   "n": 11,
   "id": "chance_floor",
   "family": "tell floors",
   "meaning": "Floor on the ulp-over-grid chance that multiplies the retail likelihood of a lean-tell hit (lo 1e-4, hi 1e-2), limiting how far a fine-grained fill is trusted as arbitrage.",
   "value": "0 (no floor on the grid chance)",
   "find": "lr=mul(lr,chance);",
   "lo": "lr=mul(lr,chance<1e14?int256(1e14):chance);",
   "hi": "lr=mul(lr,chance<1e16?int256(1e16):chance);",
   "compiled_lo": true,
   "runtime_bytes_lo": 22468,
   "source_chars_lo": 47255,
   "source_sha256_lo": "e35c0a316529e22845c8dd55edd20a7fc9445052ffd71c391ea091093e91e691",
   "compiled_hi": true,
   "runtime_bytes_hi": 22469,
   "source_chars_hi": 47255,
   "source_sha256_hi": "e87d60d8f4106e5eff468c085d4baf61daf3e350e24126083fa1f6556b6fff8f"
  },
  {
   "n": 12,
   "id": "rival_fee_bound",
   "family": "rival clip and band widths",
   "meaning": "Rival fee factor in the bound candidate c that a retail fill implies for the rival spot (lo 15 bps, hi 45 bps band).",
   "value": "997e15 (30 bps rival fee)",
   "find": "int256 c=t.isBuy?divi(mul(s,U-fb),997e15):divi(mul(s,997e15),U-fa);",
   "lo": "int256 c=t.isBuy?divi(mul(s,U-fb),9985e14):divi(mul(s,9985e14),U-fa);",
   "hi": "int256 c=t.isBuy?divi(mul(s,U-fb),9955e14):divi(mul(s,9955e14),U-fa);",
   "compiled_lo": true,
   "runtime_bytes_lo": 22440,
   "source_chars_lo": 47232,
   "source_sha256_lo": "546bd1d033876c2a842589d4458d6387d763e4325f91014821bdd3b8e8e8b7e0",
   "compiled_hi": true,
   "runtime_bytes_hi": 22440,
   "source_chars_hi": 47232,
   "source_sha256_hi": "55bca73ee303456c22356b939a76d95c04c103890920a187606b4a73c6e5611a"
  },
  {
   "n": 13,
   "id": "phase_table",
   "family": "phase thresholds",
   "meaning": "Which table pair each non-arbitrage phase reads: lo quotes phase 2 from the phase-1 tables, hi quotes phase 1 from the phase-2 tables.",
   "value": "phase 1 -> tables 1/2, phase 2 -> tables 3/4",
   "find": "tb=(ph==1?1:3)",
   "lo": "tb=(ph==1?1:1)",
   "hi": "tb=(ph==1?3:3)",
   "compiled_lo": true,
   "runtime_bytes_lo": 22440,
   "source_chars_lo": 47230,
   "source_sha256_lo": "e7f04cb083f86b70b826b4cd0495cd20ba69a7de6fd1056ec93e9152fc9cb245",
   "compiled_hi": true,
   "runtime_bytes_hi": 22440,
   "source_chars_hi": 47230,
   "source_sha256_hi": "47d228d82c5a0c19eb57363744f1ca226e73bbdda2adf1e756abc6f913258314"
  },
  {
   "n": 14,
   "id": "fee_offset",
   "family": "table levels",
   "meaning": "Constant shift of both log-fee table outputs before conversion to a fee (lo -0.5 bps, hi +0.5 bps).",
   "value": "0 bps added to the table output",
   "find": "fb=xb>0?U-exp(-xb/10000):int256(0);",
   "lo": "xb-=U/2;xa-=U/2;fb=xb>0?U-exp(-xb/10000):int256(0);",
   "hi": "xb+=U/2;xa+=U/2;fb=xb>0?U-exp(-xb/10000):int256(0);",
   "compiled_lo": true,
   "runtime_bytes_lo": 22479,
   "source_chars_lo": 47246,
   "source_sha256_lo": "8e16002b93f1422e0a409b324db04e4edb7a8f9d75ca95e385c47c284efac2b8",
   "compiled_hi": true,
   "runtime_bytes_hi": 22481,
   "source_chars_hi": 47246,
   "source_sha256_hi": "ebeae85c4c889f51d113fc76043974abea5dae2517a65ab1985c2f99e9d0828c"
  },
  {
   "n": 15,
   "id": "step_syn",
   "family": "synced-table switches",
   "meaning": "Synced flag at the start of a step: QLX5 clears it; lo carries the previous step's flag over, hi sets it when the step's first trade was read as arbitrage.",
   "value": "syn=false at every new step",
   "find": "cnt=0;syn=false;",
   "lo": "cnt=0;",
   "hi": "cnt=0;syn=arb;",
   "compiled_lo": true,
   "runtime_bytes_lo": 22431,
   "source_chars_lo": 47220,
   "source_sha256_lo": "9dffba782e00472fde90e2ce4570a6dd1b6a68fff0b537466db4d68f00361bd7",
   "compiled_hi": true,
   "runtime_bytes_hi": 22425,
   "source_chars_hi": 47228,
   "source_sha256_hi": "ecf18c6c31638df8c9c732755ee50f870211780314d65faca59b31285a2ca52a"
  },
  {
   "n": 16,
   "id": "move_floor",
   "family": "tell floors",
   "meaning": "Floor on the absolute log price move d entering the retail-size lognormal likelihood of the arbitrage tell.",
   "value": "1e9 (|ln move| floor 1e-9)",
   "find": "if(d<1e9)d=1e9;",
   "lo": "if(d<5e8)d=5e8;",
   "hi": "if(d<15e8)d=15e8;",
   "compiled_lo": true,
   "runtime_bytes_lo": 22440,
   "source_chars_lo": 47230,
   "source_sha256_lo": "aed2d3c12623589b27bd3d9e85d143e29773699c3218c35385db26eb49e290d1",
   "compiled_hi": true,
   "runtime_bytes_hi": 22440,
   "source_chars_hi": 47232,
   "source_sha256_hi": "53370a6ca74237e7605f969ed88fa34d433420754635b59e3dd286da75e1feee"
  },
  {
   "n": 17,
   "id": "window_first",
   "family": "the split test's window and candidates",
   "meaning": "Which callbacks in the window the split test is tried on: lo only the first non-arbitrage callback of the step (cnt==0), hi only the later ones.",
   "value": "split test on every non-arbitrage callback in the window",
   "find": "(s2>>128&M64)+7){int256 m0",
   "lo": "(s2>>128&M64)+7&&cnt==0){int256 m0",
   "hi": "(s2>>128&M64)+7&&cnt!=0){int256 m0",
   "compiled_lo": true,
   "runtime_bytes_lo": 22454,
   "source_chars_lo": 47238,
   "source_sha256_lo": "827f512136a69cd5b2a74e059a2cb7a60e8e007dc27313f6f7672cb4861c91b8",
   "compiled_hi": true,
   "runtime_bytes_hi": 22455,
   "source_chars_hi": 47238,
   "source_sha256_hi": "05d2878f09e0281f887338a1ff165413cbf34239ddb0cf17bb02dd6b0f84a146"
  },
  {
   "n": 18,
   "id": "rr_scale",
   "family": "rival clip and band widths",
   "meaning": "Scale of the rival offset ln r - m on the tables' column axis (lo shrinks the rival band 25%, hi widens it 25%).",
   "value": "10000 (rival offset in bps)",
   "find": "int256 rr=(ln(r)-m)*10000;",
   "lo": "int256 rr=(ln(r)-m)*7500;",
   "hi": "int256 rr=(ln(r)-m)*12500;",
   "compiled_lo": true,
   "runtime_bytes_lo": 22437,
   "source_chars_lo": 47229,
   "source_sha256_lo": "3075e2e495fecf4b87dea2dd8cfb8665e1bb94890adba3712336c7f101c2c518",
   "compiled_hi": true,
   "runtime_bytes_hi": 22437,
   "source_chars_hi": 47230,
   "source_sha256_hi": "212b65a9ce9e783c516110ab63f03887be9f226ad2f1c67c6a39bc48299a607b"
  },
  {
   "n": 19,
   "id": "step_cnt",
   "family": "phase thresholds",
   "meaning": "Phase counter at the start of a step: lo sends the callback after an arbitrage straight to phase 2, hi sends a first non-arbitrage trade of a step straight to phase 2 (phase 1 only after an arbitrage).",
   "value": "cnt=0 at every new step",
   "find": "hit,chance);cnt=0;",
   "lo": "hit,chance);cnt=arb?1:0;",
   "hi": "hit,chance);cnt=arb?0:1;",
   "compiled_lo": true,
   "runtime_bytes_lo": 22440,
   "source_chars_lo": 47236,
   "source_sha256_lo": "317c45fa1e7163ea13554f599a801e7eabc05fb5b75e6ca607c6a7980cd4f7a5",
   "compiled_hi": true,
   "runtime_bytes_hi": 22440,
   "source_chars_hi": 47236,
   "source_sha256_hi": "d2caba05b8a52071b7c7bd5b4252c49917ec1dded73ab28874f5321b22feadb4"
  },
  {
   "n": 20,
   "id": "fee_scale",
   "family": "table levels",
   "meaning": "Multiplicative scale of both log-fee table outputs before conversion (lo -3%, hi +3%, about 1 to 1.5 bps at typical fees).",
   "value": "x1 on the table output",
   "find": "fb=xb>0?U-exp(-xb/10000):int256(0);",
   "lo": "xb=xb*97/100;xa=xa*97/100;fb=xb>0?U-exp(-xb/10000):int256(0);",
   "hi": "xb=xb*103/100;xa=xa*103/100;fb=xb>0?U-exp(-xb/10000):int256(0);",
   "compiled_lo": true,
   "runtime_bytes_lo": 22182,
   "source_chars_lo": 47256,
   "source_sha256_lo": "aef200f44f05685523597971c1d5961fd94a9fb5e2e2e53e147b414b42ad3802",
   "compiled_hi": true,
   "runtime_bytes_hi": 22182,
   "source_chars_hi": 47258,
   "source_sha256_hi": "f85a0c07f696e2c56490719aafccee7246103f526d2698ae05134de872570b64"
  },
  {
   "n": 21,
   "id": "bound_syn",
   "family": "synced-table switches",
   "meaning": "Whether setting r=c marks the callback synced: lo only on an exact split-test hit, hi never.",
   "value": "syn=true when the bound binds or the split test hits",
   "find": "{r=c;syn=true;}",
   "lo": "{r=c;syn=qx;}",
   "hi": "{r=c;syn=false;}",
   "compiled_lo": true,
   "runtime_bytes_lo": 22439,
   "source_chars_lo": 47228,
   "source_sha256_lo": "f1563acf5d2e2159ecfac22102d75d46edafa181cead9a2ccc8b2f02534b64a9",
   "compiled_hi": true,
   "runtime_bytes_hi": 22441,
   "source_chars_hi": 47231,
   "source_sha256_hi": "5b15d6b9c3ad16cf82eb78fd8f2b1e500210ed46bd565777dfd5ae576b060cad"
  },
  {
   "n": 22,
   "id": "budget",
   "family": "tell floors",
   "meaning": "Budget of preimage-plus-grid candidates above which the lean tell returns 'over budget' (a miss); changing it changes leanLabel, so gate T's Python reference must use the same budget.",
   "value": "4 (lean tell budget)",
   "find": "hits>4)return 3;",
   "lo": "hits>3)return 3;",
   "hi": "hits>6)return 3;",
   "compiled_lo": true,
   "runtime_bytes_lo": 22440,
   "source_chars_lo": 47230,
   "source_sha256_lo": "709bfacdc61ac71944fcc5367c7b097196d1543675d77be5524535de439858b8",
   "compiled_hi": true,
   "runtime_bytes_hi": 22440,
   "source_chars_hi": 47230,
   "source_sha256_hi": "cd5b70ce4da4364b97483c32a240b1884a132caf54ab7df10a7a773d1a6090fb"
  },
  {
   "n": 23,
   "id": "bound_rule",
   "family": "rival clip and band widths",
   "meaning": "Rule for setting r to the bound candidate c: lo only on a split-test hit (else the pull), hi on every non-arbitrage fill (the pull never runs).",
   "value": "qx || one-sided bound (c<r on buy, c>r on sell)",
   "find": "if(qx||(t.isBuy?c<r:c>r))",
   "lo": "if(qx)",
   "hi": "if(qx||c!=r)",
   "compiled_lo": true,
   "runtime_bytes_lo": 22403,
   "source_chars_lo": 47211,
   "source_sha256_lo": "8ee034ee3608babc3b0072a37538375936b33ed8caa97e95f12957a97942b4a3",
   "compiled_hi": true,
   "runtime_bytes_hi": 22420,
   "source_chars_hi": 47217,
   "source_sha256_hi": "72e6ce1e37d4697456b646294145ccdf339c3f01eab62f8e5d986adc63d685a1"
  },
  {
   "n": 24,
   "id": "level_interp",
   "family": "table levels",
   "meaning": "How the lookup blends the two sd levels around sd: lo takes the lower level (the upper only once sd reaches it), hi the nearest level, instead of linear interpolation.",
   "value": "linear in sd between levels",
   "find": "int256 tt=clip((sd-sdl(k)*U)/(sdl(k+1)-sdl(k)),0,U);",
   "lo": "int256 tt=clip((sd-sdl(k)*U)/(sdl(k+1)-sdl(k)),0,U)>=U?U:int256(0);",
   "hi": "int256 tt=clip((sd-sdl(k)*U)/(sdl(k+1)-sdl(k)),0,U)>=U/2?U:int256(0);",
   "compiled_lo": true,
   "runtime_bytes_lo": 22481,
   "source_chars_lo": 47245,
   "source_sha256_lo": "96f99c56dae4d935905026ac509ee1eb28d03da6e3fa4c595d32cf210370ffcb",
   "compiled_hi": true,
   "runtime_bytes_hi": 22489,
   "source_chars_hi": 47247,
   "source_sha256_hi": "e1da8fcfea20db124c131d00accd0d306b3338e398ec7eed547e3f08de3a412a"
  },
  {
   "n": 25,
   "id": "cand_n",
   "family": "the split test's window and candidates",
   "meaning": "Number of denominator offsets the split test tries around the tracked m0; 5 is the most the candidate list supports, so both variants are fewer (hi 3 is QLX3's choice).",
   "value": "5 candidates (m0, +1, -1, +2, -2)",
   "find": "t.isBuy,m0,5)",
   "lo": "t.isBuy,m0,1)",
   "hi": "t.isBuy,m0,3)",
   "compiled_lo": true,
   "runtime_bytes_lo": 22440,
   "source_chars_lo": 47230,
   "source_sha256_lo": "684981efce73cba6f41ed2a03a81b25e6c48a1835a573cdf3208f523c05ff52e",
   "compiled_hi": true,
   "runtime_bytes_hi": 22488,
   "source_chars_hi": 47230,
   "source_sha256_hi": "349731ec5feef73fa1577ec5a45a74d4b19c971aef0647245e6cae8532b8f79a"
  },
  {
   "n": 26,
   "id": "rival_clip_p12",
   "family": "rival clip and band widths",
   "meaning": "Clip of the rival offset (5-bps grid units) before the phase-1/2 column warp pos2 (lo +-40 bps, hi +-80 bps).",
   "value": "+-160 grid units (+-800 bps, the warp's domain)",
   "find": "p2=pos2(w2/5);",
   "lo": "p2=pos2(clip(w2/5,-8*U,8*U));",
   "hi": "p2=pos2(clip(w2/5,-16*U,16*U));",
   "compiled_lo": true,
   "runtime_bytes_lo": 22493,
   "source_chars_lo": 47245,
   "source_sha256_lo": "1e8e7fd3e14e60f769608a20f5bdf9bf9326ada20f0ba9be8056387a045930a0",
   "compiled_hi": true,
   "runtime_bytes_hi": 22493,
   "source_chars_hi": 47247,
   "source_sha256_hi": "ed15e47d1225917a8b68859c5b4e9ef390080c6ae5da173a1e70015ef88f8533"
  },
  {
   "n": 27,
   "id": "trunc_floor",
   "family": "tell floors",
   "meaning": "Floor on the truncated-normal mass Z below which the filter treats the no-arbitrage band as missed and collapses the belief to the nearer band edge.",
   "value": "1e6 (mass 1e-12)",
   "find": "if(Z<1e6)return",
   "lo": "if(Z<1e4)return",
   "hi": "if(Z<1e8)return",
   "compiled_lo": true,
   "runtime_bytes_lo": 22439,
   "source_chars_lo": 47230,
   "source_sha256_lo": "388623aa4b6b2215dcbd69eededc25c997751da904761b058fd75471d58ea446",
   "compiled_hi": true,
   "runtime_bytes_hi": 22441,
   "source_chars_hi": 47230,
   "source_sha256_hi": "56b04ca926e2fb34d6a611835884144e1c53de2cff86c8c1a73e32f14f13678f"
  },
  {
   "n": 28,
   "id": "level_cap",
   "family": "table levels",
   "meaning": "Highest sd level index the lookup may climb to: lo caps at the 20 bps level, hi at the 26 bps level, instead of 34 bps.",
   "value": "k<6 (top level 34 bps)",
   "find": "while(k<6&&",
   "lo": "while(k<4&&",
   "hi": "while(k<5&&",
   "compiled_lo": true,
   "runtime_bytes_lo": 22440,
   "source_chars_lo": 47230,
   "source_sha256_lo": "e54b30b015deffa4340bc477c965faaedca07edef005621426d05211c4e21e6c",
   "compiled_hi": true,
   "runtime_bytes_hi": 22440,
   "source_chars_hi": 47230,
   "source_sha256_hi": "0592b87f94b518e42df5ed5acf920c3f423d14ed3cf32175beff90d975aa4553"
  },
  {
   "n": 29,
   "id": "rival_clip_p0",
   "family": "rival clip and band widths",
   "meaning": "Clip of the rival offset on table 0's column axis in phase 0; +-6 is the table's edge, so both variants are narrower (lo +-15 bps, hi +-22.5 bps).",
   "value": "+-6 grid units (+-30 bps, table 0's edge)",
   "find": "clip(w2/5,-6*U,6*U)",
   "lo": "clip(w2/5,-3*U,3*U)",
   "hi": "clip(w2/5,-45*U/10,45*U/10)",
   "compiled_lo": true,
   "runtime_bytes_lo": 22448,
   "source_chars_lo": 47230,
   "source_sha256_lo": "f0b4c0cb3011a254459f197a571bde0f06b49d8022a85419357474ede9143bd7",
   "compiled_hi": true,
   "runtime_bytes_hi": 22448,
   "source_chars_hi": 47238,
   "source_sha256_hi": "ff10131b33c7b345ffef08203246b88cf003582edbf22046be2fd6efd0426050"
  },
  {
   "n": 30,
   "id": "cand_outer",
   "family": "the split test's window and candidates",
   "meaning": "Offset of the outer candidate pair of the split test (in ulps of the denominator from m0); lo +-3, hi +-4 (the inner pair +-1 is unchanged).",
   "value": "outer pair +-2 ulps",
   "find": "i==3?int256(2):int256(-2)",
   "lo": "i==3?int256(3):int256(-3)",
   "hi": "i==3?int256(4):int256(-4)",
   "compiled_lo": true,
   "runtime_bytes_lo": 22439,
   "source_chars_lo": 47230,
   "source_sha256_lo": "cfb65b1b2e7c6cd0222eb414373e27e7d44a7f8b933a0fa9e2c03fc6abcf8f7a",
   "compiled_hi": true,
   "runtime_bytes_hi": 22440,
   "source_chars_hi": 47230,
   "source_sha256_hi": "aff120560e8d16041c226cfd97d8b8d6f3e988edf0dfe648bbca401f6bf8f61f"
  },
  {
   "n": 31,
   "id": "fee_cap",
   "family": "table levels",
   "meaning": "Ceiling on the fee returned from the tables (lo 2.5%, hi 5%).",
   "value": "U/10 (10% fee ceiling)",
   "find": "fb=clip(fb,0,U/10);fa=clip(fa,0,U/10);",
   "lo": "fb=clip(fb,0,U/40);fa=clip(fa,0,U/40);",
   "hi": "fb=clip(fb,0,U/20);fa=clip(fa,0,U/20);",
   "compiled_lo": true,
   "runtime_bytes_lo": 22438,
   "source_chars_lo": 47230,
   "source_sha256_lo": "382522394062099d194ad028e63d168f38f5b530093011bfc168e3d8ae017532",
   "compiled_hi": true,
   "runtime_bytes_hi": 22438,
   "source_chars_hi": 47230,
   "source_sha256_hi": "c9ffc3d77e735230444bb5e67f81f7029a753c9fb2fac14afaae3d6e562982c5"
  }
 ],
 "families": {
  "counts": {
   "table levels": 7,
   "phase thresholds": 4,
   "rival clip and band widths": 7,
   "synced-table switches": 4,
   "the split test's window and candidates": 5,
   "tell floors": 5
  },
  "left_out": [
   {
    "constants": "QPL table blob, qt() QT rows (knots, offsets, scales), w2l warp words",
    "why": "table compression or refit: spent line."
   },
   {
    "constants": "sdl level values 0x221a14100c080400 (0,4,8,12,16,20,26,34 bps)",
    "why": "the tables are fitted at these levels, so moving one level is a table refit; the level axis is probed instead by sd_scale, level_interp and level_cap."
   },
   {
    "constants": "pw clip w/5+160*U in [0,320*U], phase-0 column offset +6*U and nc1 12/48, pos2's +-160 domain",
    "why": "table geometry: indices outside it misaddress the fitted tables (rival clips inside the domain are kept as rival_clip_p0 and rival_clip_p12)."
   },
   {
    "constants": "893025000000 (filter diffusion per step, sigma^2)",
    "why": "per-run sigma: spent line (it is used only as a fixed predictive add in pred_var)."
   },
   {
    "constants": "retail likelihood weight 260000000000000000 and size lognormal 6801595083153746944 / 1176000000000000000",
    "why": "retail arrival and size model, next to the spent per-run rate line and not in the listed families."
   },
   {
    "constants": "filter gap cap n>12, trunc collapse v/4, pdf cutoff 10*U, ln/exp/cdf/root series constants",
    "why": "filter and numerical math, not in the listed families."
   },
   {
    "constants": "exact-arithmetic constants of ltTell, ltGrid tolerance (k0>>48), qHitX's QG/QK/QKE, LT_C, input bounds (rx>>40, ulpOverGridWad d>64)",
    "why": "exactness of the tell and split test; A/8b18deed reports that shifting QK by j ulps lowers the hit count and no single constant works."
   },
   {
    "constants": "guardFee interval 2999999999999948..3000000000000057",
    "why": "exact binary64 preimage of the Vanilla fee, not a tunable."
   },
   {
    "constants": "afterInitialize fee 2823606104386589 and initial slots",
    "why": "one-time start state, acts on the first step only."
   },
   {
    "constants": "price-belief variants (twocomp, lattice, rival pin), exact rival carry, learned residual heads, kappa",
    "why": "spent lines; no knob here changes the belief model. No constant named kappa was identified in QLX5."
   }
  ]
 },
 "not_done": [
  "No engine run and no replica run (as the brief says): no knob has a measured edge, gas peak or OOG count. Variants that add work per callback (window hi tries the split test on more callbacks, track hi, pred_var) were not gas-checked against the 245,000 afterSwap peak; QLX5's reported peak is 208366 (A/1ef80bfb).",
  "No gate (P, Q, T, F, G, E) was run. budget (n=22) changes leanLabel, so gate T needs a Python reference with the same budget.",
  "Knobs were compiled only one at a time; stacked combinations were not compiled.",
  "Variants were checked only for compiling, passing the engine validator and the size limits, not for behaviour."
 ]
}