{
 "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; this item only changes one constant of QLX5 (LEAN plus the drift-tolerant split test) and measures it. All credit for the policy is Taylor's.",
 "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;",
 "seeds": {
  "first": 10205048,
  "last": 10205175,
  "n": 128,
  "unused": 0,
  "unused_list": [],
  "burnt": [],
  "failed": [],
  "blocks_complete": 4,
  "block_size": 32,
  "run_once_in_order": true,
  "outside_range_simulated": 0
 },
 "arms": {
  "QLX5": {
   "mean_edge": 540.540017315253,
   "peak_gas": 207402,
   "out_of_gas": 0,
   "runtime_bytes": 22440,
   "source_sha256": "e183e5bc3fb794b7067703b10a7da9920267aa5f4caa968e16ca101b02338f40",
   "source_chars": 47230,
   "runtime_sha256": "903a0cf860910022916e7c16aa1ffcfb94b0db9e25074665947d786615a44ae8",
   "afterSwap_calls": 1409956,
   "afterSwap_ok": 1409956,
   "sum_ok_gas": 192520719254,
   "callback_errors_all_roles": 0,
   "engine_seconds": 32.485
  },
  "LO": {
   "mean_edge": 540.540017315253,
   "peak_gas": 207402,
   "out_of_gas": 0,
   "runtime_bytes": 22440,
   "source_sha256": "aed2d3c12623589b27bd3d9e85d143e29773699c3218c35385db26eb49e290d1",
   "source_chars": 47230,
   "runtime_sha256": "9bea665bd6e1b750c2cf9ed70ec40f202af861464c98a5f5597a84a8ab9b496e",
   "afterSwap_calls": 1409956,
   "afterSwap_ok": 1409956,
   "sum_ok_gas": 192520719254,
   "callback_errors_all_roles": 0,
   "engine_seconds": 33.833
  },
  "HI": {
   "mean_edge": 540.540017315253,
   "peak_gas": 207402,
   "out_of_gas": 0,
   "runtime_bytes": 22440,
   "source_sha256": "53370a6ca74237e7605f969ed88fa34d433420754635b59e3dd286da75e1feee",
   "source_chars": 47232,
   "runtime_sha256": "d60f4eb49e6043724677cd86c6389d64a2868583a7d7300976107b66c23cfeaa",
   "afterSwap_calls": 1409956,
   "afterSwap_ok": 1409956,
   "sum_ok_gas": 192520719254,
   "callback_errors_all_roles": 0,
   "engine_seconds": 34.865
  }
 },
 "diffs": {
  "LO-QLX5": {
   "n": 128,
   "mean_diff": 0.0,
   "se": 0.0,
   "sum_d": 0.0,
   "sum_d2": 0.0,
   "seeds_positive": 0,
   "seeds_negative": 0,
   "seeds_zero": 128,
   "min": 0.0,
   "max": 0.0
  },
  "HI-QLX5": {
   "n": 128,
   "mean_diff": 0.0,
   "se": 0.0,
   "sum_d": 0.0,
   "sum_d2": 0.0,
   "seeds_positive": 0,
   "seeds_negative": 0,
   "seeds_zero": 128,
   "min": 0.0,
   "max": 0.0
  },
  "HI-LO": {
   "n": 128,
   "mean_diff": 0.0,
   "se": 0.0,
   "sum_d": 0.0,
   "sum_d2": 0.0,
   "seeds_positive": 0,
   "seeds_negative": 0,
   "seeds_zero": 128,
   "min": 0.0,
   "max": 0.0
  }
 },
 "pass_peak": {
  "LO": true,
  "HI": true
 },
 "limits": {
  "source_chars_max": 50000,
  "runtime_bytes_max": 24576,
  "peak_gas_max": 245000,
  "LO": {
   "compiled": true,
   "source_chars": 47230,
   "within": true
  },
  "HI": {
   "compiled": true,
   "source_chars": 47232,
   "within": true
  }
 },
 "identical_per_seed": true,
 "reading": "On 128 fresh engine seeds LO (floor 5e8) and HI (floor 15e8) are bit-identical to QLX5 on every seed (all three paired differences exactly 0, se 0, with equal afterSwap call counts, peak gas and total gas), and reading the source shows why: for any d below about 8.69e9 the pdf cutoff at |z|>10 already makes the retail likelihood exactly 0, so this floor cannot move the fee at these values and the knob has no gain to offer.",
 "why_inert": {
  "source": "QLX5 update(): int256 d=ab(ln(divi(s,sp)));if(d<1e9)d=1e9; int256 pi=pdf(divi(ln(d)+6801595083153746944,1176000000000000000)); lr=divi(mul(mul(Z,260000000000000000),pi),mul(d,1176000000000000000)); and pdf(x) returns 0 when ab(x)>10*U.",
  "z_at_floor": {
   "500000000": -12.427566270708,
   "1000000000": -11.838155402884919,
   "1500000000": -11.493372147690902
  },
  "first_d_with_nonzero_pdf_arg": 8685637104,
  "argument": "With an integer port of QLX5's ln (truncating division), z=(ln(d)+6.8016)/1.176 is below -10 at d=5e8, 1e9 and 15e8 and stays below -10 for every d up to first_d_with_nonzero_pdf_arg-1 (bisection, plus 200,000 random d in between). So whenever the floor binds in any arm (d<15e8), and for any unfloored d in that band, pi=0 and lr=0 in all three arms; the denominator mul(d,1.176e18) stays nonzero for d>=5e8. The three contracts therefore return the same fees on every input; only gas could differ when the floor binds.",
  "status": "derived by reading the source and a Python integer port, not an engine measurement; the engine rows agree with it",
  "gas_note": "Total Submission afterSwap gas is identical across the three arms (same sum over 1,409,956 calls). A binding floor would change gas between LO and QLX5 (ln(5e8) takes one more doubling than ln(1e9)), so this is consistent with the floor never binding on these seeds; that was not counted directly.",
  "to_matter": "a floor would have to exceed about 8.69e9 (|ln move| 8.69e-9) before it could change lr at all"
 },
 "engine": {
  "install": "kit setup_fast.sh --platform linux-x86_64 (exit 0): amm-challenge@6b6921f8d463314aa7c96234e1be25a25245f704, amm_sim_rs 0.1.0.post1",
  "native_sha256": "ff88b6353c2aad7342f0a26194f7347e78b9c3b38d683a7449006d423978cd14",
  "compiler": "solc 0.8.24, optimizer 200, viaIR, paris (kit SolidityCompiler via the driver)",
  "driver_sha256": "d3f8646b541a76921a47e9d03247c8c9dfab594076a7c5dca79c36b6c048a282",
  "driver": "driver_zb64 of A/764c9461a9f3bab6e277178f4bb48553d1b97c6cca33bed016f7c9bfd611cc42, decoded and run unchanged: --strategy QLX5= LO= HI= --seeds 10205048 10205175 --lease 10205048 10205175 --block 32; one invocation, exit 0; each arm alone against the 30 bps VanillaStrategy, arms in order QLX5, LO, HI inside each block",
  "configs": "driver --check-configs on all 128 seeds: equal to the kit's config, no simulation",
  "engine_seconds_total": 101.183,
  "kit": "identity-md-launches/goal-3178-build-shared-evaluation-kit@45e7563d1a29ffca9d608fdf60c90bf2624d2d01"
 },
 "inputs": {
  "map_sha256": "f921f2133d55d8ce81b5d809494003e898fc2a72d1fe47cdc34606ff269d676e",
  "qlx5_source_sha256": "e183e5bc3fb794b7067703b10a7da9920267aa5f4caa968e16ca101b02338f40",
  "find_occurrences": 1,
  "variant_hashes_match_map": true
 },
 "not_done": [
  "Nothing was submitted to the leaderboard and no gate (P, Q, T, F, G, E) was run; this is a 128-seed engine measurement only.",
  "Arms were paired with QLX5 only, not with qt1 or LEAN.",
  "How often the floor binds was not counted (no counting twin was built); the gas equality only suggests it never did on these seeds.",
  "No floor above 15e8 was tried: only the map's lo and hi; a floor above about 8.69e9 is the first that could change behaviour and is untested.",
  "The inertness argument is by source reading and an integer port of ln, not a formal proof and not checked on-chain per call.",
  "Peak gas comes from these 128 seeds only.",
  "No engine seed outside 10205048..10205175 was simulated; none burnt, failed or partial; none left unused."
 ]
}