{
  "name": "The Tactic Background Table",
  "description": "Rates at which Lean tactics' proofs carry an avoidable classical dependence, across four libraries under two attribution rules, each shown against the band spanned by known-negative tactics in the same library and rule. The band is what makes a rate interpretable, and it is wide.",
  "version": "2026-08-12",
  "sha256": "4e2f817ddf0651f0f787a36dc8901afa5eaa2eed159ed2f5fd932f557687ec97",
  "url": "https://f-keys.com/gonzalgo/tactic-bands/",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "producedBy": {
    "software": "gonzalgo",
    "url": "https://pypi.org/project/gonzalgo/",
    "paper": "https://doi.org/10.5281/zenodo.21853489"
  },
  "measured": {
    "Lean 4": "4.32.1 with Mathlib v4.32.1",
    "libraries": "Mathlib, Init, Std, Batteries",
    "threshold": "cells with at least 20 proofs"
  },
  "fields": [
    "library",
    "attribution",
    "tactic",
    "proofs",
    "classical",
    "eligible",
    "rate_pct",
    "role",
    "band_low_pct",
    "band_high_pct",
    "band_widest",
    "position",
    "escapes_band",
    "controls_in_band"
  ],
  "displayed": [
    {
      "key": "library",
      "label": "library"
    },
    {
      "key": "attribution",
      "label": "rule"
    },
    {
      "key": "tactic",
      "label": "tactic"
    },
    {
      "key": "role",
      "label": "role"
    },
    {
      "key": "proofs",
      "label": "proofs"
    },
    {
      "key": "classical",
      "label": "classical"
    },
    {
      "key": "eligible",
      "label": "eligible"
    },
    {
      "key": "rate_pct",
      "label": "rate"
    },
    {
      "key": "position",
      "label": "vs band"
    }
  ],
  "rows": [
    {
      "library": "Batteries",
      "attribution": "loose",
      "tactic": "grind",
      "proofs": 182,
      "classical": 179,
      "eligible": 149,
      "rate_pct": 83.2,
      "role": "candidate",
      "band_low_pct": 23.1,
      "band_high_pct": 81.8,
      "band_widest": "refine",
      "position": "above band",
      "escapes_band": true,
      "controls_in_band": 12
    },
    {
      "library": "Batteries",
      "attribution": "loose",
      "tactic": "refine",
      "proofs": 36,
      "classical": 11,
      "eligible": 9,
      "rate_pct": 81.8,
      "role": "known-negative",
      "band_low_pct": 23.1,
      "band_high_pct": 81.8,
      "band_widest": "refine",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 12
    },
    {
      "library": "Batteries",
      "attribution": "loose",
      "tactic": "cases",
      "proofs": 111,
      "classical": 39,
      "eligible": 30,
      "rate_pct": 76.9,
      "role": "known-negative",
      "band_low_pct": 23.1,
      "band_high_pct": 81.8,
      "band_widest": "refine",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 12
    },
    {
      "library": "Batteries",
      "attribution": "loose",
      "tactic": "induction",
      "proofs": 171,
      "classical": 68,
      "eligible": 51,
      "rate_pct": 75.0,
      "role": "known-negative",
      "band_low_pct": 23.1,
      "band_high_pct": 81.8,
      "band_widest": "refine",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 12
    },
    {
      "library": "Batteries",
      "attribution": "loose",
      "tactic": "apply",
      "proofs": 94,
      "classical": 54,
      "eligible": 38,
      "rate_pct": 70.4,
      "role": "known-negative",
      "band_low_pct": 23.1,
      "band_high_pct": 81.8,
      "band_widest": "refine",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 12
    },
    {
      "library": "Batteries",
      "attribution": "loose",
      "tactic": "simp_all",
      "proofs": 32,
      "classical": 10,
      "eligible": 7,
      "rate_pct": 70.0,
      "role": "candidate",
      "band_low_pct": 23.1,
      "band_high_pct": 81.8,
      "band_widest": "refine",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 12
    },
    {
      "library": "Batteries",
      "attribution": "loose",
      "tactic": "simp",
      "proofs": 616,
      "classical": 222,
      "eligible": 151,
      "rate_pct": 68.0,
      "role": "candidate",
      "band_low_pct": 23.1,
      "band_high_pct": 81.8,
      "band_widest": "refine",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 12
    },
    {
      "library": "Batteries",
      "attribution": "loose",
      "tactic": "omega",
      "proofs": 24,
      "classical": 19,
      "eligible": 12,
      "rate_pct": 63.2,
      "role": "candidate",
      "band_low_pct": 23.1,
      "band_high_pct": 81.8,
      "band_widest": "refine",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 12
    },
    {
      "library": "Batteries",
      "attribution": "loose",
      "tactic": "rw",
      "proofs": 229,
      "classical": 99,
      "eligible": 58,
      "rate_pct": 58.6,
      "role": "known-negative",
      "band_low_pct": 23.1,
      "band_high_pct": 81.8,
      "band_widest": "refine",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 12
    },
    {
      "library": "Batteries",
      "attribution": "loose",
      "tactic": "exact",
      "proofs": 133,
      "classical": 54,
      "eligible": 30,
      "rate_pct": 55.6,
      "role": "known-negative",
      "band_low_pct": 23.1,
      "band_high_pct": 81.8,
      "band_widest": "refine",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 12
    },
    {
      "library": "Batteries",
      "attribution": "loose",
      "tactic": "unfold",
      "proofs": 49,
      "classical": 18,
      "eligible": 9,
      "rate_pct": 50.0,
      "role": "known-negative",
      "band_low_pct": 23.1,
      "band_high_pct": 81.8,
      "band_widest": "refine",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 12
    },
    {
      "library": "Batteries",
      "attribution": "loose",
      "tactic": "rfl",
      "proofs": 145,
      "classical": 39,
      "eligible": 19,
      "rate_pct": 48.7,
      "role": "known-negative",
      "band_low_pct": 23.1,
      "band_high_pct": 81.8,
      "band_widest": "refine",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 12
    },
    {
      "library": "Batteries",
      "attribution": "loose",
      "tactic": "funext",
      "proofs": 37,
      "classical": 8,
      "eligible": 3,
      "rate_pct": 37.5,
      "role": "known-negative",
      "band_low_pct": 23.1,
      "band_high_pct": 81.8,
      "band_widest": "refine",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 12
    },
    {
      "library": "Batteries",
      "attribution": "loose",
      "tactic": "ext",
      "proofs": 30,
      "classical": 17,
      "eligible": 6,
      "rate_pct": 35.3,
      "role": "known-negative",
      "band_low_pct": 23.1,
      "band_high_pct": 81.8,
      "band_widest": "refine",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 12
    },
    {
      "library": "Batteries",
      "attribution": "loose",
      "tactic": "obtain",
      "proofs": 22,
      "classical": 10,
      "eligible": 3,
      "rate_pct": 30.0,
      "role": "known-negative",
      "band_low_pct": 23.1,
      "band_high_pct": 81.8,
      "band_widest": "refine",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 12
    },
    {
      "library": "Batteries",
      "attribution": "loose",
      "tactic": "intro",
      "proofs": 34,
      "classical": 13,
      "eligible": 3,
      "rate_pct": 23.1,
      "role": "known-negative",
      "band_low_pct": 23.1,
      "band_high_pct": 81.8,
      "band_widest": "refine",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 12
    },
    {
      "library": "Batteries",
      "attribution": "loose",
      "tactic": "simpa",
      "proofs": 40,
      "classical": 23,
      "eligible": 5,
      "rate_pct": 21.7,
      "role": "not examined",
      "band_low_pct": 23.1,
      "band_high_pct": 81.8,
      "band_widest": "refine",
      "position": "below band",
      "escapes_band": false,
      "controls_in_band": 12
    },
    {
      "library": "Batteries",
      "attribution": "strict",
      "tactic": "grind",
      "proofs": 74,
      "classical": 74,
      "eligible": 69,
      "rate_pct": 93.2,
      "role": "candidate",
      "band_low_pct": 83.3,
      "band_high_pct": 83.3,
      "band_widest": "rw",
      "position": "above band",
      "escapes_band": true,
      "controls_in_band": 1
    },
    {
      "library": "Batteries",
      "attribution": "strict",
      "tactic": "rw",
      "proofs": 28,
      "classical": 12,
      "eligible": 10,
      "rate_pct": 83.3,
      "role": "known-negative",
      "band_low_pct": 83.3,
      "band_high_pct": 83.3,
      "band_widest": "rw",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 1
    },
    {
      "library": "Batteries",
      "attribution": "strict",
      "tactic": "simp",
      "proofs": 165,
      "classical": 57,
      "eligible": 42,
      "rate_pct": 73.7,
      "role": "candidate",
      "band_low_pct": 83.3,
      "band_high_pct": 83.3,
      "band_widest": "rw",
      "position": "below band",
      "escapes_band": false,
      "controls_in_band": 1
    },
    {
      "library": "Init",
      "attribution": "loose",
      "tactic": "trivial",
      "proofs": 23,
      "classical": 2,
      "eligible": 2,
      "rate_pct": 100.0,
      "role": "known-negative",
      "band_low_pct": 45.0,
      "band_high_pct": 100.0,
      "band_widest": "trivial",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 24
    },
    {
      "library": "Init",
      "attribution": "loose",
      "tactic": "norm_cast",
      "proofs": 46,
      "classical": 28,
      "eligible": 28,
      "rate_pct": 100.0,
      "role": "candidate",
      "band_low_pct": 45.0,
      "band_high_pct": 100.0,
      "band_widest": "trivial",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 24
    },
    {
      "library": "Init",
      "attribution": "loose",
      "tactic": "subst",
      "proofs": 516,
      "classical": 175,
      "eligible": 164,
      "rate_pct": 93.7,
      "role": "known-negative",
      "band_low_pct": 45.0,
      "band_high_pct": 100.0,
      "band_widest": "trivial",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 24
    },
    {
      "library": "Init",
      "attribution": "loose",
      "tactic": "assumption",
      "proofs": 150,
      "classical": 58,
      "eligible": 52,
      "rate_pct": 89.7,
      "role": "known-negative",
      "band_low_pct": 45.0,
      "band_high_pct": 100.0,
      "band_widest": "trivial",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 24
    },
    {
      "library": "Init",
      "attribution": "loose",
      "tactic": "rcases",
      "proofs": 923,
      "classical": 338,
      "eligible": 300,
      "rate_pct": 88.8,
      "role": "known-negative",
      "band_low_pct": 45.0,
      "band_high_pct": 100.0,
      "band_widest": "trivial",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 24
    },
    {
      "library": "Init",
      "attribution": "loose",
      "tactic": "constructor",
      "proofs": 367,
      "classical": 153,
      "eligible": 128,
      "rate_pct": 83.7,
      "role": "known-negative",
      "band_low_pct": 45.0,
      "band_high_pct": 100.0,
      "band_widest": "trivial",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 24
    },
    {
      "library": "Init",
      "attribution": "loose",
      "tactic": "left",
      "proofs": 38,
      "classical": 12,
      "eligible": 10,
      "rate_pct": 83.3,
      "role": "known-negative",
      "band_low_pct": 45.0,
      "band_high_pct": 100.0,
      "band_widest": "trivial",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 24
    },
    {
      "library": "Init",
      "attribution": "loose",
      "tactic": "intro",
      "proofs": 866,
      "classical": 348,
      "eligible": 285,
      "rate_pct": 81.9,
      "role": "known-negative",
      "band_low_pct": 45.0,
      "band_high_pct": 100.0,
      "band_widest": "trivial",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 24
    },
    {
      "library": "Init",
      "attribution": "loose",
      "tactic": "right",
      "proofs": 42,
      "classical": 11,
      "eligible": 9,
      "rate_pct": 81.8,
      "role": "known-negative",
      "band_low_pct": 45.0,
      "band_high_pct": 100.0,
      "band_widest": "trivial",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 24
    },
    {
      "library": "Init",
      "attribution": "loose",
      "tactic": "decide",
      "proofs": 302,
      "classical": 52,
      "eligible": 41,
      "rate_pct": 78.8,
      "role": "candidate",
      "band_low_pct": 45.0,
      "band_high_pct": 100.0,
      "band_widest": "trivial",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 24
    },
    {
      "library": "Init",
      "attribution": "loose",
      "tactic": "ext",
      "proofs": 377,
      "classical": 141,
      "eligible": 107,
      "rate_pct": 75.9,
      "role": "known-negative",
      "band_low_pct": 45.0,
      "band_high_pct": 100.0,
      "band_widest": "trivial",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 24
    },
    {
      "library": "Init",
      "attribution": "loose",
      "tactic": "contradiction",
      "proofs": 103,
      "classical": 36,
      "eligible": 27,
      "rate_pct": 75.0,
      "role": "known-negative",
      "band_low_pct": 45.0,
      "band_high_pct": 100.0,
      "band_widest": "trivial",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 24
    },
    {
      "library": "Init",
      "attribution": "loose",
      "tactic": "rintro",
      "proofs": 318,
      "classical": 113,
      "eligible": 84,
      "rate_pct": 74.3,
      "role": "known-negative",
      "band_low_pct": 45.0,
      "band_high_pct": 100.0,
      "band_widest": "trivial",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 24
    },
    {
      "library": "Init",
      "attribution": "loose",
      "tactic": "grind",
      "proofs": 42,
      "classical": 32,
      "eligible": 23,
      "rate_pct": 71.9,
      "role": "candidate",
      "band_low_pct": 45.0,
      "band_high_pct": 100.0,
      "band_widest": "trivial",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 24
    },
    {
      "library": "Init",
      "attribution": "loose",
      "tactic": "cases",
      "proofs": 1721,
      "classical": 220,
      "eligible": 158,
      "rate_pct": 71.8,
      "role": "known-negative",
      "band_low_pct": 45.0,
      "band_high_pct": 100.0,
      "band_widest": "trivial",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 24
    },
    {
      "library": "Init",
      "attribution": "loose",
      "tactic": "omega",
      "proofs": 1144,
      "classical": 654,
      "eligible": 462,
      "rate_pct": 70.6,
      "role": "candidate",
      "band_low_pct": 45.0,
      "band_high_pct": 100.0,
      "band_widest": "trivial",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 24
    },
    {
      "library": "Init",
      "attribution": "loose",
      "tactic": "simp_all",
      "proofs": 838,
      "classical": 202,
      "eligible": 141,
      "rate_pct": 69.8,
      "role": "candidate",
      "band_low_pct": 45.0,
      "band_high_pct": 100.0,
      "band_widest": "trivial",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 24
    },
    {
      "library": "Init",
      "attribution": "loose",
      "tactic": "apply",
      "proofs": 964,
      "classical": 306,
      "eligible": 210,
      "rate_pct": 68.6,
      "role": "known-negative",
      "band_low_pct": 45.0,
      "band_high_pct": 100.0,
      "band_widest": "trivial",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 24
    },
    {
      "library": "Init",
      "attribution": "loose",
      "tactic": "induction",
      "proofs": 966,
      "classical": 133,
      "eligible": 91,
      "rate_pct": 68.4,
      "role": "known-negative",
      "band_low_pct": 45.0,
      "band_high_pct": 100.0,
      "band_widest": "trivial",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 24
    },
    {
      "library": "Init",
      "attribution": "loose",
      "tactic": "funext",
      "proofs": 150,
      "classical": 25,
      "eligible": 17,
      "rate_pct": 68.0,
      "role": "known-negative",
      "band_low_pct": 45.0,
      "band_high_pct": 100.0,
      "band_widest": "trivial",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 24
    },
    {
      "library": "Init",
      "attribution": "loose",
      "tactic": "rfl",
      "proofs": 1488,
      "classical": 398,
      "eligible": 261,
      "rate_pct": 65.6,
      "role": "known-negative",
      "band_low_pct": 45.0,
      "band_high_pct": 100.0,
      "band_widest": "trivial",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 24
    },
    {
      "library": "Init",
      "attribution": "loose",
      "tactic": "rwa",
      "proofs": 179,
      "classical": 51,
      "eligible": 33,
      "rate_pct": 64.7,
      "role": "known-negative",
      "band_low_pct": 45.0,
      "band_high_pct": 100.0,
      "band_widest": "trivial",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 24
    },
    {
      "library": "Init",
      "attribution": "loose",
      "tactic": "exact",
      "proofs": 1285,
      "classical": 468,
      "eligible": 289,
      "rate_pct": 61.8,
      "role": "known-negative",
      "band_low_pct": 45.0,
      "band_high_pct": 100.0,
      "band_widest": "trivial",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 24
    },
    {
      "library": "Init",
      "attribution": "loose",
      "tactic": "refine",
      "proofs": 324,
      "classical": 145,
      "eligible": 89,
      "rate_pct": 61.4,
      "role": "known-negative",
      "band_low_pct": 45.0,
      "band_high_pct": 100.0,
      "band_widest": "trivial",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 24
    },
    {
      "library": "Init",
      "attribution": "loose",
      "tactic": "rw",
      "proofs": 3339,
      "classical": 1222,
      "eligible": 735,
      "rate_pct": 60.1,
      "role": "known-negative",
      "band_low_pct": 45.0,
      "band_high_pct": 100.0,
      "band_widest": "trivial",
      "position": "inside band",
      "escapes_band": false,
      "controls_in_band": 24
    },
    {
      "library": "Init",
      "attribution": "loose",
      "tactic": "simpa",
      "proofs": 831,
      "classical": 407,
      "eligible": 238,
      "rate_pct": 58.5,
      "role": "not examined",
      "band_low_pct": 45.0,
      "band_high_pct": 100.0,
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}