{
  "as_of": "2026-09-20",
  "unit": "model-labelled parameter assignments, with overlap across models",
  "total": "656088076618908824313107197286544515861848336008633625137803385820549666122804211668074668032",
  "entries": [
    {
      "name": "Ordinary columnar",
      "file": "coverage_summary.json",
      "cells": 338,
      "assignments": "518454579766154252339121208833120690250873497093510325137732846885467299656221982720000"
    },
    {
      "name": "Autokey columnar",
      "file": "autokey_coverage_summary.json",
      "cells": 432,
      "assignments": "1529022446773476595988542495064064000"
    },
    {
      "name": "Independent column reversal",
      "file": "reversible_coverage_summary.json",
      "cells": 44,
      "assignments": "4313644366707057999696887808000"
    },
    {
      "name": "Mixed alphabet axes",
      "file": "mixed_axis_coverage_summary.json",
      "cells": 20,
      "assignments": "935514845880975360000"
    },
    {
      "name": "Progressive keys",
      "file": "progressive_coverage_summary.json",
      "cells": 48,
      "assignments": "1872361385492742144000"
    },
    {
      "name": "Column-reset roots",
      "file": "reset_coverage_summary.json",
      "cells": 4,
      "assignments": "11702924506195034112000"
    },
    {
      "name": "Affine substitution",
      "file": "affine_coverage_summary.json",
      "cells": 20,
      "assignments": "3329234326978560000"
    },
    {
      "name": "Inverse columnar, including derived periods",
      "file": "inverse_local_period_summary.json",
      "cells": 56,
      "assignments": "656087558164329058158854858165335682741158085135136531625949221327284922838118603545837568000"
    },
    {
      "name": "K3-derived routes",
      "file": "alternatives_2m/k3_lift_results.json",
      "cells": 64,
      "assignments": "4524029526974464"
    },
    {
      "name": "Binary 7 × 7 matrices",
      "file": "continuation_5m/binary7_independent_results.json",
      "cells": 364,
      "assignments": "204913783045357568"
    }
  ],
  "k3_formula": "4 × 2 × 2 × 2 × (26^8 + 26^10)",
  "binary_formula": "2 × 26 × 7 × 2^49",
  "rules": [
    "Count complete negative cells only; omit the width-31 structural survivor.",
    "For columnar models, count labelled orders (width factorial) times all numeric keys.",
    "For reversal models, use 44 stage-deduplicated models and 2^width direction assignments.",
    "For inverse models, merge source periods 1–4 and documented destination periods, counting commuting period-1 stages once.",
    "Count only the four executed length-4 column-reset roots; the proof for all positive key lengths is not assigned a finite total.",
    "Do not add the 144 password examples, 1,746 baseline replications, repeated runs, or partial search nodes.",
    "This is a sum of labelled parameter spaces. It is not a union of unique cipher functions, plaintexts, or plausible solutions.",
    "The ring test uses a different parameterization and is reported separately. No fraction of all possible K4 methods is known."
  ],
  "tokens": {
    "recorded_lower_bound": 8770028,
    "completed_goals": 8403684,
    "goals": [
      {
        "name": "Initial run, last recorded checkpoint",
        "tokens": 366344,
        "complete": false
      },
      {
        "name": "Main cryptanalytic campaign",
        "tokens": 3417704,
        "complete": true
      },
      {
        "name": "Public-source survey",
        "tokens": 1310021,
        "complete": true
      },
      {
        "name": "Four follow-up investigations",
        "tokens": 1128952,
        "complete": true
      },
      {
        "name": "Binary-matrix and archive continuation",
        "tokens": 1233387,
        "complete": true
      },
      {
        "name": "Berlin World Clock investigation",
        "tokens": 720361,
        "complete": true
      },
      {
        "name": "K3-derived alternatives",
        "tokens": 593259,
        "complete": true
      }
    ],
    "source": "Native goal records in the original research task, deduplicated by creation timestamp; completed goal files retained in research/usage. Initial run is a checkpoint, not final usage. Planning, unbudgeted follow-up and website work are excluded."
  }
}