C529 — Assess explanatory compression

Question

Which model best explains the completed set without hiding extra choices?

Inputs

{
  "models": [
    "one scalar affine conversion",
    "independent lookup of every displayed result",
    "typed modular grammar"
  ],
  "scoring": "qualitative; no predeclared numeric description-length weights"
}

Sources

[
  "Strategy §§1,6",
  "C524–C528"
]

Opened utc

2026-09-27T22:55:20.470064+00:00

Results

{
  "models": [
    {
      "model": "one scalar affine conversion",
      "status": "rejected by current MT/LXX/SP slopes",
      "source_cost": "cannot represent the observed direction changes"
    },
    {
      "model": "independent lookup",
      "status": "can restate every datum",
      "source_cost": "stores each result and loses shared mechanisms"
    },
    {
      "model": "typed modular grammar",
      "status": "reconstructs source projections,rounded paths,Key fields,529 ladders and specified junctions",
      "source_cost": "retains source rows,phase/frame choices,partitions,anchors and exceptional inclusive conventions"
    }
  ],
  "reconstruction_reach": {
    "transfers_unchanged": [
      "row projections",
      "anchored affine laws",
      "calendar calibration",
      "529 width rule",
      "rounded path evaluator"
    ],
    "transfers_conditionally": [
      "integral endpoints require pivot residues",
      "Mirror requires a chart",
      "state changes retain source scope"
    ],
    "does_not_transfer": [
      "universal12026 across traditions",
      "MT14/15/16 field at unchanged anchor",
      "MT Noah-refinement equality in LXX"
    ],
    "not_instantiated": [
      "full LXX/SP rounded cumulative paired-path test from current source tables"
    ]
  },
  "next_family_candidate": "source-defined161/299/460 construction, with this grammar frozen before reading its test inputs"
}

Finding

The modular model explains more than an endpoint lookup and survives recorded failures without repairs. Its practical compression is demonstrated on whole families; global minimality, historical sequence and statistical rarity remain unproved. The next research should test a further named source family, not enlarge a target search.

Reassessment

Reconcile independent reviews and freeze the report’s exact scope before the final synthesis.

Checks

{
  "alternatives_compared": true,
  "failures_retained": true,
  "source_gaps_retained": true
}

Closed utc

2026-09-27T22:55:20.470440+00:00

Record provenance

Exact record hash: 03b366a52caf3a393de1f45d2efce8549fed2715ddd4ef51615b3fe1f9f5ea23

Source journal: Research_Cycles/C0482_C0531/journal.json