{
  "step": "C408",
  "status": "completed",
  "date": "2026-09-24",
  "title": "Return-path obstruction to the missing squared-E factorization",
  "previous_certificate_sha256": "a4eba6347892397aca0b10a3c950e06223f241d7539be34d2bce67a475d710da",
  "bindings": {
    "step": "STEP.json",
    "source_manifest": "SOURCE_MANIFEST.json",
    "report": "490d_C408_Return_Path_Obstruction_to_Missing_Squared_E_Factorization_20260924.md",
    "checkpoint": "490d_Mirror_Checkpoint_After_C408_20260924.md",
    "data": "evidence/DATA.json",
    "results": "evidence/RESULTS.json",
    "calculation": "evidence/CALCULATION.py",
    "verifier": "evidence/check.py",
    "next_step_decision": "NEXT_STEP_DECISION.json",
    "replay": "REPLAY.json",
    "control_integrity": "CONTROL_INTEGRITY.json",
    "readme": "README.md"
  },
  "step_sha256": "b8b3e098cbf47d4cf73b84abac8f26e8ea761f7aafec05b2abdb928dabf6da74",
  "source_manifest_sha256": "62c79e636459950c6ef9ea048e642e45577b2a79fc4ec4629c14edb91c27ebe0",
  "report_sha256": "1491118ee49185c85d7eec44f0cb092c086bcdbe350f92c51a675803eb8473d4",
  "checkpoint_sha256": "b37e9af108b6fa662dc71f160826bbf7f43f9b75f2df35808b1789601d4ed66b",
  "data_sha256": "7e286c5de4d85cd48f55b5b29f5976a7ee3dd3190371f638c4c91d875da7be24",
  "results_sha256": "c6f311e80233a986c0f3ef219352b9795ce16ffa9cba9aa9ad53640533e89fe2",
  "calculation_sha256": "a6c6f4995cfffb6ab52b5a30364066cbc0a2aab3bd901ff660eb3aee2b21722d",
  "verifier_sha256": "9f175670abb70f7819dd7f6d997ff0bef2e58df8dffd763b433f6c6cd62e332d",
  "next_step_decision_sha256": "258d9dc71a3577b837146d2a8493dc5d12a38b54d1ff3d1c9bba5140ac1b8e9a",
  "replay_sha256": "cbe8c01afba3e53b9ac161b3fdb9020e4080d4a1a7cd1a9479f9d9882cafaf81",
  "control_integrity_sha256": "9810807cb07b02f43f568f68bb82cb41a6eeff6799902254b4932e5c350ac838",
  "readme_sha256": "6a9ec630568cdfe381108e3473626b759660bc29d458f8762e634e5627b12e22",
  "assertions_passed": 59,
  "source_checks_passed": 18,
  "main_result": "C361 already supplies the translated squared-E endpoints. The new Shem graphs have exactly three slope-compatible EE paths; all six comparisons with the two target maps fail. Prime valuations exclude every longer positive E/P/J replacement. The closest companion-path discrepancy is−4/529; all48 existing-phase comparisons also fail.",
  "limits": "No new intermediate, phase or axis is adopted. The all-word exclusion applies to positive paths in the newly enumerated source graphs, not arbitrary additional operators or unreviewed source grammars.",
  "canonical_or_graph_edits": false,
  "new_independent_agent_review": false,
  "review_provenance": "Root-agent analysis and deterministic replay; no new independent-agent review",
  "next_proposed_step": "Test the newly sourced Shem return loops under both existing17K source-corner exchanges, using the frozen cumulative register and reversed inherited phases. Track how the fixed−500 regular translation changes the original2K/17K rectangle, without shifting or fitting either exchange constant.",
  "next_step_executed": false
}