{
  "step": "C456",
  "status": "completed",
  "title": "E-Square Integrality and Source Admission Gates",
  "previous_certificate_sha256": "11f6c293b48855c1b79c51bd2467d011e9e253375099c38a8090c0f6bc49e379",
  "bindings": {
    "step": "STEP.json",
    "source_manifest": "SOURCE_MANIFEST.json",
    "report": "490d_C456_E_Square_Integrality_and_Source_Gates_20260925.md",
    "checkpoint": "490d_Mirror_Checkpoint_After_C456_20260925.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": "8237aef9195b16999d1a3a0ba4f34edc8e316044219b9cdc58b8de605f3ad630",
  "source_manifest_sha256": "7d7d86854d9f9fe3aaf26d9e919f093e210a928dcda4687987bca153441d8bfa",
  "report_sha256": "ed1318102f6aa460121ac94707723be8f70ed89d5c1bdf9ffa97ba877841c396",
  "checkpoint_sha256": "d1373363f5ad183a32c9553ca49aebb40f1461a00a56822291e3202ee753dc34",
  "data_sha256": "c0bb347d11584dd4dc1d6a7778576dfed358d060422c95969a5dfe42396b54fc",
  "results_sha256": "7c87e211e2d527499a7e8cbbb4ee864bb8ae1b41a95815d0bc88d3f19bb3c810",
  "calculation_sha256": "3dee3d7bb2030006416b2eb17eefc3ecc472395410a81926c9080c81e300fe55",
  "verifier_sha256": "46964ade0128d97b589fb678853daf7b81ffff1d90eb1a99221031ba734b093f",
  "next_step_decision_sha256": "41f1dbba01a03b55ffc6b74104e6567d15ab7cde61ac7137bec5e615a72eb860",
  "replay_sha256": "bb2d1ff2f426fc2a8d8e74948c9a988afd3f4badc9a127c60a6f54067327f42b",
  "control_integrity_sha256": "24e687bf3e03c7f16c3ca2aafe4c72e9aab25f03d55fa644c44a178e698ff3df",
  "readme_sha256": "eb4c6346ab4db7f73cbdbcfe9e419487c6d3d973d5ce25783e61cf1403b9afdf",
  "assertions_passed": 4866,
  "source_checks_passed": 19,
  "main_result": "For integer input and effective pivot, a two-E output is integral exactly when the input gap is divisible by529. The13 sourced-pivot words have17 integer-output cases,15 sourced outputs and11 complete paths. Among nonzero gaps the gates narrow4→2→1; only2148→2020→1956 survives.",
  "limits": "The absence claims are restricted to the frozen source register. No missing2022,2655,2641,2657 or2643 record is generated or admitted.",
  "canonical_or_graph_edits": false,
  "new_independent_agent_review": false,
  "next_step_executed": false,
  "next_proposed_step": "Starting from all60 actual529/1058 source pairs, compute full pair reachability when the same admitted E or reflection is applied to both endpoints, preserving endpoint ancestry and every intermediate source pair."
}