{
  "step": "C403",
  "status": "completed",
  "date": "2026-09-24",
  "title": "Source E/P/J return loops, three-point path grammar and limits of 529 transport",
  "previous_certificate_sha256": "98a4c04065a1f3f995cde3a410e672207743fb344ac16670a7acdb0ebcf11094",
  "bindings": {
    "step": "STEP.json",
    "source_manifest": "SOURCE_MANIFEST.json",
    "report": "490d_C403_Source_E_P_J_Return_Loops_Three_Point_Grammar_and_529_Limits_Synthesis_20260924.md",
    "checkpoint": "490d_Mirror_Checkpoint_After_C403_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",
    "review_0": "evidence/ROOT_SECOND_METHOD.py",
    "review_1": "evidence/ROOT_SECOND_METHOD_RESULTS.json"
  },
  "step_sha256": "e39957468ea208a75ede85b91632dac245329bc3bfe667505d7b6108cb9f50ad",
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  "report_sha256": "334d20d3b8f0e6ec5eaf8844cf8597c8fc922168214e95f5d5ffd2d5170a705a",
  "checkpoint_sha256": "5c1d5ba0f2900783bf4681931a03d79626779fab9ffde1f83735035fd1a9426d",
  "data_sha256": "3fe048a371db2ecff37c530c14ca637ca46625f12a204bae9f67bd9983c800a9",
  "results_sha256": "be9d137bb1be34bb33a4768c0b3817b76395805db1d8b69df795d0acd5e56992",
  "calculation_sha256": "1e669128148081846fdd718d497c531c91aadd8fed713c820273deb97c34a852",
  "verifier_sha256": "9f175670abb70f7819dd7f6d997ff0bef2e58df8dffd763b433f6c6cd62e332d",
  "next_step_decision_sha256": "362bae52b70f4573978d795c682130ce70a991a8e58d6fc2750849ff2249463e",
  "replay_sha256": "34b5e883e3b2d8b6d9e9b33aa149a273db4f6dc59a6e4decc9d919c3468e0b24",
  "control_integrity_sha256": "9810807cb07b02f43f568f68bb82cb41a6eeff6799902254b4932e5c350ac838",
  "readme_sha256": "991385b856e56f1f3d8a7eadc1a9ec5c315a60719cee94cfac41589924b613b4",
  "review_0_sha256": "269d9251a57a66ded92e78d3c37e51e9d1690a4438f207156cb9c4b02f985ae2",
  "review_1_sha256": "ab8f6fd73c3467027bd9cf848a72b9cfa5a6866aef32910c08c628cdcc6a0b3d",
  "assertions_passed": 75,
  "source_checks_passed": 65,
  "main_result": "C394–C403 complete. The two primitive source E23→25 Noah comparisons have exact J return arrows at existing Flood pivots, but not P returns. A4096-trial coherent-family census, without529 or prior-PJ preselection, finds12 labelled E/J loops at six coordinate configurations. Two MT configurations also admit P returns and coincide with the lower-full430 common P/J repairs. Their shared G2 Noah source joins the two graphs into three vertices3031,3033,3035 and six operator arrows. Every admitted path fromu tov has affine formF(t)=v+E^e P^p J^j(t−u), with(v−u)/2=p+j−e. The402 paths through six arrows yield78 classes with endpoints retained as part of the classification; an algebraic proof gives the normal form for every finite admitted path. At each source vertex, complete P–E and J–E circuits commute with independent multipliers1750/(3K) and7500/(13K), K529. Individual E/P/J operators do not commute. The original17K branch obtained by+215 translation lacks required E pivots3271/3273. All ten common P/J source edges were checked: exactly the two lower regular edges admit an E return; no cumulative edge does. Across2238 circuit-generator/input trials in373 regular coordinates, only the fixed source point survives each circuit. Reduced denominators prove this for every nonempty positive circuit, excluding a global529-preserving chronology action. Source-table and variant reconstruction confirms all52 labelled record slots across12 loops. Endpoints, variants and scalar ratios are sourced; the new affine path grammar is a derived comparison, not an established prescription in the reviewed source passages. Whole950 biographies and a single physical seasonal action are not preserved. No new source endpoint, pivot, Gear scope or canonical graph edit was introduced.",
  "limits": "Exhaustive claims apply to the stated frozen menus, role/context conditions and positive circuits. The all-path and all-circuit extensions have explicit algebraic proofs. Source labels, repeated coordinates, verification counts and affine equalities are not independent historical witnesses or proof of intended source pairing. No global529-preserving action or source-prescribed circuit grammar is established. C404 remains unexecuted.",
  "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": "Compare the C400 three-vertex Noah return-loop grammar with the already sourced C385–C388 Noah-to-Shem E/J strips. Test whether the existing vertical E comparisons carry the admitted return paths and circuit normal forms to a source-qualified Shem graph, using only existing endpoints, pivots, chronology contexts and phases. Record any missing pivot or order obstruction. Do not extend Gear scope, add generated source points, or execute a general search.",
  "next_step_executed": false
}