# 490d — C612–C625: sequential research record

Research begun27 September2026 in the user’s local timezone; packet dated28 September UTC. Working continuation of C531. No canonical source is changed; second-order inversion and quarantined primers remain deferred.

Each step records a question before its calculation, frozen inputs, exact result, finding, and reassessment. Preparatory source extraction and review were delegated; the numbered sequence was evaluated in order. These are bounded research actions, not independent discoveries.

## C612 — Relate the989 interval to the weighted Actual bridge

**Question.** Does the cumulative Abraham–Exodus interval provide one unit for both sides of12026?

**Sources.** File60 cumulative Abraham; C545; latest File52c §3.14

**Inputs**

```json
{
  "Abraham": 2435,
  "Exodus": 1446,
  "Creation_cumulative": 14004,
  "bridge": 12026,
  "Creation_regular": 4114
}
```

**Results**

```json
{
  "unit": 989,
  "bridge_arms": [
    1978,
    7912
  ],
  "unit_coefficients": [
    2,
    8
  ],
  "expanded_unit": 1075,
  "expanded_arms": [
    2150,
    8600
  ]
}
```

**Finding.** The989-year Abraham–Exodus interval supplies2 and8 units in the Actual Creation bridge:1978+7912=10×989. E sends the common unit to1075 and the arms to2150/8600, explaining the preserved1:4 partition. This is a derived duration interface.

**Reassessment.** Assemble a compact source-input basis for every reconstructed family.

## C613 — Declare the source cost of the compact model

**Question.** Which inputs remain necessary after whole-family compression?

**Sources.** C532–C612; C531 synthesis

**Inputs**

```json
{
  "basis_policy": "retain supplied anchors, counts, phases, roles and interval data; distinguish formulas from inputs"
}
```

**Results**

```json
{
  "families": [
    "Covenant",
    "Cumulative_root",
    "Carrier",
    "Enoch_cells",
    "Enoch_grid",
    "Rounded_prior"
  ],
  "basis_artifact": {
    "path": "model/source_basis.json",
    "sha256": "c987727ba37f42d6329b321fece7ad924dc564527c6b37619c7982a0acbd3109",
    "bytes": 1913
  },
  "minimality_status": "compact candidate; no global minimum claim"
}
```

**Finding.** The compact model still pays for its source data and role selections. Explicitly including Ishmael’s137-year lifespan resolves the C551 input-label omission. Formula reuse reduces repeated construction, not the need for source premises.

**Reassessment.** Record the exact interfaces linking these family modules.

## C614 — Build the typed family interface map

**Question.** Which demonstrated relations actually join different modules?

**Sources.** C535,C545–C546,C570–C581,C605–C612; C531

**Inputs**

```json
{
  "interface_kinds": [
    "same source relation",
    "same duration",
    "endpoint-pair map",
    "same labelled coordinate",
    "evaluation equivalence"
  ]
}
```

**Results**

```json
{
  "interfaces": 13,
  "artifact": {
    "path": "model/family_interfaces.json",
    "sha256": "5d2a0654dd9eddf3a10dda6b89954024dedfbec350d10f9395d7982f284258cf",
    "bytes": 1867
  },
  "event_identity_claim": "only the explicitly labelled coordinate links identify nodes"
}
```

**Finding.** Thirteen typed interfaces make the family network connected at the level actually demonstrated. Some links identify source nodes; others identify durations or evaluated endpoints. The map preserves that distinction instead of using one undifferentiated arrow.

**Reassessment.** Determine which operations the expanded candidate grammar must expose.

## C615 — Refine the candidate generative grammar

**Question.** Does indexed carrier substitution require abandoning the existing transformation grammar?

**Sources.** C531; C552–C609

**Inputs**

```json
{
  "prior_operation_classes": 7,
  "newly_explicit_actions": [
    "indexed carrier realization",
    "bounded attribution"
  ]
}
```

**Results**

```json
{
  "artifact": {
    "path": "model/candidate_grammar.md",
    "sha256": "a3fb442c68878b387aa8843e6ebc2ed337c99ab047df99e08caf7e7638e4143b",
    "bytes": 1620
  },
  "architecture": [
    "source",
    "realization",
    "transformation",
    "comparison"
  ],
  "new_clarity": "expressions must retain counts and role offsets before evaluation"
}
```

**Finding.** The expanded grammar remains small when it acts on labelled expressions, not bare dates. Indexed carrier realization and bounded attribution make explicit two operations hidden by date-only descriptions. Minimality remains a research question.

**Reassessment.** Consolidate successful coverage and failure cases into one model assessment.

## C616 — Assess explanatory coverage and necessary distinctions

**Question.** What has the candidate grammar explained, and which simpler alternatives failed?

**Sources.** Completed journal and source reviews

**Inputs**

```json
{
  "covered_step_range": [
    532,
    615
  ]
}
```

**Results**

```json
{
  "artifact": {
    "path": "model/coverage_and_counterexamples.json",
    "sha256": "ecc4a3a750236fe5ac7f5e9996183960363264d45cea7cac04a7095946904604",
    "bytes": 1500
  },
  "covered_families": 9,
  "diagnostic_counterexamples": 5,
  "statistical_ledger_change": 0
}
```

**Finding.** The model explains complete families and records concrete failures of simpler date-only alternatives. Coverage counts describe reconstruction, not independent support; no target tally is enlarged.

**Reassessment.** Reconcile all completed review clarifications before drafting the main explanation.

## C617 — Reconcile review clarifications

**Question.** Which changes improve the explanatory account without rewriting completed research records?

**Sources.** Independent review notes in evidence/

**Inputs**

```json
{
  "reviewed_ranges": "C532–C612; conceptual artifact review in progress"
}
```

**Results**

```json
{
  "clarifications": 11,
  "artifact": {
    "path": "evidence/REVIEW_RECONCILIATION.json",
    "sha256": "c99964387bdc13282a220992516c365613b0326136017630ba704c4f58e4d264",
    "bytes": 1644
  },
  "numeric_corrections": 0
}
```

**Finding.** Reviews require no arithmetic correction through C612. Eleven explicit presentation/source clarifications are carried into the final synthesis, including the Enochian Key name and the missing lifespan premise.

**Reassessment.** Write the integrated explanatory draft with these corrections and the new interfaces.

## C618 — Draft the integrated family explanation

**Question.** Can the demonstrated interfaces be explained as one readable source-to-realization account?

**Sources.** C531 synthesis; C532–C617; source and review packets

**Inputs**

```json
{
  "deliverable": "new synthesis draft",
  "primary": "latest File52c",
  "deferred": "second decimal inversion"
}
```

**Results**

```json
{
  "draft": {
    "path": "model/draft_c618.md",
    "sha256": "7bae55be63730faccc2affac150bbb888f8ce8ac14d2718584a4f93e1b6a2957",
    "bytes": 17673
  },
  "word_count": 2355,
  "status": "first integrated version; independent editorial review follows"
}
```

**Finding.** The integrated draft now explains source measurements, Covenant and clutch shapes, calibrated Keys, Actual/Rounded interfaces, indexed Enochic carriers and shared529 widths as one account. The technical record remains separate from the main narrative.

**Reassessment.** Complete the supplemental input register identified by review before normalizing the family map.

## C619 — Complete the input register by source reference

**Question.** What supplemental inputs are needed beyond the compact core register?

**Sources.** File61/62 source tables; File68/69 source tables; C613–C618

**Inputs**

```json
{
  "review": "REVIEW_C613_C616.md",
  "policy": "retain full tables by explicit packet reference"
}
```

**Results**

```json
{
  "supplement": {
    "fixed_comparisons": {
      "regular_Joseph": [
        1915,
        1805
      ],
      "regular_Joshua": [
        1476,
        1366
      ],
      "cumulative_Joshua": [
        1406,
        1296
      ],
      "Exodus": 1446,
      "Conquest": 1406,
      "historical_Moses_birth": 1526
    },
    "additional_phase_display": {
      "whole_year_Aaron_offset": 3,
      "exact_Aaron_offset": "7/2"
    },
    "weekly_Enoch": {
      "D": [
        600,
        614
      ],
      "primary_counts": [
        10,
        8,
        6
      ],
      "residuals": [
        0,
        0,
        70
      ],
      "Lukan_transport": 140,
      "Enochic_transport": 40,
      "retained_local_gap": 70
    },
    "attribution": "All18 literal occupant pairs and72 coordinates in prep/file68_69_source_tables.json:file68_fixed_coordinate_attribution_overlay",
    "full_source_tables": [
      "prep/file61_62_tables.json",
      "prep/source63_inputs.json",
      "prep/file68_69_source_tables.json"
    ],
    "coverage_status": "core plus named tables and per-step input records; not a claim that a short register replaces the sources"
  },
  "artifact": {
    "path": "model/source_basis_completed.json",
    "sha256": "fed3a1415bf8fc354fdb9fbd3e390722d296c6cd19fd5d412b3f10b08f0f7f0e",
    "bytes": 3317
  }
}
```

**Finding.** The register now explicitly supplies fixed comparison biographies, whole-year phase, weekly residuals and overlays, and the complete attribution table. The compressed explanation remains traceable to all retained source choices.

**Reassessment.** Normalize module names and test the topology of the demonstrated interface inventory.

## C620 — Normalize the family relation graph

**Question.** Does the demonstrated relation inventory become connected under explicitly declared module names?

**Sources.** C614; REVIEW_C613_C616.md; C531

**Inputs**

```json
{
  "nodes": [
    "source_rows",
    "regular_cumulative",
    "covenant_clutch",
    "rounded",
    "carrier",
    "enochic",
    "calendar_keys",
    "forwarded_mirrors"
  ],
  "test": "weak connectivity of relation inventory, not identity or universal transport"
}
```

**Results**

```json
{
  "artifact": {
    "path": "model/family_graph_normalized.json",
    "sha256": "962ec17820b2cfea5677b158083f23ff773e3d69de9b33d38141fd31fce5a6b7",
    "bytes": 2030
  },
  "modules": 8,
  "edges": 15,
  "visited": [
    "calendar_keys",
    "carrier",
    "covenant_clutch",
    "enochic",
    "forwarded_mirrors",
    "regular_cumulative",
    "rounded",
    "source_rows"
  ],
  "weakly_connected": true
}
```

**Finding.** Explicit normalization resolves the earlier graph wording: the eight-module inventory is connected when direction is ignored. Every edge retains its own type and evidence. Connectivity describes the explanation’s organization, not a new arithmetic theorem or universal passage between events.

**Reassessment.** Finalize the exact Actual/Rounded diagram for the readable deliverable.

## C621 — Finalize the exact interface diagram

**Question.** Does the five-node visual retain the distinct paths, generated endpoint and pair adjustment?

**Sources.** C570–C572; C618 diagram

**Inputs**

```json
{
  "figure": "Actual-to-Rounded cumulative interface",
  "coordinate": "positive BC labels",
  "review": "root visually inspected1400×1250 PNG"
}
```

**Results**

```json
{
  "svg": {
    "path": "deliverables/Actual_Rounded_Interface.svg",
    "sha256": "86b6671a4c1a025000ca39443759f41384aeda40da7d05e13d07a7f0b5271043",
    "bytes": 6358
  },
  "png": {
    "path": "deliverables/Actual_Rounded_Interface.png",
    "sha256": "859a68c263d129fd372d2c072151b9cb2c791acdd13414514eeac15b157e683d",
    "bytes": 197120
  },
  "visual_QA": "legible labels; exact24552/13; five cards; unobstructed arrows; generated1404 explicitly labelled"
}
```

**Finding.** The figure presents the main bridge without losing the interior-path distinction. It is an exact vector diagram with a checked PNG companion, not a replacement for the source arithmetic.

**Reassessment.** Revise the draft using independent review and the completed source/model registers.

## C622 — Revise the synthesis after independent review

**Question.** Can the draft make the causal connections clearer while preserving every stated source distinction?

**Sources.** C618–C621; independent draft review

**Inputs**

```json
{
  "review": "REVIEW_DRAFT_C618.md",
  "changes": [
    "483 explanation",
    "475 status",
    "grid parameters",
    "weekly distance rule",
    "supplemented basis and normalized map"
  ]
}
```

**Results**

```json
{
  "draft": {
    "path": "deliverables/490d_Chronological_Families_Integrated_Draft_20260928.md",
    "sha256": "ddf2e6c86ae15d149c8e04f2e7d84ce9c15ce6a9eeba2255baa6bfa680dcf01f",
    "bytes": 19018
  },
  "word_count": 2530,
  "review_changes_applied": 6
}
```

**Finding.** The revised draft foregrounds the Actual/Rounded bridge and explains how483 carries the161/14 structure into both allocation identities. Parameters and diagnostic status are now explicit without expanding the scope-control discussion.

**Reassessment.** Bind the principal explanatory claims to exact equations and source locators.

## C623 — Bind the main claims to evidence

**Question.** Can a reader trace each principal connection to its exact calculation and controlling source?

**Sources.** Latest File52c; Files60–63,68–69; C531 and current journal

**Inputs**

```json
{
  "deliverable": "claim-to-evidence index",
  "scope": "main synthesis claims"
}
```

**Results**

```json
{
  "artifact": {
    "path": "model/claim_evidence_index.json",
    "sha256": "1db5eb7d213cc203057368f9fb1994a27be7d1bbf87b2fa5ec04d82be2de869c",
    "bytes": 2009
  },
  "principal_claims": 12,
  "source_status_labels_retained": true
}
```

**Finding.** Twelve central claims now have exact identities, step references, source locators and status labels. The index separates supplied source structure from the new algebraic explanations and from dependent coverage counts.

**Reassessment.** Identify the next useful research question beyond this100-step cycle without reopening deferred branches.

## C624 — Choose the next whole-family test

**Question.** What follow-up best advances explanation after the current families are reconstructed?

**Sources.** File70 section map; C591,C606–C607; Strategy objective

**Inputs**

```json
{
  "candidate_source": "File70 §6, Prophetic–Priestly–Enochian calendar-half bridge",
  "status": "proposal only, C632 not executed"
}
```

**Results**

```json
{
  "proposal": {
    "path": "model/NEXT_C632_PROPOSED.md",
    "sha256": "11edd7b4c8f5ca87d507771484227c0c8edb4ded70a712c75c198c90c82b87d8",
    "bytes": 1175
  },
  "next_step": 632,
  "executed": false
}
```

**Finding.** The best continuation is the next complete calendar-half family in File70, using the now explicit carrier and endpoint-role grammar. Its input packet must be frozen first; no new result or source branch is claimed in this cycle.

**Reassessment.** Create a short reading guide so the central explanation is accessible before the technical record.

## C625 — Create the short reading guide

**Question.** Can the three main advances be understood before reading the full synthesis?

**Sources.** C572,C568–C571,C587–C612; revised synthesis

**Inputs**

```json
{
  "audience": "reader seeking the Strategy’s larger picture",
  "format": "short prose with one exact comparison table"
}
```

**Results**

```json
{
  "guide": {
    "path": "deliverables/490d_Chronological_Families_Reading_Guide_20260928.md",
    "sha256": "c7e2a7506ef5507ce4f4d14e95b582ce063aacafd8febae386fee7003787cda7",
    "bytes": 4132
  },
  "word_count": 612,
  "central_results": [
    "Actual/Rounded endpoint-pair map",
    "partial E/full P and J allocation",
    "complete indexed Enoch family reconstruction"
  ]
}
```

**Finding.** The reading guide gives the larger explanation in about600 words, with a compact table and the new3430/989 connections. It lets readers start with the structure before entering the full source record.

**Reassessment.** Test the evidence packet’s portability away from the working directory.

## Evidence

Current completion:C532–C625. The accompanying archive includes the sequential journal, exact scripts, source snapshots and independent reviews. Some carried source snapshots provide future or inherited context; only the sections cited by a step are claimed as its evidence.