# How the chronological families fit together
## Reading guide · C831

The strongest current explanation is **one ordered source path, several measurements, and a small set of explicitly chosen transformations**.

MT, LXX and SP provide rows, variants and boundary conventions. Regular chronology accumulates effective begetting intervals; cumulative chronology accumulates lifespans. Rounded transforms the specified row values, then accumulates the resulting residuals. The other families join through weighted deletion, retained subdivisions, component expansion, calendar measurement, and declared shape transformations.

This explains both agreements and differences. It does not require every family to be a scaled or translated version of one date list.

| Main result | Why it matters |
|---|---|
| Complete regular–cumulative gap fields come from lifespan minus effective begetting rows. | The internal differences follow a reusable local rule, not a fitted outer offset. |
| SP with Cainan restored and native LXX share twelve birth positions across all four matched placement states. | A whole birth family agrees while its death and cumulative realizations differ predictably. |
| Rounded has a complete residual field, recoverable by adjacent differences. | An unchanged total can conceal internal movement; the row path determines the result. |
| Three binary variants have nested supports. | The eight/four/two placement pattern and unchanged intervals follow from where each source choice acts. |
| BJ’s biological and surface paths preserve the same 575 years. | Their internal differences form a zero-sum repartition, extending the same path grammar to another source family. |

The clearest worked example is the aligned SP/LXX suffix. Its births agree from Noah through Abraham, but its lifespans differ. Those differences move deaths locally and accumulate into a 574-year upstream cumulative difference. Transferred rounding changes that to 570 through two 27→25 lifespan differences. Official SP Terah 145 is retained throughout this comparison.

Three distinctions make the account precise:

1. **Measurement is not source identity.** The same source row can contribute 130 regularly and 460 cumulatively; deleting one indexed name does not itself determine a duration.
2. **A shared endpoint is not a shared full path.** Both File52c admitted paths reach 12026, and the continuation reaches 14726, because their selected components are retained. Other routes can share a total while their internal junctions differ.
3. **A date label needs a state.** MT 9890,9894 and9900 are gaps in different declared comparisons. Equal numeric labels do not identify Actual, Rounded, phase, completion or generated roles.

Several findings sharpen the sources without rewriting them. Both Methuselah and Reu exhibit the MT parts-versus-total rounding difference. BJ’s displayed Isaac–Jacob59 remains in tension with prose 70. SP’s cumulative 13406 has a useful conditional derivation as 13396+2+3+5; the supplied rectangle is established in the Strategy, while that particular provenance remains a proposed explanation.

Start with the visual, then the integrated explanation:

- [490d_Chronological_Families_Map_C831.png](sandbox:/workspace/scratch/1b40da62dcbd/c732_c831/deliverables/490d_Chronological_Families_Map_C831.png)
- [490d_Chronological_Families_Integrated_Synthesis_C831.md](sandbox:/workspace/scratch/1b40da62dcbd/c732_c831/deliverables/490d_Chronological_Families_Integrated_Synthesis_C831.md)

The evidence packet contains the exact ordered fields, source snapshots, sequential questions and reassessments, and independent reviews. The 100 actions are a research record, not 100 independent discoveries.

The next productive objective is explanatory compression: test whether this same source-path account explains another complete admitted family with its inputs fixed in advance. Latest File_52c remains primary. Second decimal inversion, the quarantined primers and further Gear transport remain outside the current scope.