# C325 independent finite endpoint and phase review

24 September 2026. Scope: the three primary same-Gear C322 biographies, their five already held roles, the two held exact phase components, and the existing C271/C314 ancestry records. No new endpoint, expansion execution, anchor fit or C326 calculation is used.

**Result:** exactly six of75 annual role comparisons satisfy all three conditions `A−B=460`, `B−C=40`, `A−C=500`. They form two role families in each Gear. Independently choosing the three phase offsets from `±1/4` gives600 comparisons, of which exactly12 succeed: both all-minus and all-plus versions of each annual match.

Here A and C are SP OFF/Terah0/full430 primary-biography endpoints; B is the corresponding same-role MT restoredON/Terah60/full430 endpoint. Flood start retains its event role and has no imported person-companion rail.

| Gear / i | A: SP anchor | B: MT same-role endpoint | C: SP terminal | BC centers A→B→C |
|---|---|---|---|---|
| G1 /3 | Noah birth | Noah birth | Shem birth |3706→3246→3206|
| G1 /3 | Flood start | Flood start | Shem death |3106→2646→2606|
| G2 /5 | Noah birth | Noah birth | Shem birth |3708→3248→3208|
| G2 /5 | Flood start | Flood start | Shem death |3108→2648→2608|
| G3 /7 | Noah birth | Noah birth | Shem birth |3710→3250→3210|
| G3 /7 | Flood start | Flood start | Shem death |3110→2650→2610|

The second family is essential to an exhaustive result: the held Flood-start→Shem-death interval is also500. Noah/Shem birth roles are not uniquely selected by the numeric condition. There are69 annual failures and588 exact-component failures; none is repaired by changing a role, phase or source state.

## Exact phase and ancestry conditions

For an annual match, write the held component coordinates as `A+pA`, `B+pB`, `C+pC`. Its three residuals are respectively `pA−pB`, `pB−pC`, `pA−pC`. Hence all legs are exact precisely when `pA=pB=pC`; the third equality is dependent. All-minus and all-plus each yield six matches. Mixed physical output phases cannot satisfy the complete triple.

| Test | Annual passes /75 | Exact-component passes /600 |
|---|---:|---:|
| A−B=460 |75|300|
| B−C=40 |6|24|
| A−C=500 |6|24|
| All three together |6|12|

Those matching output phases must not be relabeled as common cumulative ancestry. The independent audit binds each successful A to its exact C271 record and each successful C to its exact C314 record:

| Successful family | A ancestry from C271 | C ancestry retained from C314 |
|---|---|---|
| Noah birth→Shem birth | cumulative LXX_OFF Flood at `(i,p)`, with the held8993 comparison to A | inherited Shem-output ancestry `(j,−p)`, `j=10−i` |
| Flood start→Shem death | cumulative LXX_OFF Shem at `(i,p)`, with the held8993 comparison to A | inherited Shem-output ancestry `(j,−p)`, `j=10−i` |

The Gear1/2/3 pairs use `(i,j)=(3,7),(5,5),(7,3)`. Even at `i=j=5`, the inherited cumulative phase labels are opposite; no exact same-ancestry conclusion follows. The C271 Noah and Flood branches retain their different cumulative source roles. The C2718993 comparison is preserved with its existing derived-comparison status; this audit does not invent a new stored path. B retains its actual C322 source identity and physical phase, without an added ancestry claim.

## What the census establishes

Each successful40 leg follows from a held460 context translation and a held500 source-biography interval: `B−C=(A−C)−(A−B)`. The third displayed duration is therefore not an independent confirmation. Likewise, six role-labelled instances and twelve phase instances are verification counts, not independent historical witnesses.

The census positively locates existing endpoint triples with the `460+40=500` shape. It does not establish that a source prescribes applying25/23 to those regular cross-tradition endpoints. File_09's separately prescribed cumulative completion fields retain their own node classes and dependencies. No expansion was executed to create C; every C was selected from the fixed five-role SP menu before checking the arithmetic.

The best next bounded question is to complete the already admitted four-endpoint geometry for each successful family and compare its full shape and role/dependency labels with File_09's prescribed bilateral completion field. Keep all corners in the held source registers and distinguish the full outer width from overlapping interval widths. This C326 proposal remains unexecuted in this review.

## Reproduction

`C325_Independent_Audit.py --sources DIR --out DIR` uses only the standard library and frozen `C322_DATA.json`, `C314_DATA.json`, and `C271_REGISTER.json`. The JSON stores all75 annual comparisons, all600 exact component comparisons, the six/twelve successes, source identities and ancestry bindings. **349 checks passed.** No civil year zero, global Mirror replacement, cumulative Gear or imported MT/LXX companion is introduced; global paired Mirror January AD1 and local junction x=1/January AD2 remain unchanged.