# 490d Mirror checkpoint after C312

24 September 2026. Latest completed: **C312 — Same-Gear transport and cumulative field boundary.** C313 is proposed and unexecuted.

Read the C312 report and this checkpoint first. The evidence packet carries the previous C311 checkpoint for inherited synthesis, the fixed C286/C301/C302 data, current File_18, the axis report, supplemental Engine Report III and the Gear register, and the intake note. Retrieve older reports selectively; do not restart C01–C310 or follow stale next-step paragraphs.

## New C312 result

Regular MT Noah birth→Flood start uses Cainan OFF/Terah0/full430. Regular SP Shem birth→death uses OFF/Terah+60/minimum215. At each same Gear1–3:

`B_SP = B_MT +650−500+60−215−r = B_MT−5−r`,

where r=0 is SP primary and r=1 its local companion. All six regular comparisons pass. There is no single rail-blind translation; one rule with the existing rail label works for all Gears. It changes event roles and named contexts while preserving600-year pair widths.

| Gear | MT Noah→Flood | SP primary Shem life | SP companion Shem life |
| --- | --- | --- | --- |
| G3 | 3060→2460 | 3055→2455 | 3054→2454 |
| G2 | 3058→2458 | 3053→2453 | 3052→2452 |
| G1 | 3056→2456 | 3051→2451 | 3050→2450 |

Cumulative MT ON is M_i=(5896−i,5296−i); LXX OFF is L_j=(5890−j,5290−j), each restricted to indices0…7. The existing C−B=2832 condition forces **j=i−1+r**. G3 transports i4→j3/4; G2 transports i6→j5/6. These four have admitted endpoints on both cumulative sides.

G1 requires MT i8 outside the field. Its primary LXX target j7 is admitted; the companion target j8 is outside. All six regular pairs remain valid. Required MT5888/5288 and companion LXX5882/5282 are outside-field diagnostics, not added nodes. The regular rule describes all five SP targets, while only four have admitted MT ON antecedents. Do not erase this distinction.

Signed BC centers x=−B move forward5+r; existing ±1/4 phase components and pair widths survive. No harmonic expansion, new phase or Mirror attribution was applied.

## Retained conclusions and supplemental provenance

C310's unique minimum context-family cover remains MT at LXX OFF j0/2 plus SP at j3…7; LXX primary aliases add no coordinates. The missing j1 is unchanged. C311 did not locate a source rule prescribing that exact context/role switch in File_18, File_09 and the axis report. C312 establishes a uniform labelled structural relation, not such a selector.

Engine Report III §5 explicitly derives the LXX OFF Shem/Flood fields. They remain derived, not native rows printed verbatim in File_18. The seven-document supplemental ZIP is useful reference material; Engine Reports I–IV exactly match inherited archive copies. Current corrections override its older LXX182/777 regular state and mixed LXX Cainan headings. The Gear register's comparison guard remains operative. Sothic and rounded material stays background.

The inherited529 synthesis remains in C310/C311: K=529, 2K+15K=17K from598+460 and8395−460; the C287 typed four-node form retains its source membership restrictions and free common translation. C294/C295 fixed-reflection and all-K configurations remain distinct. C303–C307 path/phase compatibility limits and599/601 results are not repaired by this new600-year pair translation.

## Standing controls

Mirror and529 remain central. K=529, E=25/23, P=70/69. Global Mirror January AD1; local junction x=1, January AD2; no civil year zero. Regular Gears remain Noah/Shem/Flood only; SP−1 is local to SP Noah/Shem. No cumulative/upstream Gear operation, new endpoints or anchors, canonical/graph changes, primer reopening or global axis/z-law. Capture now; canonize later. Matched coordinates do not identify events; derived table states are not independent historical witnesses.

Retain the corrected LXX supplement: W8464 gives Creation5494 BC→AD2970, comparison to reflected ConquestAD1406 of1564→1700 by25/23; Jared4534 BC→AD3930, comparison to reflected ExodusAD1446 of2484→2700. LXX/MT Creation-to-Jared960/460 yields offsets1380/880; difference920→1000. AD3746/2300 is superseded. Awareness only.

C-series reports remain distinct from original unprefixed Reports01–10 and unestablished interrupted Reports11–25, and from Engine Reports I–IV. The original AD1905–1911 proposal remains unexecuted. C277–C310 was completed and published; no batch repetition is needed.

## Verification and next step

C312 passed33 main assertions and15 source checks, with byte-identical replay. Separate mathematical and source reviews agree. File_18/File_09, the axis source, C265 certificate, C311 predecessor and C127 graph remain unchanged; C127 has208 nodes/382 duration edges.

**C313, proposed only:** normalize the five existing SP Shem-life targets to full430/Terah0 with +155, then test the500-year Noah→Shem birth binding against SP Noah selected by17K, retaining matching Gear/rail and complete Shem-life endpoints. This connects the new relation directly to529 without repeating the earlier Noah/Flood600 test. Keep the five-case domain fixed, record failures, and do not treat a match as a source-prescribed chronology. High is sufficient. **C313 has not been executed.**