# 490d Mirror checkpoint after C434

25 September 2026. **C434 complete; C435 unexecuted.** The latest user instruction authorized one bounded step, now completed. Current decisions override stale next-step text in predecessor archives.

## Current result

The C431–C433 path `2148→2020→1956 BC`, with E pivots 3620 then 2756 and effective squared-E pivot 3206, now has a source derivation:

`25(215−130+1)+23×950=48×500=24000`.

Choose SP primary Noah birth `N=3706+2(g−1)+60T`, with Gears 1–3, Terah T0/T1, Cainan OFF and full-430. Its matched Shem birth is `H=N−500`; Noah death is `q=N−950`. The first pivot is the sourced SP companion Noah birth at Cainan ON and minimum-sojourn, `p=N+130−215−1=N−86`.

Therefore `25p+23q=48H`, giving `E_q∘E_p=(E_H)²` as a whole affine map. Relative pivot offsets are `p−H=414=18×23` and `q−H=−450=−18×25`. The existing 2K input `x=H−1058` yields intermediate `H−1186` and output `H−1250`. Gaps expand `1472→1600` and `736→800`, producing 128+64.

The MT station contexts explain the same gains: `128=130−2`, `64=60+4`, and total `192=130+60+2`. Input 2148 is MT Shem death G2/C1/T1/F1; intermediate 2020 is G3/C0/T1/F1; output 1956 is G1/C0/T0/F1.

All six Gear/Terah comparisons have sourced pivots and exact whole-map identities. Required paths are:

| Base Gear/Terah | Path, BC | Missing from the fixed register |
|---|---|---|
| G1/T0 | 2148→2020→1956 | None |
| G2/T0 | 2150→2022→1958 | 2022 |
| G3/T0 | 2152→2024→1960 | 2152, 2024 |
| G1/T1 | 2208→2080→2016 | 2208, 2080 |
| G2/T1 | 2210→2082→2018 | 2210, 2082 |
| G3/T1 | 2212→2084→2020 | 2212, 2084 |

The fixed register contains 528 labelled regular Noah/Shem/Flood records at 373 coordinates. Absence is relative to this domain, not the entire repository. No outside event was introduced to fill a missing station.

With `S(g,C,T,F)=1741+2(g−1)+130C+60T+215F`, the formal MT stations are `S(g+1,1,T+1,1)`, `S(g+2,0,T+1,1)`, and `S(g,0,T,1)`. Allowed bounds force `g=1,T=0` for a complete path. Formal G4/G5 and T2 are diagnostics, never source states. Full-register membership reveals no alternative admitted role/alias rescue.

There is one complete coordinate path and two actual-pivot label versions, choosing SP primary or theoretical LXX-OFF for the second pivot. Effective-pivot aliases are descriptive and do not multiply the executed path count. Both Noah biographies still span 950; the actual pivot separation 864 crosses contexts. The fixed-H intermediate 2056 remains absent.

Removing the SP companion shifts the effective pivot by +25/48 and breaks the identity. Using `N−502` with the same second pivot would require fractional first-pivot displacement −2246/25. Both 500/100 and 502/98 remain valid source bindings; the present identity uses 500.

## Provenance and evidence

Read the C434 report first, then `evidence/DATA.json` for all six cases and source labels. The evidence ZIP contains the report, this checkpoint, current source snapshots, the predecessor certificate and checkpoint, excerpt cards, exact-arithmetic code, alternate verification code, results and integrity records. It continues from the C433 compact restart kit; it does not replace the older complete archives.

C432 excerpt-locator correction: its `E_RULE` card pointed to File_46 lines97–113 (70/69). C434 supplies the actual 25/23 passage, L3 lines117–133. Previous calculations already used 25/23; their numerical result is unchanged. The older sealed packet is retained unchanged.

C434 passes 97 calculation checks and 38 source/predecessor checks. An alternate source-table reconstruction and integer-coefficient implementation passes 24 checks and agrees on all six cases. All three result files replay byte for byte. No independent-agent review or extra historical witness is claimed. C433 payloads/certificate, current controlling sources, C265 certificate/checkpoint and standing graph guards were authenticated.

## Inherited controls and supplemental awareness

Mirror/529 focus: K529; E25/23; P70/69. J300/299 is the File_02 gap conversion, not a Residue Protocol or calendar-date operator. Regular Gears remain Noah/Shem/Flood only. SP −1 companions remain at SP Noah/Shem person stations; Flood close is independent. SP primary Noah death retains its inclusive/harmonic qualification. Native LXX has Cainan ON; OFF is theoretical removal. Preserve modal bindings, roles, aliases and phase ancestry.

The global paired Mirror is January AD1; the local junction is January AD2; no civil year zero. No new source point, phase, fitted anchor/global axis, upstream/cumulative Gear, primer reopening or canonical graph edit. C433's four-template census and prior Mirror results remain controlling. Repeated paths and arithmetic checks are not independent witnesses.

The 25 September SKL appendix is frozen for awareness only: normal SKL Gear2/local ±2, distinct from macro ±720; `259210=490K`, `25921=49K=24K+25K`, the Exodus/Tabernacle one-year distinction and the additional13K reflected Shem-birth/Noah-death boundary. Its generated intermediate does not become a newly admitted regular source point. No SKL research was performed in C434.

The corrected LXX8464 observation also remains supplemental: 1564→1700, 2484→2700 and 920→1000; AD3746/2300 was superseded. C-series reports remain distinct from original unprefixed Reports01–10, unestablished interrupted Reports11–25 and the Engine reports.

## Best next bounded step

**C435, proposed only:** Fix the six sourced C434 pivot pairs and census all 373 existing regular coordinates as inputs, requiring a sourced intermediate and output and recording every role/context alias. This is 2,238 finite input/map comparisons. Do not fit pivots, add coordinates or enlarge the domain.

Reason: C434 explains the 2K path and its boundary. The remaining question is whether those same source-derived maps preserve a wider finite source relation. **C435 is unexecuted and requires a new instruction.**