# 490d Mirror checkpoint after C333

24 September2026. **C333 complete; C334 unexecuted.** 0 steps remain in the current authorization. Read this checkpoint and report first; frozen predecessor records retain earlier findings. Current decisions override stale archive instructions. Do not repeat completed research.

## Current result

C324–C333 complete. Allfour C287 SP paths support2K=1058=950+108. Primary gives460+490+108; companion gives459+491+108 usingactualMTNoah. Noah490 iscontext-dependent butstableunder thetwo500/502modes. Newdeathcriteria leave02/22; combinedwithtwo17K theyconditionallyselect22 at i3/5. Sourceprescription gap remains.

Latest completed: C333. C334 is unexecuted; authorization exhausted. Retain the C323 synthesis and C324–C332 source, geometry, context, modal and dependency controls. Full C287 domain remains i2…5; C332 tests only the inherited C319 i3…7 slice. Primary 950 = 460 + 490 and all-four 2K = 950 + 108 are source-qualified consequences; companion uses 459/491. Global paired Mirror: January AD1. Local junction: January AD2. No civil year zero. K = 529, E = 25/23, P = 70/69; AXIS source K = 25/23 translates to current E. Regular Gears: Noah/Shem/Flood only. SP person companion remains local; Flood close is separate. No new endpoint, phase, fitted anchor, global axis, primer, canonical or graph edit. Preserve source, modal and ancestry distinctions and the SP primary-death qualification. Corrected LXX8464 supplement remains awareness only: 1564→1700, 2484→2700, 920→1000; AD3746/2300 is superseded. Current decisions override stale next-step paragraphs. Do not rerun completed research.

**C324–C333 are complete. The principal addition is a source-qualified Noah-lifespan dissection of the existing 529 structure: 2K = 1058 = 950 + 108.** It holds across all four complete SP comparison paths in C287. The detailed 490 partition belongs to their primary states; the companion states retain different actual MT intermediates.

## The new endpoint connection

Let N be SP Noah birth, M the same-Gear restored MT Noah birth, D the matched SP Noah death, and R the already admitted next-Gear MT Flood boundary. SP is OFF/Terah0/full430; MT is restored ON/Terah60/full430. These are comparisons between source contexts, with their existing reflected-coordinate convention retained.

| C287 source path | N→M→D→R | Partition of 1058 |
|---|---|---|
| i2: SP G1 companion → MT G2 close | 3705→3246→2755→2647 | 459 + 491 + 108 |
| i3: SP G1 primary → MT G2 start | 3706→3246→2756→2648 | 460 + 490 + 108 |
| i4: SP G2 companion → MT G3 close | 3707→3248→2757→2649 | 459 + 491 + 108 |
| i5: SP G2 primary → MT G3 start | 3708→3248→2758→2650 | 460 + 490 + 108 |

Every row preserves the matched SP lifespan N−D = 950 and D−R = 108. Thus the existing 2K edge accommodates the complete Noah lifespan through an already admitted death endpoint. No death date was fitted to the desired total. Primary death retains File_18's inclusive/harmonic qualification; the companion death retains its ordinary-companion qualification.

For primary paths, MT Noah→MT Flood is 598 = 490 + 108. For companion paths it is 599 = 491 + 108. The hypothetical MT births3245/3247 needed to impose 460/490 on the companion cases are absent. Flood close remains an event boundary, not an MT person companion. Co-located LXX Noah labels remain preserved without a newly asserted LXX death-path study.

C10 already established the adjacent-Gear 1058 relation and its primary 598+460 dissection; C287 retained it. The new work makes the death endpoint and its 108 remainder explicit. This is an additional source-labelled reading of an existing relation, not another independent numerical witness. The bounded prior-art lookup does not establish archive-wide novelty.

## What survives the controls

The complete five-role census gives positive residuals40,140,490,640 after the selected 460 context leg. These come from source intervals500,600,950,1100; the two500 intervals and two600 intervals retain different event meanings. The 1100 spans Noah birth to Shem death and is not a lifespan.

| Control | Result for the Noah950 remainder |
|---|---|
| Four admitted MT Cainan/Terah contexts | 300,360,430,490; only restored ON/Terah60 gives490 |
| Explicit G2 Noah/Flood with G2 or G1 Shem | 490 survives both500/100 and502/98 bindings |
| SP primary versus companion, actual same-Gear MT Noah | 490 versus491; no imported MT companion |

The 40 remainders change to42 under the named502 binding; the 140 lifespan/Noah-age remainders remain. These controls qualify the positive finding rather than treating valid source modes as corrections of one another.

The repeated equal-interval fields also have a known dependency. The Noah/Shem birth field and Flood/Shem-death field are600 apart at each corresponding vertex, through Noah's age at the Flood and Shem's lifespan. Those are distinct source facts with equal numerical values. In each named mode,13 biography/context equations on ten coordinates have rank9; adding all25 residual equations adds no rank. This is coordinate dependence, not a historical witness count or a new global operator.

## How this relates to the local460→500 prescriptions

C324 positively located File_09's declared local cumulative460→500 endpoint completions, the AXIS report's declared-anchor example, and File_46's scoped expansion rules. Those positive source prescriptions remain intact. No explicit dependency connecting the particular regular SP→MT context translation, E=25/23 and the Noah-bound500 relation was located in the reviewed passages. That is a bounded source-audit result, not a repository-wide absence claim or a global ban on expansion.

The admitted regular four-point field has gaps460|40|460, overlap40 and outer width960. File_09's bilateral completion field has gaps40|460|40, overlap460 and outer width540. Their three-point500 subpatterns agree, while their complete metric configurations and source/generated endpoint classes differ. A common affine E map also cannot equal a biography-preserving translation across all endpoints. This does not invalidate File_09's local construction or authorize fitting a new anchor.

## What the selection test establishes

In C319's already frozen menu, a is the cumulative annual choice and b the regular Gear-coordinate choice, each0 or2. With matched SP death D=N−950, the death-to-Flood remainder is110−b. Requiring108 therefore selects b=2 and restates the right2K edge. Requiring actual MT-Noah→SP-death490 additionally selects the primary rail.

Those two conditions retain both02 and22 at i3 andi5. Their N,M,D,R source endpoints are identical; only S changes. Adding the existing two17K requirement imposes a=b, so the combined conditions select22 at those two indices. **That conditional uniqueness is valid; an independent source prescription for coupling the choices remains unestablished.**

C332 tests only C319's i3…7 slice. C287's separately admitted i2 companion remains valid and is retained in C331. C323's stricter conditional i=j5 result also remains tied to its additional joint-support requirements; this batch does not erase those requirements or turn a two-row subset into a universal domain.

## Completion and recovery

The nine predecessor steps were sealed and published incrementally, each with a report, checkpoint and evidence ZIP. Their independent archive audit verified all nine ZIPs, payloads, certificate chains and frozen sources, reproduced18/18 main outputs and9/9 independent outputs, and confirmed27 publication receipts and write markers. C333 verifies the scientific synthesis and predecessor bindings from frozen inputs. The final completion/integrity record covers C333's sealed replay and all30 individual deliverables, followed by the compact restart kit and continuation archive.

All source and standing-control hashes remain unchanged, including File_18, File_09, the C265 checkpoint/certificate and the canonical graph controls. No new endpoint, phase, fitted anchor, global axis, canonical or graph change was adopted. Original unprefixed reports, Engine reports and C-series remain distinct. The corrected LXX8464 supplement remains awareness only:1564→1700,2484→2700 and920→1000; AD3746/2300 is superseded. The earlier incomplete September17 local ZIP must not be confused with the later verified intact original.


## Retained context

C323 remains the completed predecessor synthesis. Retain the six-coordinate OFF600 rectangle family and three nativeON/restored-MT primary counterparts; the full same-Gear Noah-bound SP→MT biography translates by460, with source textual502 a distinct binding. C314 reversal requires i+j=10 and opposite cumulative phases. C313/C315 same-ancestry500/600 failures remain. C287 full domain is i2…5. The paired+2 choices produce its all-K form, but the00 control also retains two17K paths. The optional combined support criteria alone isolate i=j5. No source-prescribed selector has been established. Corrected LXX8464 supplement remains awareness only (1564→1700;2484→2700;920→1000); AD3746/2300 is superseded. Earlier reports, original unprefixed reports and Engine series remain distinct.

Mirror/529 focus: K=529, E=25/23, P=70/69. Global paired Mirror January AD1; local junction January AD2; no civil year zero. Regular Gears are Noah/Shem/Flood only. SP minus-one person companions remain local to SP Noah/Shem; Flood close is a separate boundary. No upstream/cumulative Gear, new endpoint or phase, fitted anchor, global axis, primer reopening, canonical or graph edit. Capture now; canonize later. Source identity, context, modal binding, generated coordinates and phase ancestry stay distinct.

## Verification

69 main checks and 66 frozen-input/predecessor authentication checks passed. A second main replay produced byte-identical DATA/RESULTS. Independent review and its scope are recorded in the evidence. All frozen originals and standing controls remain unchanged. Verification counts are not independent-witness counts.

## Best next bounded step

C334: Conduct a bounded source-dependency audit of whether the cumulative ON-Shem annual choice i+2 is explicitly bound to the admitted next-Gear MT Flood boundary, or whether the sources only permit those two choices separately. Use the current endpoint ledger and targeted File_09/File_18 passages and their immediate cited dependencies; add no dates, anchors or numerical search.

The new death partition fixes the regular side condition while leaving the cumulative choice open. The remaining question concerns an explicit source binding, so another numerical census would not resolve it. This is a proposal only: the ten-step authorization ends at C333.

The current authorization ends here. C334 requires a new instruction.