# 490d Mirror checkpoint after C267

24 September 2026. Latest completed step: **C267 — the 2500 midpoint and 5750/6250 seasonal bracket**. Continues the existing C01–C265 research and redirected C266; no restart.

## Direction and numbering

Dean’s comprehensive 4232/8464/12696 axis report redirected the former C266 proposal. C266 completed the 529 Axis Endpoint Ledger; C267 completed its proposed finite classification of 2500, 6250 and 7500. The earlier AD 1905–1911 historical endpoint search remains unexecuted. **C268 is proposed, not executed.**

## Fixed comparison

Use global M(x)=−x, local J₁(x)=2−x and comparison chart η(x)=1000(x−1). Center 0 is January AD 1; center 1 is January AD 2 and displays AD 1t/2n. No civil year zero. Integer pair centers carry actual components x±1/4 in t/n order.

| Profile | Translated Flood F | Translated Shem H, auxiliary | Reflected translated Shem RH |
|---|---|---|---|
| MT ON | [−6,1] | [−8,−1] | [1,8] |
| SP OFF | [−1,6] | [−3,4] | [−4,3] |
| LXX OFF | [0,7] | [−2,5] | [−5,2] |

C267 uses the 48 tagged F/RH records as its core. The 24 H records stay auxiliary. Each field contains eight annual boundary pairs. C266’s H=F−2 and RH=J₁(F), chronological 5+1+1+5+1+1 sequence, radial 5/6/7 scaffold and source-qualified Creation support path remain retained.

## C267 result to carry forward

1. **±2500 are generated LXX whole-field midpoint radii.** F_LXX midpoint 7/2 and RH_LXX midpoint −3/2 map to ±2500. These are also half of the selected SP radius-five arms. Their phasewise midpoint components are AD 4n/4t and 2n/2t BC: July-centered n/t, not January-centered t/n. No new source-event identity follows.
2. **±5750 and ±6250 are actual source-projected seasonal radii.** LXX Flood closing pair 5284t/5283n BC, translated 5290, gives center 7 and AD 7t/8n. Its components map to 5750 and 6250. LXX Shem closing pair 5884t/5883n BC, translated 5888 and reflected, gives center −5 and 6t/5n BC, mapping to −6250 and −5750. Each component also has one co-located MT interior source tag; retain both histories.
3. **The bracket is exactly 6000±250, and 6250/5750=25/23.** The axis report already states this numerical bracket. C267 establishes its explicit phase-radius realization in the frozen source projection. Macro conversion states and historical seasonal identities remain separately qualified.
4. Applying g(x)=1+(25/23)(x−1) sends the inner to outer positive component, but changes the full pair width to 25/46 and then leaves the quarter-year phase lattice. The ratio match does not preserve all source fields as a whole.
5. **7500 is a full seasonal-envelope length here.** The core phase hull is [−6.25,8.25], mapping to [−7250,7250]. The ±7500 preimages lie outside it. The two central MT envelopes each have length 7.5; their sum is 15, overlap 0.5, union 14.5. Keep 7000/Year 14 and 7500/Year 15 distinct. An auxiliary negative midpoint alone supplies no bilateral source-point extension.

The combined table now contains different roles: 2500 generated midpoint; 5000/6000/7000 source-projected pair-center radii; 5750/6250 source-projected seasonal radii; 7500 whole-envelope length. Do not flatten them into a single class of sourced endpoints.

## Evidence and controls

Eight frozen immediate inputs; 138 exact assertions; six generated outputs replayed byte identically; source-tagged phase and midpoint ledgers; independent review; certificate chained to C266; payload integrity manifest. The report and this checkpoint are authored documents, not among the six computational replay outputs. No claim is made to replay the unattached 855-check branch package.

Current File_18 SHA-256: `68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5`.

Current File_09 SHA-256: `45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e`.

The C127 208-node graph remains unchanged. Keep K=529, E=25/23, P=70/69 and ρ=radius. Regular Gears remain Noah/Shem/Flood only. No new source event, cumulative Gear, global axis, z-law or canonical amendment is asserted. Capture now, canonize later. Prior quarantines, SP official Terah 145, LXX native ON/derived OFF labels and unresolved joins remain controlling. Original unprefixed Reports 01–10 and interrupted, unestablished original Reports 11–25 remain distinct from this C-series.

## Best next bounded step

**C268:** compare the LXX seasonal-radius realization with the two retained source-qualified 6877→7475→8125 chains. Retrieve existing C01/C206 anchor and center evidence selectively; test fixed anchors, source roles and phases in addition to width ratios. Distinguish coordinate rescaling from a shared chronological endpoint map. **High is sufficient.**

Publish each completed report and incremental evidence checkpoint as work proceeds. C267 is complete; await Dean’s instruction before starting C268.