# Independent C267 classification

24 September 2026. Read C266 report, checkpoint, transformed endpoint records, radial ledger, and the explicit 5750/6250 bracket in frozen AXIS_REPORT §15. No new historical date search or source editing.

## Frozen comparison

Use eta(x)=1000(x−1), with core fields F_MT=[−6,1], F_SP=[−1,6], F_LXX=[0,7], RH_MT=[1,8], RH_SP=[−4,3], RH_LXX=[−5,2]. Every integer pair center carries its actual phases x±1/4. Unreflected H fields remain auxiliary and were not added to the core.

The core center hull is [−6,8], its phase hull is [−25/4,33/4], and their eta images are [−7000,7000] and [−7250,7250].

## Target classification

| Signed label | Preimages under eta | Frozen realization |
|---|---|---|
| ±2500 | −3/2,7/2 | Whole-field midpoints of RH_LXX and F_LXX; also half-way points along selected radius5 SP arms. Generated midpoint locations, not integer pair centers or actual source seasonal components. |
| ±6250 | −21/4,29/4 | Actual outer seasonal components at pair centers−5,+7: LXX reflected Shem closing member and translated Flood closing member. Co-located MT interior components are also present. |
| ±5750 | −19/4,27/4 | Actual inner seasonal components of those same pair centers; justified companion from AXIS_REPORT’s explicit bracket. |
| ±7500 | −13/2,17/2 | Neither core centers, phases, nor midpoints of any core points: both preimages lie outside the phase hull. 7500 remains the image of a whole7.5-year seasonal-envelope length. |

## Exact phase provenance

| eta label | Current component | LXX provenance | Co-located MT provenance |
|---:|---|---|---|
| −6250 | 6t BC, x=−21/4 | Shem5883n BC, source_index7, translated5888 then reflected | Flood5296t BC, source_index1, translated5290 |
| −5750 | 5n BC, x=−19/4 | Shem5884t BC, source_index7, translated5888 then reflected | Flood5295n BC, source_index1, translated5290 |
| +5750 | AD7t, x=27/4 | Flood5284t BC, source_index7, translated5290 | Shem5895n BC, source_index1, translated5888 then reflected |
| +6250 | AD8n, x=29/4 | Flood5283n BC, source_index7, translated5290 | Shem5896t BC, source_index1, translated5888 then reflected |

Reflection reverses the inherited Tishri/Nisan component identity, as the table records. The core has precisely two source histories per displayed phase match; they are not independent chronological witnesses.

## Midpoint and envelope safeguards

The whole-field midpoints under eta are MT ±3500, SP ±1500, LXX ±2500. Thus LXX is the unique whole-field midpoint match among the fixed six. This does not establish corpus-wide uniqueness.

Phasewise midpoint components of F_LXX are3.25 and3.75, physically AD4n andAD4t; RH_LXX gives−1.75 and−1.25, physically2n and2t BC. Their midpoint centers are half-integers. Calling their lower and upper components Tishri/Nisan by the integer-center convention would reverse their physical seasons. The midpoint values remain generated locations even where their phasewise components co-locate with admitted members.

The arithmetic residue classes give an independent exclusion: eta(integer centers) is0 mod1000; eta(actual quarter phases) is250 or750 mod1000. Both ±2500 and±7500 are500 mod1000. Full-source midpoints may supply the former; the convex-hull limit excludes the latter.

Every full seven-year field has outer seasonal width7.5, hence image length7500. For the MT adjoining pair, seasonal arms [−6.25,1.25] and[0.75,8.25] have sum15, overlap0.5, and union14.5. At1000:1 these become15000,500,14500. None gives a source radial endpoint±7500 about the fixed join x=1. The maximum core phase radius is7.25.

The source radius6 pair gives the exact quarter-phase bracket6000±250. The macro identity5290E=5750, followed by5750E=6250, therefore has a relational realization in the fixed comparison chart. Macro conversion histories do not thereby become historical phase identities. Applying E to chart radii corresponds to the declared affine coordinate map x↦1+E(x−1), which was not a pre-existing operation on the entire frozen chronology.

## Review conclusion

The bounded step strengthens the LXX realization: its field midpoints give±2500 and its outer phase components give±6250, while the already declared±6000 centers contain the explicit5750/6250 bracket. The7500 branch remains a length/completion reading within this central comparison, not an additional source point or a disjoint fifteen-year union. No z-law, new Gear operation, or original source-event identity follows.