# Independent C268 affine comparison

24 September 2026. Read immediate C267 material and the retained C01 report/results and C206 report/results. No new historical event search or C269 research. Calculations use exact rational arithmetic.

## Fixed data

Local junction c=1; local positive LXX pair center7 and actual seasonal components u=27/4 (AD7t), v=29/4 (AD8n). Their distances from c are23/4 and25/4. Local radial map g(x)=1+E(x−1), E=25/23, sends u to v. Local reflection J₁(x)=2−x exchanges the positive and negative LXX fields.

C01 supplies two distinct regular SP Creation members, a=−4419 and a=−4417. These are selections within one fixed normal Creation field, not transported Creation Gears. Their retained right-event centers are respectively2458,3056,3706 and2460,3058,3708. Relative widths are6877,7475,8125. C206 records the center operation P_a(t)=a+E(t−a), with phase separation restored separately after dilation.

## Two exact anchored fits

Define Φ_s,a(x)=a+s(x−1). Requiring Φ(1)=a and fitting the local inner/outer radii to successive widths fixes the scale uniquely:

| Fit | Widths | Scale s | Image of local center7 |
|---|---|---:|---:|
| First expansion | 6877,7475 | 1196=4×299=4×13×23 | a+7176 |
| Second expansion | 7475,8125 | 1300=4×325=4×13×25 | a+7800 |

Thus the local half-year component separation maps to598 or650. Their half-widths are299 and325. The scale ratio1300/1196=25/23 exactly.

| Creation a | Φ_1196(27/4), Φ_1196(7), Φ_1196(29/4) | Φ_1300(27/4), Φ_1300(7), Φ_1300(29/4) |
|---:|---|---|
| −4419 | 2458,2757,3056 | 3056,3381,3706 |
| −4417 | 2460,2759,3058 | 3058,3383,3708 |

In the first fit, all three images have retained source roles. They are reflected MT G2/G3 Flood start, reflected SP G2/G3 companion Noah death, and reflected MT G1/G2 Noah birth. The midpoint companion remains SP-only. It is recovered C01 source support, not a newly discovered midpoint.

In the second fit, outer images retain MT and SP G1/G2 primary Noah-birth identities. The middle images3381/3383 are generated midpoints of those births; no named event source was supplied for them in the frozen records. The test does not prove their absence from a broader corpus.

## Commutation and completeness limits

For either scale and either anchor,

Φ_s,a∘g=P_a∘Φ_s,a.

Because1300=E×1196,

Φ_1300,a=P_a∘Φ_1196,a=Φ_1196,a∘g.

These are ordinary affine conjugacy identities. They explain why the two fits agree at the shared7475 stage but are not additional independent numerical witnesses. The source qualification at particular centers is the substantive evidence.

The full three-stage macro chain does not become a three-stage local seasonal orbit. Under the1196 fit, the final8125 endpoint pulls back to

1+8125/1196=717/92=g(29/4),

which is not an actual quarter-year seasonal point. Under the1300 fit, the first6877 endpoint pulls back to

1+6877/1300=629/100=g⁻¹(27/4),

also not an actual seasonal component. Thus each adjacent pair has the exact source-backed local bracket realization, while completing all three stages with one scale introduces a generated local point.

The two Creation witnesses differ by translation2: Φ_s,a+2=T₂∘Φ_s,a and P_a+2=T₂∘P_a∘T_−2. This relationship does not authorize a Gear operation on Creation.

## Negative-side reflection

The corresponding target reflection is J_a(t)=2a−t, and

Φ_s,a∘J₁=J_a∘Φ_s,a.

It reflects about the held Creation anchor, not the global Mirror origin. The negative local LXX phase coordinates are−21/4 and−19/4; their center is−5.

| a | s | Images of negative outer, center, inner |
|---:|---:|---|
| −4419 | 1196 | −11894,−11595,−11296 |
| −4417 | 1196 | −11892,−11593,−11294 |
| −4419 | 1300 | −12544,−12219,−11894 |
| −4417 | 1300 | −12542,−12217,−11892 |

These images are generated coordinates in this finite comparison. C01/C206 does not supply event identities for them. They are not the global reflections of the positive Flood/Noah endpoints.

## Distinct centers and phases

C206’s whole-interval centers are a+w/2 for w=6877,7475,8125:

- a=−4419: −1961/2,−1363/2,−713/2.
- a=−4417: −1957/2,−1359/2,−709/2.

They are not the first-fit2757/2759 midpoint between successive right endpoints, and not the second-fit3381/3383 midpoint. The different constructions must retain distinct labels.

Most importantly, Φ maps local physical seasonal components to macro pair centers. It is not a phase-preserving map between historical seasonal components. The local pair’s0.5-year width becomes598 or650 years. Restoring±1/4 around each image event center is the separate center-first convention inherited from C206, not the full affine image of an original phase pair. Applying P_a directly to target components would instead dilate their half-year separation to25/46.

## Retained conclusion

The LXX local23:24:25 seasonal-radius bracket gives an exact affine model for the retained first C01 transition, including its already sourced SP companion Noah-death midpoint. The same bracket realizes the second transition at an E-larger scale, where its middle image is generated. Affine commutation holds, but source roles, midpoint roles, global versus anchored reflections, and physical seasonal phases do not automatically transfer through that algebra.