C290 — Dilation compatibility of the four-node source pattern
24 September2026. Tests the fixed E=25/23 against actual source and phase domains.
The scalar replacement529→575 does not carry the whole four-node pattern into admitted source records. It reproduces the cumulative Flood OFF→ON center only under an annual-offset-dependent anchoring, and it does not reproduce that field's physical seasonal pair.
There are22 distinct numerical source instances across the six rows: S,F,R throughout, plus the four supplied N records. Each is tested under global dilation q→Eq and under q→i+E(q−i), anchored at its recorded annual offset i. Cumulative targets are the four held LXX Flood/Shem ON/OFF fields; regular targets are the528 source-qualified records retained in C286.
| Operation | Source-center matches | Physical pair matches |
|---|---|---|
| Global dilation about0 | 1 | 0 |
| Dilation about each row's offset i | 6 | 0 |
The six anchored center matches are all F_OFF=−5290+i →−5750+i, the same-index native LXX ON Flood center. The other coefficients become−6900+i,2875+i and4025+i, absent from their held target domains. The global map reproduces only the opening Flood center at i=0; nonzero i acquires the factor25/23 and ceases to be an integer annual center in this small domain.
The phase obstruction is exact. An actual half-year source pair becomes width25/46 years, whereas an admitted target seasonal pair has width1/2. At the Flood center match, the components differ from the target components by±1/46 year. Reattaching ±1/4 after mapping the center would therefore be a different operation.
There is also an annual-selector obstruction. A single affine map of slope25/23 expands a one-year step to25/23 years. The true cumulative Cainan translation q→q−460 preserves the one-year spacing across the entire field. Choosing a separate dilation anchor i for every row reproduces its centers but does not define one uniform dilation of the field.
The5290→5750 scalar identity remains exact and relevant. This test identifies its permissible role: a width/center comparison whose extension to a complete source-preserving action fails in the held domain. It does not refute the source relation or alter the underlying chronology.
Twenty-seven mathematical/domain checks and seven authentication checks pass. The complete center/phase ledger replays identically. Author review only; no source or graph edits.
Best next bounded step — C291: apply the already supplied8464=16K translation to the new four-node source pattern and compare its images with the retained regular endpoints. Translation preserves actual phases, so this tests a different, already authorized bridge without adjusting its width. High is sufficient.