{"id": "c290", "title": "Dilation of the four-node source pattern", "filename": "490d_C290_Four_Node_Dilation_Compatibility_20260924.md", "role": "Research action", "step": 290, "sha256": "a213410602e804d832a5137e4bdb911caa968bce3034fe3b6d0db5cad4af72e4", "bytes": 2773, "origins": ["C01–C479/packets/C290/490d_C290_Four_Node_Dilation_Compatibility_20260924.md"], "download": "/sources/a213410602e804d832a5137e4bdb911caa968bce3034fe3b6d0db5cad4af72e4.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Mirror / 529"], "excerpt": "C290 — Dilation compatibility of the four-node source pattern\n\n24 September2026. Tests the fixed E=25/23 against actual source and phase domains.\n\nThe 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-", "content": "# C290 — Dilation compatibility of the four-node source pattern\n\n24 September2026. Tests the fixed E=25/23 against actual source and phase domains.\n\n**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.\n\nThere 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.\n\n|Operation|Source-center matches|Physical pair matches|\n|---|---:|---:|\n|Global dilation about0|1|0|\n|Dilation about each row's offset i|6|0|\n\nThe 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.\n\nThe 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.\n\nThere 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.\n\nThe5290→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.\n\nTwenty-seven mathematical/domain checks and seven authentication checks pass. The complete center/phase ledger replays identically. Author review only; no source or graph edits.\n\n**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.\n"}