490d C440 — Opposed 500-Year Transport of Two Reflection Classes
25 September 2026 UTC. Step 6 of 10, C435–C444.
The next two reflection classes are exactly paired at the coordinate level by existing source relations:
Noah birth → Shem birth: −500
Shem death → Flood start/close: +500.
Applying these opposite shifts to the two ends preserves their sum and therefore their reflection center. All16 Noah-birth/Shem-death coordinate pairs map bijectively to all16 Shem-birth/Flood-boundary pairs. No center is changed.
Primary SP and LXX Shem-death endpoints shift to Flood start. SP companion Shem-death endpoints shift to Flood close. The latter uses the source's independent Flood boundary; it does not convert Flood close into a person companion.
Source labels require care. The40 Noah-birth/Shem-death label pairs have40 unique transports preserving tradition and context on each endpoint. The target reflection class contains48 labels. Its extra eight labels are coordinate-equal LXX Flood-close aliases paired with SP companion Shem birth. They do not come from an LXX companion Shem-death state, because that rail does not exist.
| Center | Noah/Shem coordinate pairs | Noah/Shem labels | Shem/Flood labels |
|---|---|---|---|
| 3188 | 10 | 28 | 32 |
| 3190 | 2 | 8 | 8 |
| 3248 | 0 | 0 | 0 |
| 3250 | 4 | 4 | 8 |
The Noah/Shem class itself has four bounded source-sum templates. With SP/LXX normalized base3491+2391=5882, they are:
| Center | Cainan sum | Terah sum | Sojourn sum | Gear-number sum | Companion endpoints | Labels |
|---|---|---|---|---|---|---|
| 3188 | 0 | 1 | 2 | 4 | 0 | 24 |
| 3188 | 0 | 1 | 2 | 5 | 2 | 4 |
| 3190 | 0 | 1 | 2 | 6 | 0 | 8 |
| 3250 | 1 | 1 | 2 | 2 | 2 | 4 |
The complete bounded sum equation admits exactly these four templates. The all-companion rows are SP-only; primary rows retain their actual SP/LXX labels.
One transport reverses which event is the upper BC coordinate. At center3250, Noah birth3705 and Shem death2795 map to Shem birth3205 and Flood close3295. Their sum remains6500, although the Flood boundary becomes the upper coordinate. The event identities are preserved rather than sorted into a misleading chronology.
Thus two sizeable reflection classes are generated by one opposed500 correspondence, with a precise eight-label qualification. This is a comparison between selected source states, not a common500-year translation of one complete chronology.
Verification and scope
86 calculation checks and 19 source/predecessor authentication checks passed. Main result files replay byte for byte. These are root-agent checks, not an independent-agent review or independent historical witnesses.
Opposed endpoint shifts preserve a pair sum but are not a shared chronology translation. The eight extra Flood-close aliases do not license LXX person companions or independent witness counts.
Mirror/529 focus: K=529, E=25/23, P=70/69; J=300/299 remains File02 gap conversion, not a calendar date operator or Residue Protocol. Regular Gears are Noah/Shem/Flood only. SP person companions are local to Noah/Shem; Flood close is an independent event boundary. Both500/100 and502/98 bindings remain valid; SP primary Noah death retains its inclusive/harmonic qualification. LXX native Cainan is ON; OFF is theoretical removal. Global paired Mirror January AD1; local junction January AD2; no civil year zero. No new source point, phase, fitted axis, upstream/cumulative Gear, primer reopening or canonical/graph edit. Capture now; canonize later. Coordinates, source labels, context aliases and derived comparisons remain distinct. Counts are not independent historical witnesses.
Best next bounded step
C441, proposed and unexecuted: Close the C438 reflection inventory by deriving the remaining Flood-start/close, MT Noah/Gear and Noah-birth/Flood-close alias classes, then verify that the resulting source grammar accounts for every labelled and coordinate pair without double-counting aliases.
The Noah950 complement class and the paired500 classes account for216 of258 labelled pairings. Explaining the remaining42 will determine whether the entire finite reflection inventory has a compact source grammar.