490d C441 — Complete Source Grammar of the Four Local Reflection Domains

25 September 2026 UTC. Step 7 of 10, C435–C444.

The complete local-reflection inventory now has six source classes. They partition all258 labelled pairings exactly.

ClassesA–C were established in C439–C440. The remaining42 labels follow three further bounded rules, each checked against every relevant role-pair combination.

D — Flood boundaries. Both endpoints are SP or LXX, Cainan ON and Terah+60. Their sojourn flags are complementary. At center3188 their Gears are G1/G1; at3190 the Gear sums are4. Centers3248/3250 have no member of this class. The source sum is

2891+2890+2×130+2×60+215=6376,

with the required Gear increments supplying6380. The32 labels occupy eight coordinate pairs. Flood start and close retain their event-boundary identities.

E — the Noah/Flood alias. The only two coordinate pairs are3490/2890 at center3190 and3550/2950 at3250. They use SP companion Noah birth G1/C0/F0 and SP or theoretical LXX-OFF Flood close G1/C0/F0, with the same Terah state. Their600-year span is specifically birth-to-close.

The lower coordinates2890/2950 also carry Noah-death labels in a different G3/C1/F1 context, because 349=130+215+4. Consequently these pairs overlap the Noah birth/death class in coordinates, while retaining distinct event records. This is the SP/LXX-normalized counterpart of the earlier349 alias mechanism; it does not merge the biographies.

F — MT Noah Gears. Both endpoints are MT Noah births with Cainan ON, full-430 and the same Terah setting as the center. About a G2 center, G1/G3 are exchanged and G2 is fixed. About a G3 center, only G3 itself is retained; the other reflections require unavailable G4/G5. No Gear is transported to another patriarch.

The six classes total112 coordinate memberships but only106 distinct coordinate orbits. Exactly six orbits have two source-role classifications: four Noah-death/Shem-death aliases and two Noah-death/Flood-close aliases. No labelled pair is counted twice. All overlap records are listed in DATA.json.

The reflection results therefore reduce to complementary variant settings, opposed500 relations, independent Flood boundaries and the finite Gear domain. The next question is whether this local reflection structure actually preserves the two-E paths that motivated it.

Verification and scope

18 calculation checks and 20 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.

Six classes describe a finite source comparison inventory. Their coordinate overlaps do not merge event identities, and partial reflection domains do not establish a global group action.

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

C442, proposed and unexecuted: Test the reflection conjugacy R_c E_p R_c=E_q at the four sourced centers, census the reversed two-E order on the fixed373-coordinate domain, and determine whether the nonzero2K path and zero-net loop have fully sourced reflected counterparts.

The source grammar is complete. Returning to the E/529 paths will test whether the new local reflection domains support their operators, rather than inferring that from endpoint symmetries.