Research action

Source-Qualified Mirror Conjugacy of the Mixed Operator Menu

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Study sequence: Finite operator closure and sourced 2K interval ladders (C445–C469) · Mirror & 529

490d C463 — Source-Qualified Mirror Conjugacy of the Mixed Operator Menu

25 September 2026 UTC. Step 19 of 25, C445–C469.

Across490 fixed-Mirror conjugacy trials, seven arrows have sourced cumulative endpoints but only six also have sourced anchors. All six are reflections: four fixed loops and the two directions of one four-year comparison. The sole E endpoint image,−6344→−6346, requires absent pivot−6321, so no E arrow is fully sourced in this cumulative menu.

The algebraic identities X_A R_c X_A=R_(A−c) and X_A E_h X_A=E_(A−h) hold exactly for every tested arrow. Source qualification is an additional gate.

The nonzero qualified reflection is3246↔3250 about3248, carried byA−2639 to−5885↔−5889 about−5887. These are LXX-OFF cumulative Shem annual slots5,1 and3. Its four-year span is retained without calling those annual slots regular Gears.

The lone E endpoint image comes from SP-companion Noah3705→3707 about3682. Its reflected endpoints−6344 and−6346 are sourced LXX-native cumulative Shem records, but the reflected anchor−6321 is absent from the48-record menu. Endpoint availability alone would overstate the result.

The complete2K local interval ladder therefore does not gain a sourced cumulative E counterpart through these fixed exchanges. Its own source requirements should now be tested directly: the first pivot3620 is uniquely SP companion, even though the main ladder’s endpoint coordinates have primary/MT alternatives.

Verification and scope

490 calculation checks and 21 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.

The negative cumulative result is limited to the48 declared records and two fixed exchanges. No missing reflected pivot or cumulative Gear operation is added.

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

C464, proposed and unexecuted: Remove SP-companion labels as a declared sensitivity control, require every surviving operator anchor as well as its endpoints to remain sourced, and measure which529 interval ladders, local cycles and inherited corner controls survive.

The Mirror test shows why anchor provenance matters. A controlled removal of SP companions can now isolate their precise contribution without changing the accepted full-register result.

Linked sources and evidence

Edition and provenance

490d_C463_Mirror_Conjugacy_With_Anchor_Source_Gates_20260925.md

SHA-256 e312d35d7d164fe82857e20a8d15dbe1b4f9144c780594201de077c2008e74eb

C01–C479/packets/C463/490d_C463_Mirror_Conjugacy_With_Anchor_Source_Gates_20260925.md