{"id": "c467", "title": "Operator Dependence of the Interval Ladder and Local Cycles", "filename": "490d_C467_Minimal_Operator_Support_and_Deletion_Controls_20260925.md", "role": "Research action", "step": 467, "sha256": "417c75cbead006d0929ebd1628b6acbf3d8dbc40da071bfe374c802f6afaa1d2", "bytes": 3417, "origins": ["C01–C479/packets/C467/490d_C467_Minimal_Operator_Support_and_Deletion_Controls_20260925.md"], "download": "/sources/417c75cbead006d0929ebd1628b6acbf3d8dbc40da071bfe374c802f6afaa1d2.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Inverse", "Calendar Keys", "Mirror / 529"], "excerpt": "490d C467 — Operator Dependence of the Interval Ladder and Local Cycles\n\n25 September 2026 UTC. Step 23 of 25, C445–C469.\n\nThe complete interval ladder depends only on E3620 andE2756 among the12 tested operators. Deleting3620 removes all529-pair transport; deleting2756 retains the two first expansions but removes conti", "content": "# 490d C467 — Operator Dependence of the Interval Ladder and Local Cycles\n\n25 September 2026 UTC. Step 23 of 25, C445–C469.\n\nThe complete interval ladder depends only on E3620 andE2756 among the12 tested operators. Deleting3620 removes all529-pair transport; deleting2756 retains the two first expansions but removes continuation. Each reflection can be removed without changing interval transport. The ordinary and mixed cycles have separate, explicitly verified operator dependencies.\n\nAll13 scenarios—the full menu plus each single-operator deletion—retain the same source register. Every scenario still excludes a nonzero529 gap between mutually reachable endpoints.\n\n| Result | Required operators for its declared witness |\n|---|---|\n|Complete1058→1150→1250 interval ladder|E3620, E2756|\n|Ordinary four-reflection identity|R3188, R3248, R3250, R3190|\n|Mixed23-gap return cycle|R3248, R3250, E2758, E2756|\n\nRemovingE2758 preserves the positive interval ladder but splits the enlarged mixed strong component. RemovingR3248 orR3250 also destroys that mixed cycle. RemovingR3188 orR3190 destroys the ordinary four-center identity while leaving the mixed cycle’s declared word available.\n\nThus the local reflection grammar, the mixed fixed-point return and the positive interval ladder are related observations with different dependencies. The two E operators suffice for the ladder once their source records and endpoint states are fixed. Their prior source derivation remains part of the provenance; this minimal execution description does not erase that history.\n\nThe research questions of this batch are now ready for an alternate-method check, followed by the C469 synthesis and recovery package.\n\n## Verification and scope\n\n13 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.\n\nDeletion controls analyze the declared witnesses and fixed-menu reachability. They are not source edits, new operator choices or independent historical attestations.\n\nMirror/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.\n\n## Best next bounded step\n\n**C468, proposed and unexecuted:** Reconstruct the source grid and decisive finite results with a second implementation using inverse-pivot equations, bitset transitive closure, residue buckets and reverse Mirror enumeration; audit all completed packet and publication hashes.\n\nThe positive and negative findings have explicit finite domains and minimal dependencies. A different computational formulation is the most useful remaining check before freezing the25-step result.\n", "evidenceLinks": [{"id": "d-24203a4c3b282f9b", "title": "File 02"}]}