Prove R437 node509 source-quotient obstruction to a third carrier deletion

[Clear1nsight]

The next R437 carrier-deletion attempt fails a precise source boundary. Deleting helper469/SOURCE92 and injecting SOURCE92 into receiver444 would leave independent SOURCE92 and SOURCE87 rows at node509's entry. Both required outputs are their sum modulo every retained compatible external source. An invertible linear network cannot reduce that quotient rank from two to one, even with free SOURCE77 access and any number of borrowed registers returned modulo the external span.

This is a scoped necessary-condition obstruction, with no new κ, physical supplier admission or selected-frontier change. It rules out arbitrarily long linear rewrites at the declared entry/output contract. Changed SOURCE channels, delayed observations, nonreturned auxiliary rows and newly paid operations remain open.

Evidence in research/r437-carrier-quotient-cut/:

• Byte-exact current a24f9ff R437 word; independent complete659-column arbitrary-DIRTY XOR identity and636 rational-frame closure checks.
• Complete single-SOURCE-load carrier census: five remaining helpers fail immediate replacement at the unchanged current SOURCE frame.
• All659 registers scanned for the node509 frame boundary: ten compatible roles, including two targets with zero SOURCE rows. The inherited alphabet forbids target readout; allowing them is a favorable relaxation.
• All34 later frame509 insertion cuts before413 leaves509 add no external source dimension. This is an eligibility fact, not a global two-window impossibility claim.
• Independent one-column SOURCE87/92 propagation and complete GL(2,2), GL(3,2), GL(4,2) checks:6,168,20160 matrices.
• Three escape controls and an actual optimized Git-free replay with changed-source, changed-certificate and missing-notice rejections. Both registered commands pass.

A separate reviewer caught the initial omission of zero-SOURCE target roles177/185. The census was broadened to all659 roles, the certificate regenerated, and all checks rerun before publication. The reviewer independently confirmed the actual source rows, source bytes and fixed-boundary rank argument. No independent human or formal-kernel review is claimed.

The κ-directed budget gate checked PR3959's existing pooled optimum and PR1281's existing partial-width pricing first; no duplicate owner search or generic price table is presented. This attempted changed local mechanism fails even with all adapter costs relaxed to zero, so no unearned saving enters an invoice. Full physical preparation, stock, future observations and all-size cost/refinement remain inherited obligations.

Canonical main20ecf2891d80b5acf18d980b2164fb44ea7faa90 and priority revision6 were refreshed unchanged at entry and before publication. Team claim: #3967 (comment) . Explicit parallel donor assignment refines selected-packing into an actual local-word eligibility audit. Overlap coverage is partial.

Credit ai-nanachi/PR3647 for R437 and helper464 GL deletion; Ali Romman/PR1043 for SOURCE77 deletion; Sagar Thakrar/PR3700 and PR2423 for audit/OQ4; mightyOil/PR1281 for slot optimization; Rohan Arun/PR3959 for pooled R437; eumemic, DreamingOfClouds, DaysSky, Crow, chafreaky and the full retained notices. New work by Chris R / Clear1nsight with substantial OpenAI Codex assistance. Apache-2.0.

Reproduce: python3 -B scripts/research_package.py --package research/r437-carrier-quotient-cut.