[aliromman]

Any number of immutable channels of mixed Gaussian ranks 1 through 7 needs at least 65 units of rank mass to repair all eight modes of the exact F9 source. This permits arbitrary rational payloads, repeated chronological scatter and joint noise cancellation, while granting free helper restoration. For every power tariff H_r=r^q H_1, 0<q<=1, its price is at least 65/64 times the removed 8H8 allowance. No new kappa is claimed.

This resolves the lower-rank part of the released question in PR5755 and PR5745. Exact quotient-rank cuts replace the insufficient coordinate-cover test. The census has 22,585 events, 641 roles, 1,002 charts and 8,298 temporal responses. Stronger rank-mass bounds are 90 for maximum rank five and 77 for maximum rank six. A cost-62 integral cover on 17 rank-at-most-four charts reaches every coordinate but misses five of the eight target directions.

Proof, exact certificates, complete receipt, discovery limits, validation.

Verification uses Python3.12.14 and the standard library. Normal and optimized registered runs pass. The checker rebuilds all240 quotient cuts, every exact dual capacity, six support-cover primal/dual optima, the source's initial restored-Y invariant and all115 predecessor rank-one supports. Seven semantic controls, a joint-noise positive control and three actual source corruptions pass. It imports no predecessor executable or optimizer. Metadata, committed bytes/modes and the official18-file export pass. A read-only Git-free optimized replay with empty PATH passed in6.92 seconds and preserved all19 files including the manifest.

python3.12 -B scripts/research_package.py --package research/active-mixed-rank-obstruction

The contract keeps the native word and each channel's chart and payload fixed. Rank-eight/rank-nine mixtures, moving frames and changed feedback remain open. The native common-fixed-vector specialization is a retained premise; no new physical caller, compiler, precision/tape, analytic or outer theorem is supplied. Full-history preflight was not run in this shallow checkout. Hosted scientific replay and independent acceptance are not claimed. The selected frontier is unchanged.

Base canonical main: de5ec2e7a6074068452f45b1a191b5c72832df4a, priority8, refreshed before publication. Live handoffs and open-PR overlap were checked; sparse local notes and unpublished work remain limits. Canonical claim. Exact publication head: f7c198d38d5f68b0753dd0a51a2328e145b07638.

Ali Romman with substantial OpenAI Codex assistance; no subagents. Apache-2.0. Credit flyingviper/PR5755 for the restored-Y invariant and independent rank-one census, PR5720 for the active-mode proposal, PR5745 for the temporal contract and eight-H8 attainment, Cao Yifan, Cinna Davis, Dugongue and every author retained in the unchanged source archive. The new result is the arbitrary mixed-rank quotient certificate; predecessor construction credit is preserved. No merge or frontier change is requested.