[petalas]

Summary

PR2697 leaves the selected BIT caller's route temporaries as an asymptotic term. This adds a sharp source-bound storage component and a separate gather/return/scatter corollary.

route_packet live payload/key symbols, including its borrowed input
w > 1: 2v + 3H(R+J)
w = 1: 2v + 2HR + HJ

Here v=CHR, H is the complete high-cube size, R the fibre length, and J the serialized key length including delimiters. The written lifetime proof explains why decorated input, stable buckets and output coexist. Byte-exact sources are pinned to PR2697 a53fdf4bcbe33c6732f0bec1badc8c023380f9d1.

Only research/selected-route-live-volume/ is added. It contains the proof, source pins, literal live-write instrumentation, exact receipt, registered replay and open next questions. Credit Jose Manuel/jmbarrancoml for PR2697/2569, ywz65 for the separate directory/setup work, and the retained stream/hosting lineage.

Evidence

• Before: PR2697's complete charge ledger leaves route/residual/scatter temporaries by O_q(v)+O(V/W) and numerical reserve admission open.
  After: both route peaks are proved for the unchanged routine and attained in eight complete GL1/GL2 high-cube fixtures. All 1,298 Boolean origins and output bits match a separate modular oracle; a direct tape census confirms each peak.
• Registered CPython 3.12.15 replay passes 17 behavioral controls and seven integrity groups, including Git-free optimized execution, source corruption, typed receipt mutation and overwrite refusal. Optimized CPython 3.14.8 replay and six repository replay-selection tests pass. Separate internal proof/source review found no actionable issue.
• Reproduce with python3.12 scripts/research_package.py --package research/selected-route-live-volume.
• Canonical claim and handoff. Priority revision 5; the isolated branch was fast-forwarded to canonical main 6bd33bc0b87a01e9c9d8b1c01576f3ddbcaee850, with unchanged guidance, selected record and runner. Preparation provenance and scientific source pins are retained. Final overlap refresh covered 783 open PRs, 1,329 Discussion/comment/reply records and local package notes, with complete pagination and no warnings. No competing route-liveness follow-up was found; text coverage does not prove novelty.

Merge Danger

Door: two-way.

Blast Radius: research.

This counts nonblank route payload and embedded-key symbols. LEFT markers, numerical/control words, Python backing capacity, literal COPY/residual/leaf interiors and total reserve admission remain outside the result. The caller corollary covers only named routing/scatter phases and final merge. No full GL64 execution, selected cold replay, independent human/formal verification, supplier admission or new kappa is claimed. The selected frontier and predecessor files remain unchanged.