[petalas]

Summary

PR2697 leaves total caller storage open. PR2708 bounds routes and PR2731 bounds residuals. This contribution joins their actual lifetimes with the original-offset remainder peel, which processes a fibre of size V/C before fresh rows are split.

Node.run, payload and embedded route-key content
  no remainder:        3V
  positive remainder:  max(4V, 3V + 3V/C) <= 6V

The exact formula assumes the pinned successful source/completed-leaf contracts and J<=R for route keys. It counts borrowed input, retained peeled output, live families, staged/private roles, primitive interiors, scatter and merge. Numerical/control/count/directory tapes, LEFT markers and interpreter capacity remain excluded. This is a storage-category theorem, not total reserve admission, a selected supplier or new kappa.

Only research/selected-node-live-volume/ is added. It contains the proof, literal source replay, exact receipt, controls, explicit replay hook and 41 unchanged source/proof exports. Scientific sources: Jose Manuel/jmbarrancoml's PR2697 at a53fdf4bcbe33c6732f0bec1badc8c023380f9d1, Nick Petalas's PR2708 at 2982489cc00a17bd1c7ee1e206e975eda9bcb64d, and starship-s's PR2731 at 46c0c3554608a1096816ad668c755d3b5b7a8c0b. Retained notices preserve the full lineage. ywz65's PR2688 is the complementary directory component.

Task card selected-stock-envelope, priority revision 5, explicitly changed to the live Discussion2319 lifetime handoff. Started from canonical main 0374b3e6a532dac112813523d605288c416418c1, refreshed to 7b39515117fe26e75d16c268877391f1bdaa5640; guidance, selected record and replay runner were unchanged. Final complete overlap covered 754 open PRs and 1369 Discussion records without warnings, plus 1840 local records. It found no conflicting active caller-lifetime claim in the relevant excerpts; metadata searches do not prove novelty. A final post-publication compatibility read found canonical main at bd1b3bc7174cddbfa4e30ac073dc134f48aa6e77; guidance, selected record, task catalogue, replay runner and this package path remain unchanged from the pinned base. Exact provenance and remaining questions are in TASK/SOURCES/SNAPSHOTS.

Evidence

• Before: the actual positive-remainder peel rejects a 4V budget. After: its exact content peak is 6V at C=1, 4.5V at C=2 and 4V at C=3. Four literal peel fixtures measure (V,peak) = (729,4374), (1458,6561), (2187,8748), (1458,8748).
• The unchanged complete dimension-two core node, with all 48 low classes and four families, measures V=15552, peak 46656=3V. The per-write observer is checked by a separate direct cell census, independent returned-bit oracle, input/head return and numerical arena cleanup.
• Registered CPython3.12.15 replay and six behavioral/integrity control groups pass locally. The repository workflow suite passed with 70 tests run and three skipped. Controls include one-cell-underbudget rejection, an observer-bypass fault, source/manifest corruption, wrong receipt types and a Git-free read-only optimized export. Local platform: macOS27.0.1 arm64. A local internal review checked the proof, byte exports and reachable allocation sites; no human or formal-kernel review is claimed.

uv run --python 3.12 --no-project python -Werror -B scripts/research_package.py \
  --package research/selected-node-live-volume
uv run --python 3.12 --no-project python -B -m unittest discover -s tests -p 'test_research_*.py'

The selected GL64 payload, full selected cold replay, total numerical reserve and larger recursive returns remain unverified. Hosted CI is not claimed. The optional complete positive-remainder model was stopped after about 20 minutes without a result; it is outside the registered evidence. The registered positive-remainder checks execute the actual peel.

Merge Danger

Door: two-way

Additive research package with pinned predecessor bytes; no production transform, selected record or frozen predecessor changes.

Blast Radius: research