Prove exact R437 checkpoint work and lifetime backing envelope

[Clear1nsight]

The R437 physical caller currently retains conditional O_q(V) checkpoint and storage arguments. This package replaces one part of that obligation with an exact source-bound component theorem: full stream/numerical checkpoint work, lifetime parking/port backing, elementary preparation scans, and the actual chronological Program contribution. The complete production preparation term and full physical reserve coefficient remain open.

For R canonical roles and L body symbols, one complete stream park/restore costs (61L+23R+14, 26L+6R+2, 52L+20R+10) reads/writes/moves, including empty records, four-bit encoding, erasure, restoration, port scans and the real transition table. Combined with the credited PR2769 numerical invoice, the explicit auxiliary action count is 139L+51R+32S+23B+72p+C_0+C_1+59 per call occurrence.

The weighted-stack argument proves lifetime parking plus shared-port backing exactly max_active_path sum(2+R+4L+p+S) + max_record_bits + 3. Erased cells remain charged. Sibling calls reuse backing but repeat work. Numerical banks/templates, other stream-role maxima, borrowed state and finite source tables stay explicit. The R=29097 empty-body calibration visits 29100 parking cells and two port cells; it is a parameter calibration, not a valid R437 payload.

The actual children.extend serialization appends a STEP for good, pair, unit and half children. With fixed I,L,Q and starting history h0, Program bodies alone contribute 4d(2I+L+5)+4(Q+2I+90)[d*h0+d(d-1)/2] parked bits at depth d. The source length identity is credited to PR2753; this package derives its exact current-codec path and copy charges. Fixture extension checks do not execute Callback/source acceptance.

Exact capsule copy/adoption, numerical grant copies and finite-header scans are also priced. PROOF.md isolates the still-unbounded production term Pi: directory/history generation, projected extents, validation, context/geometry work and remaining cleanup. Original-width stock, root/history coupling, complete prefix multiplicity, primitive refinement and full per-role maximum extents are not discharged. No logical coefficient 11 is relabelled as physical reserve. A short comparison rejects only a particular indexed-nonempty-role encoding at a full W-family cut; no universal codec barrier is claimed.

Validation uses unchanged pinned component bodies: 32 forests with 397 complete calls, a 65-call sibling case, the 29097-role calibration, exact parent bytes/aliases, three live child grants, 18 copy/transfer pairs, four grant widths, three header schemas and 20 literal history extensions. Registered normal/optimized replay and an actual Git-free optimized CLI positive pass; all 14 live-source corruptions and a receipt mutation reject. No complete GL64 production packet, ordinary/native/router cohort, selected cold replay, Lean or Docker is claimed. The narrow loader and AST extraction boundaries are explicit.

Frozen canonical base 20ecf28, revision 6; refreshed unchanged during the session. Explicit donor assignment refines selected-stock-envelope. Canonical team claim: #3967 (comment). PR3967's current-source protocol and R=29097 inventory are attributed context, not re-executed here. Live overlap includes PR2708, PR2874, PR2882, PR3936, PR3950, PR3967 and the physical board; coverage is partial.

Credit Jose Manuel/jmbarrancoml for the physical caller and PR2769 numerical invoice; ywz65/PR2635 for the parking table; David Arias/PR2753 for logical caller, grammar, inventory and conditional reserve; Nick Petalas, Ross Richardson/PR2874, Kumagi/PR2882 and retained Word/record/continuation authors. R437 lineage: ai-nanachi/PR3647, zxv/PR3690, Ali Romman/PR1043, Sagar Thakrar/PR3700 and the credited selected/native authors. Immediate audits PR3936/3950/3967 retain their credit. New work by Chris R/Clear1nsight with substantial OpenAI Codex assistance and cross-agent review; no independent human or formal-kernel review. Apache-2.0, isolated package only.

Reproduce: python3 -B scripts/research_package.py --package research/r437-resource-envelope.

Next: bind all physical role maxima and Pi to one complete current-source producer, retaining admitted original-width stock and root/history assumptions. A further controlled returned payload does not close that join.

Published head a76ebcab36fdc78f2824fc59dceaabbeda8189ba passes exact 24-file package/input byte and canonical source-history verification plus whitespace checks. All three registered commands passed in 70.406 seconds on Python 3.12.3 with unchanged bytes. Submission refresh at 07:59 UTC confirmed canonical main unchanged; live R437 overlap now also includes the separately claimed transport PR3980.