[unpaidmoon]

Change and mathematical scope

Scoped serializer comparison. No new κ. The selected conditional exponent stays 605457647/200000000000.

RoleParking.park, from the pinned archive research/physical-ordinary-interchange/inputs/pr2809.tar, parks the bodies present on the canonical roles. It writes four bits per current symbol, blanks that symbol, and pushes once per role. The method does not name a root stream.

On a three-role schedule with a fixed 8-symbol control role and one empty role:

• root data record: 4000 bits (1000 symbols)
• child data record: 28 bits (7 symbols)
• grandchild data record: 4 bits (1 symbol)

The child cut is shorter than the root cut, so it did not recopy the root packet. The 7-symbol and 1-symbol bodies are the adopted-capsule schedule for this comparison. They are not a live GL64 measurement. Park does not compute V/(WN). The predecessor's geometric model, and §§6–7 of the archive proof, identify the parked parent frame with the current packet and the child with the capsule prepared before parking.

The pinned nested fixture charges depth * (5 * 132 + 7 * 5 + 3 * 2) steps. Those 132 bits are 4 * (4 + 13 + 12) + (1 + 3 + 12), a constant per level. The depth-1500 loop is not run.

The other reading, one fresh root-sized stream at every cut, sits outside the geometric constant 26041 already proved in research/pr2809-continuation-stack-space. Here D(2^26050) = 42857, which is greater than 26041. This package does not re-prove that constant.

Remaining obligations: marker, template, and erased-backing cells are not charged against 26041 V. Numerical PARK of live Word slots is not executed.

Task and overlap

Base 32890bc5de034ab8fc93ac88ead7279a6a416d04, priority revision 7. Task card uniform-transfer-audit. Scope status refined: the card asks for one caller-bound CrocSwap#4100 implication, and this package takes only the serializer question left open by research/pr2809-continuation-stack-space.

Session r40 of r33–r52. Eligible list rebuilt on 2026-10-25, in the order used by the earlier packages on this account: open handoffs from Discussion CrocSwap#1166 comment 19029944 first, then priority-table rows whose next decision is still open, then catalogue cards not already those rows. Closed smallest tasks, prior deliveries, open-PR coverage, and existing fork cursor/* topics were removed. Five items remained, so the assigned index is (8 - 1) mod 5 = 2, which is item 3:

1. A caller that accepts (w, q, v_N) without restoring the original source slots.
2. Unbound L561 intervals before the L546 subtraction.
3. This package. Whether one PR2809 cut parks the ancestor chain or one root-sized stream.
4. The exact fixed-tape visit count of one R437 parent blank-return.
5. A 14-point difference basis of F_2^6 with a simple closed walk of step weight at most 3.

Overlap refresh at 2026-10-25T07:18:32Z: complete local inventory of 7402 notes at this base, 393 open pull requests, and 4817 discussion records. Terms: RoleParking, root-sized stream, serializer cut, continuation serializer, PR2809. The predecessor package is the open question answered here. Open-PR search found no hit for RoleParking, root-sized stream, or serializer cut. Historical PR2809 threads are the source construction. No matches is not a novelty certificate.

The fork pull-request base is cursor/upstream-main-pin-4b1b, which is exactly that upstream commit, so the diff is this package. Fork main does not contain the commit.

Validation

Python 3.12, standard library only.

python3 scripts/research_package.py --package research/pr2809-serializer-cut --check-only
python3.12 -B scripts/research_package.py --package research/pr2809-serializer-cut

verify.py prints

PASS_PR2809_SERIALIZER_CUT root_data_bits=4000 child_data_bits=28 grandchild_data_bits=4 child_is_capsule=true child_recopies_root=false full_copy_depth=42857 no_new_kappa=true

test_verify.py prints PASS_PR2809_SERIALIZER_CUT_CONTROLS. The controls reject a child record equal to the root packet, a child length other than 28 bits, and a root length other than 4000 bits.

Not run: the GL64 macroprogram, numerical PARK, the depth-1500 nested loop, Lean, Docker, and the selected cold replay. Metadata acceptance is not mathematical acceptance.

Credit

The O_q(V) sentence is Cinna Davis's CrocSwap#4100 (research/unconditional-batched-crt/BIT.md). The serializer and §§6–7 of its proof are Jose Manuel's PR2809 archive. Mark (Matarener), with Claude Code assistance, checked BIT.md §§1–4 in research/bit-stock-recurrence-audit. The geometric constant 26041 and the open serializer question are unpaidmoon's research/pr2809-continuation-stack-space.

Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0. No independent human review and no formal-kernel acceptance are claimed.

Open next questions

1. Are the marker, template, and erased-backing cells inside the 26041 V budget? First charge one fixed template per live role against V/(G-1). Blocked because BIT.md §2 does not give the live role count.
2. Does numerical PARK of the live Word slots also avoid recopying the root templates? First meter numerical_frame.py at one cut. Blocked because this package does not execute the numerical codec.

Workflow feedback (optional)

Reconstructing the ordered eligible remainder from the 19 October index, the priority table, and later closures took longer than the serializer check. A short maintained remainder next to that index would remove the repeated reconstruction. Feedback discussion: CrocSwap#1200