[CubeJerry]

Result

Remove the rank-only positive child's stronger r*f<=parent cutoff admission
condition. For every actual selected PAID rank1..8, a literal private header
maps (f,t) to (r*f,r*t), so the unchanged numerical leaf accepts precisely
when the original parent has f<=t. Its other21 values, complete field,
owner/token, parent header and reserved geometry remain unchanged.

The source audit proves that this numerical consumer uses cutoff only for
positivity and admission; it never reaches the axis kernel, recursive work
or allocation. The original global cutoff remains unchanged for row/root
consumers. An actual row-table control demonstrates the incorrect branch
change caused by mutating that public cutoff alone. The translated header
is exclusively a positive-leaf view, not a general native descriptor.

Both products and complete restore/erase work are paid. The same39 metadata
plus349 numeric ports suffice. The two changed self-delimited values grow
the physical header by at most12 bits. Complete cost remains
F_template+O(r*f*V+(E+13)^4+388), retaining source delivery, copying,
normalization, cleanup and historical backing. No new kappa; all five
global selected assumptions remain.

Novelty and sources

The predecessor's source-complete positive child intentionally left cutoff
unchanged and required r*f<=t; parent f<=t did not suffice. This package
supplies the missing private cutoff transport and proves why the public
global threshold cannot be changed. It reuses the predecessor's rank
geometry, exact Gaussian arithmetic and source binding without reproof.

Base: 7c49fe32c55de02c2c873655c804b16e4c3fef0a.
Immediate source:
12e58df.
Row consumer provenance:
5c59d24.
All165 retained files have exact paths, blobs and hashes. Frozen predecessors
and the selected certificate are unchanged.

Verification

python3 -B scripts/research_package.py --package research/current-leaf-cutoff-transport

Four bounded normal/optimized gates execute120 literal metadata cases over
all8 ranks, exact complete-header oracles, long f/cutoff syntax, shrinking
retained-history reuse, source-use checks, real public row comparisons and
zero/rank/grant/old-table/numeric-cutoff-leak controls. The original f-only
provider's cutoff rejection is re-executed, preserving its complete input.

One separate actual rank-two leaf at source event9934 completed all4096
records with original f=t=1 and private f'=t'=2:481525381 literal actions,
388 private ports, complete field/header correctness and physical retirement,
in73.691 s under120 s. Full returned bytes and receipts are retained and
rechecked by the bounded evidence gate; that gate does not rerun the long
successful numeric call. The normalized Gaussian-character oracle is an
unchanged credited predecessor check.

Limits and next questions

The numeric fixture uses a local cutoff1 and is not a global t>=145
producer witness. Very long metadata cases prove no huge numerical admission.
The theorem retains original geometry, common-grid/signed-prefix conditions,
physical disjointness and inherited numerical source-to-machine contracts.
Changing cutoff supplies none of those premises. All row/stock/owner delivery
costs and preexisting erased backing remain charged. Materialized numerical
array extents are distinguished from visited space.

No full MOVE, enclosing product/remap caller, global recurrence or nonleaf
tariff is installed. Next: join this exact private interface to an actual
typed caller while retaining its original global descriptor; prove that
caller's f<=t, precision and stock domain; and complete literal numerical
lowering and remaining global assumptions.

Credit and assistance

Prepared for @CubeJerry. Credit the exact public packages above, selected
#6030, Gaussian work in
#3091, physical predecessor
#6293 and precision work in
#6901, with all retained notices. Substantial
OpenAI assistance supported proofs, code, experiments, review and documentation.
Shared-context AI checks are not human or proof-kernel acceptance.