[theon199]

This package prices an expanded complex-helper mechanism before attempting a
physical construction. For the thirteen original rank-nine helpers refined by
PR5599, even arbitrary positive integral target partitions, granted for free,
earn less than 0.870799206564 extra raw target moment per FULL throughout
0 <= C <= 17/5000. One additional positive-integral-rank Gaussian call costs at
least one. With all other paid work and targets fixed, the proposed edit loses
more than 0.129200793436 per FULL. No new kappa or selected-frontier change.

PR5599 adds zero recursive calls and is outside this exclusion. Its actual
binary splits remain a positive control. Fifteen fully refined H9 sources,
or forty-eight binary-split sources, are the first arithmetic endpoint
thresholds that can fund one H1; neither is a physical construction.

Evidence

python3 -I -B research/helper-refinement-budget-s29/verify.py

Expected: PASS_HELPER_REFINEMENT_BUDGET_S29 partitions=30 controls=5 independent_power_checks=2.
Normal and optimized read-only replay pass on Python 3.12.14. The package
contains a written all-partition bound, all 30 partitions of nine, rational
atanh/Taylor enclosures and independent integer-power checks of the decisive
rank-nine interval. Five controls reject omitted target debit, extra rank
mass, duplicate independent field credit, corrupt source bytes and an
out-of-scope exponent. A Git-free export and source-corruption check pass.

Scope and sources

Only research/helper-refinement-budget-s29/ is added. Publication base is
66849e1475c930fd7732b1a0067ffee7e1e95f60. Git transport was unavailable through
the configured proxy, so this uses the available checkout and byte-pinned
current sources fetched with the GitHub connector at canonical snapshot
df0137efd35e11b4445734bf612bdd4c7ebc330c. The source construction head is
09dd0965711ca7eeb169057a420abab1c9052137; its PR5565 word head is
9af814164b9dfc21f19ec737959d67cb71488c95. Source hashes match the selected
certificate, whose conditional kappa is 0.00310045 at that snapshot.

The theorem assumes the raw tariff r^(1-C), fixed other paid/target terms,
positive integral pieces of total rank nine, and honest independent-input
credit. Ordinary helper, source-access, basis, routing, restoration and
compiler work is optimistically free; actual nonnegative added work cannot
repair this raw-moment comparison. Other paid removals, other targets, a
changed tariff or exponent range, and one global call shared across eighteen
invocations are outside scope. No native replay, full source-history audit,
selected cold replay, hosted CI, compiler improvement, supplier admission or
formal multiplication theorem is claimed. The five selected framework
assumptions remain unchanged.

Seed 29 assigned the complex-supplier track. Related PR5614's hypothetical
145-split compiler target, PR5615's dyadic channel capacity and PR5632's fixed
cut ceiling are credited and not reverified. Targeted PR searches found no
matching paid-call budget result; Discussion claims could not be read through
the available connector. The claim and result are recorded locally.
zxv's PR5554 supplies related all-length fixed-local-debt stopping principles;
the added result here bounds arbitrary refinements of the thirteen H9 targets.

Attribution

Credit Ali Romman for PR5599 and the retained helper/caller lineage,
Pierre-Loic Doulcet / hexapode for PR5565, and all predecessors named in the
unaltered source proof and package README. The concave-tariff viewpoint is
established repository practice. Prepared by OpenAI Codex for Charan, using
the configured Git identity, with substantial AI assistance in proof,
implementation and verification. No independent human or proof-kernel review
is claimed. Apache-2.0.