[CubeJerry]

Why this matters

The completed serial monomial removes ordinary numerical calls on its
direct route, but retains a repeated full-field invoice. An upper invoice
alone does not prove a lower rate obstruction. This package identifies
mandatory literal work and the exact dimension, volume and cutoff
conditions for a source-specific lower consequence.

Exact result

Every successful serial invocation incurs on its public field alone at
least 4fV physical unit moves, (4/3)fV reads and fV writes. V is the
complete coded body. Each column unconditionally imports, rewinds,
exports and rewinds the entire field; all other work adds cost.

For the actual selected #6030 event9896 right monomial, an explicit
infinite admitted local zero-input family has d=9f, V=(9/2)Vraw and the
long-record condition. It excludes C V d^epsilon for epsilon<1 for this
implementation only if the full supplier admits such unbounded f and
comparable complete-field volume. Fixed-cutoff MOVE leaf wrappers admit
bounded f and are not contradicted. Literal actions and simultaneous
multitape steps are separated, with any required fixed conversion explicit.

Provenance and novelty

Canonical base: 7c49fe32c55de02c2c873655c804b16e4c3fef0a.
Serial source: CubeJerry/integer-mult-bounds@2ec95e06c2a16e73f9da9a8fe41912710135daaf.
Current monomial: 7d1ff23714e6f9182c1d0ff9214f65def2f30e04.
The serial predecessor proves an implementation and upper invoice; its
Compact-binding warning expressly excludes an algorithmic lower inference.
This adds mandatory traversals, an admitted family and the cutoff boundary.
Eleven retained files authenticate the sources and predecessor domains.

Credit remains with the original work including
#3087, #4172,
the selected #6030 source and the published current adapters. Prepared
for @CubeJerry with substantial OpenAI assistance. Separate lead review
shares sources and is model-assisted, not human or proof-kernel verification.

Verification

python -I -B scripts/research_package.py --package research/current-serial-pass-lower-bound

Both normal and optimized registered gates passed: source authentication,
actual nontrivial recipe reconstruction, literal traversal structure and
coded primitive counters, 516 descriptor members, induction premises and
nine reservation/rewind/volume/cutoff controls. Expected status:
PASS_SERIAL_MANDATORY_FIELD_PASSES. The universal theorem is proved by
control flow and induction, not finite extrapolation. No numerical
monomial, whole MOVE or complete caller is run.

Limits and next obligation

Actual full supplier/exporter admission, d/V mapping, global cost
conversion and all five foundational assumptions remain separate. Bind
one exact nonleaf caller domain or construct a different batching route.
This is not a general monomial or multiplication lower bound. No new kappa.