[CubeJerry]

Result and why it matters

The actual old Catalogue -> TensorPlan -> Sandwich.admit chain does not
admit the eventual fine-theta family. The generic old-band mismatch is
already documented by the fine-prime audit and #4029/#4142; this package
adds the exact current recovery binding and two stronger consequences.

Allowing spacing to vary independently of the literal d=D+1 still gives
no external precision at the retained fine alpha for p0>=2^200. Also
retuning alpha forces external q>(p0^2/4)(1+2log2(p0)). A hypothetical
successful relaxed port preserving those three guards and the literal
fixed-record ingress writes 4S(q+2) cells across both inputs, giving an
Omega(n log n log log n) ingress bill on the fine family. This blocks that
unchanged-policy/ABI port, not the current analytic construction, the
selected conditional theorem or alternative callers.

The package separately binds the actual total gamma and both source S
factors in #5095's strict numerical recovery guard, and specifies the
remaining complete-prefix/transform/catalogue interface needed by the
public Reference-to-ideal compression join.

Exact sources and novelty

Canonical base: 7c49fe32c55de02c2c873655c804b16e4c3fef0a.
Public proof dependencies are the production Reference gap at
9a07c08c014259bb23c0a2b5844a1b67d91892f6 and the Reference/ideal join at
4509310a9a58d4c41c74029f899cbf36be1af9a1.

OVERLAP.md credits the prior old-band failure, #3861's finite old-domain
gap, #5149's old-band prime supply, #5095's recovery caller, #5325's
conditional restored-error improvement and #6185's arbitrary-bit wrapper.
Neither a better final error bound nor an outer bit wrapper waives the
constructor's production guards. No predecessor verifier or numerical
payload is counted as new execution.

Reproduction and verification

python -B research/fine-recovery-catalogue-obstruction/verify.py
python -O -B research/fine-recovery-catalogue-obstruction/verify.py
python -B scripts/research_package.py --package research/fine-recovery-catalogue-obstruction
python -B scripts/check_research_commit.py --package research/fine-recovery-catalogue-obstruction --check-modes

The replay authenticates 16 canonical files and two public proofs. It
inspects actual source AST sites, exhausts a declared finite integer box,
checks 801 large dyadic-parameter endpoint inequalities, and independently
checks CRT/convolution/scaling/nearest/carry on four S15 fixtures. Source
mutations and exact boundary controls detect missing strictness, old
admission guards, external record width, gamma and S factors. Full receipts
and executed gate results are included in evidence/REPLAY.json and
CHECKPOINT.md. The all-size result is the written proof, not finite
extrapolation.

Limitations and remaining work

This is a scoped necessary-condition obstruction with a conditional ABI
lower bound. No actual production Tensor/CRT/Count/Tape execution, new
catalogue, source transform, selected replay, full multiplier, independent
human acceptance or proof-kernel result is claimed. Rejected literal calls
do not perform the later scans; the scan bound applies to a hypothetical
successful relaxed port keeping the named guards and representation.

The replacement needs actual encoded fine-family admission and a complete
source-bound prefix/opposite-transform error/radius/cost join with the
correct total gamma. Compression-only progress does not supply that caller
contract. No new kappa; the complete multiplication theorem remains
conditional.

Credit and AI assistance

Prepared for @CubeJerry with substantial OpenAI assistance in proof, source
audit, exact controls and packaging. Jose Manuel / jmbarrancoml (#3851/#3935),
JoyboyBrian (#5095), Tekalign / tekuuu, ToikY (#4029), unpaidmoon (#4142),
Nick Petalas (#5149/#6185), Ali Romman and Hiroki KUMAZAKI / kumagi
(#5325/#5295), Chafik Boukhalfa / chafreaky and the fine-prime contributors,
JosieElliston's audit and the retained source08/runtime authors keep their
predecessor credit. NOTICE.md records details. Lead mathematical review
is separately identified; it is not independent human or formal acceptance.