[CubeJerry]

Problem and exact result

The fine-family compression ledger and cached middle still need an actual
expansion source. The old paired production Tensor catalogue cannot admit
that family. Existing local expansion and error theorems do not by themselves
prove that the exact explicit coefficient/page producer accepts a complete
original period, or that its enlarged T-record return matches the common
codec's record clock.

This source-bound enabling/audit package proves that admission for the
unchanged explicit Tile API: q>=101, integer alpha>=2 with alpha²<q,
0<s<t<2s and metadata fitting q bits, full target [0,t), original periodic
halo [-b-1,s+b+2), b=alpha ceil(sqrt(q)), P=32768q and sigma=4096q.
It binds every actual A/K/B argument to the encoded scalar enclosure and
proves the extra strict positivity and upper-unit acceptance checks. The
kernel's near-unit case uses its actual reciprocal lower>=unit invariant,
not an invalid inference from interval containment alone.

For the already declared forward K_f>=D, exactly J=K_f-D final shift bits
spend the Tile sequence's built-in D bits. The admitted slow-reference
prefix reaches the middle's half-disk from quarter-disk ingress and has
maximum-coordinate component-l1 error below

(12*2^-J+2)*2^-q <= 14*2^-q.

Its restored contribution is funded by q>=Gamma+tau_exp+5 when the exact
normalized compression contracts. Gamma=K_f+K_c remains the existing
Gaussian dyadic restoration; both S factors and other outer recovery scales
are separate. A real native return adapter pays a new T-record clock and
the final codec shift, with borrowed encoded T and explicit q/J templates.

Novelty and predecessor credit

#3878 already covers fine theta, #5056 proves
actual inward norm, #5295 proves the five-residual error telescope, and
#6085 proves the encoded scalar enclosure. These are credited premises;
the new implication is the complete expansion producer/page admission and
its preserved-normalizer/changing-volume boundary. #5325 covers a different
old Tensor normalization. #3851/#3935 provide the unchanged native cohort
and source, and their old production guards remain untouched.

The exact public dependencies are the @CubeJerry middle
8db3cc1, ledger
76a84e1, Reference join
4509310, caller audit
9621124 and codec
73d5ada. DEPENDENCIES.json
binds their retained files; SOURCES.json pins 30 live canonical inputs
at main 7c49fe3.

Complete cost and limits

This is a declared slow reference, not a fast Broad controller. Its full
online bill is O(Tq(log T+D log²(q+2))+TJ), plus charged source preparation,
headers, page reuse and retained historical backing. Mandatory Tile writes
cost Omega(DTq), and the specified whole-axis FieldMove route costs
Omega(Tq log T) under T/S<2. These literal bounds delimit this exact port;
they are not general Gaussian lower bounds. A future grouped implementation
may reuse its certified original-coordinate target but must prove its own
source, radius, routing, normalizer and complete physical cost.

No old catalogue guard is waived. There is no broad Core implementation,
complete prefix physical replay, production GL64/O73 execution, full Fourier
or integer-recovery theorem. The remaining native/scalar/Fourier and
analytic-source obligations are explicit. No new kappa; the selected
conditional frontier and all five foundational assumptions are unchanged.

Reproduction and checks

python3 -B scripts/research_package.py --package research/fine-expansion-page-admission
python3 -B scripts/check_research_commit.py --package research/fine-expansion-page-admission --check-modes

Normal and optimized commands authenticate complete sources and 22 source
clauses, then run independently derived integer/Fraction controls across
4,320 headers, 7,557 blocks, 68,013 quadratic identities, 288,036 halo
multiplicities, 768 reciprocal-unit cases and 240 normalization budgets.
The actual T16/S9 q12/J3 native-word/public-codec output agrees exactly with
the independent signed truncation oracle, with component error 3/8192.
Short/long returns, the old S clock, borrowed metadata/work aliases,
pending returns, wrong normalizers, lost periodic multiplicity and invalid
near-unit reasoning are rejected or distinguished. The finite native
witness runs only this output seam. Its single corrected initial marker
setup failure is retained in the checkpoint; inherited guards were unchanged.

Prepared for @CubeJerry with substantial OpenAI assistance. Credit Jose
Manuel/@jmbarrancoml, JoyboyBrian, Hiroki KUMAZAKI/@kumagi, Ali Romman/
@aliromman and all retained source/archive authors in NOTICE.md.
Independent algorithmic checks and same-team lead review do not assert
independent human or proof-kernel acceptance. Exact evidence, proof,
open next questions and restart trail are in the package.