Research: structural barriers for kappa = 0.01 (no new exponent)

[huxint]

Current paired-cube refinements leave substantial data-interface and copied-center costs in place. This research package proves explicit limits on several such continuations and tests a different small-network construction. It reports no new multiplication exponent.

The new statements are:

• Keeping the pinned Pair donors to avoid parity erasure on the source-assisted v4 word: conditional κ = 6.647872e-4 #193 complex or Globally replayed source-assisted bit word: conditional kappa = 0.000661755179959122 #187 bit data calls cannot reach kappa=0.01 even if every auxiliary call and all center loss are granted for free: the ordinary-saving ceilings are below 0.008867 and 0.008898.
• A stated odd-dimensional paired-cube family remains below 0.008094 even with arbitrary local data chains and zero auxiliary entropy. The check includes an analytic infinite tail, not only a finite parameter scan.
• For paired triples with p>=5, every nonzero linear combination of coordinate stars has binary source-support span at least h-2. Consequently any factorization through exactly h copied centers costs at least h(h-2); the current stars attain equality. Overcomplete center factors and different center implementations remain open.
• A common triangular flag for every rational frame in the general finite bit contract forces s>=Wm. The argument also covers commuting frames whose common eigenbasis is not rational.
• On all 87 chronological reuses of the balanced Fano model, every completed scalar permutation obtainable from local GL(2,F2) gates is routable. This extends the earlier fixed-terminal test to every auxiliary/data output permutation in this bounded family.

Only a self-contained research package and its workflow are added to main. Inputs from the unmerged supplier PRs are small pinned profiles; reproduction does not fetch or run those suppliers and does not enlarge their validation scope. The proofs state the interface assumptions and exclusions separately. Optional vector-code solver receipts are not used as independently checked impossibility certificates.

Validation passed on a clean checkout based on main 3b6b668:

python -B -S research/percent-exponent-architecture/verify.py --deep

This regenerates the rational ceilings, checks 59,048 nonzero finite center-coefficient controls and sharp examples, runs seven adverse/unit controls, exhausts the 87 scalar/routing cases in C++17, compares the matching algorithm with eight direct full-word enumerations, and independently replays all 16 retained-demand cases with Python. Verification leaves the checkout unchanged. CI repeats the exact package on Python 3.11 and 3.14.

The whole multiplication theorem remains conditional on its inherited analytic, all-size, precision, row and fixed-tape interfaces. The existing construction, supplier certificates and claimed kappa are unchanged.

Credits and source hashes are in the package NOTICE and manifests, including the paired-cube/compiler authors, #193 and #187 suppliers, DaysSky's #192 entropy ceiling, romainhedouin's #183 assembly ceiling, and the repository's earlier Fano investigations. Prepared for huxint with substantial OpenAI Codex assistance.