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Transfer corollary · encoding-robust obstruction to every finite scaffold presentation

FPRD-T162

Cell-probe lower bounds force infinite structural transport degree

Exact statement

Let K be an (a,b)-SCA encoding of a three-stage Boolean problem in the sense of Kim and Park. If no exact deterministic cell-probe data structure has word size Theta(log n), update time O(a(n)), query time O(b(n)), and polynomial space, then Tr(K) is empty and delta_str(K)=infinity.

StatusSource-attributed corollary with explicit dependency and verification boundary
External reviewThe SCA-to-cell-probe transfer is imported from Kim and Park, arXiv:2608.29592v1. FPRD Lab has checked only the translation into its transport invariant.

Context

Raw response counts and fixed future observers do not yield universal scaffold lower bounds. The cell-probe transfer instead measures access after updates have been committed and the final query is revealed.

Hypotheses and scope

  • K satisfies the correctness, local operation-length, and polynomial total-length conditions of a Kim-Park (a,b)-SCA encoding.
  • The cell-probe exclusion applies to exact deterministic structures with Theta(log n)-bit words and polynomial space.

Proof or evidence

Finite structural degree implies K is in SCA by FPRD-T161. Kim-Park Theorem 3.5 would then give the forbidden cell-probe structure. Contraposition forces infinite degree and an empty spectrum.

Cell-probe transport obstruction →

Verification notes

The checker verifies 4,096 encoding-size rows for the Kim-Park witness and the implication orientation. It explicitly does not verify Kim-Park Theorem 3.5, Ko's lower bound, or the external Lean artifact.

Limitations

  • The theorem applies only after a suitable three-stage encoding and a matching cell-probe lower bound are supplied.
  • It does not isolate an intrinsic combinatorial obstruction inside the scaffold model.
  • The result is a direct corollary of cited work plus FPRD-T161; no independent priority claim is made.

Open work

Translate the known hard language C into the FPRD frontier model and seek an intrinsic obstruction matching its cell-probe lower bound.