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Theorem · finite hidden-choice closure with explicit transport bound

FPRD-T167

Finite causal selector covers preserve stationary transport

Exact statement

Let A have transport tuple (d,k,g,q), and let m synchronous finite-state selectors T_i with s_i states satisfy pi(A)=union_i T_i^{-1}(A). Then pi(A) has transport tuple (m*d,k,g^m,q^m product_i s_i). Thus every fixed finite online cover of the accepting hidden histories preserves bounded stationary transport.

StatusSelf-contained composition proof with exhaustive finite product audit
External reviewThe proof composes two local FPRD product constructions. No external or specialist review of the selector-cover formulation is recorded.

Context

T166 shows that one deterministic online choice is harmless. T167 identifies the maximal immediate extension: every fixed finite menu of such choices remains harmless after a Boolean product construction.

Hypotheses and scope

  • Each selector is total, deterministic, synchronous, and chooses a tagged lift of its observed input.
  • The finite family covers exactly the projected accepting language through the displayed union of inverse images.
  • A has one finite scaffolding presentation with tuple (d,k,g,q).

Proof or evidence

T166 compiles selector i with tuple (d,k,g,s_i q). T157 packs all m component graphs and accepts their union, yielding the exact displayed resource ceiling.

Finite causal selector-cover theorem →

Verification notes

The checker compares 2,666,496 packed and separate runs over 86,016 selector families, including widths one through three, all two-state binary local machines, every accepting set, and all binary inputs through length four.

Limitations

  • The resource tuple is a sufficient product bound and need not be Pareto-optimal.
  • The theorem does not cover a selector family whose size grows with the input.
  • Finite selector covers are sufficient, not necessary, for a projected language to have bounded transport.
  • The construction uses standard finite products; no literature-priority claim is made.

Open work

Replace the finite selector count by a horizon-dependent selection profile and compare its growth with scaffold access capacity.