zeroCostMode_nonempty

This module isolates the null recognition mode as the upstream recognition-theoretic object: the unique zero-cost propagating mode of the eight-tick recognition cycle, up to ratio-gauge equivalence. Physical labels such as photon, spin, polarization, or lightlike kinematics are deliberately withheld here and deferred to a separate photon module.

A propagating mode assigns a carrier event to each of the eight ticks of the recognition octave (the T7 period $2^3$). Total mode cost aggregates the per-tick reciprocal recognition cost along that cycle; vanishing total cost is the defining property of a null mode. The fundamental tick is the RS time quantum $\tau_0 = 1$. Upstream, the primary existence theorem already constructs a canonical null mode and proves its total cost is zero.

One-line term wrapper. The statement is definitionally the same as the primary null-recognition-mode existence theorem, which supplies the witness (the canonical null recognition mode) together with the lemma that its total mode cost vanishes. No further algebra or case analysis is performed.

Preserves a backward-compatible existence name so older call sites can obtain a zero-cost carrier without renaming to the null-recognition-mode API. The real content lives in the canonical construction and the total-cost-zero lemma that the primary existence theorem packages. In the RS forcing chain this sits under T7 (the eight-tick octave): a free zero-cost carrier on that cycle is the recognition-theoretic precursor of the photon, though this module refuses that identification. The dependency graph currently lists no downstream users; the companion uniqueness-up-to-gauge material in the same module is the natural next step.