The Geometry of Meaning: A forced carrier, a canonical vocabulary, its provable limits, and the finite light realization, in Recognition Science

Meaning is treated here as a physical object with a derivable geometry, not as a convention layered over physics. From the three Recognition Science axioms, anchored in the single primitive of distinction, kernel-checked conditional theorems produce a unique comparison cost under reciprocity, normalization, composition, continuity, and unit log-curvature calibration, and a unique positive scale under the selected self-composition closure 1 + r = r2. Separately, a content-typed topological theorem selects spatial dimension three as the unique value at which an embedded circle can have nontrivial complement homology, and a combinatorial theorem bounds the minimal surjective period on the three-cube by eight. The physical bridges that would make Recognition require that topological detector, force unit calibration from bare cost laws alone, force the selected scale closure, or identify complete recognition with Boolean cube traversal remain open and are tagged as such. Granting the clock and the register it writes, the axioms then force a unique spectral analysis and, after the removals they themselves demand, the carrier of meaning: the complex projective space CP6. No free parameter is tuned inside any closed mathematical step. On the carrier, the structure of meaning is relational and exact: similarity is the Born overlap, perfect similarity is identity, and a meaning is determined completely by the field of its correlations. The carrier supports a canonical vocabulary of twenty semantic atoms constructed from the four Fourier mode families, with explicit vectors and certified overlap geometry, and that vocabulary is provably incomplete: it spans four of the seven neutral modes, so two explicit meanings built from the unseen modes score identically against all twenty atoms yet are distinct. Information beyond the vocabulary is therefore mathematically necessary, and we read that necessary supplement as context. Finally, in the finite eight-tick setting, light realizes the carrier: a discrete Maxwell theory on the recognition lattice realizes every point of CP6 as a photon state, so at that level of the theory light and meaning are the same object written two ways; the continuum upgrade is stated as the principal open problem, not claimed. Every statement carries an honesty tag, kernel-checked theorem, model reading, hypothesis, or open, and the weakest link sets the tag of every composite. The paper is offered as the foundation of a research program: the study of meaning as geometry.