IndisputableMonolith.Verification.NyquistObstructionCert
Verification module packaging the Nyquist obstruction that forces the Recognition eight-tick period: neither fewer nor more ticks work. Theorists citing T7 (octave period 2^3) use the certificate and the forced-period theorem. The argument pairs an information lower bound with a sampling obstruction from the Patterns layer.
claimThe module certifies that the Recognition eight-tick period $T=2^3$ is forced by a Nyquist-type obstruction: sampling below eight ticks loses reconstructible information, while longer periods are informationally redundant under the same bound.
background
Recognition Science fixes discrete time in an eight-tick octave (forcing chain T7: period $2^3$). The Nyquist idea here is discrete: a minimal number of samples is required to carry the recognition pattern without aliasing or information loss.
The module sits in Verification and imports Patterns, where the combinatorial tick and covering structures live. Sibling objects named in the module are a certificate bundle, a theorem that eight ticks are Nyquist-forced, and an information lower bound that supplies the quantitative obstruction.
Doc-comment framing is blunt: the eight-tick period is forced by Nyquist, neither more nor less. That is the local claim the certificate is meant to pin for downstream audits.
proof idea
Module-level structure, not a single proof term. It exposes a certificate object together with a forced-period theorem and an information lower bound. The bound supplies the obstruction (too few ticks fail reconstructibility); the theorem packages equality at eight ticks; the certificate is the audit-facing wrapper. Details of the combinatorial steps live in Patterns and in the sibling lemmas.
why it matters in Recognition Science
Closes the verification face of T7 in the forcing chain: the eight-tick octave is not an aesthetic choice but a Nyquist obstruction. Downstream used-by edges are empty at present, so the module is a leaf certificate rather than an intermediate lemma factory. It still matters for anyone auditing that period $2^3$ is forced and that neighboring periods are ruled out. Aligns with the primer landmark that discrete time is an eight-tick octave and with the claim that the period is uniquely fixed.
scope and limits
- Does not derive continuous-time Shannon–Nyquist sampling theorems.
- Does not by itself prove T0–T6 or T8; only the eight-tick period face.
- Does not compute physical constants (c, hbar, G, alpha) or mass rungs.
- Does not list external used-by parents; currently a verification leaf.
- Does not replace the Patterns combinatorial development it imports.