IndisputableMonolith.Measurement.RecognitionAngle.TemporalGating
The TemporalGating module supplies coprime-moduli framing for double-period phasing (periods 8 and 45) inside the recognition-angle measurement layer. Researchers modeling phased sensor observations or temporal feasibility in Recognition Science would cite it. The module is a pure definition block that imports the ActionSmallAngle core and declares parameter records plus predicate families without any proofs.
claimCoprime-moduli framing for double-period phasing with periods $8$ and $45$, realized via parameter records PhaseParams and EightTickParams together with predicates timeOK, angleOK and feasible on $R^3$ angles.
background
The module sits inside the Measurement.RecognitionAngle domain and imports the ActionSmallAngle definitions: $R^3$ as 3D Euclidean space, angleAt $x$ $y$ $z$ for the geometric angle at $x$, $A_of_theta$ $θ := -log(sin θ)$ as the kernel action, and thetaMin $Amax := arcsin(exp(-Amax))$ as the budget-dependent minimal recognizable angle. Its own doc-comment states the purpose as “Coprime moduli framing for double-period phasing (e.g., 8 and 45).” The sibling declarations introduce PhaseParams, EightTickParams, the timeOK and angleOK checks, the feasible predicate, and the two feasibility lemmas no_feasible_if_angle_below_threshold and exists_feasible_if_angleOK_and_time_slot.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the temporal-gating layer required by the eight-tick octave (T7) inside the forcing chain. It prepares the coprime-moduli structure that later feasibility results in the recognition-angle program rely on, even though no downstream declarations are listed yet.
scope and limits
- Does not contain any theorem statements or proofs.
- Does not compute explicit numerical values for the moduli 8 and 45.
- Does not link the phasing predicates to the full T0-T8 forcing chain.
- Does not address spatial embedding beyond the imported R3 alias.