IndisputableMonolith.LightCone
Module collecting the causal light-cone structure of Recognition Science in units where c = 1. It packages the null boundary of admissible signals, the eight-tick discrete timing that forces the cone aperture, and the link from D = 3 to the usual Minkowski cone. Cite it when proving locality, no-signaling, or finite propagation speed on the phi-ladder. The module is organizational: definitions and lemmas sit here; deep uniqueness proofs live upstream in the forcing chain.
claimIn RS units with $c = 1$, the light cone is the null set $\{(t,x) : |x| = |t|\}$ in $D = 3$ spatial dimensions, discretized on the eight-tick octave (period $2^3$). Admissible recognition events lie inside or on this cone; superluminal hops are excluded by the cost functional and the self-similar fixed point $\varphi$.
background
Recognition Science fixes $c = 1$ as a unit choice and derives $D = 3$ spatial dimensions from the forcing chain (T8). The same chain forces the eight-tick octave (T7, period $2^3$), which supplies the discrete clock against which radial hops are counted. The J-cost $J(x) = (x + x^{-1})/2 - 1$ and the Recognition Composition Law penalize paths that leave the cone, so the continuum null cone emerges as the zero-cost boundary of admissible recognition.
This module sits at the interface between that discrete timing and continuum causal structure. It introduces the cone as a geometric object on the phi-ladder rather than as a postulate of special relativity, and records the elementary inclusions (timelike, null, spacelike) used by later locality and no-signaling arguments.
proof idea
This is primarily a definition and packaging module. It assembles the cone predicate, the discrete eight-tick radial bound, and the elementary comparison lemmas that relate hop count to continuum $|x|/|t|$. Nontrivial uniqueness and dimension results are imported from the forcing chain (T7–T8); the module itself does not re-prove them.
why it matters in Recognition Science
Locality, finite propagation, and no-signaling theorems in the monolith need a single, named cone object in RS units. LightCone supplies that object so downstream results can quote one interface instead of re-deriving $c = 1$ and $D = 3$ each time. It ties directly to framework landmarks T7 (eight-tick octave) and T8 ($D = 3$), and to the unit choice $c = 1$ in the RS constants. Parent developments that consume it are those establishing causal support of recognition updates and bounds on mass/energy transport along the phi-ladder.
scope and limits
- Does not re-prove T7 or T8; imports eight-tick and D = 3 from the forcing chain.
- Does not derive the numerical value of c in SI units; works entirely in c = 1.
- Does not treat curved spacetime or gravitational lensing of the cone.
- Does not encode quantum field commutators; only the geometric causal partition.