IndisputableMonolith.Physics.Planck_Length_RS
Defines the RS-native Planck length via a domain cost, a canonical positive threshold, and a certificate packing those facts. Length-scale and constant-ladder arguments in Recognition Science cite it when fixing the geometric yardstick from the assigned $c$, $\hbar$, and $G$. The module is mostly definitional: short nonnegativity and positivity lemmas plus an inhabited certificate type.
claimIn RS-native units ($c=1$, $\hbar=\varphi^{-5}$, $G=\varphi^{5}/\pi$), the module introduces a domain cost on the length scale, a canonical Planck threshold asserted positive, and a certificate type whose inhabitants witness that the threshold matches the cost evaluation and is strictly positive.
background
Recognition Science fixes the dimensionful constants in native units: $c=1$, $\hbar=\varphi^{-5}$, $G=\varphi^{5}/\pi$, with the golden ratio $\varphi$ forced as the self-similar fixed point of the J-cost (T5–T6). The ordinary Planck length $\ell_P=\sqrt{\hbar G/c^3}$ therefore collapses to an explicit $\varphi$-power once those assignments are in place.
The module sits on Constants (fundamental tick $\tau_0=1$) and Cost (J-cost and related defect infrastructure). It specializes that stack to a length-scale domain cost and a single canonical threshold intended as the RS Planck length, then packages the elementary positivity and evaluation facts into a certificate record.
proof idea
Definition-and-certificate module rather than a deep proof development. The domain cost and canonical threshold are definitions; equality-at-evaluation and nonnegativity are short lemmas; positivity of the threshold is a one-line fact; the certificate type simply bundles those propositions, and inhabitation is immediate from the lemmas already proved.
why it matters in Recognition Science
Gives physics-side code a named, certifiable handle on the Planck length once RS has fixed $c$, $\hbar$, and $G$ from the forcing chain and the Recognition Composition Law. Downstream mass-ladder and coupling work that needs a geometric yardstick can import the certificate instead of re-deriving the constant combination. No used_by edges are recorded yet; the module is a leaf certificate in the present graph, ready for length-scale or holographic claims that close against the native Planck unit.
scope and limits
- Does not re-derive $c$, $\hbar$, or $G$; it consumes the RS-native assignments.
- Does not convert the RS Planck length into SI metres.
- Does not prove uniqueness of the threshold beyond the certificate packing.
- Does not treat curvature, higher-D, or renormalization corrections.
- Does not connect the threshold to the eight-tick octave or mass rungs directly.