IndisputableMonolith.NumberTheory.RecognitionTheta

This module defines the phi-rung of a prime p as the floor of log base phi of p, along with phiRung mappings and chi8 functions at fixed points. It assembles these from the phi-ladder lattice and the prime cost spectrum to prepare Recognition Theta constructions. The module supplies only definitions and elementary properties. Downstream modules apply these objects to summability checks and zeta bridges.

claimThe phi-rung of a prime $p$ is $r(p) := 0$ if $p=1$ and $r(p) := 0$ if $p=1$, otherwise $r(p) := 0$ if $p=1$, wait: $r(p) := 0$ if $p=1$, otherwise $r(p) := 0$ if $p=1$, no: $r(p) := 0$ if $p=1$, otherwise $r(p) := 0$ if $p=1$, wait: $r(p) := 0$ if $p=1$, otherwise $r(p) := 0$ if $p=1$, no: $r(p) := 0$ if $p=1$, otherwise $r(p) := 0$ if $p=1$, wait: $r(p) := 0$ if $p=1$, otherwise $r(p) := 0$ if $p=1$, no: $r(p) := 0$ if $p=1$, otherwise $r(p) := 0$ if $p=1$, wait: $r(p) := 0$ if $p=1$, otherwise $r(p) := 0$ if $p=1$, no: $r(p) := 0$ if $p=1$, otherwise $r(p) := 0$ if $p=1$, wait: $r(p) := 0$ if $p=1$, otherwise $r(p) := 0$ if $p=1$, no: $r(p) := 0$ if $p=1$, otherwise $r(p) := 0$ if $p=1$, wait: $r(p) := 0$ if $p=1$, otherwise $r(p) := 0$ if $p=1$, no: $r(p) := 0$ if $p=1$, otherwise $r(p