cell_LQG_RungPhase
plain-language theorem explainer
Recognition Science assigns a per-rung phase delay of log φ on the recognition lattice, and that delay is strictly less than LQG's half-quantum value 1/2. Gravity-track auditors cite this cell when filling the LQG × RungPhase entry of the 4×3 discriminator matrix. The argument is a one-line term application of the certified inequality log φ < 1/2.
Claim. The RS per-rung phase delay equals $\log\varphi$ and satisfies $\log\varphi < 1/2$, so it lies strictly below loop quantum gravity's half-quantum phase threshold of $1/2$.
background
Track 6.D builds a 4×3 discriminator matrix (rivals: LQG, string, CDT, Bohmian; sectors: leading-log coefficient, echo damping, rung phase) whose cells are theorem-grade numerical bands separating Recognition Science from each rival. The RungPhase column uses the lattice phase advance per rung.
The per-rung phase delay is defined as $\log\varphi$, with $\varphi$ the golden ratio forced by the self-similarity fixed point (T6). LQG's competing half-quantum scale is the constant $1/2$. The certified comparison $\log\varphi < 1/2$ is already proved upstream as a direct corollary of the Session-90 bound on $\log\varphi$.
This module's anti-retreat standard requires every filled cell to be an inequality with no sorry and no RS-internal axiom; the LQG–RungPhase cell is one of those entries.
proof idea
One-line term proof: the goal is definitionally the statement of the upstream certificate rungPhaseDelay_below_half. That certificate unfolds the delay definition to $\mathrm{Real.log},\varphi$ and applies log_phi_lt_half. No further algebraic work occurs here.
why it matters
Fills the LQG × RungPhase cell of discriminatorMatrixFull, the structure that closes Track 6.D of the quantum-gravity master plan. Together with the LeadingLog and EchoDamping LQG cells (margins $>1/4$ and RS $>1/2$), it supplies an unambiguous numerical distinction against loop quantum gravity on an empirically named channel (rung phase). The matrix binding criterion demands at least one such cell per rival; this cell is the RungPhase witness for LQG. It sits downstream of the φ-forcing chain (T6) only through the already-certified bound $\log\varphi < 1/2$, so it does not reopen foundation work.
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