cell_LQG_EchoDamping
plain-language theorem explainer
Recognition Science predicts a per-echo amplitude damping ratio of $1/\varphi$, which is strictly larger than LQG's uniform-discreteness floor of $1/2$. Gravity-track authors cite this cell when filling the LQG row of the 4×3 discriminator matrix. The proof is a one-line wrapper of the certified inequality `echoDampingRatio_above_half`.
Claim. The RS per-echo amplitude damping ratio equals $1/\varphi$ and satisfies $1/\varphi > 1/2$, where $1/2$ is the LQG uniform-discreteness benchmark.
background
Track 6.D of the quantum-gravity master plan builds a 4×3 discriminator matrix (rivals: LQG, string, CDT, Bohmian; sectors: LeadingLog, EchoDamping, RungPhase). Each cell is a theorem-grade numerical band separating RS from the rival on an empirically accessible channel.
The EchoDamping sector compares successive black-hole echo amplitudes. In RS the per-echo damping ratio is defined as echoDampingRatio := 1/φ (from BlackHoleEchoesFromBounce), with φ the golden ratio forced at T6. LQG's uniform area discreteness supplies the competing floor 1/2.
The certified lemma echoDampingRatio_above_half (from DiscriminatorCert) already proves $1/\varphi > 1/2$. This cell simply installs that inequality into the LQG–EchoDamping slot of the matrix.
proof idea
One-line term proof: apply echoDampingRatio_above_half from DiscriminatorCert. That upstream certificate already unfolds echoDampingRatio = 1/φ and discharges $1/\varphi > 1/2$ from the known numerical bounds on φ. No further algebra is performed here.
why it matters
Fills the (LQG, EchoDamping) entry of discriminatorMatrixFull, the structural certificate that closes Track 6.D. The module doc states the binding success criterion: three or more theorem-grade discriminators from φ with named observational channels, and at least one unambiguous cell per rival. This cell supplies the explicit margin RS > 1/2 against LQG's half-quantum floor, matching the matrix row "LQG (−1/2) | … | RS > 1/2 | …".
It sits downstream of the black-hole echo construction (BlackHoleEchoesFromBounce) and the Session-93 discriminator certificates. Framework landmarks: φ is the T6 self-similar fixed point; the echo channel is an observational readout of the eight-tick / ledger dynamics. No open sorry remains on this cell.
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