cell_String_EchoDamping
plain-language theorem explainer
The RS black-hole echo damping ratio sits strictly above one half, separating the string/fuzzball proxy band from the RS rung-algebra value 1/φ. Gravity-track auditors cite it as the (String, EchoDamping) cell of the 4×3 discriminator matrix. The proof is a one-line application of the certified inequality echoDampingRatio > 1/2.
Claim. The Recognition Science echo-damping ratio satisfies $\mathrm{echoDampingRatio} > 1/2$. In the quarantined RS rung algebra this ratio equals $1/\varphi$, so the claim is the elementary separation $1/\varphi > 1/2$ against the common string/fuzzball proxy value $1/2$.
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 that separates RS from a rival on an empirically named channel.
The EchoDamping sector compares successive black-hole echo amplitudes. In RS the damping ratio is fixed by the rung algebra to $1/\varphi$ (with $\varphi$ the self-similar fixed point from the forcing chain). String/fuzzball phenomenology commonly takes a proxy near $1/2$. The cell therefore asks only whether the RS value clears that proxy.
Upstream, echoDampingRatio is the RS-side quantity from the bounce-echo module, and echoDampingRatio_above_half in DiscriminatorCert already proves the strict inequality as a certified discriminator. This declaration simply installs that fact as the matrix cell for the string row.
proof idea
One-line term proof: the goal echoDampingRatio > 1/2 is discharged by direct application of the upstream certificate echoDampingRatio_above_half from DiscriminatorCert. No local algebra is re-derived; the cell is a named packaging of that certified inequality for the string row of the matrix.
why it matters
Fills the (String, EchoDamping) entry of discriminatorMatrixFull, which assembles the full DiscriminatorMatrixCert. Together with the LQG and LeadingLog cells it meets Track 6's binding criterion: at least one unambiguous, theorem-grade distinction per rival, with three or more φ-derived discriminators on named observational channels.
The separation is algebraic ($1/\varphi > 1/2$), not a complete microphysical echo model. The module doc stresses the anti-retreat principle: rivals cannot absorb the RS band without changing their own proxy. Framework landmarks in play are the φ fixed point (T6) and the rung algebra that produces the damping ratio; the eight-tick structure sits in the broader gravity track but is not invoked in this cell.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.