BMV_coupling
plain-language theorem explainer
Identifies the Bose–Marletto–Vedral gravitational entanglement coupling with the RS Einstein coupling κ_rs = 8φ⁵. Anyone citing the G-004 no-graviton claim or the numerical BMV band (~88.7) uses this alias. The body is a one-line definitional equality to ZeroParameterGravity.kappa_rs.
Claim. The Bose–Marletto–Vedral entanglement coupling in Recognition Science is defined to be the RS gravitational coupling $\kappa_{\mathrm{rs}} := 8\phi^5$.
background
Module G-004 asks whether a graviton exists. In RS the answer is a category error: gravity is emergent curvature of the ledger lattice, not a force carried by a spin-2 gauge boson. Three concrete claims are formalized: the coupling is algebraic in φ alone, gravitational-wave polarizations equal 2 in D=3, and the BMV entanglement rate is a sharp numerical prediction.
Upstream, kappa_rs is the derived Einstein coupling $\kappa = 8\phi^5$ ("derived, not assumed"). Constants live in RS-native units with $\phi$ the self-similar fixed point forced at T6. The BMV protocol predicts that two masses become entangled at a rate set by this same $\kappa$; naming that rate BMV_coupling makes the experimental target explicit.
proof idea
Definitional one-liner: BMV_coupling is declared equal to ZeroParameterGravity.kappa_rs, which itself expands to $8\phi^5$. No tactics or lemmas; the content is the naming identification.
why it matters
Gives the BMV experiment a named RS target so downstream facts can speak in lab language. BMV_coupling_pos immediately gets $0 < \mathrm{BMV_coupling}$ from kappa_pos (entanglement should be generated). BMV_coupling_bounds places it in $(85.6, 90.4)$, the falsifiable band around $\approx 88.7$. The certificate structure NoGravitonCert records bmv_pos : 0 < BMV_coupling alongside emergent gravity, algebraic $\kappa = 8\phi^5$, and two GW polarizations. Together these close registry item G-004: if gravity were particle-mediated one would not expect a pure number-theoretic coupling fixed by $\phi$ alone.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.