Pith. sign in
module module moderate

IndisputableMonolith.Physics.ElectronAffinity_FromPhiLadder

show as:
view Lean formalization →

Module packages the Recognition Science account of electron affinity on the golden-ratio energy ladder. It defines a domain cost, a positive canonical threshold, and a certificate that the affinity sits in the predicted band. Atomic-scale RS auditors cite the certificate when matching ladder rungs to measured affinities. Structure is definitions plus sign lemmas and an inhabited certificate type, not a deep analytic derivation.

claimOn the $\varphi$-ladder, introduce a domain cost $C$, a canonical threshold $T>0$, and a certificate that electron affinity equals the RS-predicted energy defect fixed by $C$ and $T$ in native units.

background

Recognition Science places mass and atomic energy scales on a discrete $\varphi$-ladder. Here $\varphi$ is the self-similar fixed point forced after $J$-uniqueness (T5--T6), with $J(x)=(x+x^{-1})/2-1$ and the Recognition Composition Law fixing rung arithmetic. Energies are read in RS-native units built from Constants (tick $\tau_0$, and the usual $c=1$, $\hbar=\varphi^{-5}$ package) and the Cost layer.

Electron affinity is treated as an energy defect against a domain cost rather than a full many-body computation. This Physics module imports only Constants and Cost, so it stays at ladder-plus-threshold level: define the cost, fix a positive threshold, and package a certificate that the affinity claim is inhabited.

proof idea

Definition-and-certificate module, not a long tactic development. It introduces the domain cost and the canonical threshold, proves nonnegativity of the cost and positivity of the threshold, then bundles those into an electron-affinity certificate type and shows that type is inhabited. Upstream dependence is only the Constants and Cost imports; no external analytic lemma chain is required beyond those sign facts.

why it matters in Recognition Science

Fills the named electron-affinity prediction slot on the $\varphi$-ladder mass/energy formula (yardstick times $\varphi$ to a rung offset). Downstream used-by edges are empty on this page, so the module is a leaf certificate for Physics audits rather than an input to the T0--T8 forcing chain. It lets referees check that the affinity claim is stated in native units with explicit cost and threshold, separate from QED or spectroscopic fitting codes. Ties to framework landmarks only through shared $\varphi$-ladder and Constants infrastructure.

scope and limits

depends on (2)

Lean names referenced from this declaration's body.

declarations in this module (8)