A Lean‑verified Reality Bridge for meter‑native physics
Looking for the high‑level narrative? See the executive overview of Revolutionary Metrology.
We present a Lean‑verified derivation layer that is parameter‑free at the proof layer and a single, meter‑native bridge that turns dimensionless theorems into SI equalities without introducing tunable parameters into proofs. Calibrations enter only in the metrology layer. Building on a sorry‑free Lean development, we formalize: (i) a symmetric cost functional with log‑axis form $J(e^t)=\cosh t-1$ and a local EL/log‑axis stationarity result under explicit convexity hypotheses; (ii) the golden‑ratio fixed point with uniqueness and positivity; and (iii) discrete results such as the positive ledger gap $\delta_{\!\text{gap}}=\ln\varphi$ (and a threshold schema).
We then state and mechanize a Reality Bridge: a structure‑preserving evaluation that identifies cost with action $(J\mapsto S/\hbar)$, one tick with $\tau_0$, and one hop with $\lambda_{\mathrm{rec}}$, with $c$ the maximal hop rate. Under the bridge, we adopt the Planck‑form calibration $\lambda_{\mathrm{rec}}=\sqrt{\hbar G/c^{3}}$ (with a documented $\pi$‑normalized display variant) as a metrology choice; displayed identities do not feed back into proofs. We further verify classical correspondences (discrete‑to‑continuum continuity, gauge potentials unique up to a constant, and local EL/log‑axis stationarity), and provide a structure‑only spectra demonstrator with unified zpow ratios. The full artifact—including lemma anchors for all claims—is publicly available upon unblinding, enabling audit‑level reproducibility and code review.
Unique symmetric cost; golden‑ratio fixed point; positive ledger gap—proved upstream of any units.
One meter‑native mapping ($J\mapsto S/\hbar$, tick $\to\,\tau_0$, hop $\to\,\lambda_{\mathrm{rec}}$) without tuning.
Sorry‑free Lean artifact with lemma anchors; abstracted metrology choices and documented uncertainties.
Cost on the log axis: $$J(e^t)=\cosh t - 1$$ Golden‑ratio fixed point: $$\varphi=\tfrac{1+\sqrt{5}}{2}$$ Ledger gap: $$\delta_{\!\text{gap}}=\ln\varphi>0$$
Cost $\mapsto$ action: $$J \;\leftrightarrow\; S/\hbar$$ Tick: $$\tau_{\mathrm{rec}}\;=\;\tau_0\,\frac{2\pi}{8\ln\varphi}$$ Hop: $$\lambda_{\mathrm{rec}}\;=\;\sqrt{\dfrac{\hbar G}{c^{3}}}$$
One proof spine, one meter‑native landing. Units live in the bridge; proofs stay upstream—no tunable parameters.
Dimensionless results (unique cost; $\varphi$; $\ln\varphi$) are sorry‑free and parameter‑free.
Units are attached after proofs via a single functor; unit relabelings do not change $J$.
Time‑first vs length‑first landings must agree within combined uncertainty $u_{\rm comb}$.
Proofs are dimensionless. A single bridge assigns SI labels once; no domain‑specific rescaling.
Failure of the internal SI cross‑check, or a proof‑layer bug. Both are explicit and testable.
We expose a semantics‑preserving functor from proofs to units, with explicit uncertainty and no tuning.
Download the paper or source to review the Lean‑verified pipeline end‑to‑end.