From Proof to Measurement: A Reality Bridge with Falsifiable SI Landings
Recognition Science, Recognition Physics Institute, Austin, Texas, USA
Summary
This methods paper solves the crucial "last-mile" problem in theoretical physics: how to bridge dimensionless mathematical proofs to concrete SI measurements without introducing tunable parameters. Building on the Meta-Principle, it defines a Reality Bridge that maps Recognition Physics theorems to laboratory-testable statements with a single pass/fail criterion.
Abstract
This methods paper defines a proof–verified semantics that carries a strictly dimensionless derivation layer into SI displays without introducing tunable parameters. The inputs are: a unique symmetric multiplicative cost J(x)=½(x+x⁻¹)−1, a quantized tick with exact n·δ increments, an eight-phase minimal cycle in three-bit parity space, and the golden-ratio gap ln φ. We formalize a Reality Bridge that displays J additively as S/ℏ, assigns recognition tick and kinematic hop length, and provides two independent SI landings whose numerical agreement constitutes a single pass/fail criterion.
Key Contributions
- Reality Bridge Framework: Rigorous mapping from dimensionless Recognition Physics theorems to SI-native measurements
- Non-Circularity Proof: Unit relabelings factor out completely, preventing parameters from feeding back into proofs
- Two Independent SI Landings: Time-first and length-first routes that must agree within stated uncertainty
- Single Pass/Fail Test: One inequality governs success or failure with no thresholds or regression
- Complete Audit Trail: Reproducible computational pipeline with checksums and deterministic builds
Mathematical Framework
The Reality Bridge operates on four dimensionless inputs:
- Symmetric Cost Function: $J(x) = \frac{1}{2}(x + x^{-1}) - 1$ with log-axis form $J(e^t) = \cosh t - 1$
- Quantized Tick: Exact $n \cdot \delta$ increments on discrete ledger
- Eight-Tick Minimality: Complete cycle in three-bit parity space ($2^3 = 8$)
- Golden Ratio Gap: $\delta_{gap} = \ln \varphi$ where $\varphi = \frac{1+\sqrt{5}}{2}$
These map to SI displays via:
- Recognition Tick: $\tau_{rec} = \frac{2\pi}{8\ln\varphi} \tau_0$
- Kinematic Hop: $\lambda_{kin} = c \cdot \tau_{rec}$ with $c = \ell_0/\tau_0$
- Action Display: $S/\hbar = J$ (no offset, no scaling)
Experimental Method
The paper defines two independent experimental routes:
Route A: Time-First Landing
- Realize SI second using atomic clock standards
- Compute recognition tick: $\tau_{rec} = \frac{2\pi}{8\ln\varphi}\tau_0$
- Derive kinematic length: $\lambda_{kin} = c \cdot \tau_{rec}$
Route B: Length-First Landing
- Adopt conventional length anchor: $\lambda_{rec} = \sqrt{\frac{\hbar G}{c^3}}$
- Infer recognition tick: $\tau_{rec} = \lambda_{rec}/c$
- Verify consistency with Route A
Falsifiability Test
Both routes must agree within combined uncertainty:
where $u_{comb} = \sqrt{u(\lambda_{kin})^2 + u(\lambda_{rec})^2 - 2\rho u(\lambda_{kin})u(\lambda_{rec})}$
Implications
This work establishes Recognition Physics as the first theoretical framework with a completely parameter-free bridge to experimental reality. By proving non-circularity and providing two independent measurement routes, it creates an auditable path from pure mathematical theorems to falsifiable laboratory statements.
The Reality Bridge solves a fundamental problem in theoretical physics: how to connect abstract mathematical results to concrete experimental tests without introducing hidden adjustable parameters. Success validates the Recognition Physics framework; failure falsifies it—with no wiggle room for post-hoc adjustments.
Audit and Reproducibility
The paper includes complete computational reproducibility:
- Artifact Set: Source files, checksums, deterministic build instructions
- One-Command Replication: All computations reproducible without network access
- Uncertainty Accounting: Full propagation with correlation modeling
- Theorem Identifiers: Each claim has audit trail to mathematical statements
- No-Knob Policy: Mathematical proof that no parameters can be adjusted post-hoc