Derivations from first principles
Every entry below begins from the Recognition Science primitives (ledger, tick, voxel, cost composition law) and ends at a measurable consequence. Each step is a clickable Lean theorem; every empirical claim carries a named falsifier. 222 published of 246 tracked.
Recently published
-
Foundational THEOREM
Law of Logic Forces the Canonical Cost
The Law of Logic cost theorem: the canonical reciprocal cost J(x) = 1/2(x + x^-1) - 1 is the unique continuous positive-ratio cost satisfying reciprocity, normalization, the RCL...
-
Foundational THEOREM
phi forcing complete
**COMPLETE PHI FORCING THEOREM**.
-
Foundational THEOREM
The Golden Ratio as a Forced Self-Similar Scale
**THEOREM**: The unique positive closed ratio is φ.
-
Derived MODEL
f gap
Anchored in `Constants.GapWeight`.
-
Derived THEOREM
tau0 Calibrator from Constants
tau0 is calibrated against CODATA constants self-consistently.
-
Derived THEOREM
Recognition Coupling Bridge
Recognition coupling encodes the bridge between micro and macro scales.
-
Applied HYPOTHESIS
Sterile Neutrino Exclusion
Eg parametric exclusion of an eV-scale sterile neutrino.
-
Foundational THEOREM
Count Law at D=3
Counting laws on the 3-cube reproduce the standard combinatorial bounds. If `CountLaw` holds for some encoding, then the family has cardinality exactly `2 ^ D - 1`.
Quantum mechanics
Quantum mechanics as the small-tick limit of recognition dynamics.
| Derivation | Tier | Status | Anchors | Predictions |
|---|---|---|---|---|
|
Dirac Equation from RS
The Dirac equation arises as the RS spin-1/2 recognition kernel |
Foundational | THEOREM | 3 | 0 |
|
Schroedinger Equation Emerges from RS
i hbar partial_t psi = H psi appears as the small-tick limit of recognition dynamics |
Foundational | THEOREM | 4 | 0 |
|
Wavefunction Collapse as Recognition
Measurement-induced collapse is the RS recognition event in the small-tick limit |
Foundational | THEOREM | 2 | 0 |