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
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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...
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Foundational THEOREM
phi forcing complete
**COMPLETE PHI FORCING THEOREM**.
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Foundational THEOREM
The Golden Ratio as a Forced Self-Similar Scale
**THEOREM**: The unique positive closed ratio is φ.
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Derived MODEL
f gap
Anchored in `Constants.GapWeight`.
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Derived THEOREM
tau0 Calibrator from Constants
tau0 is calibrated against CODATA constants self-consistently.
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Derived THEOREM
Recognition Coupling Bridge
Recognition coupling encodes the bridge between micro and macro scales.
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Applied HYPOTHESIS
Sterile Neutrino Exclusion
Eg parametric exclusion of an eV-scale sterile neutrino.
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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`.
Applied
Engineering predictions involving phi-spacing, recognition bandwidth, and device-scale falsifiers.
| Derivation | Tier | Status | Anchors | Predictions |
|---|---|---|---|---|
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Phi-Ladder Plasmonic Modes
Plasmon resonances align with the phi-ladder |
Applied | HYPOTHESIS | 1 | 0 |
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Phi-Spaced Pulses Beat Uniform Pulses
Phi-spaced excitation produces a measurable advantage over uniform spacing |
Applied | HYPOTHESIS | 1 | 0 |
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Photonic Metamaterial from Phi
Phi-spaced photonic crystals deliver the predicted bandgaps |
Applied | HYPOTHESIS | 1 | 0 |
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Planet Strata From RS
Planetary layering follows RS recognition octaves |
Applied | HYPOTHESIS | 1 | 0 |
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Robotics Control from RS
Information-limited control gains emerge for RS-aware robotic systems |
Applied | MODEL | 1 | 0 |
Fundamental constants
Dimensionless constants and SI bridge quantities forced by J-cost, phi, and the RS unit system.
| Derivation | Tier | Status | Anchors | Predictions |
|---|---|---|---|---|
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Explicit CODATA Handles in the Canon
The canon ships concrete definitions of c, hbar, G as CODATA constants for cross-checks |
Applied | MODEL | 6 | 0 |
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External Anchors: CODATA Bridges
Empirical SI/CODATA anchors that the RS predictions are compared against |
Applied | MODEL | 4 | 0 |
Cosmology
Large-scale observables including Omega_Lambda, H0, CMB structure, baryogenesis, and inflation.
| Derivation | Tier | Status | Anchors | Predictions |
|---|---|---|---|---|
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Stellar Evolution Tracks
Main sequence to white-dwarf transitions anchored to RS phi-ladder |
Applied | HYPOTHESIS | 1 | 0 |
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Tensor-to-Scalar Ratio Bound
RS predicts r within the BICEP/Keck-respecting band |
Applied | HYPOTHESIS | 1 | 0 |
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XENON Detector Null Prediction
RS predicts a null signal in XENON-style direct detection experiments |
Applied | HYPOTHESIS | 2 | 0 |
Gravity
Spacetime, curvature, black holes, gravitational propagation, and Regge-limit derivations.
| Derivation | Tier | Status | Anchors | Predictions |
|---|---|---|---|---|
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8-Tick Resonance in Gravity
Gravitational waves exhibit an 8-tick resonance signature |
Applied | HYPOTHESIS | 1 | 0 |
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Acoustic Phase Levitation
Engineered phi-locked acoustic field induces measurable phase levitation |
Applied | HYPOTHESIS | 1 | 0 |
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Black-Hole Echoes from RS Bounce
Predicted echo amplitudes in post-merger gravitational wave data |
Applied | HYPOTHESIS | 4 | 0 |
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Gravitational Wave Amplitudes
Predicted GW amplitudes for BH/NS mergers anchored to RS energy budget |
Applied | HYPOTHESIS | 2 | 0 |
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Rotation Curves Without Dark Matter
Galactic rotation curves emerge from RS ILG kernel without invoking dark matter halos |
Applied | HYPOTHESIS | 3 | 0 |
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SPARC Galaxy Rotation Falsifier
RS predictions for ~150 SPARC galaxies fall inside a falsifier band |
Applied | HYPOTHESIS | 1 | 0 |
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Spin Foam Realization
RS realization of loop quantum gravity spin foams |
Applied | MODEL | 1 | 0 |
Mathematics & foundations
The formal forcing chain: logic, cost, phi, discreteness, dimension, arithmetic.
| Derivation | Tier | Status | Anchors | Predictions |
|---|---|---|---|---|
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Dimensional-Quantity Type System
Definitions for L, T, M dimensions and dimensioned positive quantities |
Applied | MODEL | 3 | 0 |
Particle physics
Standard-Model masses, gauge couplings, mixing matrices, and representation counts.
| Derivation | Tier | Status | Anchors | Predictions |
|---|---|---|---|---|
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Sterile Neutrino Exclusion
Eg parametric exclusion of an eV-scale sterile neutrino |
Applied | HYPOTHESIS | 1 | 0 |
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String Theory from J-Cost
If strings exist, RS forces specific compactification structure |
Applied | MODEL | 3 | 0 |
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Supersymmetry is Spontaneously Broken at the RS Scale
RS predicts a specific SUSY breaking pattern; sparticle masses lie above the EW scale |
Applied | MODEL | 1 | 0 |
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W-Mass Anomaly Structure
RS prediction for the W-mass anomaly relative to Standard-Model expectations |
Applied | HYPOTHESIS | 1 | 0 |
Quantum mechanics
Quantum mechanics as the small-tick limit of recognition dynamics.
| Derivation | Tier | Status | Anchors | Predictions |
|---|---|---|---|---|
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Superconducting Qubit Coherence
Predicted coherence times for transmon and fluxonium qubits |
Applied | HYPOTHESIS | 3 | 0 |