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 |
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Critical Recognition Loading
Phase transitions occur at canonical critical recognition loadings |
Derived | THEOREM | 1 | 0 |
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Registry Predictions Proved
The RS prediction registry forms a single proved bundle |
Derived | THEOREM | 1 | 0 |