Claim Summary · Conditionality Footer

Claim Summary

1 (ℏ identification). DERIVATION. ℏ derived as the scale factor of the minimum record. Form forced by Stone’s theorem; identification forced by uniqueness of α, uniqueness of minimum action, absence of dimensionless parameters, and indivisibility of ε (1.3). KS-Q.8 CLOSED, conditional on KS-L.4.

2 (Position-momentum uncertainty). DERIVATION. [x̂, p̂] = iℏ from the translation group on the derived manifold. ΔxΔp ≥ ℏ/2 from Robertson-Schrödinger. Axiom-first throughout. KS-L.2.

3 (Energy-time uncertainty). DERIVATION. Mandelstam-Tamm operational energy-time bound: ΔE·Δt_A ≥ ℏ/2, where Δt_A is the characteristic time for observable A to change by one standard deviation. Derived from Axiom R + Stone’s theorem. KS-L.3.

4 (Structural reading). INTERPRETATION. The pre-state algebra reads the same theorem along space and along time.

5 (Structural meaning). NON-LOAD-BEARING. The uncertainty principle as the resolution of the now.

Conditionality Footer

Dependencies

AP20 4 (axioms; fenced KS-P.1 / KS-P.2) + AP10 4 (Lorentzian signature; fenced KS-D.4). AP09 3.2 (Hilbert space). AP09 7.3 (Schrödinger equation). AP10 (N = 3). AP20 5 (AS = manifold). AP06 4 (Landauer bound, referenced).

Dependents

All AP results requiring the uncertainty bound.

AP14 (The Correction): Planck-scale commutation corrections.

AP15 (Connection): the photon’s wavelength bound.

Future treatments of decoherence and measurement at the Planck scale.

Kill switches closed

KS-Q.8 (ℏ identification): CLOSED conditional on KS-L.4.

Kill switches live

KS-L.2 (Commutation at Planck scale).

KS-L.3 (Energy-time via unitarity).

KS-L.4 (Dimensionless parameter in ℏ forcing) — strictly smaller exposure than the closed KS-Q.8.

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the420code.org

Series The 420 Code

Catalogue Ø Artist’s Proofs

Proof Number AP12

Title The Limit

Subtitle Uncertainty

Medium Physics

Artist G

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