τ-Heisenberg Uncertainty

The τ-Heisenberg uncertainty inequality is a τ-categorical theorem (`IV.T102`) stating that for every ontic defect bundle and every refinement level n, Δx · Δp ≥ ℏ_τ / 2. It is not a measurement-disturbance relation but a structural consequence of incompatible address constraints in τ-NF and the compactness of the dual lattice Ẑ.

Categorical invariant. Δx_n · Δp_n ≥ ℏ_τ / 2 on every ontic defect bundle d at every refinement level n; saturated by σ-states centered on the crossing point of L.

Primary registry anchor: IV.T102

Supporting items: IV.D14, IV.D11

1. I.K0 — Universe Postulate
2. IV.D11 — Physical Quantity Template — paired position / momentum invariants
3. IV.D14 — Uncertainty Product — incompatible address constraints in τ-NF
4. IV.T102 — τ-Heisenberg inequality — bound is attained on σ-saturated states (compactness of Ẑ)

Lean modules referenced: TauLib.BookIV.Arena.ActorsDynamics

Calibration anchor: PG-P01-neutron

Calibration chain:

1. ℏ_τ from ι_τ-chain
2. position-momentum duality at τ-natural unit scale
3. SI bridge via m_n anchor for length × momentum units

Manuscript reference: manuscript-sources/book-04/part01/ch07-beta-decay-rosetta.tex

Status: Formalized

Module: TauLib.BookIV.Arena.ActorsDynamics

Lean kind: theorem

Lean symbol: Tau.BookIV.Arena.TauheisenbergInequality

Related glossary entries

• PG-L01-tau-schrodinger τ-Schrödinger Equation
• PG-Q01-mass Mass
• PG-U01-tau-second τ-Second