Record Selection from Detector Boundary

Claim: Each detector run latches into exactly one classical record. This is not a postulate — it follows from exclusivity, latching, and calibration conditions on the detector’s metastable boundary sectors.

The Structure

A detector has a macroscopic boundary with disjoint sectors R_a — think of regions on a photographic plate, or bins in a counter. The boundary also has a null sector R_∅ (nothing detected). The key conditions:

Exclusivity: sectors R_a are disjoint — the boundary cannot
register two outcomes simultaneously.

Latching: once the boundary enters sector R_a, it stays.
Metastability prevents erasure on experimental timescales.

Calibration: each sector R_a reliably correlates with the
corresponding pointer state. The detector is a faithful recorder.

Result: dephased mixture ρ_mix = Σ_a p_a ρ_a
→ one sector latches per run → one record label a*

What This Means

The “collapse” is not a dynamical event in Hilbert space. It is the macroscopic fact that a detector boundary, once triggered, sits in one metastable sector and does not spontaneously jump to another. The Born-rule weights p_a determine which sector is entered; the boundary structure guarantees that exactly one is entered per run.

Why this matters for Barbour’s programme: Julian’s “time capsule” idea says that a present configuration contains records of its own history without requiring a preceding temporal process. This derivation gives that idea precise physical content: the detector boundary IS the time capsule. Its metastable sectors are the records. Single-record formation is a boundary condition, not a mystery. The present shape of the detector contains exactly one record — because the boundary topology permits exactly one latch per run.

Open: Explicit construction for specific detector types (photographic emulsion, silicon pixel, bubble chamber). The logical framework is closed; the concrete realisations are the next step.