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Finite Spacetime Archives

Abstract

Finite archived events retain their exact attributes and causal order beside a separate current region.

Definition 1.1 (The exact archived event domain).

Lean statement: D5/S0/History/Spacetime/ArchiveCarrier.Archive

Formalization. D5/S0/History/Spacetime/ArchiveCarrier.Archive (✓ std3).

Source. Repository-derived.

Commentary.

The finite archive contains HF event names. Time, finite-dimensional integer position, sign and source tree are functions on precisely those events. A strict transitive causal relation must increase time. The dimension is arbitrary and includes three.

Definition 1.2 (A context and its selection).

Lean statement: D5/S0/History/Spacetime/ArchiveCarrier.Rich

Formalization. D5/S0/History/Spacetime/ArchiveCarrier.Rich (✓ std3).

Source. Repository-derived.

Commentary.

A context carries an archive and a finite current region inside it; a selection is any subset of that region. Empty archives, regions and selections are permitted. Archive embeddings preserve attributes and reflect causal order without constraining current regions. Context embeddings and generated operations belong to later work.

References