Null-Boundary Qubit Ledgers and Limiting Mixed Hodge Structures: A Finite, Observer-Centred Architecture for Spacetime Bookkeeping

Motivated by black-hole thermodynamics and entanglement-based derivations of gravitational dynamics, we propose a finite, observer-local bookkeeping framework in which the primitive interface is a null boundary (light-sheet) equipped with spacelike cuts. A finite measurement-and-control protocol on such a patch carries three dimensionless ledgers in common entropy units: a geometric capacity $\X\simeq A/4G$, a modular ledger $M=\langle K\rangle$ defined relative to a chosen accessible algebra and faithful reference state, and a classical record ledger $\Nc$ counting logically irreversible updates of a finite register. The basic postulate is an event-wise balance law,$\De\X=-\De\langle K\rangle+\De\Nc$ (equivalently $\De\X=-\De M+\De\Nc$),where the modular increment is evaluated with the pre-event modular generator held fixed, as in entanglement first-law comparisons. Operational finiteness is built in: any fixed protocol admits an equivalent realization on a finite-dimensional Hilbert space, and hence an $N$-qubit ``pixel'' model coupled to a finite classical register. To separate robust protocol type data from update/event data, we also describe a cohomological encoding in which mixed Hodge graded dimensions label capacities while controlled degenerations furnish LMHS monodromy and extension invariants that can serve as canonical event labels. Compatibility of observer-local datasets across overlaps can then be implemented by explicit gluing in a colimit construction. Dynamics and continuum limits are left as model-dependent tasks.