Quantized Information Quantum Theory — Holographic

One wave function, one world.

A bounded spacetime region has only finite operational information capacity — a postulate motivated by gravitational entropy bounds. QIQT-H conjectures that this forbids it from instantiating two macroscopically distinct records at once, so after decoherence the per-run actual content is single-record, with no collapse term added to the dynamics. Whether that conjecture holds is the open crux.

A research program, not a finished theory — conditional, Born open Machine-verified in Lean 4 / Mathlib · no sorry · reproducible

The argument in five links

The whole thesis is one chain. Two links are postulates, one is the machine-verified mathematical substrate, one is a conditional theorem, and one is open. Each is labelled honestly.

What is proven, what is open

Honesty is the point. The Lean development verifies the standard modular and relative-entropy calculus underlying the regional cost χR\chi_R, not the holographic axiom, not the central conjecture, not the Born rule.

ComponentStatus
Araki relative entropy = Umegaki (finite case) machine-checked
Bounded Tomita–Takesaki: JJ, JRJ=2RJRJ=2-R, Δit\Delta^{it}, strong continuity machine-checked
One-particle CGP relative entropy + positivity S(ξ)0S(\xi)\ge 0 machine-checked
Free-field modular flow Γ(Δit)\Gamma(\Delta^{it}), σt(W(u))=W(Δitu)\sigma_t(W(u))=W(\Delta^{it}u) machine-checked
Coherent-state relative modular operator, Connes cocycle, entropy reduction machine-checked
Holographic capacity axiom (FQ): SrenQRS_{\rm ren}\le Q_R postulated
Macroscopic Definiteness Conjecture (H2) open · the crux
Born statistics from typicality open

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