The Information Substrate Theory — Volume VII: Information as the Name of Differentiatedness, and the Known Measures as Projections of One Substrate

The Information Substrate Theory (IST) — Volume VII Information as the Name of Differentiatedness, and the Known Measures as Projections of One Substrate

This volume is the seventh and final part of the αLGQV / IST research programme. Where the prior six volumes build a physics — from a dark-sector-free cosmology and the local gravitation of the quantum vacuum, through extreme curvature and the confirmed-prediction record, to the complex-algebraic apparatus of ICAST, the topology of quantum chromodynamics and nuclei on ℝP³, and the cross-scale recognition method of Structural Persistence and Coherence Analysis — Volume VII supplies the lens that reads them: the information-theoretic ontology under which each scale of that Atlas is the materialization of a projection of one differentiated substrate.

The volume begins from a claim it argues rather than assumes: that absolute nothing is impossible, so something exists, and that what exists is necessarily differentiated. From this it draws its central definition — information is the name of differentiatedness, not a substance the world is made of. The axes along which the world is read (time, space, energy) and the laws stated in their terms are facets, projections of a substrate that is itself axis-free and carries no projection value. Everything turns on one distinction, between the substrate and a projection of it, and one discipline: never mistake a projection for the substrate.

Seventeen articles in three parts develop the frame. Part I (Foundations) establishes the substrate, distinguishes it from projection, proves a projection theorem by which the known information measures descend from it, and draws the apophatic categorial boundary. Part II (The Projections) classifies the known theories of information as projections along six axes — channel (Shannon), description (Kolmogorov), regularity (effective complexity), macrostate (thermodynamic entropy), cost (Landauer), and receiver (Bateson) — relates them by inter-axis morphisms, and anchors each to a definite scale of the prior volumes. Part III (The Bridge) follows the central asymmetry — physical projection loses irreversibly, but a model-building subsystem recovers projectable structure by inference — to the arrow of time, the relocation of the simulation into the model, the incompleteness of measurement as a theorem of projective access, and the two boundaries that bound a subsystem's reach around a rich, knowable interior.

A family of standing puzzles — whether the universe computes, whether the world is made of information, whether it is a simulation, what time's arrow is, why measurement cannot be complete — is shown to be one confusion (a projection taken for the substrate) and dissolved together. The frame is an ontology and a discipline, conservative about physics: it adds no equation and affirms physical theory entirely, changing the status of its quantities rather than their content. It is not a new physics, not a speculative metaphysics, and neither idealism nor mysticism. Its central open problem, posed and left open as a conjecture, is the morphism geometry — whether one diagram of the axes and their morphisms carries both the completeness of the classification and the incompleteness floor.

• Title: The Information Substrate Theory — Volume VII: Information as the Name of Differentiatedness, and the Known Measures as Projections of One Substrate
• Authors: Kriger, Boris — Information Physics Institute; Institute of Integrative and Interdisciplinary Research, Toronto (ORCID 0009-0001-0034-2903)
• Resource type: Publication → Book
• Keywords: information substrate; substrate and projection; differentiation; information theory; Shannon; Kolmogorov complexity; effective complexity; thermodynamic entropy; Landauer's principle; arrow of time; simulation hypothesis; incompleteness of measurement; apophatic boundary; foundations of physics
• Related identifiers: is part of the αLGQV / IST programme; continues Vol. VI (doi:10.5281/zenodo.20455316)