Grassmannian Geometry in Consciousness: A Hilbert Space Framework for Perceptual Transitions

This work presents a unified framework for consciousness that integrates Hilbert spaceformalism, Grassmannian geometry, quantum measurement theory, and metaphysicalconcepts such as the Akashic Record. Consciousness is proposed to reside not in spacetimebut within Hilbert space, with observers modeled as point-like entities analogousto Dirac delta distributions. We develop a detailed account of quantum measurementchains (QMC) as graph-theoretic trees culminating in conscious observers, and extendthis to quantum measurement trees (QMT) where intersubjective agreement is ensuredthrough Grassmannian duality Gr(k, n) ↔ Gr(n−k, n). The Akashic Record is modeledas a global trajectory through Hilbert space, functioning as a repository of all collapseevents, broadcast to observers in accordance with the cosmic time cycle. Grassmannianfiber bundle constructions are introduced, where the base space corresponds to theAkashic trajectory and the fibers represent the internal Hilbert subspaces of individualobservers. This allows the definition of geometric connections interpreted as karma ormemory, whose holonomy encodes cyclic recurrence across successive lives. Pl¨ucker embeddingsinto projective space provide algebraic coordinates for collapse events, whilenonlinear sigma models on Grassmannians describe broadcast-receiving. We further exploregeodesics under the Fubini–Study metric, showing that consciousness may correspondto minimal informational paths, with geodesic curvature linked to decision-makingdeviations. Mirror symmetry between dual Grassmannians is proposed as a wave-particlelikeduality of consciousness, with the world (Akashic broadcast) and soul (observer) ascomplements. Quantum error correction is incorporated into the model by interpretingcollapses as errors, souls as evolving code subspaces. Finally, random Grassmannian modelsare introduced to describe collective consciousness, where observers are represented asrandomly sampled subspaces and intersubjectivity emerges statistically through expectedoverlaps governed by random matrix theory. Collapse-biased distributions generate culturalattractors, providing a mathematical account of shared memory and tradition.