Intersectional Singularity Interpretation (ISI): A Conjectural Geometric-Information Framework for Physical Reality

We propose the Informational Singularity Intersection (ISI) framework — a conjectural geometric-information theory in which elementary particles are intersections of singular sub-manifolds in a multi-dimensional property space, and every fundamental physical constant is a projection singularity: infinite in its native dimensional metric, finite only as seen from our observational manifold. Version 3. 7 introduces three major advances over v2. 7: (1) Three types of singularity (S1/S2/S3). ISI v3. 5 formalises three ontologically distinct singularity types: S1 (iterative singularity — born from curvature competition, iterates toward the 1-attractor), S2 (abstractum — same-space merger of S1s via Kuramoto-type synchronisation), and S3 (fractal singularity — inter-dimensional intersection, leaving projections in each participating space). (2) Curvature competition and the unification of the four forces (v3. 7). The physical mechanism of S1 formation is identified: where curvature closes topologically (∮κ dp = 2π), the first S1 forms — timeless and inevitable, providing the physical basis for the Agenesis axiom. Gravity is reinterpreted as an S3-intersection of the mass-dimension and space-dimension singularities — not a force but a projection geometry. All four fundamental forces are S3-intersections of different dimension-pairs, explaining why the Standard Model's 19 free parameters cannot be derived from first principles (IPA-8 Indescribability Postulate). (3) The 1-attractor: proved and explained (v3. 7). K5 Theorem: F (x) = x^α has unique stable fixed point x* = 1 (proved). Why 1 and not 0: ISI is multiplicative (axiom A6: Ξ·S = εₐ·εb), and 1 is the multiplicative identity; 0 is excluded by both the information conservation law and the Gödel-necessity axiom A2. Unreachability proved: xₙ = x₀^ (φ^ (−n) ) → 1 but ≠ 1 for all finite n. New falsifiable prediction P-ISI-8: Gravitational waveforms from LIGO/Virgo/KAGRA must show ISI-structured sub-Planck-scale signatures systematically deviating from pure GR templates at high-SNR binary merger events. Experimental confirmations integrated: Barontini et al. (Birmingham, 2024) — time emerges from quantum interaction (confirms A4: time as iteration). Kuramoto synchronisation — cardiac S1→S2 transition directly observable in embryonic heart cells. This upload contains two documents: Document 1 (ISI Core Hypothesis v3. 7): Formal definitions, ten axioms (A0–Aₐbs + IPA-10), S1/S2/S3 taxonomy, curvature-competition gravity model, K5 theorem, and six testable predictions with explicit falsification criteria. Document 2 (ISI Extended Framework v2. 7): Speculative extensions — biological interpretations, cosmogony, simulation equivalence, HFL research platform. Status: Pre-review conjectural hypothesis. Document 2 content is explicitly speculative and not part of the core physics claim.