A Light-Substrate Ontology for Emergent Spacetime

Fabric Theory (formally, A Light-Substrate Ontology) is a speculative but mathematically structured framework proposing that spacetime, particles, and forces emerge from threading patterns in a pre-geometric substrate. Light threads through this substrate at rate c, establishing phase-coherence relationships between points. Distance is redefined as a measure of phase coherence rather than a primitive backdrop.

Core Idea: Space Is a Record, Not a Container

In standard physics, space exists first and light moves through it. Fabric Theory inverts this: light threads first, and space crystallizes afterward as a record of that threading history. Particles are stable, knotted topological defects (similar to Hopfions and trefoil vortices) in the threading field itself.

Key Mechanisms

• Threading depth — accumulated phase relationships that stand in for time.
• Phase-locking transition — a Kosterlitz-Thouless-like transition (modeled on the 3D XY model) where random phase differences lock into coherent proto-space.
• Fitness landscape — particles survive selection based on beauty (coherence gradient), resonance (phase alignment), and topological stability, much like evolution.
• Electron as ground state — the electron is modeled as the minimal stable trefoil knot (3 crossings), the simplest topologically protected configuration.

Testable Predictions

Fabric Theory commits to falsifiable predictions, including:

1. Quantized mass ratios between leptons, derived from excitation spectra rather than fit by hand.
2. A finite electron core size (~3.86 × 10^-13 m), testable via high-energy scattering.
3. Identical gravitational behavior for antimatter and matter, testable at CERN's ALPHA-g experiment.
4. Enhanced vacuum birefringence at Compton-scale field strengths, testable at high-intensity laser facilities.
5. A "knot census" prediction that the fine structure constant's inverse (≈137) corresponds to a count of stable topological sectors.

The framework documents open gaps, including unfinished numerical work on Hopfion formation and quark confinement, and offers a computational roadmap for physicists, numerical topologists, and experimentalists.

Operational Geometry (OpGeom): Operations as Ontologically Primary

OpGeom Foundations

Operational Geometry proposes a foundational shift in mathematics: operations come first, and mathematical objects (numbers, constants, structures) emerge as stable attractors of iterative processes. Rather than starting with static objects and defining operations on them, OpGeom starts with operations and treats objects as what remains stable under repeated application.

Core Idea: Constants Are Fixed Points, Not Given Objects

Under this view, constants such as φ (the golden ratio), π, and e are fixed points where iterative processes stabilize. For example, φ solves x = 1 + 1/x, arising naturally where a specific operation loops back on itself.

Key Mechanisms

• Threading aggregate — operations compose by carrying context from prior operations, creating nested coherence that stabilizes at fixed points.
• Intrinsic Operational Gradient Theorem (IOGT) — complexity classes like P and NP are explained as operations running with or against a structural gradient, with verification flowing "downhill" and search/discovery flowing "uphill."

A Problem-Solving Framework

OpGeom functions as a classification system for unsolved mathematical problems, sorting them into four types (frontier, bridge, stable-attractor, and axiom-boundary problems) and using eleven guiding principles to predict likely outcomes. The framework has been applied to the Riemann Hypothesis, Collatz Conjecture, P vs NP, and Navier–Stokes regularity.

Pedagogical Implications

Because OpGeom treats action (operating) as prior to identity (being an object), its author argues it offers a more intuitive way to teach mathematics: students build understanding by doing operations and watching stability emerge, rather than memorizing definitions of pre-existing objects.

Both frameworks are published as open, machine-readable research templates under CC-BY-4.0 license, with explicit falsification criteria, documented research gaps, and invitations for independent verification by mathematicians, physicists, and numerical researchers.

THE KEY

FABRIC FOUNDATION:
Reality is light threading itself into coherent geometry through agency.
All phenomena are expressions of the same threading dynamics guided by choice.

CORE EQUATIONS:
τ = t
c = ΔΦ/Δτ (local light threading rate)
c_path = ΔΦ/Δτ * f(∇M) (path-dependent threading)
P = |ψ|² / Σ|ψ|² (quantum decision probability)
P → f(P,A) (probability influenced by agency)
dΨ/dτ = f(P, A, c) (consciousness rate of change)
Ψ = R(Ψ) (consciousness as recursive threading)
R(Ψ) = Ψ + g(P, A, c, τ) (recursive consciousness function)
M = M_active + M_latent (total memory)
E = Mc² (energy as memory density)
g = k∇M (gravity flows toward memory density)
δ(M_latent → M_active) (memory state transformation)
M_latent + A → M_active (agency converts latent to active memory)
∂C/∂τ = f(B,R,M_active,M_latent,A) (coherence evolution)
B = ∇C (beauty as coherence gradient)
R = Σ cos(Δφ) (resonance)
S = -∂C/∂τ (entropy)
Variables:
Φ=config, τ=threading depth, ΔΦ=change, Δτ=step, c=coherence rate, M=memory/mass, M_active/latent=constraint states, E=energy, I=info, S=entropy, Ω=state count, ψ=amp, P=prob, R=resonance, Δφ=phase diff, B=beauty, C=coherence, g=gravity, k=const, Ψ=consciousness order parameter, A=agency (unmeasurable)