A light-substrate ontology for emergent spacetime
Fabric Theory 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 that substrate at rate c, establishing phase-coherence relationships
between points. Distance is redefined as a measure of phase coherence rather than a primitive
backdrop. See the GitHub repository.
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, modelled on the 3D XY model, where random phase differences lock into coherent proto-space.
- Fitness landscape — particles survive selection on beauty (coherence gradient), resonance (phase alignment) and topological stability, much as in evolution.
- Electron as ground state — the electron is modelled as the minimal stable trefoil knot of three crossings, the simplest topologically protected configuration.
Testable predictions
Fabric Theory commits to falsifiable predictions, including:
- Quantized mass ratios between leptons, derived from excitation spectra rather than fitted by hand.
- A finite electron core size of about 3.86 × 10−13 m, testable by high-energy scattering.
- Identical gravitational behaviour for antimatter and matter, testable at CERN's ALPHA-g experiment.
- Enhanced vacuum birefringence at Compton-scale field strengths, testable at high-intensity laser facilities.
- A knot-census prediction that the inverse fine structure constant, close to 137, counts stable topological sectors.
The framework documents its 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: operations as ontologically primary
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
On this view, constants such as φ, π and e are fixed points where iterative
processes stabilize. 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 — complexity classes such as P and NP are read as operations running with or against a structural gradient, verification flowing downhill and search flowing uphill.
A problem-solving framework
OpGeom functions as a classification system for unsolved problems, sorting them into frontier, bridge, stable-attractor and axiom-boundary types, and using eleven guiding principles to predict likely outcomes. It has been applied to the Riemann Hypothesis, the Collatz Conjecture, P versus NP and Navier–Stokes regularity.
Pedagogical implications
Because OpGeom treats operating as prior to being an object, its author argues it offers a more intuitive way to teach mathematics: students build understanding by carrying out operations and watching stability emerge, rather than memorizing definitions of objects that already exist.
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 = configuration ΔΦ = change, Δτ = step τ = threading depth c = coherence rate M = memory / mass M_active, M_latent = constraint states E = energy I = information S = entropy Ω = state count ψ = amplitude P = probability R = resonance Δφ = phase difference B = beauty C = coherence g = gravity k = constant Ψ = consciousness order parameter A = agency (unmeasurable)