qedler

QEDLER — Thesis

QEDLER (Quantum Events Driven Learner) is the physics-facing extension of PEDLER (Point Event-Driven Learner, November 2001). Same substrate, different target: PEDLER is the computational/cognitive kernel; QEDLER asks what physics that substrate is obliged to produce.

Canonical thesis

QEDLER states that spacetime, quantum amplitude and gauge structure are coarse-graining artefacts of a finite typed directed event hypergraph evolved by a deterministic local rewrite algebra, and delivers the axiomatisation, the reduction map from those axioms to the target theorems of established physics, and a status-labelled register of every arrow in that map — PROVED, ARCHITECTURE, CONJECTURE or OPEN.

Abstract

The programme postulates a single primitive: a typed directed event hypergraph H = (V, E, tau, ell) evolved by a finite deterministic rewrite algebra in which every valid rewrite fires and randomness is rejected. Twelve axioms (v0.1) fix the substrate. Against these, the work does not assert derivations of general relativity, quantum mechanics, gauge theory or cosmology. It constructs the dependency graph any such derivation must traverse, states each required intermediate result as a definition, lemma or conjecture, and labels its present status. Claims previously overstated are corrected in place: spectral metric reconstruction requires an injective reconstruction map under explicit hypotheses, because isospectral manifolds exist; and the hypergraph Laplacian is not unique, so the continuum limit is choice-dependent. The programme is falsifiable mathematically before it is falsifiable experimentally — a non-confluence counterexample, or a proof that no admissible Laplacian family converges, closes it without recourse to an instrument. Six quantitative empirical signatures are stated for the case that it survives.

What is novel here, stated without inflation

Not the claim that physics might be discrete and computational; that claim has a long literature (Regge calculus, causal sets, LQG, CDT, tensor networks, the Wolfram Physics Project). What is offered is:

  1. A determinism commitment. Every valid rewrite fires; branching is structural, not stochastic. Randomness is not a primitive anywhere in the axioms.
  2. Intrinsic causality in the primitive. Hyperedges are directed, e = (S, T), so the causal partial order is carried by the ontology rather than imposed on it.
  3. A reduction map with a status label on every arrow, and a mechanical gate that refuses to publish the repository if any arrow is unlabelled. The register is the deliverable; the derivations are the programme.
  4. A prior substrate. The event-first ontology was constructed for computation and cognition in 2001 (ternary 6-tuple Turing-machine extension, Indian Patent Application 3033/CHE/2011) and is applied to physics second, not devised for it.

Falsification clause

QEDLER v0.1 is refuted by any one of the following:

  1. A rewrite algebra satisfying A1–A3 admitting no confluence characterisation under which the history quotient is determinate.
  2. A proof that no hypergraph Laplacian family satisfying A8 admits spectral convergence to the Laplace–Beltrami operator on a smooth manifold under bounded degree and bounded curvature.
  3. A demonstration that the causal DAG of A2 admits Euclidean as well as Lorentzian coarse-grainings under identical stated hypotheses.
  4. Measured exact Lorentz invariance below the graph energy scale implied by A5.

Items 1–3 are mathematical. They can close the programme before any instrument is pointed at anything. That ordering is deliberate.

Exclusions — what this work does NOT claim

No derivation of the CKM or PMNS matrices. No computation of coupling constants. No Higgs mechanism. No proof of the Born rule. No proof of the Einstein field equations. No proof that the Lorentzian signature is uniquely forced. These are TARGET THEOREMS. Their status is recorded in STATUS.md, and nowhere in this repository is a target presented as a result.

Method disclosure

Produced under Verification-Gated Human–AI Co-Development (doi:10.5281/zenodo.21264248). Authorship, every ruling and every irreversible act (push, mint) belong to the human author; machine assistance is confined to drafting and mechanical verification under executable contract.

© 1993–2026 Abhishek Choudhary. All rights reserved.

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