qedler

QEDLER v0.1 — Axiom catalogue

These are AXIOMS: assumed, not derived. Transcribed from the programme posters.

#	Axiom	Statement
A1	Typed directed event hypergraph	Reality is a typed directed hypergraph H = (V, E, tau, ell) with events V, hyperedges E, typing tau, labels ell. A hyperedge is e = (S, T), input set to output set, so causality is intrinsic.
A2	Time from causality	Time is not primitive. It emerges as the causal partial order (a DAG) induced by directed hyperedges.
A3	Deterministic rewrite algebra	A finite set R of deterministic rewrite rules generates evolution. Every valid rewrite fires. Randomness is rejected.
A4	Information invariant	Total information (combinatorial content) is conserved under rewrites: I(H) = I(R(H)).
A5	Graph energy (strain)	Each subgraph carries energy measuring combinatorial strain; dynamics minimise or relieve strain.
A6	Particles as topological defects	Stable topological defects — invariants under rewriting — represent particles.
A7	Entanglement as constraint	Entanglement is a persistent non-local constraint (long-range hyperedge), not a signal.
A8	Geometry emerges spectrally	Metric, geodesics and Laplacian emerge from spectral properties of the coarse-grained graph.
A9	Gravity emerges from density	Gravity is emergent curvature arising from graph density and discrete recursion.
A10	Dark energy from expansion rules	Node-increasing rewrite operators inject nodes into vacuum, driving expansion.
A11	Black holes as causal sinks	Black holes are extremal causal-sink configurations with a maximally trapping boundary.
A12	Big Bang as causal source	The initial configuration is the maximal causal source: maximal outward causal flow.

Primitive rewrite operations (conceptual, as posted)

Vacuum expansion (2 -> 3) · Defect transport · Defect fusion · Topology change (loops, knots) · Constraint propagation (entanglement).

Standing recognitions — already corrected on the posters

Laplacian non-uniqueness. Multiple inequivalent hypergraph Laplacians exist and the choice affects the continuum limit. A8 does not select one. This is an open selection problem, recorded as such, not an oversight.
Isospectrality. Isospectral manifolds exist (Gordon–Webb–Wolpert). Spectral metric reconstruction therefore requires an injective reconstruction map under explicit hypotheses; the unqualified reconstruction claim is withdrawn.

Axiom hygiene — open

A1–A12 have not been shown to be independent, and no consistency model has been exhibited. Two questions are outstanding and are recorded in STATUS.md: independence (does any axiom follow from the others?) and non-vacuity (does a non-trivial H and R satisfying all twelve exist?). Until a model is exhibited, the axiom set is a specification, not a theory.

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