# Spacetime Discreteness Aiwiki — Purpose

## Threat model (verbatim)

> *Demonstrate that a quantum gravity program — at its 2024–2026 frontier formulation — makes a quantitative, falsifiable prediction of spacetime discreteness that (a) survives current observational bounds (Lorentz invariance, IceCube/Fermi/HESS/MAGIC/H.E.S.S. high-energy thresholds, gravitational-wave dispersion, cosmological constant, neutron interferometry), (b) is distinguishable from continuum effective-field-theory alternatives, and (c) carries an experimental signature accessible to the current generation of detectors (CTA, IceCube-Gen2, LISA, ELT) within the next decade.*

Equivalent restatements per program:

- **Loop Quantum Gravity (LQG, full theory)**: discrete area/volume operators with eigenvalue spacing $\sim \ell_P^2$, in the *physical* Hilbert space (not just kinematical), with an observable consequence that survives semiclassical limit + matter coupling
- **Spinfoam covariant LQG (EPRL/FK lineage)**: amplitude with discrete-area input that produces a falsifiable continuum-limit prediction, not just a regulator artifact
- **Causal Dynamical Triangulations (CDT)**: dimensional flow $d_s(E) \to 2$ at small scales as a robust, observation-distinguishable signature
- **Causal Set Theory (Sorkin lineage)**: discrete causal set with sprinkling density $\rho \sim \ell_P^{-4}$ producing a signed-non-locality signature in matter propagation distinguishable from continuum
- **Asymptotic Safety / functional RG**: UV fixed point with effective dimension reduction or graviton anomalous dimension producing observable consequences in graviton-mediated processes
- **Group Field Theory (GFT)**: condensate cosmology with discrete pre-geometric building blocks producing a signature in primordial gravitational-wave spectrum
- **Effective EFT-cutoff approaches** (string-derived effective field, Padmanabhan, Verlinde-emergent gravity): cutoff-induced spacetime granularity that makes a non-trivial prediction beyond standard EFT power-counting

This excludes:

- **Pre-2024 historical anchor papers** that established the theory but make no 2024–2026-relevant prediction (covered by meta-cost M1)
- **Pure mathematical structure papers** that prove a property of the formalism without a measurable consequence (M2)
- **Phenomenological models that merely *fit* an effective discreteness scale** without deriving it from a closed quantum gravity program (M3)
- **Observable-level papers (e.g. Lorentz-violation bounds) that don't engage any specific quantum gravity program** — these go to the *watchlist* (M4)
- **Numerical simulations within a single program that don't make a predictive claim about observables** (M5)
- **Programs that require resource-unbounded simulations** (e.g., $> 10^{12}$ DOF Monte Carlo simulations infeasible on current hardware, M6) — same shape as factorization-Aiwiki M5

## Why this scope

The mass of "spacetime discreteness" claims in the 2024–2026 corpus engages one or more closure mechanisms — what does the proposed program have to *pay for* to have its discreteness claim be physically meaningful (not regulator-artifact) AND observable (not just formal)? The aiwiki maps every claim to its closure mechanism and surfaces the empty space — the claim that survives all closures and produces a genuinely falsifiable prediction.

The empty-space hypothesis predicts: **the empty space is currently empty** through 2026 — every program either pays a meta-cost (background-dependence, Lorentz-violation bound, regulator-artifact) or fails one of the bills (matter-coupling consistency, semiclassical limit, observation-distinguishability).

This is the **first physics aiwiki** under the Project 42 umbrella. It mirrors the factorization aiwiki in sharpness: small field, technically dense, closure-pattern-pure. The boundary against "string theory effective field" papers is deliberately drawn to scope out the entire string program *unless* the claimed discreteness is derived non-perturbatively from closed-string dynamics.

## Cross-aiwiki adjacency

- **factorization** aiwiki (locked v1.16): cousin in *closure-pattern purity*. Both have a small field with strong empirical anchors (factorization: $L_N(1/3, 1.923)$; spacetime: Planck length, Lorentz-violation bounds tied since ~2010s). Both predict empty signature constructions.
- **quantum_advantage** aiwiki: distant cousin via "quantum vs classical resource accounting." A quantum-gravity program that requires $> 10^{12}$ qubits to simulate the discreteness claim pays M6 here AND would trigger Bill_8 there if the simulation itself were the experiment.
- **mech_interp** aiwiki: structurally similar — both ask "when does an internal property of the formalism translate to a measurable consequence?" Mech interp's "monosemantic feature" closure-pattern is analogous to spacetime discreteness's "matter coupling consistency" requirement.

## Q-Day analog (policy-divergence panel)

This aiwiki has weak policy-timeline divergence (criterion 5 of 5 from `_methodology.md` — the lowest-scoring). The divergence is mostly *funding allocation*:

- **NSF / DOE Quantum Gravity Initiative** funding cycles (2024–2026 awards)
- **ESA / NASA observational constraints program** (LISA, CTA timelines vs theory predictions)
- **JSPS, BMBF, INFN national funding** for individual programs
- **EU FET / EIC quantum-gravity-adjacent grants**

A trigger in this aiwiki — a published clean prediction surviving all closures — would shift funding and detector-design priorities for the next decade. Not a federal-policy lever like factorization's NIST PQC migration, but a measurable scientific-funding lever.

## Out of scope (not in this aiwiki)

- Pure mathematical noncommutative geometry (Connes lineage) without a quantum-gravity prediction
- Pure cosmology / inflation papers without a quantum-gravity program backing
- Generic Lorentz-violation phenomenology (covered as M4 watch-list)
- Effective field theory of gravitons in the perturbative regime (covered by string EFT carve-out)
- Black hole microstate counting papers without a discreteness claim
- AdS/CFT correspondence papers without an explicit discreteness prediction in the bulk
- "Quantum graphity" / "emergent geometry" toy models without a continuum-limit claim
- Spin-network refinement / coarse-graining papers without an observable consequence

## In scope (this aiwiki's corpus)

- arXiv `gr-qc` 2024–2026 with keywords: `loop quantum gravity`, `spinfoam`, `causal dynamical triangulation`, `causal set`, `asymptotic safety`, `group field theory`, `discrete spacetime`, `Planck-scale discreteness`, `dimensional flow`, `non-locality`
- arXiv `hep-th` 2024–2026 same keywords + `asymptotic safety`, `Padmanabhan`, `holographic discreteness`
- IOP `Classical and Quantum Gravity` 2024–2026 (CQG canonical venue)
- AIP `Journal of Mathematical Physics` (formal LQG/CDT/causal-set papers)
- Physical Review D 2024–2026 quantum gravity sections
- *Living Reviews in Relativity* updates
- *Reports on Progress in Physics* surveys (escape gate G3)
- *Nature Physics* / *Science* / *Physical Review Letters* high-impact discreteness claims
- LOOPS conference proceedings (biennial, 2024 + 2026 editions)
- *Quantum Gravity in the Lab* / *Quantum Gravity in the Sky* workshop proceedings
- Specific lineages to track:
  - **LQG-Rovelli/Smolin/Bianchi** lineage continuations
  - **CDT-Loll/Ambjørn/Anagnostopoulos** lineage
  - **Causal sets-Sorkin/Surya/Dowker** lineage
  - **Asymptotic safety-Reuter/Saueressig/Eichhorn** lineage
  - **GFT-Oriti/Pithis/Sakellariadou** lineage
  - **Holographic discreteness-Padmanabhan-school** lineage
  - **Verlinde emergent gravity** continuations

## Adjacent corpora (the watch-list)

- IceCube / Fermi-LAT / HESS / MAGIC / H.E.S.S. high-energy Lorentz-violation bounds
- LISA gravitational-wave dispersion constraints (post-2026 launch)
- CTA observational quantum gravity phenomenology
- Atom interferometry tests of equivalence principle / Lorentz invariance
- Neutron interferometry quantum-gravity tests
- ARGO/LIGO graviton dispersion bounds
- Cosmological constant problem solutions involving discreteness
- Black hole entropy area-law derivations

## Authorship

Kevin Russell (Project 42). Scoping draft; first physics aiwiki under the methodology.

## Status

Stage 1 (SCOPE) → Stage 2 (BILLS) drafted, 2026-05-15.