# Spacetime Discreteness Aiwiki — Bills Draft (v0.1)

> Stage 2 (BILLS). **13 candidate bills + 6 meta-costs + 3 escape gates**, with **4 ★ predicted-empty** at positions 8, 10, 11, 13.
>
> Predeclared empty-space hypothesis: no 2024–2026 paper triggers Bills 8 / 10 / 11 / 13 cleanly without paying meta-costs. **One ★ more than the rl_from_rewards aiwiki** because the discreteness-prediction problem has *both* an internal-consistency closure (Bill 8) AND an external-distinguishability closure (Bill 11) that must independently pay; we predict both empty AND a third (Bill 10 — non-perturbative emergence) AND a fourth (Bill 13 — multi-program-confirmable signature) empty.

## The thirteen bills

A "bill" is a closure mechanism that any quantum-gravity discreteness claim must engage. We name them by the structural primitive they invoke.

| # | Bill | What gets paid | ★ |
|---:|---|---|:---:|
| 1 | **LQG area/volume spectrum derivation** | Area or volume operator with discrete spectrum derived from the LQG kinematical Hilbert space. Lineage: Rovelli-Smolin 1995, Ashtekar-Lewandowski. | |
| 2 | **Spinfoam continuum-limit recovery** | Spinfoam amplitude (EPRL / FK / Engle-Pereira-Rovelli-Livine) reproduces continuum GR in semiclassical limit with discrete-area input. | |
| 3 | **CDT dimensional-flow signature** | Causal dynamical triangulation produces $d_s \to 2$ at small scales as a robust signature distinguishable from artifact. Lineage: Ambjørn-Loll-Jurkiewicz. | |
| 4 | **Causal-set non-locality signature** | Causal-set sprinkling produces a measurable non-locality signature (Sorkin integral, swerve effect, signed propagators). Lineage: Sorkin-Surya-Dowker. | |
| 5 | **Asymptotic-safety UV fixed point** | Functional renormalization-group flow produces a Reuter-Saueressig-style UV fixed point with anomalous graviton dimension. Lineage: Reuter, Eichhorn, Pawlowski. | |
| 6 | **GFT condensate cosmology** | Group field theory produces an emergent FLRW cosmology from a condensate of pre-geometric building blocks with a primordial-GW signature. Lineage: Oriti-Pithis-Sakellariadou. | |
| 7 | **Holographic / emergent-gravity discreteness** | Discreteness derived from holographic entropy bounds or Verlinde-style emergent-gravity argument. Lineage: Padmanabhan, Verlinde, Jacobson. | |
| 8 | **★ Matter-coupling consistency** | Discreteness claim survives coupling to a Standard Model matter sector — i.e., the discreteness is not just a kinematic-Hilbert-space property but propagates to matter observables. Lineage attempts: Bianchi-Rovelli-Vidotto matter coupling, Eichhorn-Held QEG+SM. ★ **Empty-space candidate** — predicted no 2024–2026 paper triggers cleanly without paying M2 (formal-only) or M3 (phenomenological-fit). | ★ |
| 9 | **Background-independence preservation** | Discreteness derivation does not require fixing a background spacetime — it must hold in the diffeomorphism-invariant physical Hilbert space, not just on a kinematical fiber. | |
| 10 | **★ Non-perturbative continuum-limit emergence** | Discreteness emerges from a non-perturbative quantization (not from imposing a UV cutoff in perturbation theory) AND survives the continuum / semiclassical limit. ★ **Empty-space candidate** — predicted no 2024–2026 paper closes both perturbative-vs-non-perturbative criteria cleanly. Lineage: spinfoam continuum limit (Dittrich-Geiller-Steinhaus), CDT phase diagram (Loll-Görlich), causal set Hilbert space construction (Sorkin-Surya). | ★ |
| 11 | **★ Observation-distinguishable signature** | Predicted signature is distinguishable from continuum effective-field-theory at a measurement accessible to current-decade detectors (CTA, IceCube-Gen2, LISA, ELT, atom interferometers). Lineage: Amelino-Camelia rainbow gravity, Magueijo-Smolin DSR, Hossenfelder GUP. ★ **Empty-space candidate** — predicted no 2024–2026 paper produces a clean distinguishability without paying M3 (phenomenological-fit, not derived) or M4 (observable-without-program-backing). | ★ |
| 12 | **Lorentz-invariance bound clearance** | Predicted discreteness signature must survive published Lorentz-invariance bounds (IceCube high-E neutrino threshold $E > 10^{20}$ eV, Fermi GRB dispersion limits, HESS/MAGIC blazar spectra). | |
| 13 | **★ Multi-program convergence** | A discreteness signature is independently predicted by ≥2 programs (e.g., LQG and CDT both predict the same area-quantization scale, OR causal sets and asymptotic safety both predict the same non-locality scale). ★ **Empty-space candidate** — predicted no 2024–2026 paper demonstrates clean cross-program convergence without paying M2 (formal-coincidence-without-derivation). Cross-program agreement would be the strongest possible empirical anchor. | ★ |

★ = signature construction; empty-space hypothesis predicts no paper in 2024–2026 corpus triggers cleanly without paying meta-costs.

## Six meta-costs (disqualifying conditions)

| # | Meta-cost | Description |
|---:|---|---|
| M1 | **Pre-2024 historical anchor** | Pre-2024 paper that established the program but doesn't make a 2024–2026-relevant prediction (Rovelli-Smolin 1995, Ambjørn-Loll 2004, Sorkin 2003 historical anchors only) |
| M2 | **Formal-only / no observable** | Pure mathematical structure paper — proves a property of the formalism (e.g., representation theorem, well-definedness of an operator) without a measurable consequence |
| M3 | **Phenomenological fit** | Phenomenological model that *fits* an effective discreteness scale (e.g., GUP, rainbow gravity, DSR) without deriving it from a closed quantum-gravity program |
| M4 | **Observable-without-program-backing** | Lorentz-violation bound, neutron interferometry test, atom interferometry test, etc. that doesn't engage any specific quantum-gravity program. Important for the watch-list but not bill-triggering. |
| M5 | **Single-program-numerical** | Numerical simulation within a single program that produces internal consistency but no predictive claim about observables (e.g., CDT phase diagram exploration without a continuum-limit observable) |
| M6 | **Resource-unbounded simulation** | Claim requires $> 10^{12}$ DOF Monte Carlo simulation infeasible on current hardware, OR a non-perturbative quantization that has no current finite-time approximation. Same shape as factorization-Aiwiki M5. |

## Three escape gates

A paper that triggers no bill but also fits no meta-cost passes one of three escape gates:

1. **G1 Theoretical / proof paper** — proves a theorem about the formalism (e.g., uniqueness of LOST representation, closure of constraint algebra, well-definedness of spinfoam amplitude) without a discreteness claim
2. **G2 Tooling / simulation paper** — releases a CDT simulator, a spinfoam amplitude calculator, a causal-set Hilbert-space code package; no discreteness claim
3. **G3 Survey / review paper** — surveys the landscape of quantum gravity programs, no novel discreteness claim

## Empty-space census (★ predicted-empty bills)

Four bills are signature constructions — the empty-space hypothesis predicts no 2024–2026 paper triggers them cleanly without paying meta-costs.

| Bill | Cleanest historic candidate | Why it's expected to fail to trigger |
|---:|---|---|
| 8 ★ | Bianchi-Rovelli-Vidotto LQG matter coupling (2024 update?); Eichhorn-Held QEG+Standard Model | Most LQG matter coupling papers stay at the kinematical Hilbert level; physical-Hilbert-level matter coupling is technically open. Predicted: every paper claiming clean Bill 8 pays M2 (formal-only) or M5 (single-program-numerical). |
| 10 ★ | Dittrich-Geiller-Steinhaus spinfoam continuum limit; Loll-Görlich CDT phase diagram | Continuum-limit recovery is shown in restricted sectors only; full non-perturbative continuum limit is technically open. Predicted: every paper pays M5 (single-program-numerical) or M6 (resource-unbounded). |
| 11 ★ | Amelino-Camelia rainbow gravity GRB dispersion; Hossenfelder GUP atom-interferometry signal | Phenomenological models fit the signal but don't derive it from a closed program. Program-derived predictions (LQG dispersion, CDT dimensional flow) lie below current detector sensitivity. Predicted: every paper pays M3 (phenomenological-fit) or M4 (observable-without-program). |
| 13 ★ | Hypothetical: LQG + CDT both predicting same area scale | No 2024–2026 paper demonstrates clean cross-program convergence; all "same-scale" coincidences trace to common $\ell_P$ input. Predicted: every cross-program convergence claim pays M2 (formal-coincidence). |

## Iteration plan (8 sweeps)

- **Sweep 1101**: arXiv `gr-qc` 2024-08 to 2025-04 (LQG + spinfoam focus)
- **Sweep 1102**: arXiv `gr-qc` 2025-05 to 2026-04 (LQG + spinfoam recent)
- **Sweep 1103**: arXiv `gr-qc` 2024-08 to 2026-04 (CDT + causal sets focus)
- **Sweep 1104**: arXiv `hep-th` 2024-08 to 2026-04 (asymptotic safety + GFT focus)
- **Sweep 1105**: arXiv `hep-th` 2024-08 to 2026-04 (holographic discreteness + emergent gravity)
- **Sweep 1106**: *Classical and Quantum Gravity* + *Phys. Rev. D* + *J. Math. Phys.* 2024–2026 (journal publications)
- **Sweep 1107**: *Living Reviews in Relativity* + *Reports on Progress in Physics* + *Nature Physics / Science / PRL* (high-impact venues + reviews)
- **Sweep 1108**: Observational/phenomenology bound papers (IceCube-Gen2, Fermi-LAT, HESS, MAGIC, atom interferometry, neutron interferometry) — these are the watch-list inputs, mostly meta-cost M4

## Mandatory verification step (per Project 42 methodology, 2026-05-15)

After Stage 3 sweep batch returns:

- **Stage 3.5 — VERIFY**: dispatch a verification sweep that arxiv-lookups the top 30 flagged-low-confidence IDs from the union, plus any "clean trigger" candidates against ★ Bills. Expected hallucination rate: 50-100% based on robotics + RL precedent. **No breach claim ships without ID verification.** This is mandatory per the methodology rule added 2026-05-15 after the robotics_embodied 9/9 hallucination event.

## Cross-aiwiki coupling

- **factorization** aiwiki (locked): structurally similar — both have small fields with strong empirical anchors, both predict empty signature constructions. The factorization-Bill-7 → PQC migration pattern (when a closure is genuinely empty, the field shifts) likely applies to spacetime-Bill-11: if Bill 11 holds empty, the field shifts to *control-theory-of-quantum-gravity-detectors* rather than continuing to chase the empty target.
- **quantum_advantage** aiwiki: Bill_6 (resource-unbounded simulation) directly couples to spacetime-Bill-10 / M6 — non-perturbative quantum-gravity simulations are a quantum-advantage candidate (and currently empty there too).
- **mech_interp** aiwiki: structurally analogous — both ask "when does an internal property of the formalism translate to a measurable observable?" Mech interp's "monosemantic feature" closure is analogous to spacetime's "matter coupling consistency" requirement.

## Bridge-test commitments

- **Bills 8, 10, 11, 13 ★** are predicted empty across 2024–2026. If any surfaces a clean trigger AFTER Stage 3.5 verification, the public update timeline applies (7-day commitment per `_methodology.md`).
- **Bill 11 (observation-distinguishable signature)** is the most public-facing bill. A clean trigger would be a major astrophysics result.
- **Bill 13 (multi-program convergence)** is the cheapest empty-space candidate to test — most claimed cross-program agreements trace to common $\ell_P$ input rather than independent derivation.
- **Independent verification of any breach claim is MANDATORY** per cross-cutting methodology learning (robotics 9/9 hallucinated, RL 18/30).