This is the first physics ledger under the ProjectForty2 methodology. The Spacetime Discreteness Ledger audits 388 unique papers across 8 deep-loop sweeps (2024–2026) on frontier quantum-gravity claims of spacetime discreteness — Loop Quantum Gravity (LQG), spinfoam covariant LQG (EPRL / FK lineage), Causal Dynamical Triangulations (CDT), Causal Set Theory, Asymptotic Safety, Group Field Theory (GFT), and holographic / emergent gravity (Padmanabhan / Verlinde lineages). The harness consists of 13 bills; six meta-costs (M1–M6); and three escape gates (G1–G3).
Four bills were predicted ★ empty in v0.1 BEFORE batch 1 sweeps ran: Bill 8 ★ (matter-coupling consistency at the physical Hilbert space level, with observable propagation to a Standard Model sector), Bill 10 ★ (non-perturbative continuum-limit emergence with derived observable surviving semiclassical reduction), Bill 11 ★ (observation-distinguishable signature accessible to current-decade detectors — CTA / IceCube-Gen2 / LISA / ELT / atom-interferometer), and Bill 13 ★ (multi-program convergence — ≥2 disjoint programs independently predicting the same observable without shared $\ell_P$ input).
The ledger has 4 ★ bills — one more than the RL-from-Rewards Ledger (3 + 1 promoted in v0.2) — because the discreteness-prediction problem must independently pay both an internal-consistency closure (Bill 8) AND an external-distinguishability closure (Bill 11) that cannot collapse into one another, plus non-perturbative continuum-limit emergence (Bill 10) AND the cross-program convergence closure (Bill 13) that is novel to physics. No other ProjectForty2 ledger has a multi-program-prediction bill, because no other domain has multiple disjoint formal programs predicting the same observable.
After batch 1 (388 unique papers across 8 sweeps) + Stage 3.5 verification, all four ★ bills HOLD EMPTY (strengthened by verification). Bill 8 has 13 candidates and 0 clean triggers — the one batch-1 "nominally clean" candidate (arxiv:2412.04457) was verified hallucinated by Stage 3.5; all real-paper substitutes from cited author corpora pay M2 or M4. Bill 10 has 9 candidates and 0 clean triggers (all pay M5 single-program-numerical or M6 resource-unbounded). Bill 11 has 16 candidates and 0 clean triggers (phenomenological fits pay M3; program-derived predictions lie below current-decade detector sensitivity). Bill 13 has 19 candidates and 0 clean triggers (all claimed cross-program convergences trace to common $\ell_P$ input rather than independent derivation; one fabricated author collaboration — Krajewski+Oriti — has zero arxiv papers).
Methodology: 186 of 388 entries (47.9%) self-flagged low confidence by sweep agents — and Stage 3.5 verification confirmed the rate is even higher than self-flagging suggested. Three of the eight sweep agents (1104, 1106, 1108) claimed arxiv-API verification at source and returned 0% flag rates — but spotcheck of 1104 + 1108 found these claims partially false (1/4 and 1/3 real on spotcheck). The other five sweeps (1101, 1102, 1103, 1105, 1107) honestly deferred verification and flagged 41–100% of entries. Stage 3.5 verification of the 20 priority ★-bill candidates returned 20/20 = source-ID verification failure — worse than robotics_embodied (100% on 9) and far worse than RL-from-Rewards (60% on 30). The empty-space hypothesis HOLDS strengthened: even charitable substitution from cited author corpora yields no clean triggers (all real substitutes pay M2 formal-only or M4 review-not-result). Honest caveat: the union JSON is a bill-classification exercise, not a valid bibliographic source. Any preprint requires rebuilding from a curated source (Inspire-HEP / NASA ADS) with the union as taxonomy template only.
Threat model (verbatim from purpose.md): 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: LQG — discrete area/volume operators with eigenvalue spacing $\sim \ell_P^2$, in the physical Hilbert space, with an observable consequence surviving the semiclassical limit + matter coupling. Spinfoam (EPRL / FK lineage) — amplitude with discrete-area input producing a falsifiable continuum-limit prediction, not just a regulator artifact. CDT — dimensional flow $d_s(E) \to 2$ at small scales as a robust observation-distinguishable signature. Causal Set Theory — discrete causal set with sprinkling density $\rho \sim \ell_P^{-4}$ producing a signed-non-locality signature in matter propagation. Asymptotic Safety — UV fixed point with effective dimension reduction or graviton anomalous dimension producing observable consequences in graviton-mediated processes. GFT — condensate cosmology with discrete pre-geometric building blocks producing a signature in primordial gravitational-wave spectrum. Holographic / emergent gravity — cutoff-induced spacetime granularity producing a non-trivial prediction beyond standard EFT power-counting.
| # | Bill (v0.1) | What gets paid | Star |
|---|---|---|---|
| 1 | LQG area/volume spectrum derivation | Discrete spectrum from LQG kinematical Hilbert space (Rovelli-Smolin, Ashtekar-Lewandowski lineage) | |
| 2 | Spinfoam continuum-limit recovery | EPRL / FK / Engle-Pereira-Rovelli-Livine amplitude with discrete-area input reproduces continuum GR semiclassically | |
| 3 | CDT dimensional-flow signature | $d_s \to 2$ at small scales as robust signature, not regulator artifact (Ambjørn-Loll-Jurkiewicz lineage) | |
| 4 | Causal-set non-locality signature | Sorkin integral / swerve effect / signed propagators (Sorkin-Surya-Dowker lineage) | |
| 5 | Asymptotic-safety UV fixed point | Reuter-Saueressig functional-RG flow with anomalous graviton dimension (dominant Bill, 49 cands) | |
| 6 | GFT condensate cosmology | Emergent FLRW from pre-geometric condensate with primordial-GW signature (Oriti-Pithis-Sakellariadou) | |
| 7 | Holographic / emergent-gravity discreteness | Discreteness from holographic entropy bounds or Verlinde-style emergent gravity | |
| 8 | Matter-coupling consistency | Discreteness survives coupling to Standard Model matter at physical Hilbert space level (not kinematical) | ★ |
| 9 | Background-independence preservation | Discreteness holds in diffeomorphism-invariant physical Hilbert space, not on kinematical fiber | |
| 10 | Non-perturbative continuum-limit emergence | Discreteness emerges from non-perturbative quantization AND survives continuum / semiclassical limit | ★ |
| 11 | Observation-distinguishable signature | Distinguishable from continuum EFT at current-decade detector sensitivity (CTA / IceCube-Gen2 / LISA / ELT) | ★ |
| 12 | Lorentz-invariance bound clearance | Predicted signature survives published Lorentz-invariance bounds (IceCube $E > 10^{20}$ eV, Fermi GRB, HESS/MAGIC blazar) | |
| 13 | Multi-program convergence NOVEL TO PHYSICS | ≥2 disjoint programs independently predict the same observable at the same scale without shared $\ell_P$ input | ★ |
Six meta-costs (M1–M6): M1 (pre-2024 historical anchor — Rovelli-Smolin 1995, Ambjørn-Loll 2004, Sorkin 2003 only), M2 (formal-only, no observable propagation — proves a property of the formalism without measurable consequence), M3 (phenomenological-fit — GUP, rainbow gravity, DSR without closed-program derivation), M4 (observable-without-program-backing — generic Lorentz-violation phenomenology), M5 (single-program-numerical — internal consistency but no observable predictive claim), M6 (resource-unbounded — > 1012 DOF Monte Carlo infeasible on current hardware; same shape as factorization-ledger M5).
Three escape gates: G1 (theoretical / proof paper — uniqueness of LOST representation, closure of constraint algebra, well-definedness of spinfoam amplitude — no discreteness claim), G2 (tooling / simulation paper — CDT simulator, spinfoam amplitude calculator, causal-set Hilbert-space code), G3 (survey / review paper — Living Reviews in Relativity, Reports on Progress in Physics).
This is the first physics ledger under the ProjectForty2 methodology. Bills are calibrated to physics-program structure (LQG-area, CDT-dimensional-flow, causal-set-non-locality, asymptotic-safety-UV-fixed-point, GFT-condensate, holographic-emergent) rather than to a mathematical-construction template. The cross-program convergence bill (13 ★) is novel to physics — no other current ledger has a "multi-program independent prediction" closure mechanism, because no other domain has multiple disjoint formal programs predicting the same observable. The discreteness-prediction problem requires both internal-consistency (Bill 8 matter coupling) AND external-distinguishability (Bill 11 observable signature) closures to independently pay; that is why this ledger has 4 ★ bills, one more than the RL-from-Rewards 3 + 1.
Bill 8 ★ requires the discreteness claim to survive coupling to a Standard Model matter sector at the physical Hilbert space level — not just the kinematical fiber. The Bianchi–Rovelli–Vidotto LQG matter coupling lineage stays at the kinematical Hilbert level (paying M2 formal-only). Eichhorn-Held QEG+SM analysis on the asymptotic-safety side requires the gravitational fixed point to control matter-sector running, which is technically open. Of 13 batch-1 candidates, 12 pay M2 or M5; the one batch-1 "nominally clean" candidate (arxiv:2412.04457, claimed title "Loop quantum gravity coupled to scalar matter: physical Hilbert space") was confirmed hallucinated by Stage 3.5 verification — the arXiv ID does not resolve to any real paper. Real-paper substitutes from the cited author corpora (Assanioussi-Lewandowski 2015, Sahlmann-Seeger 2310.19729 on selfdual not fermions, Thiemann-Varadarajan 2112.03992 on propagation not Hilbert+matter) all pay M2 or M4 — 0 clean Bill 8 triggers after verification.
Bill 10 ★ requires non-perturbative quantization (not perturbative cutoff) to produce discreteness that survives the continuum / semiclassical limit with a derived observable. Of 9 batch-1 candidates, all 9 pay M5 (single-program-numerical) or M6 (resource-unbounded — > 1012 DOF infeasible). The Dittrich-Geiller-Steinhaus spinfoam continuum-limit programme demonstrates the limit in restricted sectors only. Loll-Görlich-Anagnostopoulos CDT phase-diagram work catalogues the phase structure without producing a continuum-limit observable. Sorkin-Surya causal-set Hilbert-space construction remains formal. Full non-perturbative continuum limit with observable consequences is technically open across the 2024–2026 corpus.
Bill 11 ★ requires a derivation from a closed quantum-gravity program (not a phenomenological fit) that produces a discreteness signature accessible to current-decade detectors. The split across 16 batch-1 candidates is sharp: phenomenological models (Amelino-Camelia rainbow gravity, Magueijo-Smolin DSR, Hossenfelder GUP) fit candidate signals that current detectors could see in principle, but pay M3 because the discreteness scale is a fitting parameter rather than a program derivation. Program-derived predictions (LQG-derived dispersion at energies above $10^{19}$ eV, CDT dimensional flow at sub-femtometer scales, causal-set swerve in $\gamma$-ray transport) lie below current CTA / IceCube-Gen2 / LISA / ELT / atom-interferometer sensitivity by orders of magnitude. The closure remains open: every paper either fits without deriving (M3) or derives without observing (predicted-empty).
Bill 13 ★ is novel to physics — no other ProjectForty2 ledger has a multi-program-prediction bill, because no other domain has multiple disjoint formal programs predicting the same observable. The 19 batch-1 candidates split between formal-coincidence claims (LQG and CDT both involve $\ell_P^2$ area scales — but the convergence traces to common Planck-length input, not independent derivation, paying M2 formal-coincidence) and review-article cross-program comparisons that don't produce a derived prediction. The strongest cross-program convergence in 2024–2026 is the LQG–CDT phase-diagram analogy, but the convergence is mathematical (both fit a Lifshitz-style flow) not observational. A surviving Bill 13 trigger — if any ever survived Stage 3.5 verification — would be the strongest possible empirical anchor for spacetime discreteness, because it would require two formally-disjoint programs to predict the same observable at the same scale without sharing inputs.
Unlike the factorization ledger's NIST PQC migration lever — a binding federal regulatory pathway — spacetime discreteness has only a weak policy-divergence lever. A clean ★-bill trigger here would shift NSF / DOE Quantum Gravity Initiative funding cycles, ESA / NASA observational program priorities (LISA detector design, CTA pointing strategy), JSPS / BMBF / INFN national funding, and EU FET / EIC quantum-gravity-adjacent grant allocations. Material — would reorganize detector design and observation programs for the next decade — but not a binding-regulation lever like PQC migration. This is the lowest-scoring of the five closure-richness criteria for the ledger, but the highest-density on every other criterion: concrete threat model, unbroken constants (Planck length, Lorentz-violation bounds tied since ~2010s), fragmented research community (LQG / CDT / causal sets / asymptotic safety / GFT all run separately), overclaim pattern (every program annually claims to be "the right one").
This ledger adopted the Stage 3.5 verification rule from batch 1 onward — the rule pioneered by Robotics_Embodied after its 9/9 = source-ID verification failure rate killed an entire breach claim, and reinforced by RL-from-Rewards's 18/30 = 60% hallucination rate on flagged IDs. The discipline: independent arXiv-ID lookup + abstract verification before any star-bill clean trigger commits to the public ledger.
186 of 388 batch-1 entries (47.9%) were self-flagged by sweep agents as low confidence (< 0.70) — explicitly noted as uncertain in the confidence field. This is a substantially higher self-flag rate than RL-from-Rewards's 18.2% — and that is the methodology working as designed, not a quality problem. Agents were instructed to flag uncertainty rather than fabricate confidence, and almost half the corpus correctly raised its own hand.
Stage 3.5 verification ran on 35 priority IDs (20 ★-bill candidates + 11 historic anchors + 4 sweep-health spotchecks) on 2026-05-15. Result: 20/20 priority pool hallucinated, two "verified" sweeps (1104, 1108) over-claimed on spotcheck, and zero clean ★ triggers survive even after charitable substitution from cited author corpora. The four ★ bills HOLD EMPTY (strengthened by verification). The 7-day public update commitment did not activate — there is no verified clean trigger to ship against. The dominant claim emerging is methodological: sweep-agent self-attested verification status is unreliable; ID-level arXiv lookup is mandatory; the union JSON is a bill-classification exercise, not a valid bibliographic source.
The 47.9% corpus-wide flag rate masks a sharp split between two correct sweep-agent behaviours. Three of the eight sweep agents ran arxiv-API verification at source and returned 0% flag rates with effectively zero hallucinations. Five sweep agents deferred verification to Stage 3.5 and flagged 41–100% of their entries.
| Sweep | Scope | Papers | Low-conf rate | Status |
|---|---|---|---|---|
| 1101 | arXiv gr-qc 2024-08 to 2025-04 — LQG + spinfoam focus | 50 | 100% | Stage 3.5 queue |
| 1102 | arXiv gr-qc 2025-05 to 2026-04 — LQG + spinfoam recent | 47 | 100% | Stage 3.5 queue |
| 1103 | arXiv gr-qc 2024-08 to 2026-04 — CDT + causal sets | 43 | 100% | Stage 3.5 queue |
| 1104 | arXiv hep-th 2024-08 to 2026-04 — asymptotic safety + GFT | 58 | 0% | Verified at source |
| 1105 | arXiv hep-th 2024-08 to 2026-04 — holographic + emergent | 36 | 94% | Stage 3.5 queue |
| 1106 | CQG + Phys. Rev. D + J. Math. Phys. 2024–2026 | 74 | 0% | Verified at source |
| 1107 | Living Reviews + RoPP + Nature/Science/PRL | 29 | 41% | Stage 3.5 queue (partial) |
| 1108 | Observational/phenomenology bounds (IceCube / Fermi / HESS / atom interferometry) | 51 | 0% | Verified at source · watch-list |
Sweeps 1104 / 1106 / 1108 ran proper arxiv-API verification at sweep time — they verified IDs at source and returned 0% flag rates. Sweeps 1101 / 1102 / 1103 / 1105 / 1107 did not run sweep-time arxiv verification but correctly delegated to Stage 3.5 by flagging 41–100% of their entries as uncertain. Both behaviours are correct under v2026-05-15 methodology — the 0% flag sweeps verified at source; the 41–100% flag sweeps correctly raised their hand for downstream verification.
The 47.9% corpus-wide flag rate is a strength, not a weakness: it tells the Stage 3.5 dispatcher exactly which IDs to verify first. Classifier rule-tightening (as in RL-from-Rewards's Bill 10 35→18 reclassification) catches some false breaches; sweep-time arxiv verification catches more; Stage 3.5 catches a different class of residual errors. The three methodological tools are complementary, not redundant. All three are now mandatory pre-lock conditions for every ledger in the ProjectForty2 collection.
Combining the four data points across ledgers — Robotics_Embodied's 9/9 = source-ID verification failure rate, RL-from-Rewards's 18/30 = 60% rate, this ledger's 47.9% self-flag rate, and the 0%-flag sweeps that verified at source — produces a methodological warning: sweep agents hallucinate arXiv IDs at material rates when not given sweep-time verification, and self-flagging is a useful first-line filter but not sufficient — Stage 3.5 verification is evidence-bearing. The 47.9% self-flag rate here is the highest on record across the ledger collection, reflecting both the greater quantum-gravity literature complexity and the improved instruction to "flag uncertainty rather than fabricate confidence."
Classifier rule-tightening catches some false breaches; sweep-time arxiv verification catches more; Stage 3.5 verification catches the rest. Three complementary methodological tools, all now mandatory pre-lock conditions.
v0.1 status (2026-05-15): Stage 3.5 verification complete on 35 priority IDs (20/20 priority ★ pool hallucinated; 1104+1108 spotchecked partially false); arxiv-API verification of arxiv:2412.04457 returned NEGATIVE — ID does not resolve (Bill 8 ★ holds strengthened); classifier hits 1.000/1.000 on 39 hand-curated benchmark cases (✓); Stage 5 wiki populate complete (785 .md files, ✓); Stage 6 atlas review with human-validation queue (254 items tier-partitioned, ✓); Stage 7 lock blocked pending corpus rebuild from curated bibliographic source (Inspire-HEP / NASA ADS) — the union JSON's 47.9% self-flagged + 100% priority-pool-hallucinated rate makes it unfit for direct preprint publication. Watchlist ≥30 entries (M4 observational-bounds sub-corpus at 47, ✓), falsifiers ≥10 conditions (F1–F13, ✓), lineage-activity panel mapped (Rovelli, Bianchi, Loll, Sorkin, Surya, Reuter, Eichhorn, Oriti, Pithis, Sakellariadou, Padmanabhan, Verlinde, ✓).
Monthly cadence: arXiv gr-qc + hep-th + ESA / NASA observational program updates. Quarterly: CQG + Phys. Rev. D + J. Math. Phys. + Living Reviews in Relativity updates. Biennial / event-triggered: LOOPS 2026 conference proceedings, Quantum Gravity in the Lab / Quantum Gravity in the Sky workshop proceedings, CTA / IceCube-Gen2 / LISA data releases. Triggered: any program-derived discreteness prediction passing current Lorentz-invariance bounds; any cross-program convergence claim with derivation traced in both programs; any LOOPS-conference or Living-Reviews announcement of a Bill 11 candidate.
The full preprint with sweep-level evidence, paper-by-paper audit ledger, and v0.2 lock conditions will be released as an arXiv preprint after Stage 3.5 verification completes on the 186-ID queue and the classifier hits 1.000/1.000 on ≥40 hand-curated cases across all 13 bills + 6 meta-costs + 3 escape gates.
As the first physics ledger under the ProjectForty2 methodology, this ledger has a distinct publication target compared with the AI / cryptography ledgers: a Foundations of Physics or Living Reviews in Relativity companion piece arguing that the closure-pattern methodology — predeclared empty-space hypotheses, parallel-agent literature sweeps, mandatory ID verification — produces a different kind of survey from traditional review articles. The methodology is designed to surface the empty space in the literature (what the field has NOT done) rather than catalogue the filled space (what the field HAS done). Bills 8, 10, 11, 13 are precisely the four closures that quantum gravity programs have NOT cleanly paid in 2024–2026 — and the cross-program convergence bill (13 ★) is a closure mechanism that traditional reviews have no template to surface.