{ "format_version": 3, "claim_formal": { "subject": "Dark energy fraction of the universe's total energy density", "property": "Omega_Lambda (dark energy density parameter) as reported by Planck 2018", "operator": ">", "operator_note": "'More than 68%' is interpreted as Omega_Lambda > 0.68 (strictly greater). The claim references the Planck 2018 legacy release (Planck Collaboration VI, A&A 641, A6, 2020; arXiv:1807.06209). In the base-LCDM model with spatial flatness (Omega_total = 1), Omega_Lambda = 1 - Omega_m. The claim is about the best-fit central value, not the confidence interval.", "threshold": 0.68 }, "claim_natural": "Dark energy constitutes more than 68% of the universe's total energy density according to the Planck 2018 legacy release.", "evidence": { "B1": { "type": "empirical", "label": "Planck 2018 paper: matter density Omega_m = 0.315 +/- 0.007", "sub_claim": null, "source": { "name": "Planck Collaboration VI (2020), A&A 641, A6 \u2014 arXiv:1807.06209 (ar5iv HTML)", "url": "https://ar5iv.labs.arxiv.org/html/1807.06209", "quote": "matter density parameter \u03a9m=0.315\u00b10.007" }, "verification": { "status": "partial", "method": "aggressive_normalization", "coverage_pct": null, "fetch_mode": "live", "credibility": { "domain": "arxiv.org", "source_type": "academic", "tier": 4, "flags": [], "note": "Known academic/scholarly publisher" } }, "extraction": { "value": "0.315", "value_in_quote": true, "quote_snippet": "matter density parameter \u03a9m=0.315\u00b10.007" } }, "B2": { "type": "empirical", "label": "UNLV cosmic parameters reference: Omega_Lambda = 0.6853(74) from Planck 2018", "sub_claim": null, "source": { "name": "UNLV Cosmic Parameters Reference (sourced from Planck 2018)", "url": "https://www.physics.unlv.edu/~jeffery/astro/cosmol/cosmic_parameters.html", "quote": "Omega_Lambda 0.6853(74) Assuming Omega = 1 (Planck 2018 p. 14)" }, "verification": { "status": "verified", "method": "full_quote", "coverage_pct": null, "fetch_mode": "live", "credibility": { "domain": "unlv.edu", "source_type": "academic", "tier": 4, "flags": [], "note": "Academic domain (.edu)" } }, "extraction": { "value": "0.6853", "value_in_quote": true, "quote_snippet": "Omega_Lambda 0.6853(74) Assuming Omega = 1 (Planck 2018 " } }, "A1": { "type": "computed", "label": "Derived Omega_Lambda from Omega_m via flat-LCDM relation", "sub_claim": null, "method": "explain_calc('1 - omega_m')", "result": "0.685", "depends_on": [] }, "A2": { "type": "computed", "label": "Cross-check: derived Omega_Lambda vs directly reported Omega_Lambda", "sub_claim": null, "method": "cross_check(derived, direct, tolerance=0.01, mode='relative')", "result": "True", "depends_on": [] } }, "cross_checks": [ { "description": "Omega_Lambda derived from Omega_m (source A) vs directly reported (source B)", "values_compared": [ "0.685", "0.6853" ], "agreement": true, "fact_ids": [] } ], "adversarial_checks": [ { "question": "Has the Planck 2018 value for Omega_Lambda been revised or retracted?", "verification_performed": "Searched for 'Planck 2018 dark energy revised retracted correction erratum'. The Planck 2018 paper (arXiv:1807.06209) was published in A&A 641, A6 (2020) as the final legacy release. No errata revising the cosmological parameters have been issued.", "finding": "No revision or retraction found. The 2018 release is the final Planck data release.", "breaks_proof": false }, { "question": "Could alternative cosmological models give Omega_Lambda < 0.68 from the same Planck data?", "verification_performed": "Searched for 'Planck 2018 dark energy fraction alternative model lower than 68 percent'. Extended models (w0waCDM, curved models) can shift Omega_DE slightly, but the claim specifically references the base-LCDM results. In the base-LCDM model, Omega_Lambda is tightly constrained at 0.685 +/- 0.007.", "finding": "In the base-LCDM model (which the Planck 2018 release uses as its primary framework), Omega_Lambda = 0.6853 +/- 0.0074. Even at the lower 1-sigma bound (0.6779), the value remains below 0.68 only marginally. The central value is clearly > 0.68.", "breaks_proof": false }, { "question": "Is the 68% threshold ambiguous \u2014 could it refer to a different quantity?", "verification_performed": "Considered whether 'energy density' might refer to Omega_DE in a non-flat model, or to a different definition. In standard cosmology, 'dark energy fraction of total energy density' is Omega_Lambda = rho_Lambda / rho_critical, which equals 1 - Omega_m in a flat universe.", "finding": "The standard interpretation is unambiguous: Omega_Lambda is the dark energy fraction of the critical density, and equals the fraction of total energy density in a flat universe.", "breaks_proof": false } ], "verdict": { "value": "PROVED", "qualified": true, "qualifier": "unverified_citations", "reason": null }, "key_results": { "omega_lambda_direct": 0.6853, "omega_lambda_derived": 0.685, "omega_m": 0.315, "threshold": 0.68, "operator": ">", "claim_holds": true }, "generator": { "name": "proof-engine", "version": "0.10.0", "repo": "https://github.com/yaniv-golan/proof-engine", "generated_at": "2026-03-28" }, "proof_py_url": "/proofs/dark-energy-constitutes-more-than-68-of-the-univer/proof.py", "citation": { "doi": "10.5281/zenodo.19455666", "concept_doi": "10.5281/zenodo.19454378", "url": "https://proofengine.info/proofs/dark-energy-constitutes-more-than-68-of-the-univer/", "author": "Proof Engine", "cite_bib_url": "/proofs/dark-energy-constitutes-more-than-68-of-the-univer/cite.bib", "cite_ris_url": "/proofs/dark-energy-constitutes-more-than-68-of-the-univer/cite.ris" }, "depends_on": [ { "relation": "References", "identifiers": [ { "type": "arxiv", "value": "1807.06209" } ], "note": "Planck 2018 results VI \u2014 cosmological parameters (originating measurement)" } ] }