proofs

"Dark energy constitutes more than 68% of the universe's total energy density according to the Planck 2018 legacy release."

· generated 2026-03-28 · v0.10.0
PROVED (with unverified citations) 2 citations
⬡ Verified by Proof Engine — an open-source tool that proves claims using cited sources and executable code. No LLM trust required.
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Key Findings

Claim Interpretation

Natural language: "Dark energy constitutes more than 68% of the universe's total energy density according to the Planck 2018 legacy release."

Formal interpretation: The dark energy density parameter ΩΛ (Omega Lambda), as reported in the Planck 2018 legacy release (Planck Collaboration VI, A&A 641, A6, 2020), must be strictly greater than 0.68. "More than 68%" is interpreted as ΩΛ > 0.68. In the base-ΛCDM model with spatial flatness (Ωtotal = 1), ΩΛ = 1 − Ωm. The claim is evaluated against the best-fit central value, not the confidence interval.

Source: proof.py JSON summary

evidence summary

ID Fact Verified
B1 Planck 2018 paper: matter density Ωm = 0.315 ± 0.007 Partial (aggressive normalization on ar5iv HTML rendering)
B2 UNLV cosmic parameters reference: ΩΛ = 0.6853(74) from Planck 2018 Yes
A1 Derived ΩΛ from Ωm via flat-ΛCDM relation Computed: 0.685 (= 1 − 0.315)
A2 Cross-check: derived ΩΛ vs directly reported ΩΛ Computed: True (values agree within 0.05% relative tolerance)

Source: proof.py JSON summary

Linked Sources

SourceIDVerified
Planck Collaboration VI (2020), A&A 641, A6 — arXiv:1807.06209 (ar5iv HTML) B1 Partial
UNLV Cosmic Parameters Reference (sourced from Planck 2018) B2 Yes
Derived Omega_Lambda from Omega_m via flat-LCDM relation A1 Computed
Cross-check: derived Omega_Lambda vs directly reported Omega_Lambda A2 Computed

Proof Logic

The proof proceeds in two independent paths that converge:

Path 1 — Direct report (B2): The UNLV Cosmic Parameters reference page directly reports the Planck 2018 value as "Omega_Lambda 0.6853(74) Assuming Omega = 1 (Planck 2018 p. 14)." This gives ΩΛ = 0.6853, sourced from page 14 of the Planck 2018 paper.

Path 2 — Derivation from Ωm (B1 → A1): The Planck 2018 paper abstract states "matter density parameter Ωm = 0.315 ± 0.007." In the base-ΛCDM model (spatially flat), ΩΛ = 1 − Ωm = 1 − 0.315 = 0.685 (A1).

Cross-check (A2): The derived value (0.685) and the directly reported value (0.6853) agree within 0.05% relative difference. The small discrepancy arises because Ωm = 0.315 is rounded from the full-precision value (Ωm = 0.3147 yields ΩΛ = 0.6853 exactly).

Claim evaluation: ΩΛ = 0.6853 > 0.68 = True. The claim holds.

Source: author analysis

Conclusion

PROVED (with unverified citations). The Planck 2018 legacy release reports ΩΛ = 0.6853 ± 0.0074, which is strictly greater than 0.68. The claim holds.

One citation (B1, Planck paper via ar5iv) was verified only via aggressive normalization (partial match due to LaTeX-to-HTML rendering artifacts on the ar5iv page). However, the conclusion does not depend solely on B1 — the directly reported ΩΛ value from B2 (UNLV reference, fully verified) independently establishes the claim. B1 serves as a cross-check via the matter density derivation and is consistent with B2.

Generated by proof-engine v0.10.0 on 2026-03-28.

counter-evidence search

  1. Has the Planck 2018 value been revised or retracted? Searched for errata and corrections. The Planck 2018 paper was published as the final legacy release in A&A 641 (2020). No revisions to cosmological parameters have been issued.

  2. Could alternative models give ΩΛ < 0.68? Extended models (w0waCDM, non-flat) can shift ΩDE slightly, but the claim specifically references base-ΛCDM results. In this model, ΩΛ = 0.6853 ± 0.0074 — even at the lower 1σ bound (0.6779), the central value remains clearly above 0.68.

  3. Is the 68% threshold ambiguous? In standard cosmology, "dark energy fraction of total energy density" unambiguously refers to ΩΛ = ρΛ/ρcritical, which equals the fraction of total energy in a flat universe.

Source: proof.py JSON summary

audit trail

Citation Verification 1/2 unflagged · 1 partial 1 flagged ▸

1/2 citations unflagged. 1 flagged for review:

B1 partial Planck Collaboration VI (2020), A&A 641, A6 —...
  • matched after normalization
Original audit log

B1 — Planck 2018 paper (ar5iv HTML) - Status: partial - Method: aggressive_normalization (alphanumeric-only matching). The ar5iv HTML rendering of the Planck paper uses LaTeX-to-HTML conversion that introduces formatting artifacts (subscripts, special spacing). After aggressive normalization (stripping all non-alphanumeric characters), the quote content was confirmed present. - Fetch mode: live - Impact: B1 provides Ωm for the cross-check derivation (A1). Even without B1, the directly reported ΩΛ from B2 (fully verified) independently establishes the claim. B1 adds confirmatory value but is not required for the conclusion.

B2 — UNLV Cosmic Parameters Reference - Status: verified - Method: full_quote - Fetch mode: live

Source: proof.py JSON summary; impact analysis is author analysis

Computation Traces ▸ 
Omega_Lambda (derived from Omega_m, flat LCDM): 1 - omega_m = 1 - 0.315 = 0.6850
Omega_Lambda: derived from Omega_m vs direct report: 0.685 vs 0.6853, diff=0.00029999999999996696, relative=0.000438, tolerance=0.01 -> AGREE
Omega_Lambda > 0.68: 0.6853 > 0.68 = True

Source: proof.py inline output (execution trace)

Hardening Checklist ▸
  • [x] Rule 1: Every empirical value parsed from quote text via parse_number_from_quote(), not hand-typed
  • [x] Rule 2: Every citation URL fetched and quote checked via verify_all_citations()
  • [x] Rule 3: Not time-dependent (no date computations), but date.today() used for generator timestamp
  • [x] Rule 4: Claim interpretation explicit in CLAIM_FORMAL with operator_note explaining "more than 68%" as ΩΛ > 0.68
  • [x] Rule 5: Three adversarial checks searched for revision/retraction, alternative models, and threshold ambiguity
  • [x] Rule 6: Cross-checks used independently sourced inputs (Planck paper Ωm vs UNLV reference ΩΛ)
  • [x] Rule 7: Computation uses explain_calc(), cross_check(), and compare() from computations.py
  • [x] validate_proof.py result: PASS (14/14 checks passed, 0 issues, 0 warnings)

Source: author analysis

Generated by proof-engine v0.10.0 on 2026-03-28.

Source Credibility Assessment ▸
Fact ID Domain Type Tier Note
B1 arxiv.org academic 4 Known academic/scholarly publisher
B2 unlv.edu academic 4 Academic domain (.edu)

Source: proof.py JSON summary

Linked Sources

Fact IDDomainSource URL
B1 arxiv.org https://ar5iv.labs.arxiv.org/html/1807.06209
B2 unlv.edu https://www.physics.unlv.edu/~jeffery/astro/cosmol/cosmic...
Extraction Records ▸
Fact ID Extracted Value Value in Quote Quote Snippet
B1 0.315 Yes "matter density parameter Ωm=0.315±0.007"
B2 0.6853 Yes "Omega_Lambda 0.6853(74) Assuming Omega = 1 (Planck 2018..."

Extraction method: B1 uses parse_number_from_quote() with regex [Ωo]m\s*=\s*([\d.]+) to extract Ωm from the Planck abstract. B2 uses parse_number_from_quote() with regex Omega_Lambda\s+([\d.]+) to extract ΩΛ from the UNLV table. Both extractions confirmed via verify_extraction().

Source: proof.py JSON summary; extraction method narrative is author analysis

Linked Sources

IDSource URL
B1 https://ar5iv.labs.arxiv.org/html/1807.06209
B2 https://www.physics.unlv.edu/~jeffery/astro/cosmol/cosmic...
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