Chemistry Correlation Explorer

Methodological caveat: This display shows 23 hand-curated rows from 1,703 phenomena. Selecting the highest-correlation rows from a large pool inflates apparent effect sizes by construction (multiple-comparison artifact). The 1,703 phenomena are also not statistically independent — many share underlying physical mechanisms. The r-values shown are Pearson correlations from exploratory curve-fitting, not held-out prediction accuracy. The Honest Assessment acknowledges this; the full null distribution and out-of-sample decomposition remain open research questions.

The 23 rows are not 23 independent tests. Several rows are tied together by textbook relations, so a framework that matches one of them largely matches the others for free. Sound velocity, Debye temperature, bulk modulus, Young's modulus and shear modulus are linked by elasticity (v ∝ √(modulus/density)) and by the Debye model (θ_D ∝ v). Electrical and thermal conductivity are linked in metals by the Wiedemann–Franz law. Those two groups alone reduce 7 rows to roughly 2 independent ones. Specific heat per unit mass is close to 3R/M (Dulong–Petit), which falls steadily with atomic mass and so roughly with atomic number Z. That is exactly the kind of trend the polynomial-in-Z null below reproduces. The effective number of independent tests is therefore much smaller than 23.

Null-model verdict (computed 2026-05-10): before reading any number in this table as evidence, know that a plain 2-parameter polynomial in atomic number Z, fit to the same targets, matches these correlations (|Δr| ≤ 0.07) and sometimes beats them. The targets are near-monotonic in Z, so any smooth monotonic curve scores r ≈ 1 by construction. High r here is evidence of density-monotonicity (known chemistry), not of C(ρ)-specific physics. The “47 research contributions” cited elsewhere on the site are audited and demoted, not uncharacterized (corrected 2026-07-24; this caveat previously said “not audited”): every contribution the (LLM-agent) audit examined resolved to a reparametrization, an internal-consistency finding, or a null result (top-3 swept 2026-07-03, 0/3 novel; the archive's later sessions demoted the remainder, and the count itself is a flagged ~57% overcount). What remains true is narrower: none was run against this page's polynomial null specifically. See the Research Outputs audit for the operative verdict.

What γ means here, and why the flagship row is suspect (added 2026-07-30, two visitor personas independently flagged this): γ = 2/√N_corr is audited-negative and sign-inverted for every collective system — see the γ Calculator: high γ means few correlated particles (gas-like), low γ means many(BCS-superconductor-like). This page's top result — sound velocity, r = +0.982, highest in the stiffest, most strongly-bonded, most collective solids (diamond ≈ 12,000 m/s vs air ≈ 340 m/s) — is therefore a positive correlation with γ running in the direction that formula assigns low N_corr to the most collective materials, the same inversion badged audited-negative one click away. Two readings are both live and neither is stated on this page: either the per-material γ values were computed from 2/√N_corr, in which case this table's r-column inherits the refuted sign; or γ was fit per material independently of N_corr, in which case r = 0.982 is a goodness-of-fit statistic for a free parameter, not a correlation with anything the framework predicts. Which branch applies to this dataset is an open bookkeeping question, not yet resolved here.