Chemistry Correlation Explorer
Reparametrization — r values are post-hoc fits in a γ proxy that contains the target; γ assignments and the row list are unpublished, so r carries no evidence either way until the procedure is publishedRead the r values with this caveat first: the per-material γ (or Ncorr) assignment table has not been published. If γ was set per material with the property in view, a high r between γ and that property carries no information. Until the assignments are published, treat every r on this page as unverified.
Status on the Interactive Tools index: Artifact Lesson (an operational state, not a level: a tool kept to show how a high r can come from monotonicity alone, not a verdict) · Claim status: Reparametrization, the badge above. (Added 2026-10-15, to match the index.)
Browse the chemistry phenomena tested against γ. Sort by correlation strength, filter by regime. These 23 rows were curated from a chemistry corpus of 2,671 sessions (the archive's “1,703” is a type counter read at session #1,840, not a corpus size or a count of distinct phenomena; see the note under the table).
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 (θD ∝ 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 a trend with mass, which is not the same as a trend with Z across the whole table. The effective number of independent tests is therefore much smaller than 23.
What the 23 rows are, and the null run on them: the rows are 23 properties, each a correlation over a different set of materials from a different session (n = 19–33; some include compounds). There is no single 23-material sample. On the 10 property rows that could be recovered from the session scripts, a polynomial in atomic number Z fails to reproduce the correlations: |r(property, Z)| ≤ 0.53 and a quadratic in Z reaches R ≤ 0.51, against framework r of 0.60–0.98 (site explorer, pre-registered, 2026-10-31). So the high r values do not come from a trend with Z. They come from the proxy being a renamed textbook quantity: γphonon = 2T/θD, so every correlation with 1/γphonon equals the same correlation with the Debye temperature θD, exactly; and γoptical = 13.6 eV / ionization energy, so “electronegativity vs 1/γoptical” is electronegativity against ionization energy, a relation Mulliken's definition of electronegativity builds in. That is why the Reparametrization badge stands.
Most rows do not trace to their cited session. The same audit checked each row against the archive. In the 16 high-r rows, no cited session is about the property (the closest is #83, Grüneisen, for thermal expansion), and several r values belong to other properties. One documented failure was shown as a success: electrical conductivity was listed until 2026-11-02 as +0.955 “Coherence helps”, but the session that tested it (#81) found r = −0.414 and recorded “WRONG SIGN”. The table below now has a Trace column: rows corrected to the archive value on 2026-11-02, and rows whose number could not be found (kept as rows, marked Untraced, so the gap stays visible; since 2026-11-09 they print no number, because a value that could not be traced to its own property should not read as a result). The three elastic-modulus rows rest on diamond: without it, r falls to 0.60 (Young's), 0.63 (shear) and 0.37 (bulk).
Earlier versions of this paragraph
Until 2026-10-31 this page said a polynomial-in-Z null “fit to the same targets” matched the r values within 0.07. That null was run on synthetic curves (√Z, log Z, Z1/3), not on the rows. From 2026-10-31 to 2026-11-02 it said the null had not been run on the real data; it has now been run and fails.What “Regime” means: the chemistry track's label for how each property was modelled against γ (defined on Handling Failure). Coherence helps: property modelled as rising with 1/γ (transport, stiffness). Incoherence helps: property modelled as rising with γ itself (soft-mode response such as piezoelectricity), so a positive r in this regime is a positive correlation with γ. Barrier-dominated: thermally activated, ∝ exp(−E/kT), where γ is negligible. Neutral: counting properties (coordination number CN, valence electrons) on which γ has no bearing. Hall coefficient and magnetic susceptibility also carry this label, but they are not counting properties: the label records that no correlation was found, and /gamma-boundary lists both as failures. Four rows carry two verdicts across the two chemistry pages (Hall, susceptibility, piezoelectricity, Tc); the row notes give one status each, and it is the failure (reconciled 2026-10-31, graduate-physics simulated-visitor persona). The labels were assigned after the fits, not predicted in advance.
What r is computed against (added 2026-10-22, researcher simulated-visitor persona): not C, and not one shared γ. Each r is the Pearson correlation between the property and that session's best-fitting expression in a domain-specific γ proxy (for phonon properties γphonon = 2T/θD, a Debye-temperature ratio), chosen after looking at the data. So the sign of r says whether the property rises with that expression, and the regime label says whether the expression rises with γ or with 1/γ. For example, d₃₃ = +0.940 is the fit d₃₃ ∝ γ × ε (permittivity), whence “incoherence helps” (Synchronism research archive, Research/Chemistry/Phase2_Synthesis.md and Framework_Summary.md, where the piezoelectric result is filed under chemistry session #93). For the specific-heat row (+0.756) the expression and sign convention are not recorded in the source table: the archive's heat-capacity entry quotes a different fit (r = −0.988 against the Debye form). Read that row's sign as unverified.
The top rows are close to one identity, not five correlations (added 2026-10-24, researcher simulated-visitor persona). The phonon proxy γphonon = 2T/θD contains the Debye temperature, so the “Debye temperature, r = +0.948” row correlates θD with a function of θD: high r there is by construction. Sound velocity and the three elastic moduli inherit it, because in the Debye model θD ∝ vs and vs ∝ √(modulus/density). Those five rows (marked in the table) are one definitional relation seen five ways. They show how a high r arises, which is this page's lesson; they are not evidence that coherence organizes the properties.
Read before sorting: the r column is not evidence. Each r is a post-hoc fit against a γ proxy that contains the target (null-model status above), and how γ was assigned to each material is undocumented, so the r values are not reproducible from this site: the per-material Ncorr (or γ) assignment table has not been published, and the full 1,703-row file is not linked. Per-row null values are not in this page's data, so they are not shown beside each r.
| Property | r ↓ | Category | Regime | Session | Trace |
|---|---|---|---|---|---|
| Sound velocityr(v, 1/γ_phonon) ≡ r(v, θ_D) exactly, because γ_phonon = 2T/θ_D; session was shown as #47 (material design) | +0.982 | Propagation | Coherence helps | #109 | Corrected 11-02 |
| Piezoelectricity d₃₃post-hoc fit d₃₃ ∝ γε; the direction stated in advance came out backward (Failed on /gamma-boundary). Session was shown as #110 | +0.940 | Response | Incoherence helps | #93 | Corrected 11-02 |
| ElectronegativityPauling χ vs 1/γ_optical, and γ_optical = 13.6 eV / IE: this is χ vs ionization energy (0.938 archive; 0.956 on the explorer recomputation). The 0.979 shown until 2026-11-02 was chemical softness (#118) against the same 1/IE | +0.938 | Bonding | Coherence helps | #115 | Corrected 11-02 |
| Shear modulusvs 1/γ_phonon (= θ_D); drops to 0.63 without diamond (jackknife). Shown as 0.901 (#59, no such session) until 2026-11-02 | +0.936 | Mechanical | Coherence helps | #110 | Corrected 11-02 |
| Young's modulusvs 1/γ_phonon (= θ_D); drops to 0.60 without diamond (jackknife). Shown as 0.912 (#58, fluorescence) until 2026-11-02 | +0.920 | Mechanical | Coherence helps | #110 | Corrected 11-02 |
| Thermal conductivityarchive κ result (#65); 0.883 for metals only (#108). The 0.961 shown until 2026-11-09 was redox potential E° (#72), not κ | +0.804 | Transport | Coherence helps | #65 | Corrected 11-02 |
| Bulk modulusvs 1/γ_phonon (= θ_D); drops to 0.37 without diamond (jackknife). 0.967 shown until 2026-11-02 was not found for B | +0.712 | Mechanical | Coherence helps | #110 | Corrected 11-02 |
| Electrical conductivityFailed: the session’s own verdict is “WRONG SIGN” (σ vs γ_phonon). Shown as +0.955 “Coherence helps” (#68) until 2026-11-02 | -0.414 | Transport | Coherence helps | #81 | Corrected 11-02 |
| SC penetration depth | +0.280 | Superconductivity | Coherence helps | #105 | Traced |
| Valence electron count | -0.161 | Counting | Neutral | #125 | Traced |
| Coordination number CN | +0.116 | Topology | Neutral | #123 | Traced |
| Hall coefficient R_Hno correlation: Failed (same result as /gamma-boundary; not a counting property) | +0.001 | Transport | Neutral | #102 | Traced |
| Magnetic susceptibilityno correlation: Failed (same result as /gamma-boundary; not a counting property) | 0.000 | Magnetic | Neutral | #82 | Traced |
| Debye temperatureby construction: γ_phonon = 2T/θ_D contains θ_D, so at fixed T the correlation is exactly 1 and carries nothing. The 0.948 shown until 2026-11-09 is Richard’s rule (#77); the T_c row carried the same number from the initial commit, and #62 does not contain it | — | Thermal | Coherence helps | #78 | Untraced |
| Superconducting T_cnot traced: the cited #62 (Universal Coherence Test) contains no superconductivity result (checked 2026-11-10), and the proxy behind the 0.948 is unstated. Withheld rather than printed, because a positive r against any θ_D-type proxy would have the wrong sign: across elemental superconductors T_c falls as θ_D rises (strong-coupling, soft lattices; McMillan 1968), so the expected sign is negative. The magnitude prediction is 6.5× wrong (Failed on /gamma-boundary). Shown as 0.923 (#95, electro-optic) until 2026-11-02 and as +0.948 “Coherence helps” at rank 2 until 2026-11-10, when a graduate-physics reader objected that a cell whose own footnote gives the opposite sign should not sort to the top | — | Phase transition | Coherence helps | #62 | Untraced |
| Refractive indexnot found in the archive; its refractive-index result is 0.986 (#76, Moss rule). Cited #85 is polarizability | — | Optical | Coherence helps | #85 | Untraced |
| Seebeck coefficientnot located in the archive; cited #92 is glass thermal conductivity | — | Thermoelectric | Coherence helps | #92 | Untraced |
| Specific heat C_vnot located (the archive’s 0.965 is ΔC/Cₙ); cited #80 is sound speed | — | Thermal | Incoherence helps | #80 | Untraced |
| Thermal expansionnot found; the archive has 0.940 for α vs 1/T_m (#79), a different variable. Cited #83 is Grüneisen | — | Response | Incoherence helps | #83 | Untraced |
| Boiling pointnot located; cited #100 is Fermi energy | — | Phase transition | Barrier-dominated | #100 | Untraced |
| Melting pointnot found; the archive has 0.948 for Richard’s rule (#77), a different quantity. Cited #98 is thermionic emission | — | Phase transition | Barrier-dominated | #98 | Untraced |
| Magnetic anisotropy (RE)cited #130 is an exciton session | — | Magnetic | Incoherence helps | #130 | Untraced |
| Thermionic emissionthermionic emission is session #98; cited #115 is electronegativity | — | Barrier | Barrier-dominated | #115 | Untraced |
Showing 23 of 23 curated phenomena. The archive's “1,703 phenomenon types” is not a count of distinct phenomena: from session #138 on, every chemistry session was logged as exactly one new type, so the type number equals the session number minus 137 with zero exceptions over 824 checked pairs. 1,703 is that counter at session #1,840; the corpus ran to 2,671 sessions, and pairing 1,703 with 2,671 was a partial-update error in the archive (found 2026-10-09 when a visitor saw 1,840 here and 2,671 on another page; source: whitepaper chemistry section, “phenomenon_type = session − 137”).