PostulateStatement: AI-adaptedProof: Not applicablePipeline-generated‡ sources checked 2026-10-15

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The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Zeroth law for the declared thermal-contact family

Physical scope

Transitivity of thermal-contact equilibrium only within the explicitly declared family of admissible material states and contact protocols; no numerical temperature scale or universal cross-material calibration is assumed.

Postulate

For the declared thermal-contact family $T$ and the contact relation $\sim_{T}$ of Thermal contact family and constraints, assume that $\sim_{T}$ is an equivalence relation: for all $x, y, z \in T$ ,

$x \sim_{T} x, x \sim_{T} y ⟹ y \sim_{T} x, x \sim_{T} y and y \sim_{T} z ⟹ x \sim_{T} z .$

This is an adopted physical assumption about the stated contact protocols. It does not by itself construct a real-valued thermometer reading, an absolute temperature, a differentiable temperature state function, or a common calibration across different material families. Those require further operational, entropy, regularity, and calibration hypotheses.

Depends on

Thermal contact family and constraints

Zeroth law for the declared thermal-contact family

Postulate

Depends on

Dependency tree · 2 levels

Sources