# Real-EOS Validation

## Source 1 — IAPWS-IF97 Region 1

**Authority:** International Association for the Properties of Water and Steam, R7-97(2012).

**URL:** https://www.iapws.org/relguide/IF97-Rev.html

**Region:** single-phase Region 1 compressed liquid.

**Certified pressure–entropy domain:** \(p\in[10,20]\) MPa, \(s\in[0.8,2.2]\) kJ kg\(^{-1}\) K\(^{-1}\).

**Representation:** rationalized simple-knot \(S_4\otimes S_3\), 4×4 = 16 Q43 cells.

**Exact result:** 16/16 cells VERIFIED SAFE by a standard-library-only verifier that recomputes the seven traces from the local Q43 coefficients.

**Source-validation result:** independent Region 1 implementation reproduces official IAPWS verification values.

**Approximation diagnostics:** see `results/iapws_ps_spline_result.json`.

**Proof objects:** `certificates/iapws_region1_q43/`.

## Source 2 — Timmes / AMReX-Astro Helmholtz table

**Artifact SHA-256:** `c9a57c26c6fd2b2b378b9d5295ca1214022f6fec6289d038b47bf8c8938881a1`.

**Role:** independent external evidence for third-order interpolation/reconstruction pathology, not a Q43 demonstration.

**Exact scope:** ordinary stability and boundary formal-\(G\) positivity are certified for the reconstructed formal Helmholtz cell; the formal midpoint \(G\) is negative. A separately interpolated pressure-derivative channel is positive at the same state. The result is a channel/reconstruction mismatch, not a claim that the production sound-speed implementation itself returns negative \(G\).

## Evidence separation

Mathematical theorems do not depend on either external source. IAPWS source-property comparisons use floating-point numerical diagnostics, whereas safety of the rationalized spline is established exactly. External Timmes execution is hash-gated before use.