PH-VAR-002

Name: Hyperbolic norm-equivalence conjectural

Severity: info

Input modes: adapter+dump

Scope separation (read first): PH-VAR-002 validates a diagnostic info-flag contract for the hyperbolic (wave-equation) path of physics-lint. The production rule (ph_var_002.py) does not compute against the field; it emits an info-severity PASS with a literature-pointer reason on wave-equation problems, and SKIPPED on every other PDE kind. The anchor is therefore a contract-verification test, not a numerical-reproduction test.

Per complete-v1.0 plan §21 Task 13 + user’s 2026-04-24 revised Task 13 contract (F3 absent-with-justification is acceptable for info- flag rules):

  • F1 Mathematical-legitimacy: multi-paper DPG + variational- correctness stack — Bachmayr-Dahmen-Oster 2024 + Ernst et al. 2025 (parabolic variational-correctness framework physics-lint’s shipped rules rely on); Gopalakrishnan-Sepúlveda 2019 + Ernesti- Wieners 2019 + Henning-Palitta-Simoncini-Urban 2022 + Demkowicz- Gopalakrishnan 2010/2011 (plausible DPG routes to a future tightened hyperbolic norm-equivalence). The structural argument identifies that the parabolic framework does not extend to hyperbolic problems without specialized machinery; V1’s wave- equation residual norms are therefore a conjectural extension of the parabolic framework, not a proven hyperbolic result.

  • F2 Correctness-fixture: test_anchor.py exercises the rule’s diagnostic contract: PASS + info severity + literature- pointer reason on wave PDE; SKIPPED with per-PDE reason on Laplace / Poisson / heat; PhysicsLintReport aggregation invariant (info-severity PASS does not move the exit code).

  • F3 Borrowed-credibility: absent by structure. Info-flag rules emit no numerical quantity against the field, so there is nothing to reproduce against a published baseline.

  • Supplementary calibration context: Demkowicz-Gopalakrishnan 2025 Acta Numerica DOI 10.1017/S0962492924000102 — theoretical framing for why PH-VAR-002 is conjectural-until-tightened in V1.x.

Wording discipline. Do not write “PH-VAR-002 validates hyperbolic norm-equivalence” or “PH-VAR-002 certifies wave-equation residuals.” The rule does neither. Write: “PH-VAR-002 emits an info-severity diagnostic on wave-equation problems pointing users to DPG hyperbolic norm-equivalence literature; it does not certify hyperbolic norm-equivalence and does not compute against the field.”