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Validation report

The library has no reference implementation — the paper is the oracle. This records what is checked against the literature, what is cross-checked independently, and the bug the pass found and fixed. Tests live in tests/test_validation.py (+ test_goldens.py).

1. Paper-validated (exact)

Equation What Source Result
gKPZ, β₀=−1−κ the 5 counterterms ( τ , S(τ), F(τ*))
gKPZ, β₀=−3/2−κ the full SC-tree table, 43 trees over 6 homogeneity rows tex 6024–6163 exact ✓

The gKPZ@−3/2 row counts — −3/2−κ:1, −1−2κ:2, −1/2−3κ:6, −1/2−κ:2, −2κ:9, −4κ:23 — match the paper tree-for-tree (count per row).

2. The bug this pass found (and fixed)

Matching the gKPZ@−3/2 table exposed an undercount: the engine produced 42 trees, the paper 43 — one missing at −2κ, the tree ●^{(0,1)}·𝓘ₓ[Ξ]² (a ● with an Xₓ node-decoration and two gradient-noise children).

Cause. Tree generation skipped any root whose bare homogeneity already reached the budget (if base_h.std >= bound: continue). But a node like ●^{(0,1)} (std=1=bound) is pulled below the bound by capped negative-contribution children: a gradient edge I_{(0,1)} over a noise contributes (m−|p|_𝔰)+β₀ = 1+β₀, which is < 0 once β₀<−1. The skip wrongly assumed children only raise homogeneity. It bit only at β₀<−1 (at β₀=−1 those children contribute exactly 0), so the β₀=−1 golden never caught it.

Fix (equation/generate.py): drop the premature skip — the DFS already rejects the bare node and terminates via the budget break (negative-contribution children are derivative slots with a finite cap). Corrected counts: gKPZ@−3/2 42→43, KPZ 10→11, Φ⁴₃ (via DPD) 9→13; PAM (g=0) and all β₀=−1 cases unchanged.

3. Independent cross-checks

  • Symmetry factor. S(τ) recomputed by a brute child-permutation stabiliser count (Π m_j! enumerated, not the closed formula) × node-decoration factorials, across the whole corpus — matches symmetry_factor() everywhere.
  • Subcriticality / homogeneity sanity. Every benchmark equation is subcritical and its counterterm homogeneities are the expected kβ₀ + j ladder.

4. Benchmark (sanity-checked predictions)

Post-fix counterterm counts (paper-validated where noted; others are subcritical, S=Aut-consistent predictions — the paper gives no explicit table for them):

Equation β₀ counterterms note
gKPZ d1 −1−κ 5 paper-exact (renormalised eqn)
gKPZ d1 −3/2−κ 43 paper-exact (SC table)
KPZ d1 −3/2−κ 11 homogeneity rows ⊂ paper table
gPAM d2 −1−κ 4
PAM d2 −1−κ 4
PAM d3 −3/2−κ 17
Φ⁴₂ (DPD) −2 → lift 3 lifted remainder eqn
Φ⁴₃ (DPD) −5/2 → lift 13 lifted remainder eqn

5. Honest scope of the validation

  • Exact literature validation is anchored on gKPZ (the paper's worked example); other equations are sanity-checked predictions, not cross-checked against published tables.
  • This validates the symbolic structure (which trees, homogeneities, S(τ), F(τ*)) — not the numeric renormalisation constants (Track B2, unbuilt) nor convergence.