Fix mathematical correctness across modules; add errata + verification anchors - #1
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…n anchors Independent adversarial re-audit of every quantitative claim in the library. 29 confirmed errors fixed or documented honestly (full record in ERRATA.md). Critical: - Fefferman-Graham g4: drop spurious 1/(n-4) on the algebraic term (belongs only on the Bach differential term); fix n=4 trace coefficient 1/8 -> 1/16 - Renormalized volume v2: -1/(n-2) J -> -1/2 J (n-independent), and n=2 sign Major: - Conformal Laplacian P2: add the missing curvature term -(n-2)/(4(n-1)) R (was the bare Laplacian; the term is what makes P2 conformally covariant) - n=3 holographic stress tensor: make it trace-free, (3/2)J -> J - Discrete Bach proxy: correct the stiffness-vs-pointwise rationale, add a pointwise=True option (M^-1 L M^-1 L) - Remove false discrete identity Q4 = 2K^2 - 2KH^2; relabel H^2-K as the Willmore integrand, not the 4D GJMS Q4 - README: discrete order-4 mean converges to 0 (not 6); Q4 closed form (n-1)!; P6 principal part +Delta^3 (not -Delta^3) Minor/convention: tractor mu-slot weight +1; Bach 1/(n-3) docstring; Carroll connection scope + symmetry predicate completeness; Carroll rank check; remove dead/incorrect symmetrization line; Q2 normalization caveat. Docs: ERRATA.md (per-error claim/code/correct-math/how-we-caught-it + how to contribute), docs/TOOLING_GAPS.md, README "Verify it yourself" and "Contributing corrections". Tests: 3 discrete regression anchors (160 total); PyTorch suite green.
This was referenced May 31, 2026
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Mathematical correctness audit
An independent, adversarial re-audit of every quantitative claim in the library
(symbolic and discrete) turned up 29 confirmed errors, ranging from two
critical coefficient bugs to documentation/code sign mismatches. Each is fixed
in source or — where the correction is research-level — flagged honestly in-code
with an
# ERRATA <ID>tag. The full record, including how we caught each oneand an invitation to contribute corrections, is in
ERRATA.md.Critical
g₄carried a spurious1/(n−4)on the algebraicg₂²term (that pole belongs only on the Bach differential term) and used⅛instead of1/16atn=4. Verified against the exact1/16 g₀on thehyperbolic filling of
Sⁿ.v₂was−1/(n−2) J; correct is−½J(n-independent). The two coincide at
n=4, which masked the bug.Major (selected)
P₂was the bare Laplacian — added the curvatureterm
−(n−2)/(4(n−1)) Rthat makes it conformally covariant.n=3holographic stress tensor was not traceless despite the "no anomaly"claim; coefficient
(3/2)J → J.H²−Kwas mislabeled as the 4D GJMSQ₄and the README claimedits mesh mean
→ 6; it is the Willmore integrand and→ 0. Relabeled, and afalse
Q₄ = 2K² − 2KH²"identity" removed.bi-Laplacian); added a
pointwise=Trueoption.Plus minor/convention items (tractor μ-slot weight, Bach
1/(n−3)docstring,Carroll connection scope + symmetry-predicate completeness, rank check, dead
code,
Q₂normalization caveat).Meta-finding
In most cases the code was right and the prose was wrong, or vice-versa — and
every existing test that touched a buggy function used flat /
n=2/n=4cases where the bug is invisible. That's why the bugs survived, and why
docs/TOOLING_GAPS.mdproposes a Sage-execution CIharness on curved, non-conformally-flat anchors.
Tests & docs
tests/test_discrete/test_errata_anchors.py),160 tests total; PyTorch suite passes.
ERRATA.md,docs/TOOLING_GAPS.md, README "Verify it yourself" +"Contributing corrections".