A registered result in its source context
Original ledger classification: Numerical (Hitchin reduced to finite)
Recorded statement: (U_wall) harmonic metric = FINITE linear algebra, NOT a transcendental Hitchin PDE: polystable point is unitary (Mehta-Seshadri) => Phi=0, harmonic metric = constant invariant form H. Explicit bundle: raw M_k non-unitary (||M^dag…
Statement, assumptions and sources
Paper context: Research contracts
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GATE.UWALL.04
Original ledger classification: Numerical (Hitchin reduced to finite)
Original claim text
(U_wall) harmonic metric = FINITE linear algebra, NOT a transcendental Hitchin PDE: polystable point is unitary (Mehta-Seshadri) => Phi=0, harmonic metric = constant invariant form H. Explicit bundle: raw M_k non-unitary (||M^dag M-I||~0.83) but UNIQUE invariant Hermitian form H (null dim 1) is POSITIVE-DEFINITE => unitarisable; unitarised M~_k=H^{1/2}M_k H^{-1/2} unitary (1e-8), cusp class, prod=I, clean elements {0,1/2,1/sqrt2}. So v31 'transcendental Hitchin' applies only to generic Higgs locus; at the selected point R(rho) reduces to finite unitarisation + combinatorial R (closed). RESIDUAL: final c_u/c_d needs the quark leg/hexagon-site composition; not fabricated
Original classification detail
Numerical (Hitchin reduced to finite)
Dependencies as recorded
GATE.UWALL.03; v31; v33; Mehta-Seshadri
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- Research contracts
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- Front matter / supportResearch contracts
- 2026-06-23 (the two frontier walls attacked directly: Direction A assembles the continuum chain of SEAM.EQUIV.01 theorem-by-theorem and ties its residual to the seam one-sidedness; Direction B was found ALREADY closed by v40 (harmonic metric [formula in source] finite linear algebra, not a PDE): v356)Research changelog; TFPT — Introduction and reading guide
- Research Contract 1 — [formula in source]tfpt research contracts
- 2026-07-21 (IX) ( v499 — the P2 weight-typing postulate HARDENED: the anchor [formula in source] typed as the Birkhoff–Grothendieck splitting exponents of the Deligne canonical extension, so integrality/positivity/sum- [formula in source] become theorems given the \ anchors; the v491 check-9 residual sharpened, the tfpt_2 ``balanced'' selection typed as stability; Wolfram extension [formula in source] (verified engine run); no gate closes, no marker moves — AX.P2.01 stays a declared axiom, QGEO.SYM stays )Research changelog; TFPT — Introduction and reading guide
- Front matter / supportResearch contracts
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Research Contract 1 — [formula in source]tfpt research contracts
Registered verification modules
- v40_harmonic_metric.pyRegistered verification module · uwall
Read the description recorded in the module registry
harmonic metric = finite linear algebra (polystable ⇒ unitary)
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