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Zhou weights and valuative separation by generalized Lelong numbers

Zhou weights are flat: for every plurisubharmonic germ, the normalized generalized Lelong number equals the relative type. The paper gives an analytic proof of the remaining implication (4) ⇒ (1) in Boucksom–Favre–Jonsson’s Theorem A, using mass comparison, valuation-ideal multiplicities, and controlled density of Zhou valuations. The expanded version includes background, examples, and step-by-step proofs.

AI use: the author proposed the research questions and the Zhou-weight/density organization; the proofs and exposition were developed with GPT (Astra), with background from GPT-5.6 Sol (high). Updated: September 5, 2026; 24 pages. View PDF

Generalized Lelong numbers determine valuative transforms Proves that generalized Lelong numbers for primary-ideal analytic weights determine valuative transforms. The revised proof uses ample perturbations on a fixed model and a negative-definite exceptional intersection matrix. AI use: all mathematical ideas and arguments are AI-generated; the original manuscript used GPT-5.6 Sol (high), and the corrected, expanded revision used GPT (Astra). The author takes responsibility for the mathematical content. Updated: September 5, 2026; 20 pages. View PDF

Counterexamples from Green sublevel families for higher order p-Bergman kernels Constructs explicit Green sublevel families that disprove convexity, monotonicity for p > 2, and the corresponding Lᵖ concavity statement. AI use: the first counterexample was obtained with GPT-5.6-sol (xhigh); the second and third were obtained with DeepSeek V4 flash and pro. View PDF

Counterexamples to ξ-reduction and minimal-integral duality below one Shows that both identities fail for 0 < p < 2(√2 − 1), while proving minimal-integral duality for every p ≥ 1. AI use: the counterexamples and proofs were obtained with DeepSeek V4 flash and pro. View PDF

Failure of fiberwise log-plurisubharmonicity for classical p-Bergman kernels Gives pseudoconvex Hartogs-family counterexamples for every p > 4, including bounded examples obtained by exhaustion. AI use: the construction and proof were obtained with GPT-5.6-sol (high). View PDF

A four-connected domain with no point of equality in the higher order Suita conjecture Constructs a planar domain where equality never occurs at any point or derivative order, with examples for every connectivity n ≥ 4. AI use: the counterexample was found with the assistance of DeepSeek V4 flash. View PDF

A ξ-Bergman kernel proof of the concavity of minimal L² integrals Derives Guan’s concavity theorem from fiberwise ξ-Bergman kernel variation, matrix curvature, and finite-dimensional approximation. AI use: the argument was developed with the assistance of GPT-5.6-sol (high). View PDF