Paper 2026/1989

Angular Watermarking: Sharp Leakage Bounds and Public Subspace Validation

Abstract

Fresh payloads need not hide persistent watermark geometry. For a Gaussian latent model with refreshed fair angular bits and isotropic covariance, we derive the exact fourth-order signature, the boundary of distributional hiding, and an attainable obstruction imposed by a uniform decoding margin. A fixed-probe learner has sufficient observation count O(p3 log p/c2) at fixed rank, accuracy and confidence, where c is the angular signal strength. Our central statistical result is a sharp, dimension-independent centered fourth-tensor covariance bound. It yields public finite-sample lower bounds on a frozen candidate’s carrier overlap, using independent validation directions, a carrier-dimension bound and scale information, without the secret key or payload. Exact partial-index spectra expose the tradeoff between geometric compression and validation variance. On eight fixed candidates, known- and unknown-scale lower bounds average 0.173 and 0.057, while oracle overlap averages 0.600. Population identities characterize feedback signal; a paired, budgeted MIPP comparison evaluates empirical training with independent Gaussian threshold calibration and a shared public spectral initialization control. All rank failures, zero-threshold sensitivities and negative results are reported. The guarantees concern latent subspaces under the stated iid model and exact arithmetic. They do not establish convergence of same-data adaptive training, ordered bit recovery or a neural watermark attack.

Note: Substantially revised manuscript, Updated title and scope, expanded theoretical analysis, numerical verification, and photographic experiments.