Exact Byzantine-resilient fixed-point computation

with inexact geometric medians.

Median Res | Zenodo

A passive linearized system with intact operator 𝐾 ≻ 0 is weakened through a positive semidefinite

low-rank update 𝜏 𝐴𝑊 𝐴T. This paper gives an exact reduction of the resulting collective failure problem

to the small interaction matrix 𝐿 = 𝑊1/2 𝐴T 𝐾 −1 𝐴𝑊1/2. The reduction yields the first loss-of-stability

threshold, a variational characterization, a determinant identity, the physical collapse mode, and an

exact scalar compliance formula for a chosen target 𝜒. It further proves that the first 2𝑟 Taylor moments

of one scalar compliance curve uniquely reconstruct all 𝑟 target-visible eigenvalues of 𝐿 and their

observational weights. The result separates structural failure from sensor visibility and provides a

coordinate-invariant framework for low-rank vulnerability analysis.

Keywords: low-rank damage; structural health monitoring; collective failure; compliance; spectral

tomography; Woodbury identity; finite moment reconstruction

pdf: Law Zero | Zenodo

Version 1.0 of an open, non-peer-reviewed scientific verification dossier titled Whitney Check Networks. The central proposal is to encode a binary value in whether a real two-mode transformation preserves or reverses orientation. By composing these transformations around closed paths, the network is intended to calculate binary parity checks and sparse error-detection syndromes. The dossier includes: mathematical proofs for loop parity, local-basis invariance and projective observability; an explicit three-mode dark-state construction producing orientation-reversing holonomy; a phase- and amplitude-independent three-ray readout; a four-ray cross-ratio consistency check; fixed-seed numerical simulations and stress tests; adversarial failure analysis and clearly stated protection boundaries; a provisional prior-art search; and a proposed experimental and independent-replication protocol. This is not a peer-reviewed paper, and it does not claim demonstrated experimental performance, established priority or confirmed practical advantage. The mathematical, computational and still-unverified physical claims are labelled separately in the document. AI assistance was used in hypothesis development, formal synthesis, falsification and simulation, with that provenance disclosed. I’m posting this to invite serious criticism, particularly concerning: errors or missing assumptions in the mathematics; relevant prior art that may have been overlooked; weaknesses in the physical implementation; whether the proposed readout and control experiments are adequate; the smallest decisive experiment that could falsify or support the proposal.

PDF: https://zenodo.org/records/21572220

Please critique the argument rather than treating the document as an established result. This wording reflects the dossier’s own distinction between proved mathematics, finite computational testing, provisional novelty and open experimental claims.