These notes provide an independent structural analysis of the public architecture described in: Ryan Babbush, Adam Zalcman, Craig Gidney, Michael Broughton, Tanuj Khattar, Hartmut Neven, Thiago Bergamaschi, Justin Drake, and Dan Boneh, Securing Elliptic Curve Cryptocurrencies against Quantum Vulnerabilities: Resource Estimates and Mitigations (2026). *The notes do not rederive the withheld attack circuits. Instead, they analyze the published resource-estimate architecture through Pascal whitening, shell–kernel decomposition, iterated shell extraction, and a nested QEC transport perspective. The three notes develop Pascal whitening as a structural method rather than a mere compression heuristic. Applied to the public secp256k1 ECDLP resource-estimate architecture, the method identifies a block-Pascal outer shell on the windowed point-addition axis, a candidate inner shell on the modular-multiplication recursion axis, and a QEC steady-state shell on the physical error-correction axis. Across these levels, the notes support a common conclusion: much of the visible complexity is inherited transport, while the irreducible residue is concentrated in a much smaller kernel sector.
DAVID BETZER (2026) studied this question.