tj2025 on Nostr: This geometric perspective provides rigorous proofs for the whitepaper's security ...

This geometric perspective provides rigorous proofs for the whitepaper's security claims and reveals that Bitcoin's resilience stems from topological invariants (Chern numbers, homology groups) that are preserved under its evolution. The framework suggests that Bitcoin is not merely a ledger but a topological quantum field theory of social consensus, with the whitepaper as its foundational atlas.


https://beyondturbulence.blogspot.com/2025/12/the-bitcoin-topological-manifold.html?m=1

quoting
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Abstract.

We formalize the Bitcoin system described in Nakamoto's 2008 whitepaper as a compact topological manifold B_t evolving in discrete time. The Unspent Transaction Output (UTXO) set forms a dynamic graph embedded in this manifold, while the blockchain defines a cellular decomposition.

We prove that the Nakamoto consensus protocol (proof-of-work and longest chain rule) performs a continuous gauge-fixing operation, selecting a unique representative from the cohomology class of possible histories.

The Lightning Network is shown to be a sheaf over this base manifold, implementing étale cohomology for instant payments.

Bitcoin Cash and other content-relevant forks are characterized as Dehn surgeries on the base topology. This framework provides geometric proofs for the whitepaper's security assertions and reveals hidden topological invariants governing network behavior.

https://bsky.app/profile/tcoulon2025.bsky.social/post/3m7giwhqhsc2e