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
tj2025 / Coach Taj
npub182…ug5wd
2025-12-07 21:55:18 UTC
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npub182vscmeh2w5tjnjwsnl53230dq5ggd2chur225hqs0drh52apx3qeug5wdPublished at
2025-12-07 21:55:18 UTCEvent JSON
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"content": "Abstract. \n\nWe 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. \n\nWe 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. \n\nThe Lightning Network is shown to be a sheaf over this base manifold, implementing étale cohomology for instant payments. \n\nBitcoin 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. \n\nhttps://bsky.app/profile/tcoulon2025.bsky.social/post/3m7giwhqhsc2e",
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