{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T11:48:50Z","timestamp":1792064930079,"version":"4.4.0"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T00:00:00Z","timestamp":1783987200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T00:00:00Z","timestamp":1792022400000},"content-version":"vor","delay-in-days":93,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Gossip protocols propagate information through peer-to-peer networks analogously to epidemic spreading, yet this analogy has remained informal. Here, we formalise it for blockchain consensus by means of a phase-encoding under which the dynamics reduce, at leading order and in a weak-coupling regime, to coupled-oscillator synchronisation on complex networks. Block preferences correspond to oscillator phases, communication latencies to natural frequencies, and network topology to the coupling graph. The resulting order parameter (a synchronisation measure from statistical physics) tracks simulated network consensus with a correlation of\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\rho =0.997$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    and represents it as a phase transition. Consensus disruptions then appear as phase-coherence disturbances, providing candidate anomaly signals for node isolation, network partitions, and block withholding (three typical attacks on blockchains). On real blockchain data, where continuous phase dynamics are not observable, we construct a static phase\n                    <jats:italic>proxy<\/jats:italic>\n                    from per-pool block-attribution statistics; applied to Bitcoin, this proxy-based detector identifies the 2013 chain fork at\n                    <jats:inline-formula>\n                      <jats:tex-math>$$5.1\\sigma$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    significance on unmodified data. Validation on a second protocol family confirms that the phenomenology generalises. This framework expands physicists\u2019 reach into adversarial systems, provides epidemic modellers with an empirical testbed, and offers blockchain operators a complementary, consensus-layer anomaly signal.\n                  <\/jats:p>","DOI":"10.1038\/s41598-026-61354-4","type":"journal-article","created":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T18:06:10Z","timestamp":1784052370000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Physical synchronisation for anomaly detection in epidemic blockchain consensus"],"prefix":"10.1038","volume":"16","author":[{"given":"Marcel","family":"Mordarski","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Luca","family":"Magri","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"William","family":"Knottenbelt","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,7,14]]},"reference":[{"key":"61354_CR1","unstructured":"Nakamoto, S. 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