{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:VFVXO74JSK6KWNBNPM3YBUO4VB","short_pith_number":"pith:VFVXO74J","canonical_record":{"source":{"id":"1810.02627","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2018-10-05T11:53:39Z","cross_cats_sorted":[],"title_canon_sha256":"16a773701337821ab3412a5cc60e2d31277564f156341680cf2a33224e25f98d","abstract_canon_sha256":"7a51f842649d41898e306bd7587512ba63e55cc710ed37533db0500a35e88869"},"schema_version":"1.0"},"canonical_sha256":"a96b777f8992bcab342d7b3780d1dca85b0a9842edf5b459babb511dd2950192","source":{"kind":"arxiv","id":"1810.02627","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.02627","created_at":"2026-07-05T00:19:52Z"},{"alias_kind":"arxiv_version","alias_value":"1810.02627v3","created_at":"2026-07-05T00:19:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02627","created_at":"2026-07-05T00:19:52Z"},{"alias_kind":"pith_short_12","alias_value":"VFVXO74JSK6K","created_at":"2026-07-05T00:19:52Z"},{"alias_kind":"pith_short_16","alias_value":"VFVXO74JSK6KWNBN","created_at":"2026-07-05T00:19:52Z"},{"alias_kind":"pith_short_8","alias_value":"VFVXO74J","created_at":"2026-07-05T00:19:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:VFVXO74JSK6KWNBNPM3YBUO4VB","target":"record","payload":{"canonical_record":{"source":{"id":"1810.02627","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2018-10-05T11:53:39Z","cross_cats_sorted":[],"title_canon_sha256":"16a773701337821ab3412a5cc60e2d31277564f156341680cf2a33224e25f98d","abstract_canon_sha256":"7a51f842649d41898e306bd7587512ba63e55cc710ed37533db0500a35e88869"},"schema_version":"1.0"},"canonical_sha256":"a96b777f8992bcab342d7b3780d1dca85b0a9842edf5b459babb511dd2950192","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:19:52.500916Z","signature_b64":"+eoRrNNgqnC+Ye3bTUDT6VNccv7QJTy6cWAFCex6KQKvsBFk++2jNtQtqrUSX7RagyT0M0CtNlwgVeYFQMboCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a96b777f8992bcab342d7b3780d1dca85b0a9842edf5b459babb511dd2950192","last_reissued_at":"2026-07-05T00:19:52.500374Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:19:52.500374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.02627","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:19:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2mbHC+M5TGooSeHh/XRWdNvBgMe/9tjNYuCAy6RYwi5inH41neTnvfn4C8jMPrDqcHwLL/+79jlWTtf0+v1qAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T05:06:40.082504Z"},"content_sha256":"34add331468fa0c0e9fd9d94128da8356369770158cc53c849e53e9632a0e57f","schema_version":"1.0","event_id":"sha256:34add331468fa0c0e9fd9d94128da8356369770158cc53c849e53e9632a0e57f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:VFVXO74JSK6KWNBNPM3YBUO4VB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Replica analysis of Bayesian data clustering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"Alexander Mozeika, Anthony CC Coolen","submitted_at":"2018-10-05T11:53:39Z","abstract_excerpt":"We use statistical mechanics to study model-based Bayesian data clustering. In this approach, each partition of the data into clusters is regarded as a microscopic system state, the negative data log-likelihood gives the energy of each state, and the data set realisation acts as disorder. Optimal clustering corresponds to the ground state of the system, and is hence obtained from the free energy via a low `temperature' limit. We assume that for large sample sizes the free energy density is self-averaging, and we use the replica method to compute the asymptotic free energy density. The main ord"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02627","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1810.02627/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:19:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N5hhHdvYo59VwuZViB76QnPiZtWhehX24JOrPyj1WjxBX7Wt051ULCeHb0BsT1TS2J4qv9a+BTDT6pIZuHPwCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T05:06:40.082869Z"},"content_sha256":"317c59ba49bee88c29c12efae72a7b965333fecadfb97c6c03fcb9358032c1f8","schema_version":"1.0","event_id":"sha256:317c59ba49bee88c29c12efae72a7b965333fecadfb97c6c03fcb9358032c1f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VFVXO74JSK6KWNBNPM3YBUO4VB/bundle.json","state_url":"https://pith.science/pith/VFVXO74JSK6KWNBNPM3YBUO4VB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VFVXO74JSK6KWNBNPM3YBUO4VB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-05T05:06:40Z","links":{"resolver":"https://pith.science/pith/VFVXO74JSK6KWNBNPM3YBUO4VB","bundle":"https://pith.science/pith/VFVXO74JSK6KWNBNPM3YBUO4VB/bundle.json","state":"https://pith.science/pith/VFVXO74JSK6KWNBNPM3YBUO4VB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VFVXO74JSK6KWNBNPM3YBUO4VB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VFVXO74JSK6KWNBNPM3YBUO4VB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7a51f842649d41898e306bd7587512ba63e55cc710ed37533db0500a35e88869","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2018-10-05T11:53:39Z","title_canon_sha256":"16a773701337821ab3412a5cc60e2d31277564f156341680cf2a33224e25f98d"},"schema_version":"1.0","source":{"id":"1810.02627","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.02627","created_at":"2026-07-05T00:19:52Z"},{"alias_kind":"arxiv_version","alias_value":"1810.02627v3","created_at":"2026-07-05T00:19:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02627","created_at":"2026-07-05T00:19:52Z"},{"alias_kind":"pith_short_12","alias_value":"VFVXO74JSK6K","created_at":"2026-07-05T00:19:52Z"},{"alias_kind":"pith_short_16","alias_value":"VFVXO74JSK6KWNBN","created_at":"2026-07-05T00:19:52Z"},{"alias_kind":"pith_short_8","alias_value":"VFVXO74J","created_at":"2026-07-05T00:19:52Z"}],"graph_snapshots":[{"event_id":"sha256:317c59ba49bee88c29c12efae72a7b965333fecadfb97c6c03fcb9358032c1f8","target":"graph","created_at":"2026-07-05T00:19:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1810.02627/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We use statistical mechanics to study model-based Bayesian data clustering. In this approach, each partition of the data into clusters is regarded as a microscopic system state, the negative data log-likelihood gives the energy of each state, and the data set realisation acts as disorder. Optimal clustering corresponds to the ground state of the system, and is hence obtained from the free energy via a low `temperature' limit. We assume that for large sample sizes the free energy density is self-averaging, and we use the replica method to compute the asymptotic free energy density. The main ord","authors_text":"Alexander Mozeika, Anthony CC Coolen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2018-10-05T11:53:39Z","title":"Replica analysis of Bayesian data clustering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02627","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:34add331468fa0c0e9fd9d94128da8356369770158cc53c849e53e9632a0e57f","target":"record","created_at":"2026-07-05T00:19:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7a51f842649d41898e306bd7587512ba63e55cc710ed37533db0500a35e88869","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2018-10-05T11:53:39Z","title_canon_sha256":"16a773701337821ab3412a5cc60e2d31277564f156341680cf2a33224e25f98d"},"schema_version":"1.0","source":{"id":"1810.02627","kind":"arxiv","version":3}},"canonical_sha256":"a96b777f8992bcab342d7b3780d1dca85b0a9842edf5b459babb511dd2950192","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a96b777f8992bcab342d7b3780d1dca85b0a9842edf5b459babb511dd2950192","first_computed_at":"2026-07-05T00:19:52.500374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:19:52.500374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+eoRrNNgqnC+Ye3bTUDT6VNccv7QJTy6cWAFCex6KQKvsBFk++2jNtQtqrUSX7RagyT0M0CtNlwgVeYFQMboCA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:19:52.500916Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.02627","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34add331468fa0c0e9fd9d94128da8356369770158cc53c849e53e9632a0e57f","sha256:317c59ba49bee88c29c12efae72a7b965333fecadfb97c6c03fcb9358032c1f8"],"state_sha256":"ebcceaa8b5e73330af0b0b0aeb29dd2465600e7500f2082bd80400aca70dffb1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9EJKRbwHbXkIU0I6bR8roCTsmvKL282/A/0HUk2+unQ9GDcbO4w3OdhSjVRNASa90KYmvOFmirKRy2QF3tVODw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T05:06:40.084752Z","bundle_sha256":"841cb99ec66dd9be4ff7bcd7fe049f83fdcbbf4304357c89d3cf3e91db75d2f3"}}