{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JAJJLEMP7YIX5E3QFYHL4WUYZK","short_pith_number":"pith:JAJJLEMP","canonical_record":{"source":{"id":"1304.0814","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-04-02T23:44:20Z","cross_cats_sorted":["cond-mat.dis-nn","physics.soc-ph"],"title_canon_sha256":"d79af1051e661e6b57e659a0d898b4e025534f7a3070bd68eaa11841645588a1","abstract_canon_sha256":"634fd170bdb0d5eb65fff4649f84750a91453012207bf59030519cca71cfe567"},"schema_version":"1.0"},"canonical_sha256":"481295918ffe117e93702e0ebe5a98ca83d0ed056aa8b904dd802819603211b4","source":{"kind":"arxiv","id":"1304.0814","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0814","created_at":"2026-05-18T03:29:04Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0814v1","created_at":"2026-05-18T03:29:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0814","created_at":"2026-05-18T03:29:04Z"},{"alias_kind":"pith_short_12","alias_value":"JAJJLEMP7YIX","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JAJJLEMP7YIX5E3Q","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JAJJLEMP","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JAJJLEMP7YIX5E3QFYHL4WUYZK","target":"record","payload":{"canonical_record":{"source":{"id":"1304.0814","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-04-02T23:44:20Z","cross_cats_sorted":["cond-mat.dis-nn","physics.soc-ph"],"title_canon_sha256":"d79af1051e661e6b57e659a0d898b4e025534f7a3070bd68eaa11841645588a1","abstract_canon_sha256":"634fd170bdb0d5eb65fff4649f84750a91453012207bf59030519cca71cfe567"},"schema_version":"1.0"},"canonical_sha256":"481295918ffe117e93702e0ebe5a98ca83d0ed056aa8b904dd802819603211b4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:04.966845Z","signature_b64":"I450LHasnDvoLD+VlQP6ceHPILT1o1N9z9cHyCgG6WgqyvQCYu4V3VjHov0PPDwi9NS1EePqjyepuvwiufAQDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"481295918ffe117e93702e0ebe5a98ca83d0ed056aa8b904dd802819603211b4","last_reissued_at":"2026-05-18T03:29:04.966406Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:04.966406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.0814","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:29:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DnZvZyxol2u5CNseuA3v+Vk11aHhuca/yGujwJsi5lK+mJnBbK1xT9Fl083eBPooj5M/VVkRWOepAkjUqj+wCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:33:08.015624Z"},"content_sha256":"ea5d8e6d59726cf0c3c63538c85729865d392c2b7a5251204718be15fa3a9900","schema_version":"1.0","event_id":"sha256:ea5d8e6d59726cf0c3c63538c85729865d392c2b7a5251204718be15fa3a9900"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JAJJLEMP7YIX5E3QFYHL4WUYZK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Continuous- and discrete-time Glauber dynamics. First- and second-order phase transitions in mean-field Potts models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","physics.soc-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"F. Mukhamedov, M. Ostilli","submitted_at":"2013-04-02T23:44:20Z","abstract_excerpt":"As is known, at the Gibbs-Boltzmann equilibrium, the mean-field $q$-state Potts model with a ferromagnetic coupling has only a first order phase transition when $q\\geq 3$, while there is no phase transition for an antiferromagnetic coupling. The same equilibrium is asymptotically reached when one considers the continuous time evolution according to a Glauber dynamics. In this paper we show that, when we consider instead the Potts model evolving according to a discrete-time dynamics, the Gibbs-Boltzmann equilibrium is reached only when the coupling is ferromagnetic while, when the coupling is a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0814","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T03:29:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aUolSJStUJ+Bq4XX0t30+0xOEEk4mxqi9xKsKKgVS63g90LF9YTlQY/B//acjYds7wlpvEXyUFkjCFB4knN6Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:33:08.016577Z"},"content_sha256":"5c67182194d1274f1de81e4d349ffb740d6fe2722c6c5a4eaec6e6723fb87e26","schema_version":"1.0","event_id":"sha256:5c67182194d1274f1de81e4d349ffb740d6fe2722c6c5a4eaec6e6723fb87e26"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JAJJLEMP7YIX5E3QFYHL4WUYZK/bundle.json","state_url":"https://pith.science/pith/JAJJLEMP7YIX5E3QFYHL4WUYZK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JAJJLEMP7YIX5E3QFYHL4WUYZK/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":"2026-05-31T02:33:08Z","links":{"resolver":"https://pith.science/pith/JAJJLEMP7YIX5E3QFYHL4WUYZK","bundle":"https://pith.science/pith/JAJJLEMP7YIX5E3QFYHL4WUYZK/bundle.json","state":"https://pith.science/pith/JAJJLEMP7YIX5E3QFYHL4WUYZK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JAJJLEMP7YIX5E3QFYHL4WUYZK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JAJJLEMP7YIX5E3QFYHL4WUYZK","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":"634fd170bdb0d5eb65fff4649f84750a91453012207bf59030519cca71cfe567","cross_cats_sorted":["cond-mat.dis-nn","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-04-02T23:44:20Z","title_canon_sha256":"d79af1051e661e6b57e659a0d898b4e025534f7a3070bd68eaa11841645588a1"},"schema_version":"1.0","source":{"id":"1304.0814","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0814","created_at":"2026-05-18T03:29:04Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0814v1","created_at":"2026-05-18T03:29:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0814","created_at":"2026-05-18T03:29:04Z"},{"alias_kind":"pith_short_12","alias_value":"JAJJLEMP7YIX","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JAJJLEMP7YIX5E3Q","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JAJJLEMP","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:5c67182194d1274f1de81e4d349ffb740d6fe2722c6c5a4eaec6e6723fb87e26","target":"graph","created_at":"2026-05-18T03:29:04Z","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"},"paper":{"abstract_excerpt":"As is known, at the Gibbs-Boltzmann equilibrium, the mean-field $q$-state Potts model with a ferromagnetic coupling has only a first order phase transition when $q\\geq 3$, while there is no phase transition for an antiferromagnetic coupling. The same equilibrium is asymptotically reached when one considers the continuous time evolution according to a Glauber dynamics. In this paper we show that, when we consider instead the Potts model evolving according to a discrete-time dynamics, the Gibbs-Boltzmann equilibrium is reached only when the coupling is ferromagnetic while, when the coupling is a","authors_text":"F. Mukhamedov, M. Ostilli","cross_cats":["cond-mat.dis-nn","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-04-02T23:44:20Z","title":"Continuous- and discrete-time Glauber dynamics. First- and second-order phase transitions in mean-field Potts models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0814","kind":"arxiv","version":1},"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:ea5d8e6d59726cf0c3c63538c85729865d392c2b7a5251204718be15fa3a9900","target":"record","created_at":"2026-05-18T03:29:04Z","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":"634fd170bdb0d5eb65fff4649f84750a91453012207bf59030519cca71cfe567","cross_cats_sorted":["cond-mat.dis-nn","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-04-02T23:44:20Z","title_canon_sha256":"d79af1051e661e6b57e659a0d898b4e025534f7a3070bd68eaa11841645588a1"},"schema_version":"1.0","source":{"id":"1304.0814","kind":"arxiv","version":1}},"canonical_sha256":"481295918ffe117e93702e0ebe5a98ca83d0ed056aa8b904dd802819603211b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"481295918ffe117e93702e0ebe5a98ca83d0ed056aa8b904dd802819603211b4","first_computed_at":"2026-05-18T03:29:04.966406Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:04.966406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I450LHasnDvoLD+VlQP6ceHPILT1o1N9z9cHyCgG6WgqyvQCYu4V3VjHov0PPDwi9NS1EePqjyepuvwiufAQDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:04.966845Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0814","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea5d8e6d59726cf0c3c63538c85729865d392c2b7a5251204718be15fa3a9900","sha256:5c67182194d1274f1de81e4d349ffb740d6fe2722c6c5a4eaec6e6723fb87e26"],"state_sha256":"2f35c03acd3359029211e3a2058a55312851ff74f26106948a85e05fb6357c5f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jiQQuNl0N+Dk8XSAKjX7rAWjrnLh20rAsrK0h1EExYoKhps/5PEokKQleAJXLctpDXul3UTSi2chLD//3V4HAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T02:33:08.021142Z","bundle_sha256":"89410ca8281fb11e74f08dfc4e7c12d3f94a5f92b127d7ebc407258fa71792bc"}}