{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:H4V2OMOLJE6QLQIAJ7SVN4NE26","short_pith_number":"pith:H4V2OMOL","schema_version":"1.0","canonical_sha256":"3f2ba731cb493d05c1004fe556f1a4d7911820d783a0d65b75e0e16dc982c0e1","source":{"kind":"arxiv","id":"1505.01734","version":2},"attestation_state":"computed","paper":{"title":"Emergence of a collective crystal in a classical system with long-range interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.AO"],"primary_cat":"cond-mat.stat-mech","authors_text":"Alessio Turchi, Duccio Fanelli, Xavier Leoncini","submitted_at":"2015-05-07T15:07:36Z","abstract_excerpt":"A one-dimensional long-range model of classical rotators with an extended degree of complexity, as compared to paradigmatic long-range systems, is introduced and studied. Working at constant density, in the thermodynamic limit one can prove the statistical equivalence with the Hamiltonian Mean Field model (HMF) and $\\alpha$-HMF: a second order phase transition is indeed observed at the critical energy threshold $\\varepsilon_c=0.75$. Conversely, when the thermodynamic limit is performed at infinite density (while keeping the length of the hosting interval $L$ constant), the critical energy $\\va"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1505.01734","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-05-07T15:07:36Z","cross_cats_sorted":["nlin.AO"],"title_canon_sha256":"6fb7883222c002e1aa91574fb5b1571f8f07bd75a5fe2a6309cb1bc2d66bd9f2","abstract_canon_sha256":"910616f1b824fc88adb454de5e80f5779c3c6694692ec4e5e424f78f04d6c81a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:12.798184Z","signature_b64":"FgcBAnhj5JHLxaYzbqd9V2TQLFZQh+7+gjzHPkLuiXWV6UTcTtoyqJgNebychT79u6pwPg/J2eMoEhMK/CqjDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f2ba731cb493d05c1004fe556f1a4d7911820d783a0d65b75e0e16dc982c0e1","last_reissued_at":"2026-05-18T01:34:12.797491Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:12.797491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Emergence of a collective crystal in a classical system with long-range interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.AO"],"primary_cat":"cond-mat.stat-mech","authors_text":"Alessio Turchi, Duccio Fanelli, Xavier Leoncini","submitted_at":"2015-05-07T15:07:36Z","abstract_excerpt":"A one-dimensional long-range model of classical rotators with an extended degree of complexity, as compared to paradigmatic long-range systems, is introduced and studied. Working at constant density, in the thermodynamic limit one can prove the statistical equivalence with the Hamiltonian Mean Field model (HMF) and $\\alpha$-HMF: a second order phase transition is indeed observed at the critical energy threshold $\\varepsilon_c=0.75$. Conversely, when the thermodynamic limit is performed at infinite density (while keeping the length of the hosting interval $L$ constant), the critical energy $\\va"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01734","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1505.01734","created_at":"2026-05-18T01:34:12.797607+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.01734v2","created_at":"2026-05-18T01:34:12.797607+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.01734","created_at":"2026-05-18T01:34:12.797607+00:00"},{"alias_kind":"pith_short_12","alias_value":"H4V2OMOLJE6Q","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"H4V2OMOLJE6QLQIA","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"H4V2OMOL","created_at":"2026-05-18T12:29:22.688609+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/H4V2OMOLJE6QLQIAJ7SVN4NE26","json":"https://pith.science/pith/H4V2OMOLJE6QLQIAJ7SVN4NE26.json","graph_json":"https://pith.science/api/pith-number/H4V2OMOLJE6QLQIAJ7SVN4NE26/graph.json","events_json":"https://pith.science/api/pith-number/H4V2OMOLJE6QLQIAJ7SVN4NE26/events.json","paper":"https://pith.science/paper/H4V2OMOL"},"agent_actions":{"view_html":"https://pith.science/pith/H4V2OMOLJE6QLQIAJ7SVN4NE26","download_json":"https://pith.science/pith/H4V2OMOLJE6QLQIAJ7SVN4NE26.json","view_paper":"https://pith.science/paper/H4V2OMOL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.01734&json=true","fetch_graph":"https://pith.science/api/pith-number/H4V2OMOLJE6QLQIAJ7SVN4NE26/graph.json","fetch_events":"https://pith.science/api/pith-number/H4V2OMOLJE6QLQIAJ7SVN4NE26/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H4V2OMOLJE6QLQIAJ7SVN4NE26/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H4V2OMOLJE6QLQIAJ7SVN4NE26/action/storage_attestation","attest_author":"https://pith.science/pith/H4V2OMOLJE6QLQIAJ7SVN4NE26/action/author_attestation","sign_citation":"https://pith.science/pith/H4V2OMOLJE6QLQIAJ7SVN4NE26/action/citation_signature","submit_replication":"https://pith.science/pith/H4V2OMOLJE6QLQIAJ7SVN4NE26/action/replication_record"}},"created_at":"2026-05-18T01:34:12.797607+00:00","updated_at":"2026-05-18T01:34:12.797607+00:00"}