{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:6AY5F3XF4P4SNCEKWUBCQJH4Q6","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":"3ef58ff6cc498fc5c0e056e8f28289462cba93041624d32a64e24a7926a03916","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2023-07-02T18:41:17Z","title_canon_sha256":"3c6ef3506545a5ae1f6d10ef214591f2517da953444bcaa7ffc736b9e8332a98"},"schema_version":"1.0","source":{"id":"2307.00634","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.00634","created_at":"2026-07-05T09:21:24Z"},{"alias_kind":"arxiv_version","alias_value":"2307.00634v1","created_at":"2026-07-05T09:21:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.00634","created_at":"2026-07-05T09:21:24Z"},{"alias_kind":"pith_short_12","alias_value":"6AY5F3XF4P4S","created_at":"2026-07-05T09:21:24Z"},{"alias_kind":"pith_short_16","alias_value":"6AY5F3XF4P4SNCEK","created_at":"2026-07-05T09:21:24Z"},{"alias_kind":"pith_short_8","alias_value":"6AY5F3XF","created_at":"2026-07-05T09:21:24Z"}],"graph_snapshots":[{"event_id":"sha256:9418ecda94d1d6869166bd6b9ac541f94bf76fa59e60cc9cb9503880dce33b4d","target":"graph","created_at":"2026-07-05T09:21:24Z","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/2307.00634/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The second virial coefficient for the Mie potential is evaluated using the method of brackets. This method converts a definite integral into a series in the parameters of the problem, in this case this is the temperature $T$. The results obtained here are consistent with some known special cases, such as the Lenard-Jones potential. The asymptotic properties of the second virial coefficient in molecular thermodynamic systems and complex fluid modeling are described in the limiting cases of $T \\rightarrow 0$ and $T \\rightarrow \\infty$.","authors_text":"Daniel Salinas-Arizmendi, Igor Kondrashuk, Ivan Gonzalez, Victor H. Moll","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2023-07-02T18:41:17Z","title":"Evaluation of the second virial coefficient for the Mie potential using the method of brackets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.00634","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":"sha256:9b8925c0ca4d3969dfb6fdcf49d02134d6cad6a33da7f7a2200f238a0891b8e5","target":"record","created_at":"2026-07-05T09:21:24Z","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":"3ef58ff6cc498fc5c0e056e8f28289462cba93041624d32a64e24a7926a03916","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2023-07-02T18:41:17Z","title_canon_sha256":"3c6ef3506545a5ae1f6d10ef214591f2517da953444bcaa7ffc736b9e8332a98"},"schema_version":"1.0","source":{"id":"2307.00634","kind":"arxiv","version":1}},"canonical_sha256":"f031d2eee5e3f926888ab5022824fc87989bf69df7ab74a6ab8959d23700a809","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f031d2eee5e3f926888ab5022824fc87989bf69df7ab74a6ab8959d23700a809","first_computed_at":"2026-07-05T09:21:24.674657Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:21:24.674657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3NwFtQu1FDzS2l/cTkQmsZ1UMajRVFZbjGgD1qSJb8NuzceRd0wVwD5FHiQMRqTzFqEUu+KAbLfycj32N84NBw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:21:24.675199Z","signed_message":"canonical_sha256_bytes"},"source_id":"2307.00634","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b8925c0ca4d3969dfb6fdcf49d02134d6cad6a33da7f7a2200f238a0891b8e5","sha256:9418ecda94d1d6869166bd6b9ac541f94bf76fa59e60cc9cb9503880dce33b4d"],"state_sha256":"f6a0ce77ed7532d282fdcca3633f678e77adc6633eb0a4692bbf1b0f6c4d198e"}