{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:QIDOBVK4TQRADBYJVPCVAYCJ6U","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":"c8b1206ac2b3b0e2b2ef36aa003bf86cb6436e2928fc85d16d15a84bea3cf3cf","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-04-17T17:16:39Z","title_canon_sha256":"29b15a099cc4940ec4163a63bc7fa54b5e3ec640378f2b3c5c17341f9b2f08fd"},"schema_version":"1.0","source":{"id":"0904.2744","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.2744","created_at":"2026-05-18T04:23:32Z"},{"alias_kind":"arxiv_version","alias_value":"0904.2744v2","created_at":"2026-05-18T04:23:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.2744","created_at":"2026-05-18T04:23:32Z"},{"alias_kind":"pith_short_12","alias_value":"QIDOBVK4TQRA","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"QIDOBVK4TQRADBYJ","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"QIDOBVK4","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:bd0520561f45e36c6d1704dc70bdd15706294d344d3a92298dcfe00cda6d2b3d","target":"graph","created_at":"2026-05-18T04:23:32Z","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":"We give an analytical derivation of the mass gap of the O(N) sigma models and investigate a large-order behavior of the weak coupling asymptotic expansion for the energy. For sufficiently large N the series is sign-oscillating, which is expected from the large N solution of the sigma model. However, for N=3 and N=4 the series are sign positive.","authors_text":"Dmytro Volin","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-04-17T17:16:39Z","title":"From the mass gap in O(N) to the non-Borel-summability in O(3) and O(4) sigma-models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.2744","kind":"arxiv","version":2},"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:cdceeb99ad9c8990b0a35b45dce84bffe01fd3de4ca94d6b9aca675b464d2343","target":"record","created_at":"2026-05-18T04:23:32Z","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":"c8b1206ac2b3b0e2b2ef36aa003bf86cb6436e2928fc85d16d15a84bea3cf3cf","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-04-17T17:16:39Z","title_canon_sha256":"29b15a099cc4940ec4163a63bc7fa54b5e3ec640378f2b3c5c17341f9b2f08fd"},"schema_version":"1.0","source":{"id":"0904.2744","kind":"arxiv","version":2}},"canonical_sha256":"8206e0d55c9c22018709abc5506049f50520b47bc4322b4c7c505be6da9daa70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8206e0d55c9c22018709abc5506049f50520b47bc4322b4c7c505be6da9daa70","first_computed_at":"2026-05-18T04:23:32.526305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:32.526305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ocApjPvh6u6IkKK7dH6Ulrp+Ph/f6qtj3xwMNjBLiU9+vaw/pFF6ykqrJG3mL2oOYaEiURQxVvmiMEu/kGofAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:32.526782Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.2744","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cdceeb99ad9c8990b0a35b45dce84bffe01fd3de4ca94d6b9aca675b464d2343","sha256:bd0520561f45e36c6d1704dc70bdd15706294d344d3a92298dcfe00cda6d2b3d"],"state_sha256":"c9c7b8a4414015c0ed15577b1ad0b2a4802fad551a729c443228e6896396d144"}