{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ZD3YYCQUJSR7MJ3FIFO2BU74QE","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":"2e447318762e65409bec5031dc5173d76362d21b009067d7105729681f5bde78","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2025-05-28T16:16:58Z","title_canon_sha256":"78fd6ccfb37e1365d8201a81310feef45ecce121321f7885b5c89bdb5a21cb3b"},"schema_version":"1.0","source":{"id":"2505.22530","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.22530","created_at":"2026-07-05T11:11:26Z"},{"alias_kind":"arxiv_version","alias_value":"2505.22530v1","created_at":"2026-07-05T11:11:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.22530","created_at":"2026-07-05T11:11:26Z"},{"alias_kind":"pith_short_12","alias_value":"ZD3YYCQUJSR7","created_at":"2026-07-05T11:11:26Z"},{"alias_kind":"pith_short_16","alias_value":"ZD3YYCQUJSR7MJ3F","created_at":"2026-07-05T11:11:26Z"},{"alias_kind":"pith_short_8","alias_value":"ZD3YYCQU","created_at":"2026-07-05T11:11:26Z"}],"graph_snapshots":[{"event_id":"sha256:0ce1801d3fcb46815800bb7843938f4b27d344ac884f5468d3687e7e3c46f0ed","target":"graph","created_at":"2026-07-05T11:11:26Z","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/2505.22530/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let M be a connected orientable 3-manifold, and F a compact connected orientable surface properly embedded in M. If F cuts M into two connected 3-manifolds X and Y, that is, M=X \\cup_F Y, we say that M is an amalgamation of X and Y along F; and if F cuts M into a connected 3-manifold X, we say that M is a self-amalgamation of X along F. A characterization of an amalgamation of two handlebodies along a surface, incompressible in both, to be a handlebody was obtained by Lei, Liu, Li, and Vesnin. The case of amalgamation of two handelbodies along a compressional surface was studdied by Xu, Fang, ","authors_text":"Andrei Vesnin, Fengchun Lei, Siqi Ding, Wei Lin","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2025-05-28T16:16:58Z","title":"Amalgamations along surfaces with boundary in a handlebody"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.22530","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":"sha256:1f8a46f93e8e6bcc3af65348ab7e6cde6c0f0061ec8afa4b2d860f2667806a2e","target":"record","created_at":"2026-07-05T11:11:26Z","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":"2e447318762e65409bec5031dc5173d76362d21b009067d7105729681f5bde78","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2025-05-28T16:16:58Z","title_canon_sha256":"78fd6ccfb37e1365d8201a81310feef45ecce121321f7885b5c89bdb5a21cb3b"},"schema_version":"1.0","source":{"id":"2505.22530","kind":"arxiv","version":1}},"canonical_sha256":"c8f78c0a144ca3f62765415da0d3fc8138476ed1f4f42581967e42c9beeb1b8a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8f78c0a144ca3f62765415da0d3fc8138476ed1f4f42581967e42c9beeb1b8a","first_computed_at":"2026-07-05T11:11:26.121353Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:11:26.121353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"87F3wEhb4C5QsAGYsbX4vDJmd1wWo1KomBs+rAkaI1gDjkvj6sdGMFlX6ah+WOwLO6bRSwYxkdeje+P64p+qBw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:11:26.121854Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.22530","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f8a46f93e8e6bcc3af65348ab7e6cde6c0f0061ec8afa4b2d860f2667806a2e","sha256:0ce1801d3fcb46815800bb7843938f4b27d344ac884f5468d3687e7e3c46f0ed"],"state_sha256":"365e263910c2e080b9040502657a7839d3e927b621d02df81f662981c92f4d16"}