{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:DN6RDIY3DSK2MK4CYLLHDOSK2N","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":"a68151dfdaa2386f9ddf6a3baba00225fa3776884f6f84feb0e3af7f1e1186f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-09-11T16:56:34Z","title_canon_sha256":"2bae09a08efa30757a99a20937b5e9ddccd095ed7bd181ff86085d6b8f64f391"},"schema_version":"1.0","source":{"id":"2509.09615","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.09615","created_at":"2026-07-05T12:09:39Z"},{"alias_kind":"arxiv_version","alias_value":"2509.09615v1","created_at":"2026-07-05T12:09:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.09615","created_at":"2026-07-05T12:09:39Z"},{"alias_kind":"pith_short_12","alias_value":"DN6RDIY3DSK2","created_at":"2026-07-05T12:09:39Z"},{"alias_kind":"pith_short_16","alias_value":"DN6RDIY3DSK2MK4C","created_at":"2026-07-05T12:09:39Z"},{"alias_kind":"pith_short_8","alias_value":"DN6RDIY3","created_at":"2026-07-05T12:09:39Z"}],"graph_snapshots":[{"event_id":"sha256:86d964dffd1134df21cab5fdfd6394840b3a63e6c5da9238b16a326212b032ce","target":"graph","created_at":"2026-07-05T12:09:39Z","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/2509.09615/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Extending the notion of monodromies associated with open books of $3$-manifolds, we consider monodromies for all incompressible surfaces in $3$-manifolds as partial self-maps of the arc set of the surfaces. We use them to develop a primeness criterion for incompressible surfaces constructed as iterative Murasugi sums in irreducible $3$-manifolds.\n  We also consider a suitable notion of right-veeringness for monodromies of incompressible surfaces. We show strongly quasipositive surfaces are right-veering, thereby generalizing the corresponding result for open books and providing a proof that do","authors_text":"Lukas Lewark, Miguel Orbegozo Rodriguez, Peter Feller","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-09-11T16:56:34Z","title":"Monodromies of surfaces in 3-manifolds, right-veeringness, and primeness of links"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.09615","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:e308ec128f5260f618b7011158565e6de17fa5495e596c4850aca5cfe57249ec","target":"record","created_at":"2026-07-05T12:09:39Z","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":"a68151dfdaa2386f9ddf6a3baba00225fa3776884f6f84feb0e3af7f1e1186f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-09-11T16:56:34Z","title_canon_sha256":"2bae09a08efa30757a99a20937b5e9ddccd095ed7bd181ff86085d6b8f64f391"},"schema_version":"1.0","source":{"id":"2509.09615","kind":"arxiv","version":1}},"canonical_sha256":"1b7d11a31b1c95a62b82c2d671ba4ad36fdbce32a9cf8432b8a26fd024b061ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b7d11a31b1c95a62b82c2d671ba4ad36fdbce32a9cf8432b8a26fd024b061ef","first_computed_at":"2026-07-05T12:09:39.499144Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:09:39.499144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bJELu7TQnJbJLxbq3pRQ3kT2LbwNT0DMbwkJx4YFnjlnnC65hnhycRerU/675XB+iiiANyjIMBgDxzOAzHJ+BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T12:09:39.499638Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.09615","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e308ec128f5260f618b7011158565e6de17fa5495e596c4850aca5cfe57249ec","sha256:86d964dffd1134df21cab5fdfd6394840b3a63e6c5da9238b16a326212b032ce"],"state_sha256":"15aff11c229a3a92fffcc307b7a4b3cc9068173a200df10e4fd0992043a33f0f"}