{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:533IHREIRQNTV2X35BNY7NP5AY","short_pith_number":"pith:533IHREI","schema_version":"1.0","canonical_sha256":"eef683c4888c1b3aeafbe85b8fb5fd060f9edb1f0b4c3026ad233987615e50b0","source":{"kind":"arxiv","id":"2203.16605","version":1},"attestation_state":"computed","paper":{"title":"Non-orientable Lagrangian fillings of Legendrian knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.SG","authors_text":"Braeden Reinoso, Grant Crider-Phillips, Joshua M. Sabloff, Leyu Yau, Linyi Chen","submitted_at":"2022-03-30T18:36:51Z","abstract_excerpt":"We investigate when a Legendrian knot in standard contact $\\mathbb{R}^3$ has a non-orientable exact Lagrangian filling. We prove analogs of several results in the orientable setting, develop new combinatorial obstructions to fillability, and determine when several families of knots have such fillings. In particular, we determine completely when an alternating knot (and more generally a plus-adequate knot) is decomposably non-orientably fillable, and classify the fillability of most torus and 3-strand pretzel knots. We also describe rigidity phenomena of decomposable non-orientable fillings, in"},"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":"2203.16605","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2022-03-30T18:36:51Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"863ee7972a9834fcf705ee6ff9f7777e6b1284575898d96ead991f7e9009ca6a","abstract_canon_sha256":"1dd41311be166b72d7d2358acc223b76dea3c3f67c7394ecbf6fc07e1dfca4ca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:10:14.133076Z","signature_b64":"YbizpzM5JXBLSDc1pikSEMEhjYIwCZGo37y9Trf88lO/39kvFzGMwWzDNSTSH+1mDJEBlfaofXd4p3G0jXm9DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eef683c4888c1b3aeafbe85b8fb5fd060f9edb1f0b4c3026ad233987615e50b0","last_reissued_at":"2026-07-05T04:10:14.132726Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:10:14.132726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-orientable Lagrangian fillings of Legendrian knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.SG","authors_text":"Braeden Reinoso, Grant Crider-Phillips, Joshua M. Sabloff, Leyu Yau, Linyi Chen","submitted_at":"2022-03-30T18:36:51Z","abstract_excerpt":"We investigate when a Legendrian knot in standard contact $\\mathbb{R}^3$ has a non-orientable exact Lagrangian filling. We prove analogs of several results in the orientable setting, develop new combinatorial obstructions to fillability, and determine when several families of knots have such fillings. In particular, we determine completely when an alternating knot (and more generally a plus-adequate knot) is decomposably non-orientably fillable, and classify the fillability of most torus and 3-strand pretzel knots. We also describe rigidity phenomena of decomposable non-orientable fillings, in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.16605","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2203.16605/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2203.16605","created_at":"2026-07-05T04:10:14.132781+00:00"},{"alias_kind":"arxiv_version","alias_value":"2203.16605v1","created_at":"2026-07-05T04:10:14.132781+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.16605","created_at":"2026-07-05T04:10:14.132781+00:00"},{"alias_kind":"pith_short_12","alias_value":"533IHREIRQNT","created_at":"2026-07-05T04:10:14.132781+00:00"},{"alias_kind":"pith_short_16","alias_value":"533IHREIRQNTV2X3","created_at":"2026-07-05T04:10:14.132781+00:00"},{"alias_kind":"pith_short_8","alias_value":"533IHREI","created_at":"2026-07-05T04:10:14.132781+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.03357","citing_title":"Rationally Convex Surfaces with hyperbolic complex tangencies","ref_index":2,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/533IHREIRQNTV2X35BNY7NP5AY","json":"https://pith.science/pith/533IHREIRQNTV2X35BNY7NP5AY.json","graph_json":"https://pith.science/api/pith-number/533IHREIRQNTV2X35BNY7NP5AY/graph.json","events_json":"https://pith.science/api/pith-number/533IHREIRQNTV2X35BNY7NP5AY/events.json","paper":"https://pith.science/paper/533IHREI"},"agent_actions":{"view_html":"https://pith.science/pith/533IHREIRQNTV2X35BNY7NP5AY","download_json":"https://pith.science/pith/533IHREIRQNTV2X35BNY7NP5AY.json","view_paper":"https://pith.science/paper/533IHREI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2203.16605&json=true","fetch_graph":"https://pith.science/api/pith-number/533IHREIRQNTV2X35BNY7NP5AY/graph.json","fetch_events":"https://pith.science/api/pith-number/533IHREIRQNTV2X35BNY7NP5AY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/533IHREIRQNTV2X35BNY7NP5AY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/533IHREIRQNTV2X35BNY7NP5AY/action/storage_attestation","attest_author":"https://pith.science/pith/533IHREIRQNTV2X35BNY7NP5AY/action/author_attestation","sign_citation":"https://pith.science/pith/533IHREIRQNTV2X35BNY7NP5AY/action/citation_signature","submit_replication":"https://pith.science/pith/533IHREIRQNTV2X35BNY7NP5AY/action/replication_record"}},"created_at":"2026-07-05T04:10:14.132781+00:00","updated_at":"2026-07-05T04:10:14.132781+00:00"}