{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:533IHREIRQNTV2X35BNY7NP5AY","short_pith_number":"pith:533IHREI","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"},"canonical_sha256":"eef683c4888c1b3aeafbe85b8fb5fd060f9edb1f0b4c3026ad233987615e50b0","source":{"kind":"arxiv","id":"2203.16605","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.16605","created_at":"2026-07-05T04:10:14Z"},{"alias_kind":"arxiv_version","alias_value":"2203.16605v1","created_at":"2026-07-05T04:10:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.16605","created_at":"2026-07-05T04:10:14Z"},{"alias_kind":"pith_short_12","alias_value":"533IHREIRQNT","created_at":"2026-07-05T04:10:14Z"},{"alias_kind":"pith_short_16","alias_value":"533IHREIRQNTV2X3","created_at":"2026-07-05T04:10:14Z"},{"alias_kind":"pith_short_8","alias_value":"533IHREI","created_at":"2026-07-05T04:10:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:533IHREIRQNTV2X35BNY7NP5AY","target":"record","payload":{"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"},"canonical_sha256":"eef683c4888c1b3aeafbe85b8fb5fd060f9edb1f0b4c3026ad233987615e50b0","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"},"source_kind":"arxiv","source_id":"2203.16605","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:10:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6lpoStxGxJvZCQ2AN+Jpn/bcoenlGjnl8wKtJloSjfhYKadtJaOATRSaR7iXskG5o+vrddqBv3tCS16ViuyDDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T05:33:39.299992Z"},"content_sha256":"21f0d5b4dcba5dc5a0169a4f20fc6ed846eb09d77d8972ca3e64c76d7513f600","schema_version":"1.0","event_id":"sha256:21f0d5b4dcba5dc5a0169a4f20fc6ed846eb09d77d8972ca3e64c76d7513f600"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:533IHREIRQNTV2X35BNY7NP5AY","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:10:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"taL0Em+9VAy5eW82AfnX6mgOymZbgqMJjrxTPGIrkkrfRHIG0jksb/N6Q1uh0Lg83HJ8UDnAHksm67GvfIWhDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T05:33:39.300647Z"},"content_sha256":"aaf772e24c980412a1018b745f2a0161317e55dcc8987b1f74fef6c1c564b9a1","schema_version":"1.0","event_id":"sha256:aaf772e24c980412a1018b745f2a0161317e55dcc8987b1f74fef6c1c564b9a1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/533IHREIRQNTV2X35BNY7NP5AY/bundle.json","state_url":"https://pith.science/pith/533IHREIRQNTV2X35BNY7NP5AY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/533IHREIRQNTV2X35BNY7NP5AY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-20T05:33:39Z","links":{"resolver":"https://pith.science/pith/533IHREIRQNTV2X35BNY7NP5AY","bundle":"https://pith.science/pith/533IHREIRQNTV2X35BNY7NP5AY/bundle.json","state":"https://pith.science/pith/533IHREIRQNTV2X35BNY7NP5AY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/533IHREIRQNTV2X35BNY7NP5AY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:533IHREIRQNTV2X35BNY7NP5AY","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":"1dd41311be166b72d7d2358acc223b76dea3c3f67c7394ecbf6fc07e1dfca4ca","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2022-03-30T18:36:51Z","title_canon_sha256":"863ee7972a9834fcf705ee6ff9f7777e6b1284575898d96ead991f7e9009ca6a"},"schema_version":"1.0","source":{"id":"2203.16605","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.16605","created_at":"2026-07-05T04:10:14Z"},{"alias_kind":"arxiv_version","alias_value":"2203.16605v1","created_at":"2026-07-05T04:10:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.16605","created_at":"2026-07-05T04:10:14Z"},{"alias_kind":"pith_short_12","alias_value":"533IHREIRQNT","created_at":"2026-07-05T04:10:14Z"},{"alias_kind":"pith_short_16","alias_value":"533IHREIRQNTV2X3","created_at":"2026-07-05T04:10:14Z"},{"alias_kind":"pith_short_8","alias_value":"533IHREI","created_at":"2026-07-05T04:10:14Z"}],"graph_snapshots":[{"event_id":"sha256:aaf772e24c980412a1018b745f2a0161317e55dcc8987b1f74fef6c1c564b9a1","target":"graph","created_at":"2026-07-05T04:10:14Z","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/2203.16605/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Braeden Reinoso, Grant Crider-Phillips, Joshua M. Sabloff, Leyu Yau, Linyi Chen","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2022-03-30T18:36:51Z","title":"Non-orientable Lagrangian fillings of Legendrian knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.16605","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":"sha256:21f0d5b4dcba5dc5a0169a4f20fc6ed846eb09d77d8972ca3e64c76d7513f600","target":"record","created_at":"2026-07-05T04:10:14Z","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":"1dd41311be166b72d7d2358acc223b76dea3c3f67c7394ecbf6fc07e1dfca4ca","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2022-03-30T18:36:51Z","title_canon_sha256":"863ee7972a9834fcf705ee6ff9f7777e6b1284575898d96ead991f7e9009ca6a"},"schema_version":"1.0","source":{"id":"2203.16605","kind":"arxiv","version":1}},"canonical_sha256":"eef683c4888c1b3aeafbe85b8fb5fd060f9edb1f0b4c3026ad233987615e50b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eef683c4888c1b3aeafbe85b8fb5fd060f9edb1f0b4c3026ad233987615e50b0","first_computed_at":"2026-07-05T04:10:14.132726Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:10:14.132726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YbizpzM5JXBLSDc1pikSEMEhjYIwCZGo37y9Trf88lO/39kvFzGMwWzDNSTSH+1mDJEBlfaofXd4p3G0jXm9DA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:10:14.133076Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.16605","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21f0d5b4dcba5dc5a0169a4f20fc6ed846eb09d77d8972ca3e64c76d7513f600","sha256:aaf772e24c980412a1018b745f2a0161317e55dcc8987b1f74fef6c1c564b9a1"],"state_sha256":"53ea71279a110e5bb05652c32e393618d8b76712f1d7e4cb18f8b59c4f595fc0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rQwO78eAdBp42nnxn9+aYY16P/j86NRwLZ55+GLRmwq3+txaax6UptQDhdmE5wUppd3AC+ms+YFQ/C9AJXXkAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T05:33:39.304803Z","bundle_sha256":"c44b108de98fa7bfe09cb70036bc04fb4f2e8fac29a47b97617fe06609545f70"}}