{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:VB2RGH7XJXG7ELXQSCP7KDWUVP","short_pith_number":"pith:VB2RGH7X","canonical_record":{"source":{"id":"1610.06977","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2016-10-21T23:54:02Z","cross_cats_sorted":["math.AG","math.GT"],"title_canon_sha256":"5e9f21e6a6ef6f25ec81e5f6317c4deae41510f7f86fde19c5b0e5d22e9f08e0","abstract_canon_sha256":"5b700719ad165fea76df908d36ae86e0dead1e98c8eb5915f0b7ea160a0064ff"},"schema_version":"1.0"},"canonical_sha256":"a875131ff74dcdf22ef0909ff50ed4abc2dfd2501cfca6dda83e7715fddcf51b","source":{"kind":"arxiv","id":"1610.06977","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06977","created_at":"2026-05-17T23:51:00Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06977v1","created_at":"2026-05-17T23:51:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06977","created_at":"2026-05-17T23:51:00Z"},{"alias_kind":"pith_short_12","alias_value":"VB2RGH7XJXG7","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VB2RGH7XJXG7ELXQ","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VB2RGH7X","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:VB2RGH7XJXG7ELXQSCP7KDWUVP","target":"record","payload":{"canonical_record":{"source":{"id":"1610.06977","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2016-10-21T23:54:02Z","cross_cats_sorted":["math.AG","math.GT"],"title_canon_sha256":"5e9f21e6a6ef6f25ec81e5f6317c4deae41510f7f86fde19c5b0e5d22e9f08e0","abstract_canon_sha256":"5b700719ad165fea76df908d36ae86e0dead1e98c8eb5915f0b7ea160a0064ff"},"schema_version":"1.0"},"canonical_sha256":"a875131ff74dcdf22ef0909ff50ed4abc2dfd2501cfca6dda83e7715fddcf51b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:00.467354Z","signature_b64":"uhRLdnRXBo5YLs+HjHu0wFImFfelzp8aduUC29BT2WwiNwnbahg2ZqGuF8+1N6D/eFnOe2d2cVN+PVX6xy+cDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a875131ff74dcdf22ef0909ff50ed4abc2dfd2501cfca6dda83e7715fddcf51b","last_reissued_at":"2026-05-17T23:51:00.466814Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:00.466814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.06977","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":"2026-05-17T23:51:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m6OfdIM+Ddh4urgHjM+nUIYDGKvIUhL33++xApsCBozsaTpuqS7YNb0aTmed1Fxzlw/71wnf6ddjsxXmIFTaDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T18:48:42.745842Z"},"content_sha256":"87588f248089abf0e2d52abd16e2c91109e5e2d2a7e51289d91c0165824b0907","schema_version":"1.0","event_id":"sha256:87588f248089abf0e2d52abd16e2c91109e5e2d2a7e51289d91c0165824b0907"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:VB2RGH7XJXG7ELXQSCP7KDWUVP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Legendrian Fronts for Affine Varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.GT"],"primary_cat":"math.SG","authors_text":"Emmy Murphy, Roger Casals","submitted_at":"2016-10-21T23:54:02Z","abstract_excerpt":"In this article we study Weinstein structures endowed with a Lefschetz fibration in terms of the Legendrian front projection. First we provide a systematic recipe for translating from a Weinstein Lefschetz bifibration to a Legendrian handlebody. Then we present several applications of this technique to symplectic topology. This includes the detection of flexibility and rigidity for several families of Weinstein manifolds and the existence of closed exact Lagrangian submanifolds. In addition, we prove that the Koras--Russell cubic is Stein deformation equivalent to affine complex 3-space and ve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06977","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":""},"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":"2026-05-17T23:51:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MM6+evcdBszjKMlC6rvk7YfSaLyzCfc5sTJF95tjxyJN4DdKZtScVACUyf6J/bThU0vhjhfxBnD1Ti6KRJRRCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T18:48:42.746510Z"},"content_sha256":"2a9c1f0c3eaa57eb41e98ecb054e8e53931a296835f75d29a81087bd97331199","schema_version":"1.0","event_id":"sha256:2a9c1f0c3eaa57eb41e98ecb054e8e53931a296835f75d29a81087bd97331199"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VB2RGH7XJXG7ELXQSCP7KDWUVP/bundle.json","state_url":"https://pith.science/pith/VB2RGH7XJXG7ELXQSCP7KDWUVP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VB2RGH7XJXG7ELXQSCP7KDWUVP/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":"2026-06-11T18:48:42Z","links":{"resolver":"https://pith.science/pith/VB2RGH7XJXG7ELXQSCP7KDWUVP","bundle":"https://pith.science/pith/VB2RGH7XJXG7ELXQSCP7KDWUVP/bundle.json","state":"https://pith.science/pith/VB2RGH7XJXG7ELXQSCP7KDWUVP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VB2RGH7XJXG7ELXQSCP7KDWUVP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VB2RGH7XJXG7ELXQSCP7KDWUVP","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":"5b700719ad165fea76df908d36ae86e0dead1e98c8eb5915f0b7ea160a0064ff","cross_cats_sorted":["math.AG","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2016-10-21T23:54:02Z","title_canon_sha256":"5e9f21e6a6ef6f25ec81e5f6317c4deae41510f7f86fde19c5b0e5d22e9f08e0"},"schema_version":"1.0","source":{"id":"1610.06977","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06977","created_at":"2026-05-17T23:51:00Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06977v1","created_at":"2026-05-17T23:51:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06977","created_at":"2026-05-17T23:51:00Z"},{"alias_kind":"pith_short_12","alias_value":"VB2RGH7XJXG7","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VB2RGH7XJXG7ELXQ","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VB2RGH7X","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:2a9c1f0c3eaa57eb41e98ecb054e8e53931a296835f75d29a81087bd97331199","target":"graph","created_at":"2026-05-17T23:51:00Z","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":"In this article we study Weinstein structures endowed with a Lefschetz fibration in terms of the Legendrian front projection. First we provide a systematic recipe for translating from a Weinstein Lefschetz bifibration to a Legendrian handlebody. Then we present several applications of this technique to symplectic topology. This includes the detection of flexibility and rigidity for several families of Weinstein manifolds and the existence of closed exact Lagrangian submanifolds. In addition, we prove that the Koras--Russell cubic is Stein deformation equivalent to affine complex 3-space and ve","authors_text":"Emmy Murphy, Roger Casals","cross_cats":["math.AG","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2016-10-21T23:54:02Z","title":"Legendrian Fronts for Affine Varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06977","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":"sha256:87588f248089abf0e2d52abd16e2c91109e5e2d2a7e51289d91c0165824b0907","target":"record","created_at":"2026-05-17T23:51:00Z","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":"5b700719ad165fea76df908d36ae86e0dead1e98c8eb5915f0b7ea160a0064ff","cross_cats_sorted":["math.AG","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2016-10-21T23:54:02Z","title_canon_sha256":"5e9f21e6a6ef6f25ec81e5f6317c4deae41510f7f86fde19c5b0e5d22e9f08e0"},"schema_version":"1.0","source":{"id":"1610.06977","kind":"arxiv","version":1}},"canonical_sha256":"a875131ff74dcdf22ef0909ff50ed4abc2dfd2501cfca6dda83e7715fddcf51b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a875131ff74dcdf22ef0909ff50ed4abc2dfd2501cfca6dda83e7715fddcf51b","first_computed_at":"2026-05-17T23:51:00.466814Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:00.466814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uhRLdnRXBo5YLs+HjHu0wFImFfelzp8aduUC29BT2WwiNwnbahg2ZqGuF8+1N6D/eFnOe2d2cVN+PVX6xy+cDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:00.467354Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.06977","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87588f248089abf0e2d52abd16e2c91109e5e2d2a7e51289d91c0165824b0907","sha256:2a9c1f0c3eaa57eb41e98ecb054e8e53931a296835f75d29a81087bd97331199"],"state_sha256":"542718a3168704edc019c447950cb4a9d23dba8d3b54602a124b57cf93ab8d2e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2YuL4po7UjGKsMuObI7NeptCVyPKmltwTgBYSHGN64i4cxQH4ZLBe6B1Zn6Py2IQMZluE5wa/wox6oOrzQ6PCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T18:48:42.751031Z","bundle_sha256":"c1074e1636ece38fbac301aeb4973d0862bd63d711d35852bd238bdc25f7487c"}}