{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:LX4GBLMRQDPBCTVUO2K55APUII","short_pith_number":"pith:LX4GBLMR","canonical_record":{"source":{"id":"1010.0665","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-04T19:33:38Z","cross_cats_sorted":[],"title_canon_sha256":"6c27664de29522257280de854a138126fd539d204b440730cbcf474b2df45514","abstract_canon_sha256":"da689cf39e81a6417c37df06bd1a4abf6485be781e310dbccdc11f7097f085a0"},"schema_version":"1.0"},"canonical_sha256":"5df860ad9180de114eb47695de81f44219f903d3c275f53e34793f15f3abfc7c","source":{"kind":"arxiv","id":"1010.0665","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0665","created_at":"2026-05-18T04:03:57Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0665v3","created_at":"2026-05-18T04:03:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0665","created_at":"2026-05-18T04:03:57Z"},{"alias_kind":"pith_short_12","alias_value":"LX4GBLMRQDPB","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"LX4GBLMRQDPBCTVU","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"LX4GBLMR","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:LX4GBLMRQDPBCTVUO2K55APUII","target":"record","payload":{"canonical_record":{"source":{"id":"1010.0665","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-04T19:33:38Z","cross_cats_sorted":[],"title_canon_sha256":"6c27664de29522257280de854a138126fd539d204b440730cbcf474b2df45514","abstract_canon_sha256":"da689cf39e81a6417c37df06bd1a4abf6485be781e310dbccdc11f7097f085a0"},"schema_version":"1.0"},"canonical_sha256":"5df860ad9180de114eb47695de81f44219f903d3c275f53e34793f15f3abfc7c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:57.051695Z","signature_b64":"DQLqy0EC0BnoeK2m4fn4xacCbfY48jEDSR5ZaxTDWOlFdXBPA0MSfLRJCpS/sTifjNlTs8YvykoIpqQQUgzLDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5df860ad9180de114eb47695de81f44219f903d3c275f53e34793f15f3abfc7c","last_reissued_at":"2026-05-18T04:03:57.050985Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:57.050985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.0665","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:03:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sMftuxBslRM7+frSOxTrwQCfnHXrXUJc+Ki7F0lenetgX5SK5MzW66Xm4RXO89MwMTMeD5u1gMZ7HswpdmBGBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T14:45:33.295767Z"},"content_sha256":"0ab4da72bbefc891a0e8bcc68b3e3c792886b5278c0d4fe68f50f101daf97865","schema_version":"1.0","event_id":"sha256:0ab4da72bbefc891a0e8bcc68b3e3c792886b5278c0d4fe68f50f101daf97865"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:LX4GBLMRQDPBCTVUO2K55APUII","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Secant Conjecture in the real Schubert calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Abraham Martin del Campo, Christopher J. Hillar, Frank Sottile, James Ruffo, Luis Garcia-Puente, Nickolas Hein, Zach Teitler","submitted_at":"2010-10-04T19:33:38Z","abstract_excerpt":"We formulate the Secant Conjecture, which is a generalization of the Shapiro Conjecture for Grassmannians. It asserts that an intersection of Schubert varieties in a Grassmannian is transverse with all points real, if the flags defining the Schubert varieties are secant along disjoint intervals of a rational normal curve. We present theoretical evidence for it as well as computational evidence obtained in over one terahertz-year of computing, and we discuss some phenomena we observed in our data."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0665","kind":"arxiv","version":3},"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":"2026-05-18T04:03:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jvWgdHnkEALr0xp0EkknfJLtpOe1ajec6Vo3jDeikV2uU3Ik0Vfvim4m51B3cXKjwrFXsc2/Acch0gqnSZ8YAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T14:45:33.296109Z"},"content_sha256":"5b9c0356e38f54ee02642549fa779afc7ec8f480b86f2abb10403eff4534527c","schema_version":"1.0","event_id":"sha256:5b9c0356e38f54ee02642549fa779afc7ec8f480b86f2abb10403eff4534527c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LX4GBLMRQDPBCTVUO2K55APUII/bundle.json","state_url":"https://pith.science/pith/LX4GBLMRQDPBCTVUO2K55APUII/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LX4GBLMRQDPBCTVUO2K55APUII/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":"2026-06-20T14:45:33Z","links":{"resolver":"https://pith.science/pith/LX4GBLMRQDPBCTVUO2K55APUII","bundle":"https://pith.science/pith/LX4GBLMRQDPBCTVUO2K55APUII/bundle.json","state":"https://pith.science/pith/LX4GBLMRQDPBCTVUO2K55APUII/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LX4GBLMRQDPBCTVUO2K55APUII/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:LX4GBLMRQDPBCTVUO2K55APUII","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":"da689cf39e81a6417c37df06bd1a4abf6485be781e310dbccdc11f7097f085a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-04T19:33:38Z","title_canon_sha256":"6c27664de29522257280de854a138126fd539d204b440730cbcf474b2df45514"},"schema_version":"1.0","source":{"id":"1010.0665","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0665","created_at":"2026-05-18T04:03:57Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0665v3","created_at":"2026-05-18T04:03:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0665","created_at":"2026-05-18T04:03:57Z"},{"alias_kind":"pith_short_12","alias_value":"LX4GBLMRQDPB","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"LX4GBLMRQDPBCTVU","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"LX4GBLMR","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:5b9c0356e38f54ee02642549fa779afc7ec8f480b86f2abb10403eff4534527c","target":"graph","created_at":"2026-05-18T04:03:57Z","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":"We formulate the Secant Conjecture, which is a generalization of the Shapiro Conjecture for Grassmannians. It asserts that an intersection of Schubert varieties in a Grassmannian is transverse with all points real, if the flags defining the Schubert varieties are secant along disjoint intervals of a rational normal curve. We present theoretical evidence for it as well as computational evidence obtained in over one terahertz-year of computing, and we discuss some phenomena we observed in our data.","authors_text":"Abraham Martin del Campo, Christopher J. Hillar, Frank Sottile, James Ruffo, Luis Garcia-Puente, Nickolas Hein, Zach Teitler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-04T19:33:38Z","title":"The Secant Conjecture in the real Schubert calculus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0665","kind":"arxiv","version":3},"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":"sha256:0ab4da72bbefc891a0e8bcc68b3e3c792886b5278c0d4fe68f50f101daf97865","target":"record","created_at":"2026-05-18T04:03:57Z","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":"da689cf39e81a6417c37df06bd1a4abf6485be781e310dbccdc11f7097f085a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-04T19:33:38Z","title_canon_sha256":"6c27664de29522257280de854a138126fd539d204b440730cbcf474b2df45514"},"schema_version":"1.0","source":{"id":"1010.0665","kind":"arxiv","version":3}},"canonical_sha256":"5df860ad9180de114eb47695de81f44219f903d3c275f53e34793f15f3abfc7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5df860ad9180de114eb47695de81f44219f903d3c275f53e34793f15f3abfc7c","first_computed_at":"2026-05-18T04:03:57.050985Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:57.050985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DQLqy0EC0BnoeK2m4fn4xacCbfY48jEDSR5ZaxTDWOlFdXBPA0MSfLRJCpS/sTifjNlTs8YvykoIpqQQUgzLDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:57.051695Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.0665","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ab4da72bbefc891a0e8bcc68b3e3c792886b5278c0d4fe68f50f101daf97865","sha256:5b9c0356e38f54ee02642549fa779afc7ec8f480b86f2abb10403eff4534527c"],"state_sha256":"cbff72ee493c6da18285a535352a6ceed13532193d83f5a25e8941c4a4e65bc7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AFLuop8VS1aTZgihqDqqx8+uULsUJ00XaA19AtYo+R6E8oYZyQyjb9F/9Qt0aj4J3NDq0nyD2a6WPyyhhVADDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T14:45:33.298052Z","bundle_sha256":"994d0866e06b01115d74a70536dc78e5b204dc616851e52c269864e88da135df"}}