{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:3FQEASNFTB76EQFQD36LIJTUPI","short_pith_number":"pith:3FQEASNF","canonical_record":{"source":{"id":"1908.01620","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-05T13:48:06Z","cross_cats_sorted":[],"title_canon_sha256":"551af997d345fd819581e024383467428d20a67e835ad83c06b63f5caba27203","abstract_canon_sha256":"23f277f67ab58e20eb1bcf55b66b07eab82f9e1983217459e936d3c836c903f9"},"schema_version":"1.0"},"canonical_sha256":"d9604049a5987fe240b01efcb426747a00cc5d35b9e7c6b132757ab1350e6d0d","source":{"kind":"arxiv","id":"1908.01620","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.01620","created_at":"2026-07-04T23:51:32Z"},{"alias_kind":"arxiv_version","alias_value":"1908.01620v1","created_at":"2026-07-04T23:51:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01620","created_at":"2026-07-04T23:51:32Z"},{"alias_kind":"pith_short_12","alias_value":"3FQEASNFTB76","created_at":"2026-07-04T23:51:32Z"},{"alias_kind":"pith_short_16","alias_value":"3FQEASNFTB76EQFQ","created_at":"2026-07-04T23:51:32Z"},{"alias_kind":"pith_short_8","alias_value":"3FQEASNF","created_at":"2026-07-04T23:51:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:3FQEASNFTB76EQFQD36LIJTUPI","target":"record","payload":{"canonical_record":{"source":{"id":"1908.01620","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-05T13:48:06Z","cross_cats_sorted":[],"title_canon_sha256":"551af997d345fd819581e024383467428d20a67e835ad83c06b63f5caba27203","abstract_canon_sha256":"23f277f67ab58e20eb1bcf55b66b07eab82f9e1983217459e936d3c836c903f9"},"schema_version":"1.0"},"canonical_sha256":"d9604049a5987fe240b01efcb426747a00cc5d35b9e7c6b132757ab1350e6d0d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:51:32.293139Z","signature_b64":"o53j3YTQVWkzmwMVES6T6qloHMPEsFXa34L/rqec7qACohuYhapLDIOeMUhwsmzcbCty0qsOprPNaBko/sdMDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9604049a5987fe240b01efcb426747a00cc5d35b9e7c6b132757ab1350e6d0d","last_reissued_at":"2026-07-04T23:51:32.292800Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:51:32.292800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.01620","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":"2026-07-04T23:51:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VP9lvwTjuvoH1IgKxcBRaX6WgM/QANWN00WL1pMRN3r94609YNTudPP7o93ley1DRuJ+tqenjzDFJGXeVLTCAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T17:44:49.012122Z"},"content_sha256":"2c99ee17ce5b6e09097e0ef6dced1d289b8be5fb922a3fb4b9c28f24ba24c4cf","schema_version":"1.0","event_id":"sha256:2c99ee17ce5b6e09097e0ef6dced1d289b8be5fb922a3fb4b9c28f24ba24c4cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:3FQEASNFTB76EQFQD36LIJTUPI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on $r$ hypersurfaces intersecting in $\\mathbb{P}^r$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dennis Tseng","submitted_at":"2019-08-05T13:48:06Z","abstract_excerpt":"We consider the locus of $r$-tuples of homogeneous forms of some fixed degree whose common vanishing locus in $\\mathbb{P}^r$ is positive dimensional. We show that any component of maximal dimension of that locus either consists of homogeneous forms all vanishing on some line or homogeneous forms where a proper subset fail to intersect properly."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01620","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/1908.01620/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":"2026-07-04T23:51:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jzUWuGD2oj41ajxzUdL0iTnvq6eYu8tGkvocYIvyq5n1j0hcHJw1ef8F9tmtKJzWfuy1uWLB2J6BfGqNL0ZBAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T17:44:49.013048Z"},"content_sha256":"28ef32b76427e18bb322eb1d83efa572ca66aa9657f43aa1aed0d0b5f78de449","schema_version":"1.0","event_id":"sha256:28ef32b76427e18bb322eb1d83efa572ca66aa9657f43aa1aed0d0b5f78de449"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3FQEASNFTB76EQFQD36LIJTUPI/bundle.json","state_url":"https://pith.science/pith/3FQEASNFTB76EQFQD36LIJTUPI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3FQEASNFTB76EQFQD36LIJTUPI/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":"2026-08-16T17:44:49Z","links":{"resolver":"https://pith.science/pith/3FQEASNFTB76EQFQD36LIJTUPI","bundle":"https://pith.science/pith/3FQEASNFTB76EQFQD36LIJTUPI/bundle.json","state":"https://pith.science/pith/3FQEASNFTB76EQFQD36LIJTUPI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3FQEASNFTB76EQFQD36LIJTUPI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:3FQEASNFTB76EQFQD36LIJTUPI","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":"23f277f67ab58e20eb1bcf55b66b07eab82f9e1983217459e936d3c836c903f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-05T13:48:06Z","title_canon_sha256":"551af997d345fd819581e024383467428d20a67e835ad83c06b63f5caba27203"},"schema_version":"1.0","source":{"id":"1908.01620","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.01620","created_at":"2026-07-04T23:51:32Z"},{"alias_kind":"arxiv_version","alias_value":"1908.01620v1","created_at":"2026-07-04T23:51:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01620","created_at":"2026-07-04T23:51:32Z"},{"alias_kind":"pith_short_12","alias_value":"3FQEASNFTB76","created_at":"2026-07-04T23:51:32Z"},{"alias_kind":"pith_short_16","alias_value":"3FQEASNFTB76EQFQ","created_at":"2026-07-04T23:51:32Z"},{"alias_kind":"pith_short_8","alias_value":"3FQEASNF","created_at":"2026-07-04T23:51:32Z"}],"graph_snapshots":[{"event_id":"sha256:28ef32b76427e18bb322eb1d83efa572ca66aa9657f43aa1aed0d0b5f78de449","target":"graph","created_at":"2026-07-04T23:51:32Z","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/1908.01620/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the locus of $r$-tuples of homogeneous forms of some fixed degree whose common vanishing locus in $\\mathbb{P}^r$ is positive dimensional. We show that any component of maximal dimension of that locus either consists of homogeneous forms all vanishing on some line or homogeneous forms where a proper subset fail to intersect properly.","authors_text":"Dennis Tseng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-05T13:48:06Z","title":"A note on $r$ hypersurfaces intersecting in $\\mathbb{P}^r$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01620","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":"sha256:2c99ee17ce5b6e09097e0ef6dced1d289b8be5fb922a3fb4b9c28f24ba24c4cf","target":"record","created_at":"2026-07-04T23:51:32Z","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":"23f277f67ab58e20eb1bcf55b66b07eab82f9e1983217459e936d3c836c903f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-05T13:48:06Z","title_canon_sha256":"551af997d345fd819581e024383467428d20a67e835ad83c06b63f5caba27203"},"schema_version":"1.0","source":{"id":"1908.01620","kind":"arxiv","version":1}},"canonical_sha256":"d9604049a5987fe240b01efcb426747a00cc5d35b9e7c6b132757ab1350e6d0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9604049a5987fe240b01efcb426747a00cc5d35b9e7c6b132757ab1350e6d0d","first_computed_at":"2026-07-04T23:51:32.292800Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:51:32.292800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o53j3YTQVWkzmwMVES6T6qloHMPEsFXa34L/rqec7qACohuYhapLDIOeMUhwsmzcbCty0qsOprPNaBko/sdMDw==","signature_status":"signed_v1","signed_at":"2026-07-04T23:51:32.293139Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.01620","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c99ee17ce5b6e09097e0ef6dced1d289b8be5fb922a3fb4b9c28f24ba24c4cf","sha256:28ef32b76427e18bb322eb1d83efa572ca66aa9657f43aa1aed0d0b5f78de449"],"state_sha256":"f1905f12bb31851cc03cbb834b16f5003a46479c6388c306505b3deb842c906b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5zYkVWxZViQKOxI8qJHkl++GKscTh69PTBkOUailfZE07eze/SH3a89/Q4VMdoz5vVp1lWL4+vdqAzRX/umLAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T17:44:49.038467Z","bundle_sha256":"01449a7fc32c8ad49be4515e1b8f40b3fd61aa24f99b39c1fddca5ea0efea1cb"}}