{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:EFYNLFBMJN2NNUY42QKHNY3A6C","short_pith_number":"pith:EFYNLFBM","canonical_record":{"source":{"id":"1909.13136","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-09-28T19:21:18Z","cross_cats_sorted":[],"title_canon_sha256":"5944c383ca989ad67222a7aa7450d3a9a0677fc623aed8ab8977930ce3c42707","abstract_canon_sha256":"42ebf4be9d55784e511748896f75b96e9709fb35580c3c1eb6bbd222a74119e1"},"schema_version":"1.0"},"canonical_sha256":"2170d5942c4b74d6d31cd41476e360f0b375e9fedf957e89b2afa47502af2b7a","source":{"kind":"arxiv","id":"1909.13136","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.13136","created_at":"2026-07-05T00:07:56Z"},{"alias_kind":"arxiv_version","alias_value":"1909.13136v1","created_at":"2026-07-05T00:07:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.13136","created_at":"2026-07-05T00:07:56Z"},{"alias_kind":"pith_short_12","alias_value":"EFYNLFBMJN2N","created_at":"2026-07-05T00:07:56Z"},{"alias_kind":"pith_short_16","alias_value":"EFYNLFBMJN2NNUY4","created_at":"2026-07-05T00:07:56Z"},{"alias_kind":"pith_short_8","alias_value":"EFYNLFBM","created_at":"2026-07-05T00:07:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:EFYNLFBMJN2NNUY42QKHNY3A6C","target":"record","payload":{"canonical_record":{"source":{"id":"1909.13136","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-09-28T19:21:18Z","cross_cats_sorted":[],"title_canon_sha256":"5944c383ca989ad67222a7aa7450d3a9a0677fc623aed8ab8977930ce3c42707","abstract_canon_sha256":"42ebf4be9d55784e511748896f75b96e9709fb35580c3c1eb6bbd222a74119e1"},"schema_version":"1.0"},"canonical_sha256":"2170d5942c4b74d6d31cd41476e360f0b375e9fedf957e89b2afa47502af2b7a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:07:56.397844Z","signature_b64":"GW9+swJnmjCSsWzoLIti3UWGjHUJHHon1VKe+fur+rtYS7EJdQhgNYFMksNWCU047W6QGeDeRdu5vRHasH90CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2170d5942c4b74d6d31cd41476e360f0b375e9fedf957e89b2afa47502af2b7a","last_reissued_at":"2026-07-05T00:07:56.397488Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:07:56.397488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1909.13136","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":"2026-07-05T00:07:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o5LWuvPCKsV4Vw5Mt2X7hWdmz8Sf+VhqJC/cKSBVjeq4w5hULGTUXkDx3aJAkDi+IC/ysNTDvWAqx6R/mfkBAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T06:19:28.175187Z"},"content_sha256":"97572513edb55ccc5003a9f99d774df75cbadfe583d787d594785a2e57b543c5","schema_version":"1.0","event_id":"sha256:97572513edb55ccc5003a9f99d774df75cbadfe583d787d594785a2e57b543c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:EFYNLFBMJN2NNUY42QKHNY3A6C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Loxodromic unit vector field on punctured spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Adriana V. Nicoli, Giovanni N. Nunes, Jackeline Conrado","submitted_at":"2019-09-28T19:21:18Z","abstract_excerpt":"In these short notes we characterize the loxodromic unit vector fields on antipodally punctured Euclidean spheres as the only ones achieving a lower bound for the volume functional depending on the Poincar\\'e indexes around their singularities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.13136","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/1909.13136/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":"2026-07-05T00:07:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0+CYkO1bNLIGfpdNfs2vQWwQsx3UoypkNIJ3n7w3H54lSwDT04J9a0NJfbG+8fsklEWdEmz67G1vnKFxD8EcBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T06:19:28.175566Z"},"content_sha256":"e0d84c42d10284e0aae7bd7a831cd968ae9338e9855b2c7c6f0a334a1ace38a9","schema_version":"1.0","event_id":"sha256:e0d84c42d10284e0aae7bd7a831cd968ae9338e9855b2c7c6f0a334a1ace38a9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EFYNLFBMJN2NNUY42QKHNY3A6C/bundle.json","state_url":"https://pith.science/pith/EFYNLFBMJN2NNUY42QKHNY3A6C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EFYNLFBMJN2NNUY42QKHNY3A6C/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":"2026-07-08T06:19:28Z","links":{"resolver":"https://pith.science/pith/EFYNLFBMJN2NNUY42QKHNY3A6C","bundle":"https://pith.science/pith/EFYNLFBMJN2NNUY42QKHNY3A6C/bundle.json","state":"https://pith.science/pith/EFYNLFBMJN2NNUY42QKHNY3A6C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EFYNLFBMJN2NNUY42QKHNY3A6C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:EFYNLFBMJN2NNUY42QKHNY3A6C","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":"42ebf4be9d55784e511748896f75b96e9709fb35580c3c1eb6bbd222a74119e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-09-28T19:21:18Z","title_canon_sha256":"5944c383ca989ad67222a7aa7450d3a9a0677fc623aed8ab8977930ce3c42707"},"schema_version":"1.0","source":{"id":"1909.13136","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.13136","created_at":"2026-07-05T00:07:56Z"},{"alias_kind":"arxiv_version","alias_value":"1909.13136v1","created_at":"2026-07-05T00:07:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.13136","created_at":"2026-07-05T00:07:56Z"},{"alias_kind":"pith_short_12","alias_value":"EFYNLFBMJN2N","created_at":"2026-07-05T00:07:56Z"},{"alias_kind":"pith_short_16","alias_value":"EFYNLFBMJN2NNUY4","created_at":"2026-07-05T00:07:56Z"},{"alias_kind":"pith_short_8","alias_value":"EFYNLFBM","created_at":"2026-07-05T00:07:56Z"}],"graph_snapshots":[{"event_id":"sha256:e0d84c42d10284e0aae7bd7a831cd968ae9338e9855b2c7c6f0a334a1ace38a9","target":"graph","created_at":"2026-07-05T00:07:56Z","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/1909.13136/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In these short notes we characterize the loxodromic unit vector fields on antipodally punctured Euclidean spheres as the only ones achieving a lower bound for the volume functional depending on the Poincar\\'e indexes around their singularities.","authors_text":"Adriana V. Nicoli, Giovanni N. Nunes, Jackeline Conrado","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-09-28T19:21:18Z","title":"Loxodromic unit vector field on punctured spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.13136","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":"sha256:97572513edb55ccc5003a9f99d774df75cbadfe583d787d594785a2e57b543c5","target":"record","created_at":"2026-07-05T00:07:56Z","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":"42ebf4be9d55784e511748896f75b96e9709fb35580c3c1eb6bbd222a74119e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-09-28T19:21:18Z","title_canon_sha256":"5944c383ca989ad67222a7aa7450d3a9a0677fc623aed8ab8977930ce3c42707"},"schema_version":"1.0","source":{"id":"1909.13136","kind":"arxiv","version":1}},"canonical_sha256":"2170d5942c4b74d6d31cd41476e360f0b375e9fedf957e89b2afa47502af2b7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2170d5942c4b74d6d31cd41476e360f0b375e9fedf957e89b2afa47502af2b7a","first_computed_at":"2026-07-05T00:07:56.397488Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:07:56.397488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GW9+swJnmjCSsWzoLIti3UWGjHUJHHon1VKe+fur+rtYS7EJdQhgNYFMksNWCU047W6QGeDeRdu5vRHasH90CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:07:56.397844Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.13136","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97572513edb55ccc5003a9f99d774df75cbadfe583d787d594785a2e57b543c5","sha256:e0d84c42d10284e0aae7bd7a831cd968ae9338e9855b2c7c6f0a334a1ace38a9"],"state_sha256":"4ebf0bc1dd02487d5d3db23b3a86853783eaa6b5b60f25d85b964bc932b874d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VmRhdMXeBcgZbonjPmrvy09xZryePp3ha4UOzWkmqEsSXrRrUCrSx0tOOBf7jrBFiLsIwAu2QbqhxlSsbVs7BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-08T06:19:28.177614Z","bundle_sha256":"b7889cfdc5955df8efe8f8148bf9c4a0f0855a56db76fe0554fd047f9497b914"}}