{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:TW3VQWESHAXMM2LEMIY5ZQ3A47","short_pith_number":"pith:TW3VQWES","canonical_record":{"source":{"id":"1104.0050","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-31T23:50:43Z","cross_cats_sorted":[],"title_canon_sha256":"23d1ae2e05830746a162f082b2de008ee3dbf28161afb8fb913933ba41c61700","abstract_canon_sha256":"5c10e6893734555339fb8de0b7c1af9d8dcfda45362f26ea950bc7d83ab62fa8"},"schema_version":"1.0"},"canonical_sha256":"9db7585892382ec669646231dcc360e7c5b529d4898e8a876e7d155002edc62d","source":{"kind":"arxiv","id":"1104.0050","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0050","created_at":"2026-05-18T04:19:54Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0050v3","created_at":"2026-05-18T04:19:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0050","created_at":"2026-05-18T04:19:54Z"},{"alias_kind":"pith_short_12","alias_value":"TW3VQWESHAXM","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TW3VQWESHAXMM2LE","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TW3VQWES","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:TW3VQWESHAXMM2LEMIY5ZQ3A47","target":"record","payload":{"canonical_record":{"source":{"id":"1104.0050","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-31T23:50:43Z","cross_cats_sorted":[],"title_canon_sha256":"23d1ae2e05830746a162f082b2de008ee3dbf28161afb8fb913933ba41c61700","abstract_canon_sha256":"5c10e6893734555339fb8de0b7c1af9d8dcfda45362f26ea950bc7d83ab62fa8"},"schema_version":"1.0"},"canonical_sha256":"9db7585892382ec669646231dcc360e7c5b529d4898e8a876e7d155002edc62d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:54.502394Z","signature_b64":"9T8fwOqqfjZKGiKg4gAcO06Fga9N4GTN2Ez5q22eMRz1eYjCMsEno2UYZXqfiHwn0ITpotAz4Vtww06Wmz/0AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9db7585892382ec669646231dcc360e7c5b529d4898e8a876e7d155002edc62d","last_reissued_at":"2026-05-18T04:19:54.501703Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:54.501703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.0050","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":"2026-05-18T04:19:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XZ69MfNmxVbLK1v7/OwddyKElJtEGFXXY7InHr86PlGD2zVSjkS84wJiTdE+1cVN43ImlH5M3UgNkkzD8dGbDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:38:19.549759Z"},"content_sha256":"0a5fe3b0a00b42cae66f568b8acd2ac650079dec4b9d2a778b990da51ebf79e4","schema_version":"1.0","event_id":"sha256:0a5fe3b0a00b42cae66f568b8acd2ac650079dec4b9d2a778b990da51ebf79e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:TW3VQWESHAXMM2LEMIY5ZQ3A47","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classification of constant angle hypersurfaces in warped products via eikonal functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Eugenio Garnica, Gabriel Ruiz-Hernandez, Oscar Palmas","submitted_at":"2011-03-31T23:50:43Z","abstract_excerpt":"Given a warped product of the real line with a Riemannian manifold of arbitrary dimension, we classify the hypersurfaces whose tangent spaces make a constant angle with the vector field tangent to the real direction. We show that this is a natural setting in which to extend previous results in this direction made by several authors. Moreover, when the constant angle hypersurface is a graph over the Riemannian manifold, we show that the function involved satisfies a generalized eikonal equation, which we solve via a geometric method. In the final part of this paper we prove that minimal constan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0050","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":"2026-05-18T04:19:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DK+J4N1z3qCQz/AyMSfD7f5yQW5oxsfPFJOYJeac9hBFQKGH5zaHlzka1CZ53+2c1UyYZ71s5I5hxNcBPbcnDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:38:19.550086Z"},"content_sha256":"e2d9251cbb846d3b88c41fcc1ddc8083ace0e559e93037b659739f1a434fa1e8","schema_version":"1.0","event_id":"sha256:e2d9251cbb846d3b88c41fcc1ddc8083ace0e559e93037b659739f1a434fa1e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TW3VQWESHAXMM2LEMIY5ZQ3A47/bundle.json","state_url":"https://pith.science/pith/TW3VQWESHAXMM2LEMIY5ZQ3A47/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TW3VQWESHAXMM2LEMIY5ZQ3A47/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":"2026-06-20T07:38:19Z","links":{"resolver":"https://pith.science/pith/TW3VQWESHAXMM2LEMIY5ZQ3A47","bundle":"https://pith.science/pith/TW3VQWESHAXMM2LEMIY5ZQ3A47/bundle.json","state":"https://pith.science/pith/TW3VQWESHAXMM2LEMIY5ZQ3A47/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TW3VQWESHAXMM2LEMIY5ZQ3A47/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TW3VQWESHAXMM2LEMIY5ZQ3A47","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":"5c10e6893734555339fb8de0b7c1af9d8dcfda45362f26ea950bc7d83ab62fa8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-31T23:50:43Z","title_canon_sha256":"23d1ae2e05830746a162f082b2de008ee3dbf28161afb8fb913933ba41c61700"},"schema_version":"1.0","source":{"id":"1104.0050","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0050","created_at":"2026-05-18T04:19:54Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0050v3","created_at":"2026-05-18T04:19:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0050","created_at":"2026-05-18T04:19:54Z"},{"alias_kind":"pith_short_12","alias_value":"TW3VQWESHAXM","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TW3VQWESHAXMM2LE","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TW3VQWES","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:e2d9251cbb846d3b88c41fcc1ddc8083ace0e559e93037b659739f1a434fa1e8","target":"graph","created_at":"2026-05-18T04:19:54Z","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":"Given a warped product of the real line with a Riemannian manifold of arbitrary dimension, we classify the hypersurfaces whose tangent spaces make a constant angle with the vector field tangent to the real direction. We show that this is a natural setting in which to extend previous results in this direction made by several authors. Moreover, when the constant angle hypersurface is a graph over the Riemannian manifold, we show that the function involved satisfies a generalized eikonal equation, which we solve via a geometric method. In the final part of this paper we prove that minimal constan","authors_text":"Eugenio Garnica, Gabriel Ruiz-Hernandez, Oscar Palmas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-31T23:50:43Z","title":"Classification of constant angle hypersurfaces in warped products via eikonal functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0050","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":"sha256:0a5fe3b0a00b42cae66f568b8acd2ac650079dec4b9d2a778b990da51ebf79e4","target":"record","created_at":"2026-05-18T04:19:54Z","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":"5c10e6893734555339fb8de0b7c1af9d8dcfda45362f26ea950bc7d83ab62fa8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-31T23:50:43Z","title_canon_sha256":"23d1ae2e05830746a162f082b2de008ee3dbf28161afb8fb913933ba41c61700"},"schema_version":"1.0","source":{"id":"1104.0050","kind":"arxiv","version":3}},"canonical_sha256":"9db7585892382ec669646231dcc360e7c5b529d4898e8a876e7d155002edc62d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9db7585892382ec669646231dcc360e7c5b529d4898e8a876e7d155002edc62d","first_computed_at":"2026-05-18T04:19:54.501703Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:54.501703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9T8fwOqqfjZKGiKg4gAcO06Fga9N4GTN2Ez5q22eMRz1eYjCMsEno2UYZXqfiHwn0ITpotAz4Vtww06Wmz/0AA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:54.502394Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.0050","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a5fe3b0a00b42cae66f568b8acd2ac650079dec4b9d2a778b990da51ebf79e4","sha256:e2d9251cbb846d3b88c41fcc1ddc8083ace0e559e93037b659739f1a434fa1e8"],"state_sha256":"5da74c64deeae55a8b670339d45ef446ffe903d439a0d9a56a9c570708ace5b7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a499DumycAGRQIrRPv/5eq1LMXAmo7VKxzTKNw5KxxykkxWC55wMFoKn3WYhViL6p+iUa9evDr/Wp8cPmvH0CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T07:38:19.551965Z","bundle_sha256":"0793d9d976a682b60675429ea463e9de5cdfc1b92abbc13fd61b6beea61da003"}}