{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:DQSFLHYK343QYA7C46ST4OZQVI","short_pith_number":"pith:DQSFLHYK","canonical_record":{"source":{"id":"1110.2201","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-10T21:18:57Z","cross_cats_sorted":[],"title_canon_sha256":"ba26ac047914a17f5a91d909f9b090c306d9351c801d85f11662705191e59b63","abstract_canon_sha256":"25d7284d001eb0cfb2ffff98bb668ea892269e0dc7f240b2d930151b59a5042d"},"schema_version":"1.0"},"canonical_sha256":"1c24559f0adf370c03e2e7a53e3b30aa10d23d13dd84dc9655462aa8654172c5","source":{"kind":"arxiv","id":"1110.2201","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2201","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2201v1","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2201","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"pith_short_12","alias_value":"DQSFLHYK343Q","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DQSFLHYK343QYA7C","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DQSFLHYK","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:DQSFLHYK343QYA7C46ST4OZQVI","target":"record","payload":{"canonical_record":{"source":{"id":"1110.2201","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-10T21:18:57Z","cross_cats_sorted":[],"title_canon_sha256":"ba26ac047914a17f5a91d909f9b090c306d9351c801d85f11662705191e59b63","abstract_canon_sha256":"25d7284d001eb0cfb2ffff98bb668ea892269e0dc7f240b2d930151b59a5042d"},"schema_version":"1.0"},"canonical_sha256":"1c24559f0adf370c03e2e7a53e3b30aa10d23d13dd84dc9655462aa8654172c5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:17.406147Z","signature_b64":"MV1q4iMKZ3nrvcB6tBrAsL02iDjgFheEYGZ2uIIaGYGjb1oR1WgAM6uBbN4mEeIGXnFus0oxNBHtrg/QdwoVDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c24559f0adf370c03e2e7a53e3b30aa10d23d13dd84dc9655462aa8654172c5","last_reissued_at":"2026-05-18T04:11:17.405592Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:17.405592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.2201","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":"2026-05-18T04:11:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GQV7zp5Cmud0weGloNK68tM9vmiXecbZ3ezcpQOUEe6UFQQNh2c9lsXXdPSoxn0AgfzdeTEbMebzsk+smjOCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:57:43.088792Z"},"content_sha256":"fee54a39341573bca697c0476ef70e6bc5bc3627dd6af1060d2bb14b8e0aecb1","schema_version":"1.0","event_id":"sha256:fee54a39341573bca697c0476ef70e6bc5bc3627dd6af1060d2bb14b8e0aecb1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:DQSFLHYK343QYA7C46ST4OZQVI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hypersurfaces with a canonical principal direction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Eugenio Garnica, Gabriel Ruiz-Hern\\'andez, Oscar Palmas","submitted_at":"2011-10-10T21:18:57Z","abstract_excerpt":"Given a vector field $X$ in a Riemannian manifold, a hypersurface is said to have a canonical principal direction relative to $X$ if the projection of $X$ onto the tangent space of the hypersurface gives a principal direction. We give different ways for building these hypersurfaces, as well as a number of useful characterizations. In particular, we relate them with transnormal functions and eikonal equations. With the further condition of having constant mean curvature (CMC) we obtain a characterization of the canonical principal direction surfaces in Euclidean space as Delaunay surfaces. We a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2201","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":"2026-05-18T04:11:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5EJHwNdei3wL2wh1dIBR+a/+E3ZV/y0Qzg9kgxVbiyQJv3NwSu2B5OC4+hezJr3g7p7UtuAPUuRiTVkUJVbOCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:57:43.089131Z"},"content_sha256":"24c53cf6db430a8a502412655812d9b3673098e96b57dc4b8bd1776b255c8610","schema_version":"1.0","event_id":"sha256:24c53cf6db430a8a502412655812d9b3673098e96b57dc4b8bd1776b255c8610"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DQSFLHYK343QYA7C46ST4OZQVI/bundle.json","state_url":"https://pith.science/pith/DQSFLHYK343QYA7C46ST4OZQVI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DQSFLHYK343QYA7C46ST4OZQVI/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":"2026-06-20T06:57:43Z","links":{"resolver":"https://pith.science/pith/DQSFLHYK343QYA7C46ST4OZQVI","bundle":"https://pith.science/pith/DQSFLHYK343QYA7C46ST4OZQVI/bundle.json","state":"https://pith.science/pith/DQSFLHYK343QYA7C46ST4OZQVI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DQSFLHYK343QYA7C46ST4OZQVI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DQSFLHYK343QYA7C46ST4OZQVI","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":"25d7284d001eb0cfb2ffff98bb668ea892269e0dc7f240b2d930151b59a5042d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-10T21:18:57Z","title_canon_sha256":"ba26ac047914a17f5a91d909f9b090c306d9351c801d85f11662705191e59b63"},"schema_version":"1.0","source":{"id":"1110.2201","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2201","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2201v1","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2201","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"pith_short_12","alias_value":"DQSFLHYK343Q","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DQSFLHYK343QYA7C","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DQSFLHYK","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:24c53cf6db430a8a502412655812d9b3673098e96b57dc4b8bd1776b255c8610","target":"graph","created_at":"2026-05-18T04:11:17Z","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 vector field $X$ in a Riemannian manifold, a hypersurface is said to have a canonical principal direction relative to $X$ if the projection of $X$ onto the tangent space of the hypersurface gives a principal direction. We give different ways for building these hypersurfaces, as well as a number of useful characterizations. In particular, we relate them with transnormal functions and eikonal equations. With the further condition of having constant mean curvature (CMC) we obtain a characterization of the canonical principal direction surfaces in Euclidean space as Delaunay surfaces. We a","authors_text":"Eugenio Garnica, Gabriel Ruiz-Hern\\'andez, Oscar Palmas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-10T21:18:57Z","title":"Hypersurfaces with a canonical principal direction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2201","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:fee54a39341573bca697c0476ef70e6bc5bc3627dd6af1060d2bb14b8e0aecb1","target":"record","created_at":"2026-05-18T04:11:17Z","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":"25d7284d001eb0cfb2ffff98bb668ea892269e0dc7f240b2d930151b59a5042d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-10T21:18:57Z","title_canon_sha256":"ba26ac047914a17f5a91d909f9b090c306d9351c801d85f11662705191e59b63"},"schema_version":"1.0","source":{"id":"1110.2201","kind":"arxiv","version":1}},"canonical_sha256":"1c24559f0adf370c03e2e7a53e3b30aa10d23d13dd84dc9655462aa8654172c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c24559f0adf370c03e2e7a53e3b30aa10d23d13dd84dc9655462aa8654172c5","first_computed_at":"2026-05-18T04:11:17.405592Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:17.405592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MV1q4iMKZ3nrvcB6tBrAsL02iDjgFheEYGZ2uIIaGYGjb1oR1WgAM6uBbN4mEeIGXnFus0oxNBHtrg/QdwoVDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:17.406147Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.2201","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fee54a39341573bca697c0476ef70e6bc5bc3627dd6af1060d2bb14b8e0aecb1","sha256:24c53cf6db430a8a502412655812d9b3673098e96b57dc4b8bd1776b255c8610"],"state_sha256":"843e8ca51eab0e5156c1b484cec79ee4318f240972ba96b7efc86db9e9f8a896"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ylLlPr5vgb1NATRipHVXeycahfOVQTMyeNd/P17J3PlRxManOlFBu/cJVNgoltEzjm7Pg4AIyObzdeHtOa2gDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T06:57:43.091001Z","bundle_sha256":"19e021b87bf1ed362e47b52e2dd4eafad530ec5e62ae857f5d18d06faaebd438"}}