{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:LDI434FZ7EPVQOY7BKOKZR4WHL","short_pith_number":"pith:LDI434FZ","canonical_record":{"source":{"id":"1306.1655","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-06-07T08:55:38Z","cross_cats_sorted":[],"title_canon_sha256":"502efbf3480f186fea0836b1928ac21c18b22fa3783a7e2f9c72936ecc7a2653","abstract_canon_sha256":"ac59cd7ab053370d6478bc574f8307d87d63b458757735eabee9727a344cfb20"},"schema_version":"1.0"},"canonical_sha256":"58d1cdf0b9f91f583b1f0a9cacc7963ad18e6a4326f61585eb07fb0fffb24689","source":{"kind":"arxiv","id":"1306.1655","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1655","created_at":"2026-05-18T03:21:32Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1655v1","created_at":"2026-05-18T03:21:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1655","created_at":"2026-05-18T03:21:32Z"},{"alias_kind":"pith_short_12","alias_value":"LDI434FZ7EPV","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LDI434FZ7EPVQOY7","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LDI434FZ","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:LDI434FZ7EPVQOY7BKOKZR4WHL","target":"record","payload":{"canonical_record":{"source":{"id":"1306.1655","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-06-07T08:55:38Z","cross_cats_sorted":[],"title_canon_sha256":"502efbf3480f186fea0836b1928ac21c18b22fa3783a7e2f9c72936ecc7a2653","abstract_canon_sha256":"ac59cd7ab053370d6478bc574f8307d87d63b458757735eabee9727a344cfb20"},"schema_version":"1.0"},"canonical_sha256":"58d1cdf0b9f91f583b1f0a9cacc7963ad18e6a4326f61585eb07fb0fffb24689","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:32.785471Z","signature_b64":"xkg609iZh3VAGh8bnS3UWqnLC2ygfnBYgzdugGgU83WMOqwduCRIf+OZ+nEOg1p2P6FBjnLOhJTDYpUbMf/PDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58d1cdf0b9f91f583b1f0a9cacc7963ad18e6a4326f61585eb07fb0fffb24689","last_reissued_at":"2026-05-18T03:21:32.784714Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:32.784714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.1655","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":"2026-05-18T03:21:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FUpnkrKChG7gf3mZRahtxFqXvEG/C6bleq/usGr7aWgm8eP8y0kgsRwtQt+1XdSZ9SmwAyoGFpfL64ewDD2TAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:43:58.440652Z"},"content_sha256":"232cb810956503b8639686fb63d9823ae1395612d416ed6aafbcf1a86b4becc5","schema_version":"1.0","event_id":"sha256:232cb810956503b8639686fb63d9823ae1395612d416ed6aafbcf1a86b4becc5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:LDI434FZ7EPVQOY7BKOKZR4WHL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some relationships between intrinsic and extrinsic invariants of submanifolds in generalized S-space-forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ana M. Fuentes, Luis M. Fern\\'Andez","submitted_at":"2013-06-07T08:55:38Z","abstract_excerpt":"We establish some inequalities of Chen's type between certain intrinsic invariants (involving sectional, Ricci and scalar curvatures) and the squared mean curvature of submanifolds tangent to the structure vector fields of a generalized S-space-form and we discuss the equality cases of them. We apply the obtained results to slant submanifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1655","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":"2026-05-18T03:21:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qsFY24WHOtwP9PldWVWVUvjPDybrIGuMafyDv5aZDklU4JzIMB0YdApxGkuciDQxgNyxWfHTmbo6siaLNmjMBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:43:58.441003Z"},"content_sha256":"cf0d147720d2566918ba7fd956de1db27e1bc2f408475fa7eb1c58ad54987d61","schema_version":"1.0","event_id":"sha256:cf0d147720d2566918ba7fd956de1db27e1bc2f408475fa7eb1c58ad54987d61"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LDI434FZ7EPVQOY7BKOKZR4WHL/bundle.json","state_url":"https://pith.science/pith/LDI434FZ7EPVQOY7BKOKZR4WHL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LDI434FZ7EPVQOY7BKOKZR4WHL/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":"2026-06-25T19:43:58Z","links":{"resolver":"https://pith.science/pith/LDI434FZ7EPVQOY7BKOKZR4WHL","bundle":"https://pith.science/pith/LDI434FZ7EPVQOY7BKOKZR4WHL/bundle.json","state":"https://pith.science/pith/LDI434FZ7EPVQOY7BKOKZR4WHL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LDI434FZ7EPVQOY7BKOKZR4WHL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LDI434FZ7EPVQOY7BKOKZR4WHL","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":"ac59cd7ab053370d6478bc574f8307d87d63b458757735eabee9727a344cfb20","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-06-07T08:55:38Z","title_canon_sha256":"502efbf3480f186fea0836b1928ac21c18b22fa3783a7e2f9c72936ecc7a2653"},"schema_version":"1.0","source":{"id":"1306.1655","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1655","created_at":"2026-05-18T03:21:32Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1655v1","created_at":"2026-05-18T03:21:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1655","created_at":"2026-05-18T03:21:32Z"},{"alias_kind":"pith_short_12","alias_value":"LDI434FZ7EPV","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LDI434FZ7EPVQOY7","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LDI434FZ","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:cf0d147720d2566918ba7fd956de1db27e1bc2f408475fa7eb1c58ad54987d61","target":"graph","created_at":"2026-05-18T03:21:32Z","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"},"paper":{"abstract_excerpt":"We establish some inequalities of Chen's type between certain intrinsic invariants (involving sectional, Ricci and scalar curvatures) and the squared mean curvature of submanifolds tangent to the structure vector fields of a generalized S-space-form and we discuss the equality cases of them. We apply the obtained results to slant submanifolds.","authors_text":"Ana M. Fuentes, Luis M. Fern\\'Andez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-06-07T08:55:38Z","title":"Some relationships between intrinsic and extrinsic invariants of submanifolds in generalized S-space-forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1655","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":"sha256:232cb810956503b8639686fb63d9823ae1395612d416ed6aafbcf1a86b4becc5","target":"record","created_at":"2026-05-18T03:21:32Z","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":"ac59cd7ab053370d6478bc574f8307d87d63b458757735eabee9727a344cfb20","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-06-07T08:55:38Z","title_canon_sha256":"502efbf3480f186fea0836b1928ac21c18b22fa3783a7e2f9c72936ecc7a2653"},"schema_version":"1.0","source":{"id":"1306.1655","kind":"arxiv","version":1}},"canonical_sha256":"58d1cdf0b9f91f583b1f0a9cacc7963ad18e6a4326f61585eb07fb0fffb24689","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58d1cdf0b9f91f583b1f0a9cacc7963ad18e6a4326f61585eb07fb0fffb24689","first_computed_at":"2026-05-18T03:21:32.784714Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:32.784714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xkg609iZh3VAGh8bnS3UWqnLC2ygfnBYgzdugGgU83WMOqwduCRIf+OZ+nEOg1p2P6FBjnLOhJTDYpUbMf/PDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:32.785471Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.1655","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:232cb810956503b8639686fb63d9823ae1395612d416ed6aafbcf1a86b4becc5","sha256:cf0d147720d2566918ba7fd956de1db27e1bc2f408475fa7eb1c58ad54987d61"],"state_sha256":"693cfce34a7aa8bafe2430cb5160f2fea36088934cbaea200626eb53f9f993e1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ctzi1QPIJOLp1ziyUSZtHBthKiyuUCZ+wdq7vsCKlfHlmrYFKenGfkEqB+89YR7juI3Cm6K3/+ZWGHX1n6jWCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T19:43:58.442981Z","bundle_sha256":"18664b2351b1ee4f77fd5302f3abb1c92b0432420ab844d3b567c928f779f2b7"}}