{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:3L2EZAR4NXTQVSVQP6RB3RM4E7","short_pith_number":"pith:3L2EZAR4","canonical_record":{"source":{"id":"1105.3153","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-05-16T17:23:33Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"3f4731fbc3a984c2cd691929689d8fdd5263e052fc33f0bb8493f9129fbb1d70","abstract_canon_sha256":"907336fcb7afe545060131a8ea230c9d7cf651c0f52b1cbe7f1b43fd3c58ffd3"},"schema_version":"1.0"},"canonical_sha256":"daf44c823c6de70acab07fa21dc59c27c324baae3254be378c275a40d01529df","source":{"kind":"arxiv","id":"1105.3153","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.3153","created_at":"2026-05-18T04:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"1105.3153v2","created_at":"2026-05-18T04:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3153","created_at":"2026-05-18T04:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"3L2EZAR4NXTQ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3L2EZAR4NXTQVSVQ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3L2EZAR4","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:3L2EZAR4NXTQVSVQP6RB3RM4E7","target":"record","payload":{"canonical_record":{"source":{"id":"1105.3153","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-05-16T17:23:33Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"3f4731fbc3a984c2cd691929689d8fdd5263e052fc33f0bb8493f9129fbb1d70","abstract_canon_sha256":"907336fcb7afe545060131a8ea230c9d7cf651c0f52b1cbe7f1b43fd3c58ffd3"},"schema_version":"1.0"},"canonical_sha256":"daf44c823c6de70acab07fa21dc59c27c324baae3254be378c275a40d01529df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:49.446654Z","signature_b64":"ssrSKLR2tl+nnhBGMTyWOOVv3QupBSV0ISfJOlfL06YGG2FWrphbAMtDIdfQnUhTM3Z4oLCCHcawNgGRYavZCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"daf44c823c6de70acab07fa21dc59c27c324baae3254be378c275a40d01529df","last_reissued_at":"2026-05-18T04:20:49.445943Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:49.445943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.3153","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:20:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1pj7xkELeLRV6gOkT+N2CF1sA+DC9jUTkQw6A0Ezpf1ATmHgFZQFIAEUTcUhN9Qfv10BqKbFg+D4VbkYGdhrAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T22:32:51.367333Z"},"content_sha256":"5e68f85e1a99d6c947c421e301c32329cf39902215edf5da5a00d0657503ea31","schema_version":"1.0","event_id":"sha256:5e68f85e1a99d6c947c421e301c32329cf39902215edf5da5a00d0657503ea31"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:3L2EZAR4NXTQVSVQP6RB3RM4E7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cauchy-Riemann inequalities on 2-spheres of $\\mathbb{R}^7$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.DG","authors_text":"Isabel M.C. Salavessa","submitted_at":"2011-05-16T17:23:33Z","abstract_excerpt":"We prove that an integral Cauchy-Riemann inequality holds for any pair of smooth functions $(f,h)$ on the 2-sphere $\\mathbb{S}^2$, and equality holds iff $f$ and $h$ are related $\\lambda_1$-eigenfunctions. We extend such inequality to 4-tuples of functions, only valid on the $L^2$-orthogonal complement of a suitable nonzero finite dimensional space of functions. As a consequence we prove that 2-spheres are not $\\Omega$-stable surfaces with parallel mean curvature in $\\mathbb{R}^7$ for the associative calibration $\\Omega$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3153","kind":"arxiv","version":2},"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":"2026-05-18T04:20:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DQAQn1XGN4Y7ZdLVTZyL9mJ3aCOqxRf87mCxPkNVXEvyBbFJas3awohFrozFfZ5GdXLsL0KeT+IdC2HGl8GeDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T22:32:51.367679Z"},"content_sha256":"d2f22e21f329b035735c88c2041ec8b4919f1b435049c6effe815569515b7ea3","schema_version":"1.0","event_id":"sha256:d2f22e21f329b035735c88c2041ec8b4919f1b435049c6effe815569515b7ea3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3L2EZAR4NXTQVSVQP6RB3RM4E7/bundle.json","state_url":"https://pith.science/pith/3L2EZAR4NXTQVSVQP6RB3RM4E7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3L2EZAR4NXTQVSVQP6RB3RM4E7/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":"2026-06-08T22:32:51Z","links":{"resolver":"https://pith.science/pith/3L2EZAR4NXTQVSVQP6RB3RM4E7","bundle":"https://pith.science/pith/3L2EZAR4NXTQVSVQP6RB3RM4E7/bundle.json","state":"https://pith.science/pith/3L2EZAR4NXTQVSVQP6RB3RM4E7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3L2EZAR4NXTQVSVQP6RB3RM4E7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3L2EZAR4NXTQVSVQP6RB3RM4E7","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":"907336fcb7afe545060131a8ea230c9d7cf651c0f52b1cbe7f1b43fd3c58ffd3","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-05-16T17:23:33Z","title_canon_sha256":"3f4731fbc3a984c2cd691929689d8fdd5263e052fc33f0bb8493f9129fbb1d70"},"schema_version":"1.0","source":{"id":"1105.3153","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.3153","created_at":"2026-05-18T04:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"1105.3153v2","created_at":"2026-05-18T04:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3153","created_at":"2026-05-18T04:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"3L2EZAR4NXTQ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3L2EZAR4NXTQVSVQ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3L2EZAR4","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:d2f22e21f329b035735c88c2041ec8b4919f1b435049c6effe815569515b7ea3","target":"graph","created_at":"2026-05-18T04:20:49Z","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 prove that an integral Cauchy-Riemann inequality holds for any pair of smooth functions $(f,h)$ on the 2-sphere $\\mathbb{S}^2$, and equality holds iff $f$ and $h$ are related $\\lambda_1$-eigenfunctions. We extend such inequality to 4-tuples of functions, only valid on the $L^2$-orthogonal complement of a suitable nonzero finite dimensional space of functions. As a consequence we prove that 2-spheres are not $\\Omega$-stable surfaces with parallel mean curvature in $\\mathbb{R}^7$ for the associative calibration $\\Omega$.","authors_text":"Isabel M.C. Salavessa","cross_cats":["math-ph","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-05-16T17:23:33Z","title":"Cauchy-Riemann inequalities on 2-spheres of $\\mathbb{R}^7$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3153","kind":"arxiv","version":2},"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":"sha256:5e68f85e1a99d6c947c421e301c32329cf39902215edf5da5a00d0657503ea31","target":"record","created_at":"2026-05-18T04:20:49Z","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":"907336fcb7afe545060131a8ea230c9d7cf651c0f52b1cbe7f1b43fd3c58ffd3","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-05-16T17:23:33Z","title_canon_sha256":"3f4731fbc3a984c2cd691929689d8fdd5263e052fc33f0bb8493f9129fbb1d70"},"schema_version":"1.0","source":{"id":"1105.3153","kind":"arxiv","version":2}},"canonical_sha256":"daf44c823c6de70acab07fa21dc59c27c324baae3254be378c275a40d01529df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"daf44c823c6de70acab07fa21dc59c27c324baae3254be378c275a40d01529df","first_computed_at":"2026-05-18T04:20:49.445943Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:49.445943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ssrSKLR2tl+nnhBGMTyWOOVv3QupBSV0ISfJOlfL06YGG2FWrphbAMtDIdfQnUhTM3Z4oLCCHcawNgGRYavZCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:49.446654Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.3153","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e68f85e1a99d6c947c421e301c32329cf39902215edf5da5a00d0657503ea31","sha256:d2f22e21f329b035735c88c2041ec8b4919f1b435049c6effe815569515b7ea3"],"state_sha256":"f700503578b39a697881bea54f427648c91b102195b52f034a5fbb6764c5ac9d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jw6C6apMNhtWAcmZ7Dd6wNvgprDpRFjbNYN3sXf6VtvImpvMbBeM0PT8Nzefm0YEmnnP4pGTPaZc4+Rn3244CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T22:32:51.369551Z","bundle_sha256":"e8c11dd384e9abfebc4fa315f7f65e9c1654b6befadc55d27ad44f7dee68c3ae"}}