{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:VOP4V34XWL5IZIMHLMCHY5MYOB","short_pith_number":"pith:VOP4V34X","canonical_record":{"source":{"id":"0911.4689","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-11-24T18:12:07Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"7e1397a823b2e25abb1b431b5643348b1cc020de758c8a27df8176885b93d8fa","abstract_canon_sha256":"a82efca01b5371d137df3b62eb9a60ba9cc7cb74017faec601a940dc2379e487"},"schema_version":"1.0"},"canonical_sha256":"ab9fcaef97b2fa8ca1875b047c7598705d3be2c7b16a40c53f2447dc33abef15","source":{"kind":"arxiv","id":"0911.4689","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.4689","created_at":"2026-05-18T04:38:59Z"},{"alias_kind":"arxiv_version","alias_value":"0911.4689v6","created_at":"2026-05-18T04:38:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.4689","created_at":"2026-05-18T04:38:59Z"},{"alias_kind":"pith_short_12","alias_value":"VOP4V34XWL5I","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VOP4V34XWL5IZIMH","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VOP4V34X","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:VOP4V34XWL5IZIMHLMCHY5MYOB","target":"record","payload":{"canonical_record":{"source":{"id":"0911.4689","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-11-24T18:12:07Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"7e1397a823b2e25abb1b431b5643348b1cc020de758c8a27df8176885b93d8fa","abstract_canon_sha256":"a82efca01b5371d137df3b62eb9a60ba9cc7cb74017faec601a940dc2379e487"},"schema_version":"1.0"},"canonical_sha256":"ab9fcaef97b2fa8ca1875b047c7598705d3be2c7b16a40c53f2447dc33abef15","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:59.272722Z","signature_b64":"Y98Dy6MPvVg+d/Dju61iQ7XgAWdRUHHpkoVZwpSqL6bqj1gRSwjzBlTbncP1oMuZe38AZw22TGYLzYx88KnGAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab9fcaef97b2fa8ca1875b047c7598705d3be2c7b16a40c53f2447dc33abef15","last_reissued_at":"2026-05-18T04:38:59.272278Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:59.272278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0911.4689","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:38:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FMCfJ82IsW6fAWGiVKWc4rTPlVu3K2eEXVddm3Lt/m+SRAY2DApGhbx33Im35Ia42I557/mcVgNjt61K8liZBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T22:35:23.927744Z"},"content_sha256":"08b8c69a82541a8bf0144b7917980be2de5040aee373724ffc37777b51d4e798","schema_version":"1.0","event_id":"sha256:08b8c69a82541a8bf0144b7917980be2de5040aee373724ffc37777b51d4e798"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:VOP4V34XWL5IZIMHLMCHY5MYOB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability of submanifolds with parallel mean curvature in calibrated manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Isabel M.C. Salavessa","submitted_at":"2009-11-24T18:12:07Z","abstract_excerpt":"On a Riemannian manifold $\\bar{M}^{m+n}$ with an $(m+1)$-calibration $\\Omega$, we prove that an $m$-submanifold $M$ with constant mean curvature $H$ and calibrated extended tangent space $\\mathbb{R}H\\oplus TM$ is a critical point of the area functional for variations that preserve the enclosed $\\Omega$-volume. This recovers the case described by Barbosa, do Carmo and Eschenburg, when $n=1$ and $\\Omega$ is the volume element of $\\bar{M}$. To the second variation we associate an $\\Omega$-Jacobi operator and define $\\Omega$-stablility. Under natural conditions, we prove that the Euclidean $m$-sph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.4689","kind":"arxiv","version":6},"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":"2026-05-18T04:38:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9DvbTrIw1oCZnMFVWykSi+uBYX40bN7QD8FdjiIJsNld5MsmjyrMk+kJfZr4bTb/4A0Zm776uK2oe+DzFu/2AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T22:35:23.928082Z"},"content_sha256":"5f246642066dcdafbbe2861b01caf1742abc08e21c790e1b2c90fa92bb56dab8","schema_version":"1.0","event_id":"sha256:5f246642066dcdafbbe2861b01caf1742abc08e21c790e1b2c90fa92bb56dab8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VOP4V34XWL5IZIMHLMCHY5MYOB/bundle.json","state_url":"https://pith.science/pith/VOP4V34XWL5IZIMHLMCHY5MYOB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VOP4V34XWL5IZIMHLMCHY5MYOB/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":"2026-06-08T22:35:23Z","links":{"resolver":"https://pith.science/pith/VOP4V34XWL5IZIMHLMCHY5MYOB","bundle":"https://pith.science/pith/VOP4V34XWL5IZIMHLMCHY5MYOB/bundle.json","state":"https://pith.science/pith/VOP4V34XWL5IZIMHLMCHY5MYOB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VOP4V34XWL5IZIMHLMCHY5MYOB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:VOP4V34XWL5IZIMHLMCHY5MYOB","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":"a82efca01b5371d137df3b62eb9a60ba9cc7cb74017faec601a940dc2379e487","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-11-24T18:12:07Z","title_canon_sha256":"7e1397a823b2e25abb1b431b5643348b1cc020de758c8a27df8176885b93d8fa"},"schema_version":"1.0","source":{"id":"0911.4689","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.4689","created_at":"2026-05-18T04:38:59Z"},{"alias_kind":"arxiv_version","alias_value":"0911.4689v6","created_at":"2026-05-18T04:38:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.4689","created_at":"2026-05-18T04:38:59Z"},{"alias_kind":"pith_short_12","alias_value":"VOP4V34XWL5I","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VOP4V34XWL5IZIMH","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VOP4V34X","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:5f246642066dcdafbbe2861b01caf1742abc08e21c790e1b2c90fa92bb56dab8","target":"graph","created_at":"2026-05-18T04:38:59Z","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":"On a Riemannian manifold $\\bar{M}^{m+n}$ with an $(m+1)$-calibration $\\Omega$, we prove that an $m$-submanifold $M$ with constant mean curvature $H$ and calibrated extended tangent space $\\mathbb{R}H\\oplus TM$ is a critical point of the area functional for variations that preserve the enclosed $\\Omega$-volume. This recovers the case described by Barbosa, do Carmo and Eschenburg, when $n=1$ and $\\Omega$ is the volume element of $\\bar{M}$. To the second variation we associate an $\\Omega$-Jacobi operator and define $\\Omega$-stablility. Under natural conditions, we prove that the Euclidean $m$-sph","authors_text":"Isabel M.C. Salavessa","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-11-24T18:12:07Z","title":"Stability of submanifolds with parallel mean curvature in calibrated manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.4689","kind":"arxiv","version":6},"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":"sha256:08b8c69a82541a8bf0144b7917980be2de5040aee373724ffc37777b51d4e798","target":"record","created_at":"2026-05-18T04:38:59Z","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":"a82efca01b5371d137df3b62eb9a60ba9cc7cb74017faec601a940dc2379e487","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-11-24T18:12:07Z","title_canon_sha256":"7e1397a823b2e25abb1b431b5643348b1cc020de758c8a27df8176885b93d8fa"},"schema_version":"1.0","source":{"id":"0911.4689","kind":"arxiv","version":6}},"canonical_sha256":"ab9fcaef97b2fa8ca1875b047c7598705d3be2c7b16a40c53f2447dc33abef15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab9fcaef97b2fa8ca1875b047c7598705d3be2c7b16a40c53f2447dc33abef15","first_computed_at":"2026-05-18T04:38:59.272278Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:59.272278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y98Dy6MPvVg+d/Dju61iQ7XgAWdRUHHpkoVZwpSqL6bqj1gRSwjzBlTbncP1oMuZe38AZw22TGYLzYx88KnGAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:59.272722Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.4689","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08b8c69a82541a8bf0144b7917980be2de5040aee373724ffc37777b51d4e798","sha256:5f246642066dcdafbbe2861b01caf1742abc08e21c790e1b2c90fa92bb56dab8"],"state_sha256":"104cbfaaee2fba20c8e6b5e5801c1f8e29cc85abf5b877e62c1073dc30c79c24"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0kZeaW9nth4dFC9HNvwZKrWIwCCsmR7EOQ/OQgDszoMG9sEx4FjqMMJn1f9+0qoJwVY0zBZuGIPLM+HZJIjEDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T22:35:23.929977Z","bundle_sha256":"c62fde2eb94ea482307b75d7404a6548be2b640daf4ad438379661b3e7d9201b"}}