{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:LXPYE4INOOIW3LMTBDDS7TE66U","short_pith_number":"pith:LXPYE4IN","canonical_record":{"source":{"id":"1511.06944","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-22T01:28:32Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"066d2de3694b5a8233a63205c35ead9e8e4bedc851cce5249e712c664cd1986f","abstract_canon_sha256":"ba3acb5f234431be80160729ccf2575cd256682d54895508f3dc549aaf0fe412"},"schema_version":"1.0"},"canonical_sha256":"5ddf82710d73916dad9308c72fcc9ef526bf0c7ac6cc81ebab12bd1731539171","source":{"kind":"arxiv","id":"1511.06944","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.06944","created_at":"2026-05-17T23:49:57Z"},{"alias_kind":"arxiv_version","alias_value":"1511.06944v4","created_at":"2026-05-17T23:49:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.06944","created_at":"2026-05-17T23:49:57Z"},{"alias_kind":"pith_short_12","alias_value":"LXPYE4INOOIW","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LXPYE4INOOIW3LMT","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LXPYE4IN","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:LXPYE4INOOIW3LMTBDDS7TE66U","target":"record","payload":{"canonical_record":{"source":{"id":"1511.06944","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-22T01:28:32Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"066d2de3694b5a8233a63205c35ead9e8e4bedc851cce5249e712c664cd1986f","abstract_canon_sha256":"ba3acb5f234431be80160729ccf2575cd256682d54895508f3dc549aaf0fe412"},"schema_version":"1.0"},"canonical_sha256":"5ddf82710d73916dad9308c72fcc9ef526bf0c7ac6cc81ebab12bd1731539171","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:57.681191Z","signature_b64":"fY3t0dUXuDu0uJdFOsNNJH8Av3MamPUpMy69DbTFNSyuq6EmLgg+1WqowoXYfR22FH2fRvQ9jIPeVp3oM2CfAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ddf82710d73916dad9308c72fcc9ef526bf0c7ac6cc81ebab12bd1731539171","last_reissued_at":"2026-05-17T23:49:57.680687Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:57.680687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.06944","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:49:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sRnNYzIe7H+J58fOp5CWYDOWzvJsjNnLtDHp9fle4nym5e4HfLyfrGmjlH0MnpvwmAOfEn5vW7N98DdqOc4tAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T19:10:11.323675Z"},"content_sha256":"9628a74d377cb82b236c1aa30cd3c883d4018d910914511f0df82e73c057d02a","schema_version":"1.0","event_id":"sha256:9628a74d377cb82b236c1aa30cd3c883d4018d910914511f0df82e73c057d02a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:LXPYE4INOOIW3LMTBDDS7TE66U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the evolution by fractional mean curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Enrico Valdinoci, Mariel S\\'aez","submitted_at":"2015-11-22T01:28:32Z","abstract_excerpt":"In this paper we study smooth solutions to a fractional mean curvature flow equation. We establish a comparison principle and consequences such as uniqueness and finite extinction time for compact solutions. We also establish evolutions equations for fractional geometric quantities that yield preservation of certain quantities (such as positive fractional curvature) and smoothness of graphical evolutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06944","kind":"arxiv","version":4},"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":"2026-05-17T23:49:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j5d2r0VyAOL8cik3AyvBGwkODyBwzuLWEadAP5+LLALHmBX69Tu5r6lHbnIdluyHVAgv+QuPIzDBb4Pjhi8ZAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T19:10:11.324013Z"},"content_sha256":"40fb4a27962c4fb6d5b580dc22e7a5e973eb1f396510b14b6565ea342a3949e5","schema_version":"1.0","event_id":"sha256:40fb4a27962c4fb6d5b580dc22e7a5e973eb1f396510b14b6565ea342a3949e5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LXPYE4INOOIW3LMTBDDS7TE66U/bundle.json","state_url":"https://pith.science/pith/LXPYE4INOOIW3LMTBDDS7TE66U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LXPYE4INOOIW3LMTBDDS7TE66U/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":"2026-07-08T19:10:11Z","links":{"resolver":"https://pith.science/pith/LXPYE4INOOIW3LMTBDDS7TE66U","bundle":"https://pith.science/pith/LXPYE4INOOIW3LMTBDDS7TE66U/bundle.json","state":"https://pith.science/pith/LXPYE4INOOIW3LMTBDDS7TE66U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LXPYE4INOOIW3LMTBDDS7TE66U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LXPYE4INOOIW3LMTBDDS7TE66U","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":"ba3acb5f234431be80160729ccf2575cd256682d54895508f3dc549aaf0fe412","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-22T01:28:32Z","title_canon_sha256":"066d2de3694b5a8233a63205c35ead9e8e4bedc851cce5249e712c664cd1986f"},"schema_version":"1.0","source":{"id":"1511.06944","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.06944","created_at":"2026-05-17T23:49:57Z"},{"alias_kind":"arxiv_version","alias_value":"1511.06944v4","created_at":"2026-05-17T23:49:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.06944","created_at":"2026-05-17T23:49:57Z"},{"alias_kind":"pith_short_12","alias_value":"LXPYE4INOOIW","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LXPYE4INOOIW3LMT","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LXPYE4IN","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:40fb4a27962c4fb6d5b580dc22e7a5e973eb1f396510b14b6565ea342a3949e5","target":"graph","created_at":"2026-05-17T23:49:57Z","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":"In this paper we study smooth solutions to a fractional mean curvature flow equation. We establish a comparison principle and consequences such as uniqueness and finite extinction time for compact solutions. We also establish evolutions equations for fractional geometric quantities that yield preservation of certain quantities (such as positive fractional curvature) and smoothness of graphical evolutions.","authors_text":"Enrico Valdinoci, Mariel S\\'aez","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-22T01:28:32Z","title":"On the evolution by fractional mean curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06944","kind":"arxiv","version":4},"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":"sha256:9628a74d377cb82b236c1aa30cd3c883d4018d910914511f0df82e73c057d02a","target":"record","created_at":"2026-05-17T23:49:57Z","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":"ba3acb5f234431be80160729ccf2575cd256682d54895508f3dc549aaf0fe412","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-22T01:28:32Z","title_canon_sha256":"066d2de3694b5a8233a63205c35ead9e8e4bedc851cce5249e712c664cd1986f"},"schema_version":"1.0","source":{"id":"1511.06944","kind":"arxiv","version":4}},"canonical_sha256":"5ddf82710d73916dad9308c72fcc9ef526bf0c7ac6cc81ebab12bd1731539171","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ddf82710d73916dad9308c72fcc9ef526bf0c7ac6cc81ebab12bd1731539171","first_computed_at":"2026-05-17T23:49:57.680687Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:57.680687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fY3t0dUXuDu0uJdFOsNNJH8Av3MamPUpMy69DbTFNSyuq6EmLgg+1WqowoXYfR22FH2fRvQ9jIPeVp3oM2CfAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:57.681191Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.06944","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9628a74d377cb82b236c1aa30cd3c883d4018d910914511f0df82e73c057d02a","sha256:40fb4a27962c4fb6d5b580dc22e7a5e973eb1f396510b14b6565ea342a3949e5"],"state_sha256":"2e6582b83ae9d7603c940e6d9cb6511fd72e585b28e27fbce4432c6a0908c30f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TuhcY8ArizETPev65RV8ThCqG/pSoiZh47KGRiJ4B8kRgaqy93T2knByU4R2kJ7BH0UXdUbPtqH7/x0AL1kZBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-08T19:10:11.326042Z","bundle_sha256":"ef0a0529bfffd8956aa7d028447cf798598eeb87e620f0b00cfd88a5bdfa2c31"}}