{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:6QWDAWAGJBUXBQVU526UZKZ4FG","short_pith_number":"pith:6QWDAWAG","canonical_record":{"source":{"id":"1604.07559","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-26T08:12:51Z","cross_cats_sorted":[],"title_canon_sha256":"a711612dd51774645f3d2f507c4fde2fbfa89e3d87b4b569e7ff20af1b657cf9","abstract_canon_sha256":"81793e9066d66ba7d5dde10cd0eb562a3813c2ce347cb5486f034871911f35ad"},"schema_version":"1.0"},"canonical_sha256":"f42c305806486970c2b4eebd4cab3c29a33a41a893c38d9da53c43cfa46834f6","source":{"kind":"arxiv","id":"1604.07559","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.07559","created_at":"2026-05-18T01:16:19Z"},{"alias_kind":"arxiv_version","alias_value":"1604.07559v1","created_at":"2026-05-18T01:16:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.07559","created_at":"2026-05-18T01:16:19Z"},{"alias_kind":"pith_short_12","alias_value":"6QWDAWAGJBUX","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6QWDAWAGJBUXBQVU","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6QWDAWAG","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:6QWDAWAGJBUXBQVU526UZKZ4FG","target":"record","payload":{"canonical_record":{"source":{"id":"1604.07559","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-26T08:12:51Z","cross_cats_sorted":[],"title_canon_sha256":"a711612dd51774645f3d2f507c4fde2fbfa89e3d87b4b569e7ff20af1b657cf9","abstract_canon_sha256":"81793e9066d66ba7d5dde10cd0eb562a3813c2ce347cb5486f034871911f35ad"},"schema_version":"1.0"},"canonical_sha256":"f42c305806486970c2b4eebd4cab3c29a33a41a893c38d9da53c43cfa46834f6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:19.494160Z","signature_b64":"0kFn4ZTWCuQEIG1kIZk3+743SisItTKK6vBAi7AxNQdRX1I/RWp11nkJ8jKuzY3bGWY1EWxCCUWP85Focre7Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f42c305806486970c2b4eebd4cab3c29a33a41a893c38d9da53c43cfa46834f6","last_reissued_at":"2026-05-18T01:16:19.493653Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:19.493653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.07559","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":"2026-05-18T01:16:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QbezP//991ZgE3EuNeNOrL+zlL2lDUiUbsCjfDLqNIC0yK4ufaBOk0e9JuFzrCErlhuZ8Fik8XzSx+lUm9S0Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:17:06.955974Z"},"content_sha256":"4dfb74e7bb460563875e480f8d8a8ed5ea21d435a019850b4cbe3bb4265b8041","schema_version":"1.0","event_id":"sha256:4dfb74e7bb460563875e480f8d8a8ed5ea21d435a019850b4cbe3bb4265b8041"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:6QWDAWAGJBUXBQVU526UZKZ4FG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The {\\L}ojasiewicz-Simon gradient inequality for open elastic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Adrian Spener, Anna Dall'Acqua, Paola Pozzi","submitted_at":"2016-04-26T08:12:51Z","abstract_excerpt":"In this paper we consider the elastic energy for open curves in Euclidean space subject to clamped boundary conditions and obtain the \\L ojasiewicz-Simon gradient inequality for this energy functional. Thanks to this inequality we can prove that a (suitably reparametrized) solution to the associated $L^2$-gradient flow converges for large time to an elastica, that is to a critical point of the functional."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07559","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":"2026-05-18T01:16:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wanacPd2cBR/BJDsKAfzIdutL1kvT+k7PkJPomEAtLUV8b4AlaneYJXrw97L5TvQdsCQ0p0MwDm/d52IMT/QBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:17:06.956328Z"},"content_sha256":"32b43f85164bc382623628becdd09ddecbcd5ad6f55485010854a2ff2ad0ab7b","schema_version":"1.0","event_id":"sha256:32b43f85164bc382623628becdd09ddecbcd5ad6f55485010854a2ff2ad0ab7b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6QWDAWAGJBUXBQVU526UZKZ4FG/bundle.json","state_url":"https://pith.science/pith/6QWDAWAGJBUXBQVU526UZKZ4FG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6QWDAWAGJBUXBQVU526UZKZ4FG/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":"2026-06-02T02:17:06Z","links":{"resolver":"https://pith.science/pith/6QWDAWAGJBUXBQVU526UZKZ4FG","bundle":"https://pith.science/pith/6QWDAWAGJBUXBQVU526UZKZ4FG/bundle.json","state":"https://pith.science/pith/6QWDAWAGJBUXBQVU526UZKZ4FG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6QWDAWAGJBUXBQVU526UZKZ4FG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6QWDAWAGJBUXBQVU526UZKZ4FG","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":"81793e9066d66ba7d5dde10cd0eb562a3813c2ce347cb5486f034871911f35ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-26T08:12:51Z","title_canon_sha256":"a711612dd51774645f3d2f507c4fde2fbfa89e3d87b4b569e7ff20af1b657cf9"},"schema_version":"1.0","source":{"id":"1604.07559","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.07559","created_at":"2026-05-18T01:16:19Z"},{"alias_kind":"arxiv_version","alias_value":"1604.07559v1","created_at":"2026-05-18T01:16:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.07559","created_at":"2026-05-18T01:16:19Z"},{"alias_kind":"pith_short_12","alias_value":"6QWDAWAGJBUX","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6QWDAWAGJBUXBQVU","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6QWDAWAG","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:32b43f85164bc382623628becdd09ddecbcd5ad6f55485010854a2ff2ad0ab7b","target":"graph","created_at":"2026-05-18T01:16:19Z","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 consider the elastic energy for open curves in Euclidean space subject to clamped boundary conditions and obtain the \\L ojasiewicz-Simon gradient inequality for this energy functional. Thanks to this inequality we can prove that a (suitably reparametrized) solution to the associated $L^2$-gradient flow converges for large time to an elastica, that is to a critical point of the functional.","authors_text":"Adrian Spener, Anna Dall'Acqua, Paola Pozzi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-26T08:12:51Z","title":"The {\\L}ojasiewicz-Simon gradient inequality for open elastic curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07559","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":"sha256:4dfb74e7bb460563875e480f8d8a8ed5ea21d435a019850b4cbe3bb4265b8041","target":"record","created_at":"2026-05-18T01:16:19Z","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":"81793e9066d66ba7d5dde10cd0eb562a3813c2ce347cb5486f034871911f35ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-26T08:12:51Z","title_canon_sha256":"a711612dd51774645f3d2f507c4fde2fbfa89e3d87b4b569e7ff20af1b657cf9"},"schema_version":"1.0","source":{"id":"1604.07559","kind":"arxiv","version":1}},"canonical_sha256":"f42c305806486970c2b4eebd4cab3c29a33a41a893c38d9da53c43cfa46834f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f42c305806486970c2b4eebd4cab3c29a33a41a893c38d9da53c43cfa46834f6","first_computed_at":"2026-05-18T01:16:19.493653Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:19.493653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0kFn4ZTWCuQEIG1kIZk3+743SisItTKK6vBAi7AxNQdRX1I/RWp11nkJ8jKuzY3bGWY1EWxCCUWP85Focre7Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:19.494160Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.07559","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4dfb74e7bb460563875e480f8d8a8ed5ea21d435a019850b4cbe3bb4265b8041","sha256:32b43f85164bc382623628becdd09ddecbcd5ad6f55485010854a2ff2ad0ab7b"],"state_sha256":"e485e6425f23f3a18e96806c87e34851f72ebb5f091cd50a02e184995048b6cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nlSPZ0o5oYdS4vrrZragbRdgp2+OgR9+T0LHCpfQ8VSbj4bWrXypT6BumVxiddxFdtK7HlXUxfVZDIiffAUBBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T02:17:06.958301Z","bundle_sha256":"fb4bbda005b519b0b27a921285178a53fa11152b4de0062b65881264200d968d"}}