{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:XVYQUZ7JI2A7O5RGXTWR3S7HQM","short_pith_number":"pith:XVYQUZ7J","canonical_record":{"source":{"id":"1609.09337","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-09-29T13:43:37Z","cross_cats_sorted":[],"title_canon_sha256":"93444935a661360e574c5ef5902243569c0648b1e4a80059826ba214554495d0","abstract_canon_sha256":"c8c060497d821ecf43002b7ecdf00b3c44d07bac926b3d6d0df8fa49b77e21e6"},"schema_version":"1.0"},"canonical_sha256":"bd710a67e94681f77626bced1dcbe78314acc8c9bc8798d89d1fd13c67e5e4ec","source":{"kind":"arxiv","id":"1609.09337","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.09337","created_at":"2026-05-18T01:03:38Z"},{"alias_kind":"arxiv_version","alias_value":"1609.09337v1","created_at":"2026-05-18T01:03:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.09337","created_at":"2026-05-18T01:03:38Z"},{"alias_kind":"pith_short_12","alias_value":"XVYQUZ7JI2A7","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XVYQUZ7JI2A7O5RG","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XVYQUZ7J","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:XVYQUZ7JI2A7O5RGXTWR3S7HQM","target":"record","payload":{"canonical_record":{"source":{"id":"1609.09337","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-09-29T13:43:37Z","cross_cats_sorted":[],"title_canon_sha256":"93444935a661360e574c5ef5902243569c0648b1e4a80059826ba214554495d0","abstract_canon_sha256":"c8c060497d821ecf43002b7ecdf00b3c44d07bac926b3d6d0df8fa49b77e21e6"},"schema_version":"1.0"},"canonical_sha256":"bd710a67e94681f77626bced1dcbe78314acc8c9bc8798d89d1fd13c67e5e4ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:38.144101Z","signature_b64":"lstwGOgSK4ShTEHz+nCKJLQeLDKwWYIOsiHFw6VurW4ScJmIjRGzqc4wcwjf9ruhxFIZSUy/0cq9WBOMcFgZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd710a67e94681f77626bced1dcbe78314acc8c9bc8798d89d1fd13c67e5e4ec","last_reissued_at":"2026-05-18T01:03:38.143637Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:38.143637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.09337","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":"2026-05-18T01:03:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cgF4nxUExJbwR8HJUuXXuZc0siCXMhU/Xh+6XF0itilDt9l6Flj/kw23fqlKqcs2Kps/qan4dfapMKKy5JZJAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:35:01.591181Z"},"content_sha256":"e8c7e9c4e7ed7f873e0a6dc92f2edea315941565e4e19807df819d146b23e125","schema_version":"1.0","event_id":"sha256:e8c7e9c4e7ed7f873e0a6dc92f2edea315941565e4e19807df819d146b23e125"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:XVYQUZ7JI2A7O5RGXTWR3S7HQM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Kurdyka-{\\L}ojasiewicz-Simon inequality and stabilisation in nonsmooth infinite-dimensional gradient systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ralph Chill, Sebastian Mildner","submitted_at":"2016-09-29T13:43:37Z","abstract_excerpt":"We state and prove a stabilisation result for solutions of abstract gradient systems associated with nonsmooth energy functions on infinite dimensional Hilbert spaces. One feature is that in this general setting the assumption on the range of the solution can be considerably relaxed, which considerably simplifies the applicability of the stabilisation result even in the case of smooth energies."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.09337","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":"2026-05-18T01:03:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fjrk79XbpU0gsMbdPabYzkGyI/UGy0EdQLxSy9Y7PF8pn7wnlVKrzW/bBrPX4K6lxQ17H+DD1HNbXSMKX2EXCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:35:01.591540Z"},"content_sha256":"68c4d28e2aba01f0eee68000d2134cd6254aa53ac26319a4bbf78673ec115694","schema_version":"1.0","event_id":"sha256:68c4d28e2aba01f0eee68000d2134cd6254aa53ac26319a4bbf78673ec115694"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XVYQUZ7JI2A7O5RGXTWR3S7HQM/bundle.json","state_url":"https://pith.science/pith/XVYQUZ7JI2A7O5RGXTWR3S7HQM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XVYQUZ7JI2A7O5RGXTWR3S7HQM/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":"2026-06-26T14:35:01Z","links":{"resolver":"https://pith.science/pith/XVYQUZ7JI2A7O5RGXTWR3S7HQM","bundle":"https://pith.science/pith/XVYQUZ7JI2A7O5RGXTWR3S7HQM/bundle.json","state":"https://pith.science/pith/XVYQUZ7JI2A7O5RGXTWR3S7HQM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XVYQUZ7JI2A7O5RGXTWR3S7HQM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XVYQUZ7JI2A7O5RGXTWR3S7HQM","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":"c8c060497d821ecf43002b7ecdf00b3c44d07bac926b3d6d0df8fa49b77e21e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-09-29T13:43:37Z","title_canon_sha256":"93444935a661360e574c5ef5902243569c0648b1e4a80059826ba214554495d0"},"schema_version":"1.0","source":{"id":"1609.09337","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.09337","created_at":"2026-05-18T01:03:38Z"},{"alias_kind":"arxiv_version","alias_value":"1609.09337v1","created_at":"2026-05-18T01:03:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.09337","created_at":"2026-05-18T01:03:38Z"},{"alias_kind":"pith_short_12","alias_value":"XVYQUZ7JI2A7","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XVYQUZ7JI2A7O5RG","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XVYQUZ7J","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:68c4d28e2aba01f0eee68000d2134cd6254aa53ac26319a4bbf78673ec115694","target":"graph","created_at":"2026-05-18T01:03:38Z","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 state and prove a stabilisation result for solutions of abstract gradient systems associated with nonsmooth energy functions on infinite dimensional Hilbert spaces. One feature is that in this general setting the assumption on the range of the solution can be considerably relaxed, which considerably simplifies the applicability of the stabilisation result even in the case of smooth energies.","authors_text":"Ralph Chill, Sebastian Mildner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-09-29T13:43:37Z","title":"The Kurdyka-{\\L}ojasiewicz-Simon inequality and stabilisation in nonsmooth infinite-dimensional gradient systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.09337","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:e8c7e9c4e7ed7f873e0a6dc92f2edea315941565e4e19807df819d146b23e125","target":"record","created_at":"2026-05-18T01:03:38Z","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":"c8c060497d821ecf43002b7ecdf00b3c44d07bac926b3d6d0df8fa49b77e21e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-09-29T13:43:37Z","title_canon_sha256":"93444935a661360e574c5ef5902243569c0648b1e4a80059826ba214554495d0"},"schema_version":"1.0","source":{"id":"1609.09337","kind":"arxiv","version":1}},"canonical_sha256":"bd710a67e94681f77626bced1dcbe78314acc8c9bc8798d89d1fd13c67e5e4ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd710a67e94681f77626bced1dcbe78314acc8c9bc8798d89d1fd13c67e5e4ec","first_computed_at":"2026-05-18T01:03:38.143637Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:38.143637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lstwGOgSK4ShTEHz+nCKJLQeLDKwWYIOsiHFw6VurW4ScJmIjRGzqc4wcwjf9ruhxFIZSUy/0cq9WBOMcFgZBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:38.144101Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.09337","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8c7e9c4e7ed7f873e0a6dc92f2edea315941565e4e19807df819d146b23e125","sha256:68c4d28e2aba01f0eee68000d2134cd6254aa53ac26319a4bbf78673ec115694"],"state_sha256":"db61b3d3ce659d9f6957a27f5fb01f72c786f21836fba578059449bb3a15596e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JhQuVw7sjXph01OKiy+Tv4yjAzSWJbQxV5bZJWCF+dlFZOTgWzINhntj5F/3Wa9ZFP1/DmdN9fYxwp4ih2wjBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T14:35:01.593516Z","bundle_sha256":"98d1b7d86218f9f7488488fce6027000f7fd9d5e8d373da04f4e0523f00ad478"}}