{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:AWA33KALEYFVVJ24SC4J5VLJ3F","short_pith_number":"pith:AWA33KAL","canonical_record":{"source":{"id":"2506.11705","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-06-13T12:19:46Z","cross_cats_sorted":[],"title_canon_sha256":"ecf2926722f5924aff25c4184ab931d2ca26e96292a20b26d89ff47307e4f28e","abstract_canon_sha256":"5f7e0c200a0c9ad5e7b06d43133789c1010377dcfc102bca988d5fbf84c01363"},"schema_version":"1.0"},"canonical_sha256":"0581bda80b260b5aa75c90b89ed569d976feef84e786f772ee422fd3f3bb0f9a","source":{"kind":"arxiv","id":"2506.11705","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.11705","created_at":"2026-07-05T11:21:09Z"},{"alias_kind":"arxiv_version","alias_value":"2506.11705v1","created_at":"2026-07-05T11:21:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.11705","created_at":"2026-07-05T11:21:09Z"},{"alias_kind":"pith_short_12","alias_value":"AWA33KALEYFV","created_at":"2026-07-05T11:21:09Z"},{"alias_kind":"pith_short_16","alias_value":"AWA33KALEYFVVJ24","created_at":"2026-07-05T11:21:09Z"},{"alias_kind":"pith_short_8","alias_value":"AWA33KAL","created_at":"2026-07-05T11:21:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:AWA33KALEYFVVJ24SC4J5VLJ3F","target":"record","payload":{"canonical_record":{"source":{"id":"2506.11705","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-06-13T12:19:46Z","cross_cats_sorted":[],"title_canon_sha256":"ecf2926722f5924aff25c4184ab931d2ca26e96292a20b26d89ff47307e4f28e","abstract_canon_sha256":"5f7e0c200a0c9ad5e7b06d43133789c1010377dcfc102bca988d5fbf84c01363"},"schema_version":"1.0"},"canonical_sha256":"0581bda80b260b5aa75c90b89ed569d976feef84e786f772ee422fd3f3bb0f9a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:21:09.471582Z","signature_b64":"VdmlxJq0D5UgO3eQIyB2T+FDds6mpGrKgSs8kWm9v9cmVl9WmqW+o0SFd1GrSXdVHndgU5vRUSlGW05YcLAMAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0581bda80b260b5aa75c90b89ed569d976feef84e786f772ee422fd3f3bb0f9a","last_reissued_at":"2026-07-05T11:21:09.471139Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:21:09.471139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.11705","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":"2026-07-05T11:21:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CkSdg3vEpT5NKNxNPNpsWxLraPR43F5lxSl0bbiotKxGassSu/LlLREvWn9NL915D3Ai1Z4J2+nv2VDSAK1xCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T08:28:46.225249Z"},"content_sha256":"acf8407a5524fbb4df44c159c1e9a3eda8833aa93e785a14ee091d18c90859bc","schema_version":"1.0","event_id":"sha256:acf8407a5524fbb4df44c159c1e9a3eda8833aa93e785a14ee091d18c90859bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:AWA33KALEYFVVJ24SC4J5VLJ3F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Heavy-ball dynamics with Hessian-driven damping for non-convex optimization under the {\\L}ojasiewicz condition","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Theodoros G. Tsironis, Vasiliki Mavrogeorgou, Vassilis Apidopoulos","submitted_at":"2025-06-13T12:19:46Z","abstract_excerpt":"In this paper, we examine the convergence properties of heavy-ball dynamics with Hessian-driven damping in smooth non-convex optimization problems satisfying a {\\L}ojasiewicz condition. In this general setting, we provide a series of tight, worst-case optimal convergence rate guarantees as a function of the dynamics' friction coefficients and the {\\L}ojasiewicz exponent of the problem's objective function. Importantly, the linear rates that we obtain improve on previous available rates and they suggest a different tuning of the dynamics' damping terms, even in the strongly convex regime. We co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.11705","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.11705/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:21:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JvLAHJA2RHn3qOJhbSkI6SuRH0cWWp4/DfIJTaDarLopQxgrAehwDfAMXWhjPD+We6ZZFdHfic+xUKgl+DNYDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T08:28:46.225888Z"},"content_sha256":"bd54979d7ef061925a966814c1cdb5047489b1b2bb3917c6ef5a82ec7776dd85","schema_version":"1.0","event_id":"sha256:bd54979d7ef061925a966814c1cdb5047489b1b2bb3917c6ef5a82ec7776dd85"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AWA33KALEYFVVJ24SC4J5VLJ3F/bundle.json","state_url":"https://pith.science/pith/AWA33KALEYFVVJ24SC4J5VLJ3F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AWA33KALEYFVVJ24SC4J5VLJ3F/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":"2026-08-08T08:28:46Z","links":{"resolver":"https://pith.science/pith/AWA33KALEYFVVJ24SC4J5VLJ3F","bundle":"https://pith.science/pith/AWA33KALEYFVVJ24SC4J5VLJ3F/bundle.json","state":"https://pith.science/pith/AWA33KALEYFVVJ24SC4J5VLJ3F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AWA33KALEYFVVJ24SC4J5VLJ3F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:AWA33KALEYFVVJ24SC4J5VLJ3F","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":"5f7e0c200a0c9ad5e7b06d43133789c1010377dcfc102bca988d5fbf84c01363","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-06-13T12:19:46Z","title_canon_sha256":"ecf2926722f5924aff25c4184ab931d2ca26e96292a20b26d89ff47307e4f28e"},"schema_version":"1.0","source":{"id":"2506.11705","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.11705","created_at":"2026-07-05T11:21:09Z"},{"alias_kind":"arxiv_version","alias_value":"2506.11705v1","created_at":"2026-07-05T11:21:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.11705","created_at":"2026-07-05T11:21:09Z"},{"alias_kind":"pith_short_12","alias_value":"AWA33KALEYFV","created_at":"2026-07-05T11:21:09Z"},{"alias_kind":"pith_short_16","alias_value":"AWA33KALEYFVVJ24","created_at":"2026-07-05T11:21:09Z"},{"alias_kind":"pith_short_8","alias_value":"AWA33KAL","created_at":"2026-07-05T11:21:09Z"}],"graph_snapshots":[{"event_id":"sha256:bd54979d7ef061925a966814c1cdb5047489b1b2bb3917c6ef5a82ec7776dd85","target":"graph","created_at":"2026-07-05T11:21:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.11705/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we examine the convergence properties of heavy-ball dynamics with Hessian-driven damping in smooth non-convex optimization problems satisfying a {\\L}ojasiewicz condition. In this general setting, we provide a series of tight, worst-case optimal convergence rate guarantees as a function of the dynamics' friction coefficients and the {\\L}ojasiewicz exponent of the problem's objective function. Importantly, the linear rates that we obtain improve on previous available rates and they suggest a different tuning of the dynamics' damping terms, even in the strongly convex regime. We co","authors_text":"Theodoros G. Tsironis, Vasiliki Mavrogeorgou, Vassilis Apidopoulos","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-06-13T12:19:46Z","title":"Heavy-ball dynamics with Hessian-driven damping for non-convex optimization under the {\\L}ojasiewicz condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.11705","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:acf8407a5524fbb4df44c159c1e9a3eda8833aa93e785a14ee091d18c90859bc","target":"record","created_at":"2026-07-05T11:21:09Z","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":"5f7e0c200a0c9ad5e7b06d43133789c1010377dcfc102bca988d5fbf84c01363","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-06-13T12:19:46Z","title_canon_sha256":"ecf2926722f5924aff25c4184ab931d2ca26e96292a20b26d89ff47307e4f28e"},"schema_version":"1.0","source":{"id":"2506.11705","kind":"arxiv","version":1}},"canonical_sha256":"0581bda80b260b5aa75c90b89ed569d976feef84e786f772ee422fd3f3bb0f9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0581bda80b260b5aa75c90b89ed569d976feef84e786f772ee422fd3f3bb0f9a","first_computed_at":"2026-07-05T11:21:09.471139Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:21:09.471139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VdmlxJq0D5UgO3eQIyB2T+FDds6mpGrKgSs8kWm9v9cmVl9WmqW+o0SFd1GrSXdVHndgU5vRUSlGW05YcLAMAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:21:09.471582Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.11705","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:acf8407a5524fbb4df44c159c1e9a3eda8833aa93e785a14ee091d18c90859bc","sha256:bd54979d7ef061925a966814c1cdb5047489b1b2bb3917c6ef5a82ec7776dd85"],"state_sha256":"2ccbfbf2a244fb1a20e48a3da27718e9d470d899a8a6165c3d0d8e4922a9aadf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qIRm72Fe3sjWXRaN/o9iXOHHanzahtbn7G7hJhbsemf1Ym6GQjj4Ng6rHq8pBnPISrhm9wAWzpnTXziyOekRDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T08:28:46.231351Z","bundle_sha256":"7b3fc3cafc7337f82df5170cf011239379742a2dcb27df61f27380b1085f821a"}}