{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:53EYEVVKAF54FHZX3X4LMPI6MG","short_pith_number":"pith:53EYEVVK","canonical_record":{"source":{"id":"2505.22180","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2025-05-28T09:56:18Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"8735a5c8261f30417db41bebb86440fe41c785d89036a1ee94451d20223dbe20","abstract_canon_sha256":"e6be7b1237da318733ba187a2d5a369bf06e11289d6dd3a95714b363380ac4dd"},"schema_version":"1.0"},"canonical_sha256":"eec98256aa017bc29f37ddf8b63d1e618d92b50396ab044ae5d597e4fe57476b","source":{"kind":"arxiv","id":"2505.22180","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.22180","created_at":"2026-07-05T11:11:10Z"},{"alias_kind":"arxiv_version","alias_value":"2505.22180v1","created_at":"2026-07-05T11:11:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.22180","created_at":"2026-07-05T11:11:10Z"},{"alias_kind":"pith_short_12","alias_value":"53EYEVVKAF54","created_at":"2026-07-05T11:11:10Z"},{"alias_kind":"pith_short_16","alias_value":"53EYEVVKAF54FHZX","created_at":"2026-07-05T11:11:10Z"},{"alias_kind":"pith_short_8","alias_value":"53EYEVVK","created_at":"2026-07-05T11:11:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:53EYEVVKAF54FHZX3X4LMPI6MG","target":"record","payload":{"canonical_record":{"source":{"id":"2505.22180","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2025-05-28T09:56:18Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"8735a5c8261f30417db41bebb86440fe41c785d89036a1ee94451d20223dbe20","abstract_canon_sha256":"e6be7b1237da318733ba187a2d5a369bf06e11289d6dd3a95714b363380ac4dd"},"schema_version":"1.0"},"canonical_sha256":"eec98256aa017bc29f37ddf8b63d1e618d92b50396ab044ae5d597e4fe57476b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:11:10.999459Z","signature_b64":"0SXgeb1zLLLQrcGnRfozC8hiLR+t+ChOU4dTx9TDADDCjS9JldfsV2qAfm5VLoN4AKS330VTpQ/lijVxE+LFBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eec98256aa017bc29f37ddf8b63d1e618d92b50396ab044ae5d597e4fe57476b","last_reissued_at":"2026-07-05T11:11:10.998988Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:11:10.998988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.22180","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":"2026-07-05T11:11:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HD094WMu5UM/in8nIsKnjwlfXhhYKCptT+jyiL59Knxrzmupu2R48swjofYdSRp/v7WhYymsdcN6AjbeDINoAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T02:31:45.472119Z"},"content_sha256":"b2db42bfbc774b6577b72a8ee8bf04c85455d1c7e7ec918954af10b4d94e1214","schema_version":"1.0","event_id":"sha256:b2db42bfbc774b6577b72a8ee8bf04c85455d1c7e7ec918954af10b4d94e1214"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:53EYEVVKAF54FHZX3X4LMPI6MG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some iterative algorithms on Riemannian manifolds and Banach spaces with good global convergence guarantee","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OC","authors_text":"Tuyen Trung Truong","submitted_at":"2025-05-28T09:56:18Z","abstract_excerpt":"In this paper, we introduce some new iterative optimisation algorithms on Riemannian manifolds and Hilbert spaces which have good global convergence guarantees to local minima. More precisely, these algorithms have the following properties: If $\\{x_n\\}$ is a sequence constructed by one such algorithm then:\n  - Finding critical points: Any cluster point of $\\{x_n\\}$ is a critical point of the cost function $f$.\n  - Convergence guarantee: Under suitable assumptions, the sequence $\\{x_n\\}$ either converges to a point $x^*$, or diverges to $\\infty$.\n  - Avoidance of saddle points: If $x_0$ is rand"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.22180","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/2505.22180/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":"2026-07-05T11:11:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I8fWJH3qo5TMsAyg5ELYcGYC56uRAddEDFDgXoaKiKOG83lHR/xFf5CNho6W8nQmtvLiWP8vFAdAm9IrqxLCAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T02:31:45.472639Z"},"content_sha256":"c07a638d0dcc586ccfea68a328f77bda2d6fda82e5b7514119ff48ffcf704de6","schema_version":"1.0","event_id":"sha256:c07a638d0dcc586ccfea68a328f77bda2d6fda82e5b7514119ff48ffcf704de6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/53EYEVVKAF54FHZX3X4LMPI6MG/bundle.json","state_url":"https://pith.science/pith/53EYEVVKAF54FHZX3X4LMPI6MG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/53EYEVVKAF54FHZX3X4LMPI6MG/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":"2026-08-08T02:31:45Z","links":{"resolver":"https://pith.science/pith/53EYEVVKAF54FHZX3X4LMPI6MG","bundle":"https://pith.science/pith/53EYEVVKAF54FHZX3X4LMPI6MG/bundle.json","state":"https://pith.science/pith/53EYEVVKAF54FHZX3X4LMPI6MG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/53EYEVVKAF54FHZX3X4LMPI6MG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:53EYEVVKAF54FHZX3X4LMPI6MG","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":"e6be7b1237da318733ba187a2d5a369bf06e11289d6dd3a95714b363380ac4dd","cross_cats_sorted":["math.DS"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2025-05-28T09:56:18Z","title_canon_sha256":"8735a5c8261f30417db41bebb86440fe41c785d89036a1ee94451d20223dbe20"},"schema_version":"1.0","source":{"id":"2505.22180","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.22180","created_at":"2026-07-05T11:11:10Z"},{"alias_kind":"arxiv_version","alias_value":"2505.22180v1","created_at":"2026-07-05T11:11:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.22180","created_at":"2026-07-05T11:11:10Z"},{"alias_kind":"pith_short_12","alias_value":"53EYEVVKAF54","created_at":"2026-07-05T11:11:10Z"},{"alias_kind":"pith_short_16","alias_value":"53EYEVVKAF54FHZX","created_at":"2026-07-05T11:11:10Z"},{"alias_kind":"pith_short_8","alias_value":"53EYEVVK","created_at":"2026-07-05T11:11:10Z"}],"graph_snapshots":[{"event_id":"sha256:c07a638d0dcc586ccfea68a328f77bda2d6fda82e5b7514119ff48ffcf704de6","target":"graph","created_at":"2026-07-05T11:11:10Z","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/2505.22180/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we introduce some new iterative optimisation algorithms on Riemannian manifolds and Hilbert spaces which have good global convergence guarantees to local minima. More precisely, these algorithms have the following properties: If $\\{x_n\\}$ is a sequence constructed by one such algorithm then:\n  - Finding critical points: Any cluster point of $\\{x_n\\}$ is a critical point of the cost function $f$.\n  - Convergence guarantee: Under suitable assumptions, the sequence $\\{x_n\\}$ either converges to a point $x^*$, or diverges to $\\infty$.\n  - Avoidance of saddle points: If $x_0$ is rand","authors_text":"Tuyen Trung Truong","cross_cats":["math.DS"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2025-05-28T09:56:18Z","title":"Some iterative algorithms on Riemannian manifolds and Banach spaces with good global convergence guarantee"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.22180","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:b2db42bfbc774b6577b72a8ee8bf04c85455d1c7e7ec918954af10b4d94e1214","target":"record","created_at":"2026-07-05T11:11:10Z","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":"e6be7b1237da318733ba187a2d5a369bf06e11289d6dd3a95714b363380ac4dd","cross_cats_sorted":["math.DS"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2025-05-28T09:56:18Z","title_canon_sha256":"8735a5c8261f30417db41bebb86440fe41c785d89036a1ee94451d20223dbe20"},"schema_version":"1.0","source":{"id":"2505.22180","kind":"arxiv","version":1}},"canonical_sha256":"eec98256aa017bc29f37ddf8b63d1e618d92b50396ab044ae5d597e4fe57476b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eec98256aa017bc29f37ddf8b63d1e618d92b50396ab044ae5d597e4fe57476b","first_computed_at":"2026-07-05T11:11:10.998988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:11:10.998988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0SXgeb1zLLLQrcGnRfozC8hiLR+t+ChOU4dTx9TDADDCjS9JldfsV2qAfm5VLoN4AKS330VTpQ/lijVxE+LFBA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:11:10.999459Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.22180","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2db42bfbc774b6577b72a8ee8bf04c85455d1c7e7ec918954af10b4d94e1214","sha256:c07a638d0dcc586ccfea68a328f77bda2d6fda82e5b7514119ff48ffcf704de6"],"state_sha256":"f544fb5010836087ba27f45b8eafe301f875a23fb5bd003355b30d9bd8668456"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0OuAnoPYp+KMIrCcdglGOj7hJo8LFNl3HAMnYtGPZpiEWvrROHbRWcrGQhTODlN54nEP6G37EICG1SI1Fj1KBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T02:31:45.478791Z","bundle_sha256":"373c611788703b8bf80cf6cd4666476559bb66b4c9dff061e39ebdd48a2bc446"}}