{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JGPDTGWDRBJCGCQBBMZNTDMGCA","short_pith_number":"pith:JGPDTGWD","canonical_record":{"source":{"id":"1607.08875","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-29T17:42:04Z","cross_cats_sorted":["math.OC","physics.comp-ph"],"title_canon_sha256":"7740a793f3e91b6bd03dd3761d1a6f825c20fa5e6407731957ffbea1cd267a2f","abstract_canon_sha256":"0b58c08cd56118c4b4e228483955b45bb396a6d68e6cba9e6df33401133b616b"},"schema_version":"1.0"},"canonical_sha256":"499e399ac38852230a010b32d98d861039c2a42e744c2a156c12e848c3d3acaf","source":{"kind":"arxiv","id":"1607.08875","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.08875","created_at":"2026-05-18T01:10:15Z"},{"alias_kind":"arxiv_version","alias_value":"1607.08875v1","created_at":"2026-05-18T01:10:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.08875","created_at":"2026-05-18T01:10:15Z"},{"alias_kind":"pith_short_12","alias_value":"JGPDTGWDRBJC","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JGPDTGWDRBJCGCQB","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JGPDTGWD","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JGPDTGWDRBJCGCQBBMZNTDMGCA","target":"record","payload":{"canonical_record":{"source":{"id":"1607.08875","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-29T17:42:04Z","cross_cats_sorted":["math.OC","physics.comp-ph"],"title_canon_sha256":"7740a793f3e91b6bd03dd3761d1a6f825c20fa5e6407731957ffbea1cd267a2f","abstract_canon_sha256":"0b58c08cd56118c4b4e228483955b45bb396a6d68e6cba9e6df33401133b616b"},"schema_version":"1.0"},"canonical_sha256":"499e399ac38852230a010b32d98d861039c2a42e744c2a156c12e848c3d3acaf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:15.695505Z","signature_b64":"XalZ1clraHC6UtWctVCePf/Da4nh7sTH+qi5NiIw0bi22zj1U9tETrsb/reUpthRJQgsZAqdRLLC1tuxq6HlCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"499e399ac38852230a010b32d98d861039c2a42e744c2a156c12e848c3d3acaf","last_reissued_at":"2026-05-18T01:10:15.694872Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:15.694872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.08875","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":"2026-05-18T01:10:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FiKbeo7Xs0zo3ISxuxRksjIWcNLMjvAjFMBWhLgAvKc/rSLRBwz/vuj2n4EwjBjmmVdDrS8IQo5VRkICOFFqCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T04:51:36.779558Z"},"content_sha256":"6ba0576667ce4fcfa75f10f2218480f1049e7c4dfad851a4b0ee776c7be4629d","schema_version":"1.0","event_id":"sha256:6ba0576667ce4fcfa75f10f2218480f1049e7c4dfad851a4b0ee776c7be4629d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JGPDTGWDRBJCGCQBBMZNTDMGCA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence and Cycling in Walker-type Saddle Search Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Antoine Levitt, Christoph Ortner","submitted_at":"2016-07-29T17:42:04Z","abstract_excerpt":"Algorithms for computing local minima of smooth objective functions enjoy a mature theory as well as robust and efficient implementations. By comparison, the theory and practice of saddle search is destitute. In this paper we present results for idealized versions of the dimer and gentlest ascent (GAD) saddle search algorithms that show-case the limitations of what is theoretically achievable within the current class of saddle search algorithms: (1) we present an improved estimate on the region of attraction of saddles; and (2) we construct quasi-periodic solutions which indicate that it is im"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08875","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":"2026-05-18T01:10:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PDROhEC9crRpjacObLj4D5/Nk1r0QhI8N+CrwA9AuO2bbYOtymrM0T+WJtgRaOHnbz4jBTh4I7iovhlRy3VlAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T04:51:36.780263Z"},"content_sha256":"841ddc4acac9961a163d5ed6a111df39c4ba47cbfc89a0276b8313be1c2cadc7","schema_version":"1.0","event_id":"sha256:841ddc4acac9961a163d5ed6a111df39c4ba47cbfc89a0276b8313be1c2cadc7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JGPDTGWDRBJCGCQBBMZNTDMGCA/bundle.json","state_url":"https://pith.science/pith/JGPDTGWDRBJCGCQBBMZNTDMGCA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JGPDTGWDRBJCGCQBBMZNTDMGCA/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":"2026-06-05T04:51:36Z","links":{"resolver":"https://pith.science/pith/JGPDTGWDRBJCGCQBBMZNTDMGCA","bundle":"https://pith.science/pith/JGPDTGWDRBJCGCQBBMZNTDMGCA/bundle.json","state":"https://pith.science/pith/JGPDTGWDRBJCGCQBBMZNTDMGCA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JGPDTGWDRBJCGCQBBMZNTDMGCA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JGPDTGWDRBJCGCQBBMZNTDMGCA","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":"0b58c08cd56118c4b4e228483955b45bb396a6d68e6cba9e6df33401133b616b","cross_cats_sorted":["math.OC","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-29T17:42:04Z","title_canon_sha256":"7740a793f3e91b6bd03dd3761d1a6f825c20fa5e6407731957ffbea1cd267a2f"},"schema_version":"1.0","source":{"id":"1607.08875","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.08875","created_at":"2026-05-18T01:10:15Z"},{"alias_kind":"arxiv_version","alias_value":"1607.08875v1","created_at":"2026-05-18T01:10:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.08875","created_at":"2026-05-18T01:10:15Z"},{"alias_kind":"pith_short_12","alias_value":"JGPDTGWDRBJC","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JGPDTGWDRBJCGCQB","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JGPDTGWD","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:841ddc4acac9961a163d5ed6a111df39c4ba47cbfc89a0276b8313be1c2cadc7","target":"graph","created_at":"2026-05-18T01:10:15Z","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":"Algorithms for computing local minima of smooth objective functions enjoy a mature theory as well as robust and efficient implementations. By comparison, the theory and practice of saddle search is destitute. In this paper we present results for idealized versions of the dimer and gentlest ascent (GAD) saddle search algorithms that show-case the limitations of what is theoretically achievable within the current class of saddle search algorithms: (1) we present an improved estimate on the region of attraction of saddles; and (2) we construct quasi-periodic solutions which indicate that it is im","authors_text":"Antoine Levitt, Christoph Ortner","cross_cats":["math.OC","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-29T17:42:04Z","title":"Convergence and Cycling in Walker-type Saddle Search Algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08875","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":"sha256:6ba0576667ce4fcfa75f10f2218480f1049e7c4dfad851a4b0ee776c7be4629d","target":"record","created_at":"2026-05-18T01:10:15Z","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":"0b58c08cd56118c4b4e228483955b45bb396a6d68e6cba9e6df33401133b616b","cross_cats_sorted":["math.OC","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-29T17:42:04Z","title_canon_sha256":"7740a793f3e91b6bd03dd3761d1a6f825c20fa5e6407731957ffbea1cd267a2f"},"schema_version":"1.0","source":{"id":"1607.08875","kind":"arxiv","version":1}},"canonical_sha256":"499e399ac38852230a010b32d98d861039c2a42e744c2a156c12e848c3d3acaf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"499e399ac38852230a010b32d98d861039c2a42e744c2a156c12e848c3d3acaf","first_computed_at":"2026-05-18T01:10:15.694872Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:15.694872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XalZ1clraHC6UtWctVCePf/Da4nh7sTH+qi5NiIw0bi22zj1U9tETrsb/reUpthRJQgsZAqdRLLC1tuxq6HlCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:15.695505Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.08875","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ba0576667ce4fcfa75f10f2218480f1049e7c4dfad851a4b0ee776c7be4629d","sha256:841ddc4acac9961a163d5ed6a111df39c4ba47cbfc89a0276b8313be1c2cadc7"],"state_sha256":"6f7ff609a586b118f4829aedb60e2bf23a83dcda06d6615003185b5426bc07cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HVxvlcjTDmSlh/l6ub9uPG6aHi2L4zrNn40tTcpeopBaw+chZUVDDSzLr9YvixfczFJ3DNB02AZd1ns5DKXPDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T04:51:36.784049Z","bundle_sha256":"a7132a3a942cca04f7dc2f7851373a36323cee5d4ebcd2a361b2c526c8c70738"}}