{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:VCNGXL2GVKLOHL2KQDH5GF3LGO","short_pith_number":"pith:VCNGXL2G","canonical_record":{"source":{"id":"1602.04243","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-30T19:21:19Z","cross_cats_sorted":["nlin.CD","physics.flu-dyn"],"title_canon_sha256":"6b2489522a805d7a88eff7d41d3741311f8b1505c4a7f0039e304aadb80893ef","abstract_canon_sha256":"7970020d8fd01de68b698e92060fe5f1b7fd9e11d6aec49edcd3f93d259b4ecf"},"schema_version":"1.0"},"canonical_sha256":"a89a6baf46aa96e3af4a80cfd3176b33913fb55ec63c6a38f38c61068103fdb2","source":{"kind":"arxiv","id":"1602.04243","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04243","created_at":"2026-05-18T01:20:51Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04243v1","created_at":"2026-05-18T01:20:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04243","created_at":"2026-05-18T01:20:51Z"},{"alias_kind":"pith_short_12","alias_value":"VCNGXL2GVKLO","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VCNGXL2GVKLOHL2K","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VCNGXL2G","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:VCNGXL2GVKLOHL2KQDH5GF3LGO","target":"record","payload":{"canonical_record":{"source":{"id":"1602.04243","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-30T19:21:19Z","cross_cats_sorted":["nlin.CD","physics.flu-dyn"],"title_canon_sha256":"6b2489522a805d7a88eff7d41d3741311f8b1505c4a7f0039e304aadb80893ef","abstract_canon_sha256":"7970020d8fd01de68b698e92060fe5f1b7fd9e11d6aec49edcd3f93d259b4ecf"},"schema_version":"1.0"},"canonical_sha256":"a89a6baf46aa96e3af4a80cfd3176b33913fb55ec63c6a38f38c61068103fdb2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:51.466926Z","signature_b64":"2V3dRXnyg6C5bllO5cX2heGCtx3HftEI8ExK2t2FYZe3IV0FQYvy3bLAavnVqIiBglEreXRStfWaPerys4KZDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a89a6baf46aa96e3af4a80cfd3176b33913fb55ec63c6a38f38c61068103fdb2","last_reissued_at":"2026-05-18T01:20:51.466340Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:51.466340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.04243","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":"2026-05-18T01:20:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GKCe1Dna7TZir2uLEaaXTcA9jKRV6l3Kas3KE5iJ8+Hy446TaoNwxpK98gdYv6ewG0y8p4NP1MU2/E5J5im+Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:50:42.717626Z"},"content_sha256":"b9842f6f8bee212f149e139c234920139cbb0e9aebfe57259bcefa360aa172c9","schema_version":"1.0","event_id":"sha256:b9842f6f8bee212f149e139c234920139cbb0e9aebfe57259bcefa360aa172c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:VCNGXL2GVKLOHL2KQDH5GF3LGO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Response to: \"Limitations of the Method of Lagrangian Descriptors\" [arXiv:1510.04838]","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD","physics.flu-dyn"],"primary_cat":"math.DS","authors_text":"A. M. Mancho, C. Lopesino, C. Mendoza, F. Balibrea-Iniesta, J. Curbelo, S. Wiggins, V. J. Garc\\'ia-Garrido","submitted_at":"2016-01-30T19:21:19Z","abstract_excerpt":"This Response is concerned with the recent Comment of Ruiz-Herrera, \"Limitations of the Method of Lagrangian Descriptors\" [arXiv:1510.04838], criticising the method of Lagrangian Descriptors. In spite of the significant body of literature asserting the contrary, Ruiz-Herrera claims that the method fails to reveal the presence of stable and unstable manifolds of hyperbolic trajectories in incompressible systems and in almost all linear systems. He supports this claim by considering the method of Lagrangian descriptors applied to three specific examples. However in this response we show that Rui"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04243","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":"2026-05-18T01:20:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D/3+yYdSeiWS7HiH69aayP1ht9wm3p2LkWSJ/nshjNp2ot3c/kiHjCAhy5VlvJXP2ZOxqaJeQzN4L7XhuBthAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:50:42.717969Z"},"content_sha256":"723335cc529edcf882abbc83b48c1e0759bc5a73b7993f50013670c5a5e37694","schema_version":"1.0","event_id":"sha256:723335cc529edcf882abbc83b48c1e0759bc5a73b7993f50013670c5a5e37694"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VCNGXL2GVKLOHL2KQDH5GF3LGO/bundle.json","state_url":"https://pith.science/pith/VCNGXL2GVKLOHL2KQDH5GF3LGO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VCNGXL2GVKLOHL2KQDH5GF3LGO/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":"2026-06-22T09:50:42Z","links":{"resolver":"https://pith.science/pith/VCNGXL2GVKLOHL2KQDH5GF3LGO","bundle":"https://pith.science/pith/VCNGXL2GVKLOHL2KQDH5GF3LGO/bundle.json","state":"https://pith.science/pith/VCNGXL2GVKLOHL2KQDH5GF3LGO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VCNGXL2GVKLOHL2KQDH5GF3LGO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VCNGXL2GVKLOHL2KQDH5GF3LGO","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":"7970020d8fd01de68b698e92060fe5f1b7fd9e11d6aec49edcd3f93d259b4ecf","cross_cats_sorted":["nlin.CD","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-30T19:21:19Z","title_canon_sha256":"6b2489522a805d7a88eff7d41d3741311f8b1505c4a7f0039e304aadb80893ef"},"schema_version":"1.0","source":{"id":"1602.04243","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04243","created_at":"2026-05-18T01:20:51Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04243v1","created_at":"2026-05-18T01:20:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04243","created_at":"2026-05-18T01:20:51Z"},{"alias_kind":"pith_short_12","alias_value":"VCNGXL2GVKLO","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VCNGXL2GVKLOHL2K","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VCNGXL2G","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:723335cc529edcf882abbc83b48c1e0759bc5a73b7993f50013670c5a5e37694","target":"graph","created_at":"2026-05-18T01:20:51Z","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":"This Response is concerned with the recent Comment of Ruiz-Herrera, \"Limitations of the Method of Lagrangian Descriptors\" [arXiv:1510.04838], criticising the method of Lagrangian Descriptors. In spite of the significant body of literature asserting the contrary, Ruiz-Herrera claims that the method fails to reveal the presence of stable and unstable manifolds of hyperbolic trajectories in incompressible systems and in almost all linear systems. He supports this claim by considering the method of Lagrangian descriptors applied to three specific examples. However in this response we show that Rui","authors_text":"A. M. Mancho, C. Lopesino, C. Mendoza, F. Balibrea-Iniesta, J. Curbelo, S. Wiggins, V. J. Garc\\'ia-Garrido","cross_cats":["nlin.CD","physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-30T19:21:19Z","title":"Response to: \"Limitations of the Method of Lagrangian Descriptors\" [arXiv:1510.04838]"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04243","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:b9842f6f8bee212f149e139c234920139cbb0e9aebfe57259bcefa360aa172c9","target":"record","created_at":"2026-05-18T01:20:51Z","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":"7970020d8fd01de68b698e92060fe5f1b7fd9e11d6aec49edcd3f93d259b4ecf","cross_cats_sorted":["nlin.CD","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-30T19:21:19Z","title_canon_sha256":"6b2489522a805d7a88eff7d41d3741311f8b1505c4a7f0039e304aadb80893ef"},"schema_version":"1.0","source":{"id":"1602.04243","kind":"arxiv","version":1}},"canonical_sha256":"a89a6baf46aa96e3af4a80cfd3176b33913fb55ec63c6a38f38c61068103fdb2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a89a6baf46aa96e3af4a80cfd3176b33913fb55ec63c6a38f38c61068103fdb2","first_computed_at":"2026-05-18T01:20:51.466340Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:51.466340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2V3dRXnyg6C5bllO5cX2heGCtx3HftEI8ExK2t2FYZe3IV0FQYvy3bLAavnVqIiBglEreXRStfWaPerys4KZDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:51.466926Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.04243","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9842f6f8bee212f149e139c234920139cbb0e9aebfe57259bcefa360aa172c9","sha256:723335cc529edcf882abbc83b48c1e0759bc5a73b7993f50013670c5a5e37694"],"state_sha256":"b886f4ba1690a214a20e2205ea5ebd18de0612289de50c0074bd1f6e53b6daac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lnNkeUjyWj4gbymNKudfk6HXmTVJzLVh5EiSUnDEkDwmz+YtDJo3oQGGXxti3TUjjJck+BrimdA7NJGdpUg0Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T09:50:42.719990Z","bundle_sha256":"0126e0ec62c6636ac3b13843000d46fcbc14bcb6250c072c935763fb1617210f"}}