{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:IJ2A5NQOUM2H7VRHMQXHGW3D7L","short_pith_number":"pith:IJ2A5NQO","canonical_record":{"source":{"id":"0905.2134","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-05-13T15:32:09Z","cross_cats_sorted":["cs.NA","math.NA","math.SG","math.SP"],"title_canon_sha256":"79c6d17778c94b77b95b20c070b81e01d7fbb1b592668374b1bb7ebc46b2c573","abstract_canon_sha256":"15bdde202dec7c9b6ad1fa760a2b1d6734e88ca5b9f66522654f3950b0545725"},"schema_version":"1.0"},"canonical_sha256":"42740eb60ea3347fd627642e735b63fae0714da12f816a9307ff97c205bc90d9","source":{"kind":"arxiv","id":"0905.2134","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.2134","created_at":"2026-06-03T23:06:26Z"},{"alias_kind":"arxiv_version","alias_value":"0905.2134v1","created_at":"2026-06-03T23:06:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.2134","created_at":"2026-06-03T23:06:26Z"},{"alias_kind":"pith_short_12","alias_value":"IJ2A5NQOUM2H","created_at":"2026-06-03T23:06:26Z"},{"alias_kind":"pith_short_16","alias_value":"IJ2A5NQOUM2H7VRH","created_at":"2026-06-03T23:06:26Z"},{"alias_kind":"pith_short_8","alias_value":"IJ2A5NQO","created_at":"2026-06-03T23:06:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:IJ2A5NQOUM2H7VRHMQXHGW3D7L","target":"record","payload":{"canonical_record":{"source":{"id":"0905.2134","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-05-13T15:32:09Z","cross_cats_sorted":["cs.NA","math.NA","math.SG","math.SP"],"title_canon_sha256":"79c6d17778c94b77b95b20c070b81e01d7fbb1b592668374b1bb7ebc46b2c573","abstract_canon_sha256":"15bdde202dec7c9b6ad1fa760a2b1d6734e88ca5b9f66522654f3950b0545725"},"schema_version":"1.0"},"canonical_sha256":"42740eb60ea3347fd627642e735b63fae0714da12f816a9307ff97c205bc90d9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T23:06:26.166229Z","signature_b64":"kbFAGxJd4agD2ZB81x1tPUgKSQk7T4thK3pi7pmErGjTaHZRiwoYkSdr/bnVYR9bnnClL3VBKgIMlcxfEoqeCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42740eb60ea3347fd627642e735b63fae0714da12f816a9307ff97c205bc90d9","last_reissued_at":"2026-06-03T23:06:26.165795Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T23:06:26.165795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0905.2134","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":"2026-06-03T23:06:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tJlfc3FrIBSses64f9d3zLPbE92bFLtl1YaCt7va/97j/mhM/34StlwdMGi3s2KiaA8gSjM9reaLAuFcUxYfBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T04:00:09.518176Z"},"content_sha256":"fa94cb4ce59a7dc6e670285dd153aeaa5620d26116ae2cd5d7cedfb89ff6c4b7","schema_version":"1.0","event_id":"sha256:fa94cb4ce59a7dc6e670285dd153aeaa5620d26116ae2cd5d7cedfb89ff6c4b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:IJ2A5NQOUM2H7VRHMQXHGW3D7L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computational aspects of the Maslov index of solitary waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","math.SG","math.SP"],"primary_cat":"math.AP","authors_text":"Fr\\'ed\\'eric Chardard (CMLA), Fr\\'ed\\'eric Dias (CMLA), Thomas J. Bridges","submitted_at":"2009-05-13T15:32:09Z","abstract_excerpt":"When solitary waves are characterized as homoclinic orbits of a finite-dimensional Hamiltonian system, they have an integer-valued topological invariant, the Maslov index. We are interested in developing a robust numerical algorithm to compute the Maslov index, to understand its properties, and to study the implications for the stability of solitary waves. The algorithms reported here are developed in the exterior algebra representation, which leads to a robust and fast algorithm with some novel properties. We use two different representations for the Maslov index, one based on an intersection"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.2134","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/0905.2134/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":"2026-06-03T23:06:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AR62jfANnKg/M3+pKC5V0DFNQscBxVVJO8Ke2C0IOB6ZGtGjkyj+wMfoei820QnG7q4rNt6KGuzzTYDZa5wYBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T04:00:09.518995Z"},"content_sha256":"21f84a0f9c67034ac56d7dcd467f92ba1d1cd961c0e42e07e79fb14614e7a7df","schema_version":"1.0","event_id":"sha256:21f84a0f9c67034ac56d7dcd467f92ba1d1cd961c0e42e07e79fb14614e7a7df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IJ2A5NQOUM2H7VRHMQXHGW3D7L/bundle.json","state_url":"https://pith.science/pith/IJ2A5NQOUM2H7VRHMQXHGW3D7L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IJ2A5NQOUM2H7VRHMQXHGW3D7L/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":"2026-06-11T04:00:09Z","links":{"resolver":"https://pith.science/pith/IJ2A5NQOUM2H7VRHMQXHGW3D7L","bundle":"https://pith.science/pith/IJ2A5NQOUM2H7VRHMQXHGW3D7L/bundle.json","state":"https://pith.science/pith/IJ2A5NQOUM2H7VRHMQXHGW3D7L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IJ2A5NQOUM2H7VRHMQXHGW3D7L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:IJ2A5NQOUM2H7VRHMQXHGW3D7L","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":"15bdde202dec7c9b6ad1fa760a2b1d6734e88ca5b9f66522654f3950b0545725","cross_cats_sorted":["cs.NA","math.NA","math.SG","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-05-13T15:32:09Z","title_canon_sha256":"79c6d17778c94b77b95b20c070b81e01d7fbb1b592668374b1bb7ebc46b2c573"},"schema_version":"1.0","source":{"id":"0905.2134","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.2134","created_at":"2026-06-03T23:06:26Z"},{"alias_kind":"arxiv_version","alias_value":"0905.2134v1","created_at":"2026-06-03T23:06:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.2134","created_at":"2026-06-03T23:06:26Z"},{"alias_kind":"pith_short_12","alias_value":"IJ2A5NQOUM2H","created_at":"2026-06-03T23:06:26Z"},{"alias_kind":"pith_short_16","alias_value":"IJ2A5NQOUM2H7VRH","created_at":"2026-06-03T23:06:26Z"},{"alias_kind":"pith_short_8","alias_value":"IJ2A5NQO","created_at":"2026-06-03T23:06:26Z"}],"graph_snapshots":[{"event_id":"sha256:21f84a0f9c67034ac56d7dcd467f92ba1d1cd961c0e42e07e79fb14614e7a7df","target":"graph","created_at":"2026-06-03T23:06:26Z","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/0905.2134/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"When solitary waves are characterized as homoclinic orbits of a finite-dimensional Hamiltonian system, they have an integer-valued topological invariant, the Maslov index. We are interested in developing a robust numerical algorithm to compute the Maslov index, to understand its properties, and to study the implications for the stability of solitary waves. The algorithms reported here are developed in the exterior algebra representation, which leads to a robust and fast algorithm with some novel properties. We use two different representations for the Maslov index, one based on an intersection","authors_text":"Fr\\'ed\\'eric Chardard (CMLA), Fr\\'ed\\'eric Dias (CMLA), Thomas J. Bridges","cross_cats":["cs.NA","math.NA","math.SG","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-05-13T15:32:09Z","title":"Computational aspects of the Maslov index of solitary waves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.2134","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:fa94cb4ce59a7dc6e670285dd153aeaa5620d26116ae2cd5d7cedfb89ff6c4b7","target":"record","created_at":"2026-06-03T23:06:26Z","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":"15bdde202dec7c9b6ad1fa760a2b1d6734e88ca5b9f66522654f3950b0545725","cross_cats_sorted":["cs.NA","math.NA","math.SG","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-05-13T15:32:09Z","title_canon_sha256":"79c6d17778c94b77b95b20c070b81e01d7fbb1b592668374b1bb7ebc46b2c573"},"schema_version":"1.0","source":{"id":"0905.2134","kind":"arxiv","version":1}},"canonical_sha256":"42740eb60ea3347fd627642e735b63fae0714da12f816a9307ff97c205bc90d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42740eb60ea3347fd627642e735b63fae0714da12f816a9307ff97c205bc90d9","first_computed_at":"2026-06-03T23:06:26.165795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T23:06:26.165795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kbFAGxJd4agD2ZB81x1tPUgKSQk7T4thK3pi7pmErGjTaHZRiwoYkSdr/bnVYR9bnnClL3VBKgIMlcxfEoqeCg==","signature_status":"signed_v1","signed_at":"2026-06-03T23:06:26.166229Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.2134","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa94cb4ce59a7dc6e670285dd153aeaa5620d26116ae2cd5d7cedfb89ff6c4b7","sha256:21f84a0f9c67034ac56d7dcd467f92ba1d1cd961c0e42e07e79fb14614e7a7df"],"state_sha256":"3410c3039f1a2df65c5fb2afbc4b822e0d81b6824bad3f289e737878ca630396"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qDXqznc4MqfgFWh59IpBebG4LBCNUrOZLJBpMH4rqI4bQau4B4c9Ze35vt0JqMS+TcZJSXW7i5eT4Ot3p283DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T04:00:09.523079Z","bundle_sha256":"fd269e88ec5e7680dbfe14702246e7414a5de324d6e521dcd43d6a5c99ba1915"}}