{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:IGED3WEUB2EAXIULHA74WW3O5O","short_pith_number":"pith:IGED3WEU","canonical_record":{"source":{"id":"1603.07131","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-23T10:57:04Z","cross_cats_sorted":[],"title_canon_sha256":"69b2aa802cfb636cc593d1579e537fccb813a633a58ecc2d6135e44e31a48292","abstract_canon_sha256":"c45942cef35af7d580c6e8ad8ce34c506b3bb60c1855e34a5188f9fcaaf38ff0"},"schema_version":"1.0"},"canonical_sha256":"41883dd8940e880ba28b383fcb5b6eeb8e9a8f139670b8acaccb2e09c5f1e724","source":{"kind":"arxiv","id":"1603.07131","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07131","created_at":"2026-05-18T01:18:24Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07131v1","created_at":"2026-05-18T01:18:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07131","created_at":"2026-05-18T01:18:24Z"},{"alias_kind":"pith_short_12","alias_value":"IGED3WEUB2EA","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IGED3WEUB2EAXIUL","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IGED3WEU","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:IGED3WEUB2EAXIULHA74WW3O5O","target":"record","payload":{"canonical_record":{"source":{"id":"1603.07131","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-23T10:57:04Z","cross_cats_sorted":[],"title_canon_sha256":"69b2aa802cfb636cc593d1579e537fccb813a633a58ecc2d6135e44e31a48292","abstract_canon_sha256":"c45942cef35af7d580c6e8ad8ce34c506b3bb60c1855e34a5188f9fcaaf38ff0"},"schema_version":"1.0"},"canonical_sha256":"41883dd8940e880ba28b383fcb5b6eeb8e9a8f139670b8acaccb2e09c5f1e724","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:24.354010Z","signature_b64":"dsRBPpKN9YOzKShrAclyUjIMEWB4XlyuWWCysTnVsilkO/ygOYp4yPX5Ecz/2TqRN9xszVD6HjANmVkvsEOVCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41883dd8940e880ba28b383fcb5b6eeb8e9a8f139670b8acaccb2e09c5f1e724","last_reissued_at":"2026-05-18T01:18:24.353302Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:24.353302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.07131","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":"2026-05-18T01:18:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yu/CGerG+xrctWx+aDM5Uqd04equkBkvySuFJ61iaqGxcJ/22qL6ukzn0lArdIqD8UNCaTktxQ9FphNgRTwVAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T00:30:05.447188Z"},"content_sha256":"1299fe440e2b748e3971e46bfbd971c3e5701a6e39f93d0a6c14f12d627de867","schema_version":"1.0","event_id":"sha256:1299fe440e2b748e3971e46bfbd971c3e5701a6e39f93d0a6c14f12d627de867"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:IGED3WEUB2EAXIULHA74WW3O5O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Beyond the Melnikov method: a computer assisted approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Maciej J. Capinski, Piotr Zgliczynski","submitted_at":"2016-03-23T10:57:04Z","abstract_excerpt":"We present a Melnikov type approach for establishing transversal intersections of stable/unstable manifolds of perturbed normally hyperbolic invariant manifolds (NHIMs). The method is based on a new geometric proof of the normally hyperbolic invariant manifold theorem, which establishes the existence of a NHIM, together with its associated invariant manifolds and bounds on their first and second derivatives. We do not need to know the explicit formulas for the homoclinic orbits prior to the perturbation. We also do not need to compute any integrals along such homoclinics. All needed bounds are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07131","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":"2026-05-18T01:18:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tCAXYAKAKiX6+fD1ybmjdPArBx1xAEBirBpARNv2B2dpeD4jliBaafGQ+U3N5oDnLhVS9zT4JdlI6jwG9jnVAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T00:30:05.447551Z"},"content_sha256":"f9d8bac6049f58498365610dde61693ad986a051a30aeed3271d0bdeb3ab4f26","schema_version":"1.0","event_id":"sha256:f9d8bac6049f58498365610dde61693ad986a051a30aeed3271d0bdeb3ab4f26"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IGED3WEUB2EAXIULHA74WW3O5O/bundle.json","state_url":"https://pith.science/pith/IGED3WEUB2EAXIULHA74WW3O5O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IGED3WEUB2EAXIULHA74WW3O5O/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":"2026-06-04T00:30:05Z","links":{"resolver":"https://pith.science/pith/IGED3WEUB2EAXIULHA74WW3O5O","bundle":"https://pith.science/pith/IGED3WEUB2EAXIULHA74WW3O5O/bundle.json","state":"https://pith.science/pith/IGED3WEUB2EAXIULHA74WW3O5O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IGED3WEUB2EAXIULHA74WW3O5O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IGED3WEUB2EAXIULHA74WW3O5O","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":"c45942cef35af7d580c6e8ad8ce34c506b3bb60c1855e34a5188f9fcaaf38ff0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-23T10:57:04Z","title_canon_sha256":"69b2aa802cfb636cc593d1579e537fccb813a633a58ecc2d6135e44e31a48292"},"schema_version":"1.0","source":{"id":"1603.07131","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07131","created_at":"2026-05-18T01:18:24Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07131v1","created_at":"2026-05-18T01:18:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07131","created_at":"2026-05-18T01:18:24Z"},{"alias_kind":"pith_short_12","alias_value":"IGED3WEUB2EA","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IGED3WEUB2EAXIUL","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IGED3WEU","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:f9d8bac6049f58498365610dde61693ad986a051a30aeed3271d0bdeb3ab4f26","target":"graph","created_at":"2026-05-18T01:18:24Z","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":"We present a Melnikov type approach for establishing transversal intersections of stable/unstable manifolds of perturbed normally hyperbolic invariant manifolds (NHIMs). The method is based on a new geometric proof of the normally hyperbolic invariant manifold theorem, which establishes the existence of a NHIM, together with its associated invariant manifolds and bounds on their first and second derivatives. We do not need to know the explicit formulas for the homoclinic orbits prior to the perturbation. We also do not need to compute any integrals along such homoclinics. All needed bounds are","authors_text":"Maciej J. Capinski, Piotr Zgliczynski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-23T10:57:04Z","title":"Beyond the Melnikov method: a computer assisted approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07131","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":"sha256:1299fe440e2b748e3971e46bfbd971c3e5701a6e39f93d0a6c14f12d627de867","target":"record","created_at":"2026-05-18T01:18:24Z","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":"c45942cef35af7d580c6e8ad8ce34c506b3bb60c1855e34a5188f9fcaaf38ff0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-23T10:57:04Z","title_canon_sha256":"69b2aa802cfb636cc593d1579e537fccb813a633a58ecc2d6135e44e31a48292"},"schema_version":"1.0","source":{"id":"1603.07131","kind":"arxiv","version":1}},"canonical_sha256":"41883dd8940e880ba28b383fcb5b6eeb8e9a8f139670b8acaccb2e09c5f1e724","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41883dd8940e880ba28b383fcb5b6eeb8e9a8f139670b8acaccb2e09c5f1e724","first_computed_at":"2026-05-18T01:18:24.353302Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:24.353302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dsRBPpKN9YOzKShrAclyUjIMEWB4XlyuWWCysTnVsilkO/ygOYp4yPX5Ecz/2TqRN9xszVD6HjANmVkvsEOVCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:24.354010Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.07131","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1299fe440e2b748e3971e46bfbd971c3e5701a6e39f93d0a6c14f12d627de867","sha256:f9d8bac6049f58498365610dde61693ad986a051a30aeed3271d0bdeb3ab4f26"],"state_sha256":"251d914f57d0f824d34bde11ab617ce9d7919c092491704bd0490f06f67e4f3b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2MVNuqMd7S9Evdqh+ffcXCdsiEYhKDj+l7di+Tzyt3SItFkF38unaMEO8fSAXzIm4OXdH1lddZn2gTendSgGAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T00:30:05.449486Z","bundle_sha256":"6688e6a640f6ce66a9a6c509fd1d033ae59acc3afd522565fca3fac0e0d8289f"}}