{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:D72BFWENKFRQE2LFR2HL2KK4BG","short_pith_number":"pith:D72BFWEN","canonical_record":{"source":{"id":"1512.02148","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-07T18:10:56Z","cross_cats_sorted":[],"title_canon_sha256":"02096d70de19812160838c4e85878343dd615d3626a40717e6e6d5c75a53022e","abstract_canon_sha256":"fb35f4d2ccd9a8e175e9c2f6760018afc29ed1c45d1b898d6ae8628804285c80"},"schema_version":"1.0"},"canonical_sha256":"1ff412d88d51630269658e8ebd295c09853e2952c544779e174bee51a7672f2e","source":{"kind":"arxiv","id":"1512.02148","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02148","created_at":"2026-05-18T01:04:21Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02148v1","created_at":"2026-05-18T01:04:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02148","created_at":"2026-05-18T01:04:21Z"},{"alias_kind":"pith_short_12","alias_value":"D72BFWENKFRQ","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"D72BFWENKFRQE2LF","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"D72BFWEN","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:D72BFWENKFRQE2LFR2HL2KK4BG","target":"record","payload":{"canonical_record":{"source":{"id":"1512.02148","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-07T18:10:56Z","cross_cats_sorted":[],"title_canon_sha256":"02096d70de19812160838c4e85878343dd615d3626a40717e6e6d5c75a53022e","abstract_canon_sha256":"fb35f4d2ccd9a8e175e9c2f6760018afc29ed1c45d1b898d6ae8628804285c80"},"schema_version":"1.0"},"canonical_sha256":"1ff412d88d51630269658e8ebd295c09853e2952c544779e174bee51a7672f2e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:21.989262Z","signature_b64":"/IeBm1T3ueKDZq+cXYvS5ryN84crrW3NQGwKiLw+oW1FWNCLFL7ILtH+T8W1JcnfAwMFIJjA8AXaBkOc/x92Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ff412d88d51630269658e8ebd295c09853e2952c544779e174bee51a7672f2e","last_reissued_at":"2026-05-18T01:04:21.988613Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:21.988613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.02148","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":"2026-05-18T01:04:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uaqZUY+xbPLK/7iRieShLsNTrL4US6LI+soj4b/SLFz2KgT/4Y7BT3NJPq/N2yHY6DgLwsJKKUoZfy+a9QM9BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:40:19.153685Z"},"content_sha256":"00228a346fff7dea240da54deb104019eb0a9940405df16a0f878226856dc225","schema_version":"1.0","event_id":"sha256:00228a346fff7dea240da54deb104019eb0a9940405df16a0f878226856dc225"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:D72BFWENKFRQE2LFR2HL2KK4BG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On homoclinic orbits to center manifolds of elliptic-hyperbolic equilibria in Hamiltonian systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dmitry Turaev, Jeroen Lamb, William Giles","submitted_at":"2015-12-07T18:10:56Z","abstract_excerpt":"We consider a Hamiltonian system which has an elliptic-hyperbolic equilibrium with a homoclinic loop. We identify the set of orbits which are homoclinic to the center manifold of the equilibrium via a Lyapunov- Schmidt reduction procedure. This leads to the study of a singularity which inherits certain structure from the Hamiltonian nature of the system. Under non-degeneracy assumptions, we classify the possible Morse indices of this singularity, permitting a local description of the set of homoclinic orbits. We also consider the case of time-reversible Hamiltonian systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02148","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":"2026-05-18T01:04:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E6ivll+R4tZPC0NZXnLazDFlGnGrt3Eo7Q+FJhvkMHOmFRvHOyIjYs1z/U7PffQChOyM5ba5QU4bv6jDSscUAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:40:19.154022Z"},"content_sha256":"deca95202ff9a32b0c98c8896aa5ae65e7292bffeaefe6676d4b92bcebbeae92","schema_version":"1.0","event_id":"sha256:deca95202ff9a32b0c98c8896aa5ae65e7292bffeaefe6676d4b92bcebbeae92"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D72BFWENKFRQE2LFR2HL2KK4BG/bundle.json","state_url":"https://pith.science/pith/D72BFWENKFRQE2LFR2HL2KK4BG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D72BFWENKFRQE2LFR2HL2KK4BG/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":"2026-06-01T09:40:19Z","links":{"resolver":"https://pith.science/pith/D72BFWENKFRQE2LFR2HL2KK4BG","bundle":"https://pith.science/pith/D72BFWENKFRQE2LFR2HL2KK4BG/bundle.json","state":"https://pith.science/pith/D72BFWENKFRQE2LFR2HL2KK4BG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D72BFWENKFRQE2LFR2HL2KK4BG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:D72BFWENKFRQE2LFR2HL2KK4BG","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":"fb35f4d2ccd9a8e175e9c2f6760018afc29ed1c45d1b898d6ae8628804285c80","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-07T18:10:56Z","title_canon_sha256":"02096d70de19812160838c4e85878343dd615d3626a40717e6e6d5c75a53022e"},"schema_version":"1.0","source":{"id":"1512.02148","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02148","created_at":"2026-05-18T01:04:21Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02148v1","created_at":"2026-05-18T01:04:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02148","created_at":"2026-05-18T01:04:21Z"},{"alias_kind":"pith_short_12","alias_value":"D72BFWENKFRQ","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"D72BFWENKFRQE2LF","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"D72BFWEN","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:deca95202ff9a32b0c98c8896aa5ae65e7292bffeaefe6676d4b92bcebbeae92","target":"graph","created_at":"2026-05-18T01:04:21Z","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 consider a Hamiltonian system which has an elliptic-hyperbolic equilibrium with a homoclinic loop. We identify the set of orbits which are homoclinic to the center manifold of the equilibrium via a Lyapunov- Schmidt reduction procedure. This leads to the study of a singularity which inherits certain structure from the Hamiltonian nature of the system. Under non-degeneracy assumptions, we classify the possible Morse indices of this singularity, permitting a local description of the set of homoclinic orbits. We also consider the case of time-reversible Hamiltonian systems.","authors_text":"Dmitry Turaev, Jeroen Lamb, William Giles","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-07T18:10:56Z","title":"On homoclinic orbits to center manifolds of elliptic-hyperbolic equilibria in Hamiltonian systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02148","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":"sha256:00228a346fff7dea240da54deb104019eb0a9940405df16a0f878226856dc225","target":"record","created_at":"2026-05-18T01:04:21Z","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":"fb35f4d2ccd9a8e175e9c2f6760018afc29ed1c45d1b898d6ae8628804285c80","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-07T18:10:56Z","title_canon_sha256":"02096d70de19812160838c4e85878343dd615d3626a40717e6e6d5c75a53022e"},"schema_version":"1.0","source":{"id":"1512.02148","kind":"arxiv","version":1}},"canonical_sha256":"1ff412d88d51630269658e8ebd295c09853e2952c544779e174bee51a7672f2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ff412d88d51630269658e8ebd295c09853e2952c544779e174bee51a7672f2e","first_computed_at":"2026-05-18T01:04:21.988613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:21.988613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/IeBm1T3ueKDZq+cXYvS5ryN84crrW3NQGwKiLw+oW1FWNCLFL7ILtH+T8W1JcnfAwMFIJjA8AXaBkOc/x92Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:21.989262Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.02148","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00228a346fff7dea240da54deb104019eb0a9940405df16a0f878226856dc225","sha256:deca95202ff9a32b0c98c8896aa5ae65e7292bffeaefe6676d4b92bcebbeae92"],"state_sha256":"88ec7f7eaa9ff25591caebb735620de4f2973ea92a7fcf32d59fae04d4320e7f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HNhB4Cvsg7m5kG9vHpgNZNAJuOKycdVOPkIcs0wrryMdwSI0hrQlhP5NyiVQZHutnW28zXtLi7vBDP72fxYXCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T09:40:19.155928Z","bundle_sha256":"b575642ba08584a6edd48116feb3bb731ffa96aee5540afb49e86ea0f6288469"}}