{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5PTCKY6QLELKNGNKTH37U36MFR","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":"d54efdb6380f680cfb74dea9ab5f59142d984c44f002521331398f4b1d5945b3","cross_cats_sorted":["math.CA","math.DS","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-13T03:46:52Z","title_canon_sha256":"ec9ee117dc1882f7e1d84018ce0401b92eeb1299ff1a51f38c61a80b593067ee"},"schema_version":"1.0","source":{"id":"1604.03645","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.03645","created_at":"2026-05-17T23:56:00Z"},{"alias_kind":"arxiv_version","alias_value":"1604.03645v2","created_at":"2026-05-17T23:56:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.03645","created_at":"2026-05-17T23:56:00Z"},{"alias_kind":"pith_short_12","alias_value":"5PTCKY6QLELK","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5PTCKY6QLELKNGNK","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5PTCKY6Q","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:726f69188454a41a3351fff9b672bbf0472a414743f6fdd89af22ef2d017e9fa","target":"graph","created_at":"2026-05-17T23:56:00Z","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 revisit the existence problem of heteroclinic connections in $\\mathbb{R}^N$ associated with Hamiltonian systems involving potentials $W:\\mathbb{R}^N\\to \\mathbb{R}$ having several global minima. Under very mild assumptions on $W$ we present a simple variational approach to first find geodesics minimizing length of curves joining any two of the potential wells, where length is computed with respect to a degenerate metric having conformal factor $\\sqrt{W}.$ Then we show that when such a minimizing geodesic avoids passing through other wells of the potential at intermediate times, it gives rise","authors_text":"Andres Zuniga, Peter Sternberg","cross_cats":["math.CA","math.DS","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-13T03:46:52Z","title":"On the heteroclinic connection problem for multi-well gradient systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03645","kind":"arxiv","version":2},"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":"sha256:07edb9981d3d242d3f0171ea9a8b8684bf4e329cc7f577231c0b60e7a2eaa0b2","target":"record","created_at":"2026-05-17T23:56:00Z","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":"d54efdb6380f680cfb74dea9ab5f59142d984c44f002521331398f4b1d5945b3","cross_cats_sorted":["math.CA","math.DS","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-13T03:46:52Z","title_canon_sha256":"ec9ee117dc1882f7e1d84018ce0401b92eeb1299ff1a51f38c61a80b593067ee"},"schema_version":"1.0","source":{"id":"1604.03645","kind":"arxiv","version":2}},"canonical_sha256":"ebe62563d05916a699aa99f7fa6fcc2c4355fcff8f5beaa297fbb522e8e8dfdf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ebe62563d05916a699aa99f7fa6fcc2c4355fcff8f5beaa297fbb522e8e8dfdf","first_computed_at":"2026-05-17T23:56:00.820491Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:00.820491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RSLJJDqcQ9VWav1R4NRgJVtkZ9WEGEMiBOTjEy5NePiBvP1xCmr8U5xEfoc6H4T+sOzQmI28oZ9h5vr4VulFBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:00.821184Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.03645","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07edb9981d3d242d3f0171ea9a8b8684bf4e329cc7f577231c0b60e7a2eaa0b2","sha256:726f69188454a41a3351fff9b672bbf0472a414743f6fdd89af22ef2d017e9fa"],"state_sha256":"24c17b9bdeb9f0e3553d71b4c10ba6a5d51c98d6eb14bee0344606097668a08b"}