{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NQTOVJWAS3KNAF4YNI2Z2MHDZ2","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":"445ff397a256029d3596ea5e50feae40e216c6024c2b749f5a0e3e4f9f209fa8","cross_cats_sorted":["math.FA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-07T07:38:19Z","title_canon_sha256":"333fce391bf9e7c2ff179a38530212a4c39e8ec432cc21db1503857255d1fcb0"},"schema_version":"1.0","source":{"id":"1709.02117","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.02117","created_at":"2026-05-18T00:35:50Z"},{"alias_kind":"arxiv_version","alias_value":"1709.02117v1","created_at":"2026-05-18T00:35:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.02117","created_at":"2026-05-18T00:35:50Z"},{"alias_kind":"pith_short_12","alias_value":"NQTOVJWAS3KN","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NQTOVJWAS3KNAF4Y","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NQTOVJWA","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:b3771b7766dbe5b769bc1e47074dc689ab5ba6bdbcb4f29d858414220a69a129","target":"graph","created_at":"2026-05-18T00:35:50Z","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 the minimal action problem min \\int\\_R 1/2 |$\\gamma$'|^2 + W($\\gamma$) dt among curves lying in a non-locally-compact metric space and connecting two given zeros of W $\\ge$ 0. For this problem, the optimal curves are usually called heteroclinic connections. We reduce it, following a standard method, to a geodesic problem of the form min \\int\\_0^1 K($\\gamma$)|$\\gamma$'| dt with K = (2W)^(1/2). We then prove existence of curves minimizing this new action under some suitable compactness assumptions on K, which are minimal. The method allows to solve some PDE problems in unbounded doma","authors_text":"Antonin Monteil, Filippo Santambrogio (LM-Orsay)","cross_cats":["math.FA","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-07T07:38:19Z","title":"Metric methods for heteroclinic connections in infinite dimensional spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02117","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":"sha256:1e41ee659fbe28dea523b0573d968605d9e2c6d9f64cfd64549eb631b19b707f","target":"record","created_at":"2026-05-18T00:35:50Z","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":"445ff397a256029d3596ea5e50feae40e216c6024c2b749f5a0e3e4f9f209fa8","cross_cats_sorted":["math.FA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-07T07:38:19Z","title_canon_sha256":"333fce391bf9e7c2ff179a38530212a4c39e8ec432cc21db1503857255d1fcb0"},"schema_version":"1.0","source":{"id":"1709.02117","kind":"arxiv","version":1}},"canonical_sha256":"6c26eaa6c096d4d017986a359d30e3ce8da9bf535ab54999f89270a9ebbd5bee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c26eaa6c096d4d017986a359d30e3ce8da9bf535ab54999f89270a9ebbd5bee","first_computed_at":"2026-05-18T00:35:50.109009Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:50.109009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nfJTy5jdi8NDvjBfkeGmVefc9TPo7o3k9L96QKf8Iw5Z5zAM4FOVt2lUkCMSMrvP0FinaXJYKGdnTr2qN32hCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:50.109720Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.02117","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e41ee659fbe28dea523b0573d968605d9e2c6d9f64cfd64549eb631b19b707f","sha256:b3771b7766dbe5b769bc1e47074dc689ab5ba6bdbcb4f29d858414220a69a129"],"state_sha256":"a60c298f2bfd4d604e648a88cb6463bfd637cd73bb75ba82200056a63874229b"}