{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SNPTOB25SDY7MPKDRCD746CN7M","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":"0272a380920a2ba207ca841cdc60d6732aec066708c7630b2183d3f848dba310","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-09T00:34:48Z","title_canon_sha256":"c5d11906453402d9db08ddd239f74c1d16a651587b067f1040277e181d521484"},"schema_version":"1.0","source":{"id":"1512.02703","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02703","created_at":"2026-05-18T01:24:43Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02703v1","created_at":"2026-05-18T01:24:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02703","created_at":"2026-05-18T01:24:43Z"},{"alias_kind":"pith_short_12","alias_value":"SNPTOB25SDY7","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SNPTOB25SDY7MPKD","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SNPTOB25","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:faffc2c6e7565949fead6808db4a603edc912ef7cff4c148c09fca638605d440","target":"graph","created_at":"2026-05-18T01:24:43Z","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 develop a \"metrically selfdual\" variational calculus for $c$-monotone vector fields between general manifolds $X$ and $Y$, where $c$ is a coupling on $X\\times Y$. Remarkably, many of the key properties of classical monotone operators known to hold in a linear context, extend to this non-linear setting. This includes an integral representation of $c$-monotone vector fields in terms of $c$-convex selfdual Lagrangians, their characterization as a partial $c$-gradients of antisymmetric Hamiltonians, as well as the property that these vector fields are generically single-valued. We also use a sy","authors_text":"Abbas Moameni, Nassif Ghoussoub","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-09T00:34:48Z","title":"Metric Selfduality and Monotone Vector Fields on Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02703","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":"sha256:26fe02d75693b087d9b80cb7154a9e1308c4d792595dc1c0af18ca5a26ce5fb0","target":"record","created_at":"2026-05-18T01:24:43Z","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":"0272a380920a2ba207ca841cdc60d6732aec066708c7630b2183d3f848dba310","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-09T00:34:48Z","title_canon_sha256":"c5d11906453402d9db08ddd239f74c1d16a651587b067f1040277e181d521484"},"schema_version":"1.0","source":{"id":"1512.02703","kind":"arxiv","version":1}},"canonical_sha256":"935f37075d90f1f63d438887fe784dfb15a3b48bf34f804b284efb81bca0a441","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"935f37075d90f1f63d438887fe784dfb15a3b48bf34f804b284efb81bca0a441","first_computed_at":"2026-05-18T01:24:43.315074Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:43.315074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XeFwv5yZzgy+bWlldzszfo/n4tf37Gi6k3LkWd4XEDVVodgyBo0TIuDNzFL9sJEDtZKTvm6GcItyJrNkfMUlDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:43.315520Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.02703","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26fe02d75693b087d9b80cb7154a9e1308c4d792595dc1c0af18ca5a26ce5fb0","sha256:faffc2c6e7565949fead6808db4a603edc912ef7cff4c148c09fca638605d440"],"state_sha256":"7df363c7f7c44db9ec237b1fd5768383920573021c41c2d140652b1997a244e5"}