{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZY6EOOIJWQRA6NAR5HEC2NLQYC","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":"e1706e95699fdc977264e7b441c241c6ce08ba5728891a4673dbd34ccf3136a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-10-14T22:41:23Z","title_canon_sha256":"eaff6dbb05bf8e7b4b3ab7af1db3cfec97f4e0d7ced918019c3ce6ebd62a4e01"},"schema_version":"1.0","source":{"id":"1310.3874","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.3874","created_at":"2026-05-18T01:22:24Z"},{"alias_kind":"arxiv_version","alias_value":"1310.3874v2","created_at":"2026-05-18T01:22:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3874","created_at":"2026-05-18T01:22:24Z"},{"alias_kind":"pith_short_12","alias_value":"ZY6EOOIJWQRA","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZY6EOOIJWQRA6NAR","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZY6EOOIJ","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:67bb53521044bde1b55575d3b2a9e50b9f971ca2f986c443231352e32bfdd1ff","target":"graph","created_at":"2026-05-18T01:22:24Z","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 provide new bounds on a flux integral over the portion of the boundary of one regular domain contained inside a second regular domain, based on properties of the second domain rather than the first one. This bound is amenable to numerical computation of a flux through the boundary of a domain, for example, when there is a large variation in the normal vector near a point. We present applications of this result to occupational measures and two-dimensional differential equations, including a new proof that all minimal invariant sets in the plane are trivial.","authors_text":"Ido Bright, John M. Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-10-14T22:41:23Z","title":"A Note on Flux Integrals over Smooth Regular Domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3874","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":"sha256:8af7a050db5b2e446a0ff2b07732de0efb5cf55890cc6b40d4dbfe6940bf3a9d","target":"record","created_at":"2026-05-18T01:22:24Z","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":"e1706e95699fdc977264e7b441c241c6ce08ba5728891a4673dbd34ccf3136a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-10-14T22:41:23Z","title_canon_sha256":"eaff6dbb05bf8e7b4b3ab7af1db3cfec97f4e0d7ced918019c3ce6ebd62a4e01"},"schema_version":"1.0","source":{"id":"1310.3874","kind":"arxiv","version":2}},"canonical_sha256":"ce3c473909b4220f3411e9c82d3570c0bce344085714aed6e26226711f08a012","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce3c473909b4220f3411e9c82d3570c0bce344085714aed6e26226711f08a012","first_computed_at":"2026-05-18T01:22:24.768917Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:24.768917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IjdD74Zh8Wlj8spdrmiJlX5cOcyOcoqf7XNyyW5/b/rdRXEqeRM+Lrf9NeAnv50VVziprtom22/OG/EgpUUVCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:24.769600Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.3874","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8af7a050db5b2e446a0ff2b07732de0efb5cf55890cc6b40d4dbfe6940bf3a9d","sha256:67bb53521044bde1b55575d3b2a9e50b9f971ca2f986c443231352e32bfdd1ff"],"state_sha256":"c11c780f74c4432c72e857a0718276967d9eef7af60d85ec8100fdec92d6289e"}