{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RQGRMN3ZOCOSZ7NAMVVZKGR3VF","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":"6b69658905eadda72f3c74bf18ff864d9ee4556a9dd162cefdec435ed174dbcd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-28T06:48:36Z","title_canon_sha256":"80c13c1800475f2b4970df221143329acfdc2541871cd9068b73e601f841b74a"},"schema_version":"1.0","source":{"id":"1603.08324","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08324","created_at":"2026-05-18T01:18:11Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08324v1","created_at":"2026-05-18T01:18:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08324","created_at":"2026-05-18T01:18:11Z"},{"alias_kind":"pith_short_12","alias_value":"RQGRMN3ZOCOS","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RQGRMN3ZOCOSZ7NA","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RQGRMN3Z","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:87452684598d4568a1f5aed546798109426aa53822b060b8bcd36ad238d2e7bb","target":"graph","created_at":"2026-05-18T01:18:11Z","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 investigate centers of a body (the closure of a bounded open set) defined as maximum points of potentials. In particular, we study centers defined by the Riesz potential and by Poisson's integral. These centers, in general, depend on parameters and move with respect to the parameters. We give a necessary and sufficient condition for the existence of a center independent of a parameter.","authors_text":"Shigehiro Sakata","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-28T06:48:36Z","title":"Stationary radial centers and characterization of convex polyhedrons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08324","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:f32d17f85a6d8b5772751d84c10388c78ee6357a613f769aa0a451ae05601f93","target":"record","created_at":"2026-05-18T01:18:11Z","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":"6b69658905eadda72f3c74bf18ff864d9ee4556a9dd162cefdec435ed174dbcd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-28T06:48:36Z","title_canon_sha256":"80c13c1800475f2b4970df221143329acfdc2541871cd9068b73e601f841b74a"},"schema_version":"1.0","source":{"id":"1603.08324","kind":"arxiv","version":1}},"canonical_sha256":"8c0d163779709d2cfda0656b951a3ba940118a5a7a458c79a4c09f86d220736f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c0d163779709d2cfda0656b951a3ba940118a5a7a458c79a4c09f86d220736f","first_computed_at":"2026-05-18T01:18:11.018226Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:11.018226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5qbBxdqLzm4CVTb0TEGNsNcFHy8sQwo2ToGGUcti9kBP8ezpUGCVB6Tf45jnLPKwVqrfPPXigUg8aWTLnwQDDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:11.018694Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.08324","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f32d17f85a6d8b5772751d84c10388c78ee6357a613f769aa0a451ae05601f93","sha256:87452684598d4568a1f5aed546798109426aa53822b060b8bcd36ad238d2e7bb"],"state_sha256":"2f7ebe415755d7833ba4e08bdd98b49d3c294c21b9c252dcf18ae8c6f32e36dc"}