{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:OPGR6KIJ7I6FK4YFDJDBXUGQ4I","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":"2c53ed50ecf78441fd5fcd2dab51a7b0b9efddf9884ab92e2cd52e6ede5d5d0e","cross_cats_sorted":["math.AP","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-02-15T06:13:01Z","title_canon_sha256":"a3c8cae2c67934cbaae7ef6e3b0b586e2eb74fceba2a237d1a3d70d37f45af63"},"schema_version":"1.0","source":{"id":"2502.10686","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.10686","created_at":"2026-07-05T10:14:56Z"},{"alias_kind":"arxiv_version","alias_value":"2502.10686v1","created_at":"2026-07-05T10:14:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.10686","created_at":"2026-07-05T10:14:56Z"},{"alias_kind":"pith_short_12","alias_value":"OPGR6KIJ7I6F","created_at":"2026-07-05T10:14:56Z"},{"alias_kind":"pith_short_16","alias_value":"OPGR6KIJ7I6FK4YF","created_at":"2026-07-05T10:14:56Z"},{"alias_kind":"pith_short_8","alias_value":"OPGR6KIJ","created_at":"2026-07-05T10:14:56Z"}],"graph_snapshots":[{"event_id":"sha256:2ae2b6a18d787d1091f027e8b208f8ffb217a76a809b25055a1d55158e74e7f4","target":"graph","created_at":"2026-07-05T10:14:56Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2502.10686/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove bounds on approximate incidences between families of circles and families of points in the plane. As a consequence, we prove a lower bound for the dimension of circular $(u,v)$-Furstenberg sets, which is new for large $u$ and $v$.","authors_text":"John Green, Kevin Ren, Sarah Tammen, Terence L. J. Harris, Yumeng Ou","cross_cats":["math.AP","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-02-15T06:13:01Z","title":"Incidence bounds related to circular Furstenberg sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.10686","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":"sha256:08cad3c4f1febd6fd1eb5fd4af9ee64d523391b0c96b5d599be499b5663f7957","target":"record","created_at":"2026-07-05T10:14:56Z","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":"2c53ed50ecf78441fd5fcd2dab51a7b0b9efddf9884ab92e2cd52e6ede5d5d0e","cross_cats_sorted":["math.AP","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-02-15T06:13:01Z","title_canon_sha256":"a3c8cae2c67934cbaae7ef6e3b0b586e2eb74fceba2a237d1a3d70d37f45af63"},"schema_version":"1.0","source":{"id":"2502.10686","kind":"arxiv","version":1}},"canonical_sha256":"73cd1f2909fa3c5573051a461bd0d0e22c9862b62412319b90e2d249c980c605","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73cd1f2909fa3c5573051a461bd0d0e22c9862b62412319b90e2d249c980c605","first_computed_at":"2026-07-05T10:14:56.463992Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:14:56.463992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vfYZYkm3qh72EI15kWDIs6ZfbFmaWVqIhKsj9/3UbF5Sc84ngt/pHZSZZGEFScDA3kFndpN7KEICLoIXEImrBg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:14:56.464487Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.10686","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08cad3c4f1febd6fd1eb5fd4af9ee64d523391b0c96b5d599be499b5663f7957","sha256:2ae2b6a18d787d1091f027e8b208f8ffb217a76a809b25055a1d55158e74e7f4"],"state_sha256":"3e3aeb4f197dd4fc4ee494c07dd2e00ab34997a88719d67c350e9f9b79824e39"}