{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:OPGR6KIJ7I6FK4YFDJDBXUGQ4I","short_pith_number":"pith:OPGR6KIJ","canonical_record":{"source":{"id":"2502.10686","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-02-15T06:13:01Z","cross_cats_sorted":["math.AP","math.CO"],"title_canon_sha256":"a3c8cae2c67934cbaae7ef6e3b0b586e2eb74fceba2a237d1a3d70d37f45af63","abstract_canon_sha256":"2c53ed50ecf78441fd5fcd2dab51a7b0b9efddf9884ab92e2cd52e6ede5d5d0e"},"schema_version":"1.0"},"canonical_sha256":"73cd1f2909fa3c5573051a461bd0d0e22c9862b62412319b90e2d249c980c605","source":{"kind":"arxiv","id":"2502.10686","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:OPGR6KIJ7I6FK4YFDJDBXUGQ4I","target":"record","payload":{"canonical_record":{"source":{"id":"2502.10686","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-02-15T06:13:01Z","cross_cats_sorted":["math.AP","math.CO"],"title_canon_sha256":"a3c8cae2c67934cbaae7ef6e3b0b586e2eb74fceba2a237d1a3d70d37f45af63","abstract_canon_sha256":"2c53ed50ecf78441fd5fcd2dab51a7b0b9efddf9884ab92e2cd52e6ede5d5d0e"},"schema_version":"1.0"},"canonical_sha256":"73cd1f2909fa3c5573051a461bd0d0e22c9862b62412319b90e2d249c980c605","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:14:56.464487Z","signature_b64":"vfYZYkm3qh72EI15kWDIs6ZfbFmaWVqIhKsj9/3UbF5Sc84ngt/pHZSZZGEFScDA3kFndpN7KEICLoIXEImrBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73cd1f2909fa3c5573051a461bd0d0e22c9862b62412319b90e2d249c980c605","last_reissued_at":"2026-07-05T10:14:56.463992Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:14:56.463992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.10686","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:14:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5d5SMC+dGGyipcqCSTZfH1AVdQLq7fg97DVTs6ADOI073/1i7IHdwEjF5QnitFaoKS0dEZVzTuBEMa2rEBkfAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T06:14:04.958464Z"},"content_sha256":"08cad3c4f1febd6fd1eb5fd4af9ee64d523391b0c96b5d599be499b5663f7957","schema_version":"1.0","event_id":"sha256:08cad3c4f1febd6fd1eb5fd4af9ee64d523391b0c96b5d599be499b5663f7957"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:OPGR6KIJ7I6FK4YFDJDBXUGQ4I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Incidence bounds related to circular Furstenberg sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CO"],"primary_cat":"math.CA","authors_text":"John Green, Kevin Ren, Sarah Tammen, Terence L. J. Harris, Yumeng Ou","submitted_at":"2025-02-15T06:13:01Z","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 $v$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.10686","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.10686/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:14:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EzLacrdfzmNfyulWQPNAPUr24guh/VQHdBTIuhrKVtBB6/Xzp2fmCs46Zal7AeEpPyu3h/touVKFQH11A9J0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T06:14:04.958974Z"},"content_sha256":"2ae2b6a18d787d1091f027e8b208f8ffb217a76a809b25055a1d55158e74e7f4","schema_version":"1.0","event_id":"sha256:2ae2b6a18d787d1091f027e8b208f8ffb217a76a809b25055a1d55158e74e7f4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OPGR6KIJ7I6FK4YFDJDBXUGQ4I/bundle.json","state_url":"https://pith.science/pith/OPGR6KIJ7I6FK4YFDJDBXUGQ4I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OPGR6KIJ7I6FK4YFDJDBXUGQ4I/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-09T06:14:04Z","links":{"resolver":"https://pith.science/pith/OPGR6KIJ7I6FK4YFDJDBXUGQ4I","bundle":"https://pith.science/pith/OPGR6KIJ7I6FK4YFDJDBXUGQ4I/bundle.json","state":"https://pith.science/pith/OPGR6KIJ7I6FK4YFDJDBXUGQ4I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OPGR6KIJ7I6FK4YFDJDBXUGQ4I/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n+CyUaN2HIceRvaImGbC5ZdwDJlc2SwNlVeFgeXEy1d595zAGVb92ii0MMjOcN7Q7a0DQ3gIVd0xEs8HJtyYAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T06:14:04.963442Z","bundle_sha256":"6ab6ec74b6f8e67481483eda15809ed91ec3b1df21cd1c006a519a75a6fec754"}}