{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:WNC3U5N72H4B2JBZB5OXREXXRU","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":"116150ca4fe22ea52f13f3cb31acdcd0ffad314c77a055b78ddfca81cde2c767","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-08-07T15:15:02Z","title_canon_sha256":"cd4df36e384bfaa96b0cdaface69c9076d313f684cc793a4b5ac7716cc4494f1"},"schema_version":"1.0","source":{"id":"2508.05475","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.05475","created_at":"2026-07-05T11:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"2508.05475v1","created_at":"2026-07-05T11:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.05475","created_at":"2026-07-05T11:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"WNC3U5N72H4B","created_at":"2026-07-05T11:50:13Z"},{"alias_kind":"pith_short_16","alias_value":"WNC3U5N72H4B2JBZ","created_at":"2026-07-05T11:50:13Z"},{"alias_kind":"pith_short_8","alias_value":"WNC3U5N7","created_at":"2026-07-05T11:50:13Z"}],"graph_snapshots":[{"event_id":"sha256:af7ef4a4270cb66faefdceee7d95fd365830afc751ab0241370eb33814547626","target":"graph","created_at":"2026-07-05T11:50:13Z","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/2508.05475/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a detailed outline of the proof that the Kakeya conjecture follows from the sticky case. This proof is due to Wang and Zahl and appears in a recent paper. The sticky case was proven in earlier work of Wang-Zahl, building on an approach suggested by Katz-Tao.","authors_text":"Larry Guth","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-08-07T15:15:02Z","title":"Outline of the Wang-Zahl proof of the Kakeya conjecture in $\\mathbb{R}^3$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.05475","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:b9bc1ecf5dc08baaa709d8a2604e6959e4ef79a1bdccb2cd8e88a5565d2eec8b","target":"record","created_at":"2026-07-05T11:50:13Z","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":"116150ca4fe22ea52f13f3cb31acdcd0ffad314c77a055b78ddfca81cde2c767","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-08-07T15:15:02Z","title_canon_sha256":"cd4df36e384bfaa96b0cdaface69c9076d313f684cc793a4b5ac7716cc4494f1"},"schema_version":"1.0","source":{"id":"2508.05475","kind":"arxiv","version":1}},"canonical_sha256":"b345ba75bfd1f81d24390f5d7892f78d1937b57797ef15fdfbdacd04f6ecb2d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b345ba75bfd1f81d24390f5d7892f78d1937b57797ef15fdfbdacd04f6ecb2d0","first_computed_at":"2026-07-05T11:50:13.879115Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:50:13.879115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BphcyNtfPBUNMYOLYz17WGu6A+q68vtWYwbzRBaEUT1c/IIuYR5CQyThTIZlZ+kyFhVVDqelhmRTbfR5fGI+BA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:50:13.879620Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.05475","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9bc1ecf5dc08baaa709d8a2604e6959e4ef79a1bdccb2cd8e88a5565d2eec8b","sha256:af7ef4a4270cb66faefdceee7d95fd365830afc751ab0241370eb33814547626"],"state_sha256":"a1c80d23c5f9f07fcbf08c840f61f88c991da5bbe19328f87851179f9532d6ea"}