{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:B3DMD3Q2CEWZXNVLAYAK3BBSLS","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":"a1a3e13996b5768cce3afe7ee9efc4ba872988c47399e87d4e6a96bcbc623876","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-10T12:29:47Z","title_canon_sha256":"50143a39fef88ee4577af379aabc53b7bf5bc423207f5bfe777b7d420f856551"},"schema_version":"1.0","source":{"id":"1204.2121","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2121","created_at":"2026-05-18T02:07:32Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2121v3","created_at":"2026-05-18T02:07:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2121","created_at":"2026-05-18T02:07:32Z"},{"alias_kind":"pith_short_12","alias_value":"B3DMD3Q2CEWZ","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"B3DMD3Q2CEWZXNVL","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"B3DMD3Q2","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:92b3ed512967a2967b85594c2eaee04a3bd29226e9386e33dc496fde6079b992","target":"graph","created_at":"2026-05-18T02:07:32Z","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 consider several classical results related to the Hausdorff dimension of exceptional sets of orthogonal projections and try to find out whether they have reasonable formulations in terms of packing dimension. We also investigate the existence of category versions for Marstrand and Falconer-Howroyd-type projection results.","authors_text":"Tuomas Orponen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-10T12:29:47Z","title":"On the Packing Dimension and Category of Exceptional Sets of Orthogonal Projections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2121","kind":"arxiv","version":3},"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":"sha256:2eca16728fe9743672975c69baffa34d4cb0ef795dc35182efb4d93d6c0726d8","target":"record","created_at":"2026-05-18T02:07:32Z","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":"a1a3e13996b5768cce3afe7ee9efc4ba872988c47399e87d4e6a96bcbc623876","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-10T12:29:47Z","title_canon_sha256":"50143a39fef88ee4577af379aabc53b7bf5bc423207f5bfe777b7d420f856551"},"schema_version":"1.0","source":{"id":"1204.2121","kind":"arxiv","version":3}},"canonical_sha256":"0ec6c1ee1a112d9bb6ab0600ad84325cb0178963d61f8eeb971024879c7cea78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ec6c1ee1a112d9bb6ab0600ad84325cb0178963d61f8eeb971024879c7cea78","first_computed_at":"2026-05-18T02:07:32.587153Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:07:32.587153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+eQdr0J3bsYlGPksGAXAFCXdUd1u6wLZdlrGjfJ/V5lgyYP1LIa4nwOc7EVO2OWj1lStRJ5BNeIAPIwjmlPoCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:07:32.587778Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.2121","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2eca16728fe9743672975c69baffa34d4cb0ef795dc35182efb4d93d6c0726d8","sha256:92b3ed512967a2967b85594c2eaee04a3bd29226e9386e33dc496fde6079b992"],"state_sha256":"5ee5e75b08f2963d2afebf210b6387007ec6a8ea6c7da098f1c2dc7faef84489"}