{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:637EQ6KA4OMOBJ2ASSI6X5IZVZ","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":"54d0974cb58eeda38020dee97ee01d972ae2b818749a5d7b639ba8ee50f04b3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-09-24T12:57:12Z","title_canon_sha256":"f855f83645f230f7cf81800414c9db09d07c12860aec7b12ce430ac19097153c"},"schema_version":"1.0","source":{"id":"1509.07347","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.07347","created_at":"2026-05-18T01:20:50Z"},{"alias_kind":"arxiv_version","alias_value":"1509.07347v2","created_at":"2026-05-18T01:20:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07347","created_at":"2026-05-18T01:20:50Z"},{"alias_kind":"pith_short_12","alias_value":"637EQ6KA4OMO","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"637EQ6KA4OMOBJ2A","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"637EQ6KA","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:c697c670a50a4347610dc0a700c24d064505d78ec97f01569ed009e214778351","target":"graph","created_at":"2026-05-18T01:20:50Z","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":"This is a short introduction to Hilbert space frame theory and its applications for those outside the area who want to enter the subject. We will emphasize finite frame theory since it is the easiest way to get into the subject.","authors_text":"Peter G. Casazza, Richard G. Lynch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-09-24T12:57:12Z","title":"A brief introduction to Hilbert space frame theory and its applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07347","kind":"arxiv","version":2},"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":"sha256:35e58a5a281e184d20b4cee862e492deb02774d2766cc993a47825857440bc48","target":"record","created_at":"2026-05-18T01:20:50Z","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":"54d0974cb58eeda38020dee97ee01d972ae2b818749a5d7b639ba8ee50f04b3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-09-24T12:57:12Z","title_canon_sha256":"f855f83645f230f7cf81800414c9db09d07c12860aec7b12ce430ac19097153c"},"schema_version":"1.0","source":{"id":"1509.07347","kind":"arxiv","version":2}},"canonical_sha256":"f6fe487940e398e0a7409491ebf519ae46b50e0794f1ff66c9306c1790abb3a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6fe487940e398e0a7409491ebf519ae46b50e0794f1ff66c9306c1790abb3a3","first_computed_at":"2026-05-18T01:20:50.276079Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:50.276079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3sgD4oQ+CvITXzDHmc1A62W82aKn6saZRKcspjWVkdX1ShGdZ8If1uxuQ/0kY77PwPait2/CueP7FM3FCM6aCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:50.276586Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.07347","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35e58a5a281e184d20b4cee862e492deb02774d2766cc993a47825857440bc48","sha256:c697c670a50a4347610dc0a700c24d064505d78ec97f01569ed009e214778351"],"state_sha256":"d67c77ee49a5ab2631e023f64ac2d223d266db4860984862c57d76f7a7de3bc3"}