{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OCNXE74JE6NIKXIREL7MYTQYHC","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":"5ec6cc63e341a761ec7dfa87af61ca07f778167feca9461cfdf5e9322a709781","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-12-11T10:35:12Z","title_canon_sha256":"fbd01eb7c643d8a074c5150b976613db537002802a5cc7ec0db5b45df50851de"},"schema_version":"1.0","source":{"id":"1212.2375","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.2375","created_at":"2026-05-18T03:38:45Z"},{"alias_kind":"arxiv_version","alias_value":"1212.2375v1","created_at":"2026-05-18T03:38:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.2375","created_at":"2026-05-18T03:38:45Z"},{"alias_kind":"pith_short_12","alias_value":"OCNXE74JE6NI","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OCNXE74JE6NIKXIR","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OCNXE74J","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:675443e856d99634a26b2b14b03159785edeccbb021b45e8f16bf9f7a858661c","target":"graph","created_at":"2026-05-18T03:38:45Z","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 continue our earlier investigations of radial subspaces of Besov and Lizorkin-Triebel spaces on $\\R^d$. This time we study characterizations of these subspaces by differences.","authors_text":"Jan Vybiral, Leszek Skrzypczak, Winfried Sickel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-12-11T10:35:12Z","title":"The Characterization of Radial Subspaces of Besov- and Lizorkin-Triebel Spaces by Differences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2375","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":"sha256:9dab44fc292a97fb65da76e9f2a3b1ea7e3c3b05e037e11c6970a698cb94cde9","target":"record","created_at":"2026-05-18T03:38:45Z","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":"5ec6cc63e341a761ec7dfa87af61ca07f778167feca9461cfdf5e9322a709781","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-12-11T10:35:12Z","title_canon_sha256":"fbd01eb7c643d8a074c5150b976613db537002802a5cc7ec0db5b45df50851de"},"schema_version":"1.0","source":{"id":"1212.2375","kind":"arxiv","version":1}},"canonical_sha256":"709b727f89279a855d1122fecc4e1838a75dadab560e3c0b6724f2f660b4287e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"709b727f89279a855d1122fecc4e1838a75dadab560e3c0b6724f2f660b4287e","first_computed_at":"2026-05-18T03:38:45.100532Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:45.100532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wjwTxhUbm2e+T1Md+6OIrHWztSFs1Jgygt61SHX/5tLIfOliwn8IZRsXFR0CTyMPAJpmH1Xv9JpfJ7agoGLyBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:45.101295Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.2375","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9dab44fc292a97fb65da76e9f2a3b1ea7e3c3b05e037e11c6970a698cb94cde9","sha256:675443e856d99634a26b2b14b03159785edeccbb021b45e8f16bf9f7a858661c"],"state_sha256":"dd33eaf88e0f47e41763ca39ea934f89a2284de825b169618a137a6307d3eb84"}