{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KQZ6BJM2PWQJWHIHT5NKJ3IZOB","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":"d13c2b13b4b65e09cf12604d180b20393002d591b91ee73eedfb03358184f541","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-01-12T20:37:14Z","title_canon_sha256":"9543f5ac3c556d93f9626163a745adf69f8c2a599d977cdba22f607cb61c8da8"},"schema_version":"1.0","source":{"id":"1601.03024","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.03024","created_at":"2026-05-18T01:06:40Z"},{"alias_kind":"arxiv_version","alias_value":"1601.03024v2","created_at":"2026-05-18T01:06:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.03024","created_at":"2026-05-18T01:06:40Z"},{"alias_kind":"pith_short_12","alias_value":"KQZ6BJM2PWQJ","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KQZ6BJM2PWQJWHIH","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KQZ6BJM2","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:3073491e65575f7994f988bc976a6646c9014ba8481376707942d2fb2d124ff1","target":"graph","created_at":"2026-05-18T01:06:40Z","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":"In this paper we extend the notion of approximate dual to fusion frames and present some approaches to obtain dual and approximate alternate dual fusion frames. Also, we study the stability of dual and approximate alternate dual fusion frames.","authors_text":"Ali Akbar Arefijamaal, Fahimeh Arabyani Neyshaburi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-01-12T20:37:14Z","title":"Some properties of dual and approximate dual of fusion frames"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03024","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":"sha256:0fb6ef4be53f60fa7ea9f2a8bf1e671bf6010a6885bf68453d3e8946fdb90e30","target":"record","created_at":"2026-05-18T01:06:40Z","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":"d13c2b13b4b65e09cf12604d180b20393002d591b91ee73eedfb03358184f541","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-01-12T20:37:14Z","title_canon_sha256":"9543f5ac3c556d93f9626163a745adf69f8c2a599d977cdba22f607cb61c8da8"},"schema_version":"1.0","source":{"id":"1601.03024","kind":"arxiv","version":2}},"canonical_sha256":"5433e0a59a7da09b1d079f5aa4ed19706e7d0659247337b8c3afb908034b10db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5433e0a59a7da09b1d079f5aa4ed19706e7d0659247337b8c3afb908034b10db","first_computed_at":"2026-05-18T01:06:40.852031Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:40.852031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oUlJhijH3J9pWfSUPSKosGneyWrDT1yicgeJqS+ISQacQJMbtr1Qh51XLcsILtmAzZG6iKYGl/MCqJtQAw6jCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:40.852621Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.03024","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fb6ef4be53f60fa7ea9f2a8bf1e671bf6010a6885bf68453d3e8946fdb90e30","sha256:3073491e65575f7994f988bc976a6646c9014ba8481376707942d2fb2d124ff1"],"state_sha256":"55cd6caf9e2b938678fe929b917a71f24382baa40a62701a2994cf2fed48997d"}