{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YQHGL5RNIBQZS457KLCUKJCMLC","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":"52ba1d6681e3a6b249c360df3d28fb88c05df6c5b94693bd2db3b06ed7684daf","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-04T03:13:32Z","title_canon_sha256":"5faba8c25eef79513b0d664d96568c410ea8a1e5d6cadd50d5a5d0b435be3144"},"schema_version":"1.0","source":{"id":"1805.01594","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.01594","created_at":"2026-05-18T00:16:47Z"},{"alias_kind":"arxiv_version","alias_value":"1805.01594v1","created_at":"2026-05-18T00:16:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.01594","created_at":"2026-05-18T00:16:47Z"},{"alias_kind":"pith_short_12","alias_value":"YQHGL5RNIBQZ","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YQHGL5RNIBQZS457","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YQHGL5RN","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:85adb39d91caa1fb9e662305ba40e6aa57dba71dd8dd0a8ba51819094b975894","target":"graph","created_at":"2026-05-18T00:16:47Z","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 note, following the complex theory, we examine discrete controlled frames, discrete weighted frames and frame multipliers in a non-commutative setting, namely in a left quaternionic Hilbert space. In particular, we show that the controlled frames are equivalent to usual frames under certain conditions. We also study connection between frame multipliers and weighted frames in the same Hilbert space.","authors_text":"K. Thirulogasanthar, M. Khokulan","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-04T03:13:32Z","title":"Frame Multipliers for discrete frames on Quaternionic Hilbert Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01594","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":"sha256:4ce403392115966b673308fb25df1ed6414ccb6a2fdae73e13bb68fd65907f31","target":"record","created_at":"2026-05-18T00:16:47Z","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":"52ba1d6681e3a6b249c360df3d28fb88c05df6c5b94693bd2db3b06ed7684daf","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-04T03:13:32Z","title_canon_sha256":"5faba8c25eef79513b0d664d96568c410ea8a1e5d6cadd50d5a5d0b435be3144"},"schema_version":"1.0","source":{"id":"1805.01594","kind":"arxiv","version":1}},"canonical_sha256":"c40e65f62d40619973bf52c545244c58838784346235b9d0160b221cd21377ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c40e65f62d40619973bf52c545244c58838784346235b9d0160b221cd21377ba","first_computed_at":"2026-05-18T00:16:47.353039Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:47.353039Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Iw67ZtaFJ8alXvX57wS8g8xChoQiQpTEf+jhf2EO2xFCx42M8NsTOV0qJA5Bd2s5xMHmt+mtegQyGfDH3FyNDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:47.353756Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.01594","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ce403392115966b673308fb25df1ed6414ccb6a2fdae73e13bb68fd65907f31","sha256:85adb39d91caa1fb9e662305ba40e6aa57dba71dd8dd0a8ba51819094b975894"],"state_sha256":"9a5ffc6cca57df3f4687dbbcca80e44de79201c9debac73e45e1863f024f1074"}