{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:2P7XYIOSY7XRZG2ULDBB57SWYY","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":"26190d472d2bbc0bd96738c4da60bc8eaf72c67618657bbc1bef161c446acd22","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-08-06T13:40:11Z","title_canon_sha256":"e09c89e3d63d99fd3d4c97aa2909acdeb8a145f7f615a6197aad30a0598083a3"},"schema_version":"1.0","source":{"id":"2608.06032","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.06032","created_at":"2026-08-07T00:55:09Z"},{"alias_kind":"arxiv_version","alias_value":"2608.06032v1","created_at":"2026-08-07T00:55:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.06032","created_at":"2026-08-07T00:55:09Z"},{"alias_kind":"pith_short_12","alias_value":"2P7XYIOSY7XR","created_at":"2026-08-07T00:55:09Z"},{"alias_kind":"pith_short_16","alias_value":"2P7XYIOSY7XRZG2U","created_at":"2026-08-07T00:55:09Z"},{"alias_kind":"pith_short_8","alias_value":"2P7XYIOS","created_at":"2026-08-07T00:55:09Z"}],"graph_snapshots":[{"event_id":"sha256:13aa352fb89aeec6b3b6e394ee984fab39c3abde27722249f2ccab8a5ce77ebc","target":"graph","created_at":"2026-08-07T00:55:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.06032/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this note, we observe that the class of unbounded subnormal operators on quaternionic Hilbert spaces is a solution of quaternionic quantum harmonic q-oscillator whose complex case is addressed by Szefraniec in [19]. We also address the connection of unbounded subnormal operators on quaternionic Hilbert spaces, quaternionic quantum harmonic q-oscillator and quaternionic quantum economics using model theory of unbounded subnormal operators.","authors_text":"E. Shine Lal, K Krishnan, T. Prasad","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-08-06T13:40:11Z","title":"Quaternionic Quantum q-Oscillator And Unbounded Subnormal Operators In Quantum Economics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.06032","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":"sha256:2d42114ea707d501099568b157384665b4ede9205a10e1312de6760e9999dd8c","target":"record","created_at":"2026-08-07T00:55:09Z","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":"26190d472d2bbc0bd96738c4da60bc8eaf72c67618657bbc1bef161c446acd22","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-08-06T13:40:11Z","title_canon_sha256":"e09c89e3d63d99fd3d4c97aa2909acdeb8a145f7f615a6197aad30a0598083a3"},"schema_version":"1.0","source":{"id":"2608.06032","kind":"arxiv","version":1}},"canonical_sha256":"d3ff7c21d2c7ef1c9b5458c21efe56c621ffa0ba4c8f7512a88eca0fb94f209a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3ff7c21d2c7ef1c9b5458c21efe56c621ffa0ba4c8f7512a88eca0fb94f209a","first_computed_at":"2026-08-07T00:55:09.153578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-07T00:55:09.153578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vC42PkXhy//fxeR7JT9EpqxR5L6IQj7W9usfpEdf5EuojtXx4Wj3kE7VljV8dM+nNPmYNjT6FS5Ro8QhDxHHBQ==","signature_status":"signed_v1","signed_at":"2026-08-07T00:55:09.155007Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.06032","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d42114ea707d501099568b157384665b4ede9205a10e1312de6760e9999dd8c","sha256:13aa352fb89aeec6b3b6e394ee984fab39c3abde27722249f2ccab8a5ce77ebc"],"state_sha256":"05ceba84c2a5003b8d0cfca936698241025fafd6b12047c99edd39bc9fa9bde3"}