{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:2E4224FGQU3WNUIEDWDZBXD7V5","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":"1226f9021ea1e3a2ae940b6314b08bc012e388b7bda995dd14f44824b5b9fc04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-06-11T14:41:40Z","title_canon_sha256":"0e9c92760098feb2bba7abdf4481db41def24bc14fe69791ee41eebbdee0b9c5"},"schema_version":"1.0","source":{"id":"2506.09799","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.09799","created_at":"2026-07-05T11:19:57Z"},{"alias_kind":"arxiv_version","alias_value":"2506.09799v1","created_at":"2026-07-05T11:19:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.09799","created_at":"2026-07-05T11:19:57Z"},{"alias_kind":"pith_short_12","alias_value":"2E4224FGQU3W","created_at":"2026-07-05T11:19:57Z"},{"alias_kind":"pith_short_16","alias_value":"2E4224FGQU3WNUIE","created_at":"2026-07-05T11:19:57Z"},{"alias_kind":"pith_short_8","alias_value":"2E4224FG","created_at":"2026-07-05T11:19:57Z"}],"graph_snapshots":[{"event_id":"sha256:f1b92313ab3959baff7d7cc58491cedccd4c3e1bc9692713472b1d990162af4e","target":"graph","created_at":"2026-07-05T11:19:57Z","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/2506.09799/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Complex numbers play a pivotal role in both mathematics and physics, particularly in quantum mechanics, and are extensively utilized to depict the behavior of microscopic particles. Recognizing the significance of complex numbers, a framework of imaginarity resource theory has recently been established. In this work, we propose two types of imaginarity monotones induced by the unified $(\\alpha,\\beta)$-relative entropy and investigate their properties. Moreover, we give explicit examples to illustrate our results.","authors_text":"Chuanfa Wu, Zhaoqi Wu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-06-11T14:41:40Z","title":"Two imaginarity monotones induced by unified $(\\alpha,\\beta)$-relative entropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.09799","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":"sha256:88f25951918879eb263481658dd6bed6b1e5e014ae9a1c38d594e8ccdd33fbdd","target":"record","created_at":"2026-07-05T11:19:57Z","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":"1226f9021ea1e3a2ae940b6314b08bc012e388b7bda995dd14f44824b5b9fc04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-06-11T14:41:40Z","title_canon_sha256":"0e9c92760098feb2bba7abdf4481db41def24bc14fe69791ee41eebbdee0b9c5"},"schema_version":"1.0","source":{"id":"2506.09799","kind":"arxiv","version":1}},"canonical_sha256":"d139ad70a6853766d1041d8790dc7faf5b4f3b341280603a7b1f1f7ffb309ca4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d139ad70a6853766d1041d8790dc7faf5b4f3b341280603a7b1f1f7ffb309ca4","first_computed_at":"2026-07-05T11:19:57.170071Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:19:57.170071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5WMHI7j615Kh/bYtHi7Ks7OzUSQ2ELnCQX/jWSuj1kVn2hP6eDfBIrZgMDY5cEDVPp0KLBesqf0nS+EOy1qMAg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:19:57.170685Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.09799","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88f25951918879eb263481658dd6bed6b1e5e014ae9a1c38d594e8ccdd33fbdd","sha256:f1b92313ab3959baff7d7cc58491cedccd4c3e1bc9692713472b1d990162af4e"],"state_sha256":"e9e86581d31266c664443fe46480ff51b9fbd1fcdc1c6f7c23154109af803ec8"}