{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:STFFY5NT2NTC4TWNDHDSBPJRKO","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":"0dcfabb41f2da9f5428e96c72886e522e28d46010f674e32b947113af346907d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-09-27T11:25:21Z","title_canon_sha256":"bd2983c793c84534b0dfa05a9292ef74bab39bc58ef426c8211af64d4fd42fa6"},"schema_version":"1.0","source":{"id":"1509.08085","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.08085","created_at":"2026-05-18T00:28:57Z"},{"alias_kind":"arxiv_version","alias_value":"1509.08085v2","created_at":"2026-05-18T00:28:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08085","created_at":"2026-05-18T00:28:57Z"},{"alias_kind":"pith_short_12","alias_value":"STFFY5NT2NTC","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"STFFY5NT2NTC4TWN","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"STFFY5NT","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:5f04507f041b8f2e311a6929fe736c6309b15358063c285432a4b8c99a9bc5c8","target":"graph","created_at":"2026-05-18T00:28:57Z","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"},"paper":{"abstract_excerpt":"We derive suitable uncertainty relations for characteristics functions of phase and number variables obtained from the Weyl form of commutation relations. This is applied to finite-dimensional spin- like systems, which is the case when describing the phase difference between two field modes, as well as to the phase and number of a single-mode field. Some contradictions between the product and sums of characteristic functions are noted.","authors_text":"Alfredo Luis, Gonzalo Donoso","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-09-27T11:25:21Z","title":"Phase-number uncertainty from Weyl commutation relations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08085","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":"sha256:315324a427ee92477b9ebe9cca47152cddf0313a92503f05c0c7fbefc57bcd9f","target":"record","created_at":"2026-05-18T00:28:57Z","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":"0dcfabb41f2da9f5428e96c72886e522e28d46010f674e32b947113af346907d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-09-27T11:25:21Z","title_canon_sha256":"bd2983c793c84534b0dfa05a9292ef74bab39bc58ef426c8211af64d4fd42fa6"},"schema_version":"1.0","source":{"id":"1509.08085","kind":"arxiv","version":2}},"canonical_sha256":"94ca5c75b3d3662e4ecd19c720bd3153ae18e978d7dca0e72144c61efd005ef5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94ca5c75b3d3662e4ecd19c720bd3153ae18e978d7dca0e72144c61efd005ef5","first_computed_at":"2026-05-18T00:28:57.183391Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:57.183391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/T5+o0BYz1IW5TaVq6rwHIoIYaS78ugVW+cjN83g77tJ+n46k/D7Vt9EW5LaQXBl7CJC73uWiUJpgGrL/Z8pAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:57.183816Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.08085","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:315324a427ee92477b9ebe9cca47152cddf0313a92503f05c0c7fbefc57bcd9f","sha256:5f04507f041b8f2e311a6929fe736c6309b15358063c285432a4b8c99a9bc5c8"],"state_sha256":"766f130e3f7b29ebdbecc916f9e6e561fc5c91ac9fa55c282583f4b0e7fe5e03"}