{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:B4DXWRUEXIPKSQF2NLCXMIIZXA","short_pith_number":"pith:B4DXWRUE","schema_version":"1.0","canonical_sha256":"0f077b4684ba1ea940ba6ac5762119b82d31ca608b531465aafb5b9cb4c4245e","source":{"kind":"arxiv","id":"2607.14920","version":1},"attestation_state":"computed","paper":{"title":"A Three-Point Continuous-Variable Quantum MacWilliams Identity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Yinzi Xiao","submitted_at":"2026-07-16T12:38:52Z","abstract_excerpt":"We construct the three-point continuous-variable (CV) quantum MacWilliams identity, extending the two-point framework of Burchards, and give its closed-form integral kernel. Its configuration space carries a symplectic invariant with no classical counterpart, which encodes the GKP quantization condition and a three-point sign phase. Using the identity, we derive the semidefinite-programming bounds it supports on the dimension of CV quantum error-correcting codes, and we prove, in two collapse theorems, that the three-point apparatus does not improve on the two-point bound. For GKP lattice code"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.14920","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-16T12:38:52Z","cross_cats_sorted":[],"title_canon_sha256":"ea0a09d20a1a104d388b960779e9b16156e3d5bdffb2fcbdfabae90c22c4be97","abstract_canon_sha256":"f7ec2eeb2e607a9a2a96a644731ecba2ddb9dfc2f53559db7f3f8e24752c3b03"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-17T01:21:58.794538Z","signature_b64":"BJf4BMVMsOgP9HeHprHJfGGpqfEuBFCjZybl2OYWFeAkqKxY9BY2A0ioqbvLvmP1d6EjVKO5H2gn78gGF8xCBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f077b4684ba1ea940ba6ac5762119b82d31ca608b531465aafb5b9cb4c4245e","last_reissued_at":"2026-07-17T01:21:58.793698Z","signature_status":"signed_v1","first_computed_at":"2026-07-17T01:21:58.793698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Three-Point Continuous-Variable Quantum MacWilliams Identity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Yinzi Xiao","submitted_at":"2026-07-16T12:38:52Z","abstract_excerpt":"We construct the three-point continuous-variable (CV) quantum MacWilliams identity, extending the two-point framework of Burchards, and give its closed-form integral kernel. Its configuration space carries a symplectic invariant with no classical counterpart, which encodes the GKP quantization condition and a three-point sign phase. Using the identity, we derive the semidefinite-programming bounds it supports on the dimension of CV quantum error-correcting codes, and we prove, in two collapse theorems, that the three-point apparatus does not improve on the two-point bound. For GKP lattice code"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14920","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.14920/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.14920","created_at":"2026-07-17T01:21:58.794132+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.14920v1","created_at":"2026-07-17T01:21:58.794132+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.14920","created_at":"2026-07-17T01:21:58.794132+00:00"},{"alias_kind":"pith_short_12","alias_value":"B4DXWRUEXIPK","created_at":"2026-07-17T01:21:58.794132+00:00"},{"alias_kind":"pith_short_16","alias_value":"B4DXWRUEXIPKSQF2","created_at":"2026-07-17T01:21:58.794132+00:00"},{"alias_kind":"pith_short_8","alias_value":"B4DXWRUE","created_at":"2026-07-17T01:21:58.794132+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/B4DXWRUEXIPKSQF2NLCXMIIZXA","json":"https://pith.science/pith/B4DXWRUEXIPKSQF2NLCXMIIZXA.json","graph_json":"https://pith.science/api/pith-number/B4DXWRUEXIPKSQF2NLCXMIIZXA/graph.json","events_json":"https://pith.science/api/pith-number/B4DXWRUEXIPKSQF2NLCXMIIZXA/events.json","paper":"https://pith.science/paper/B4DXWRUE"},"agent_actions":{"view_html":"https://pith.science/pith/B4DXWRUEXIPKSQF2NLCXMIIZXA","download_json":"https://pith.science/pith/B4DXWRUEXIPKSQF2NLCXMIIZXA.json","view_paper":"https://pith.science/paper/B4DXWRUE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.14920&json=true","fetch_graph":"https://pith.science/api/pith-number/B4DXWRUEXIPKSQF2NLCXMIIZXA/graph.json","fetch_events":"https://pith.science/api/pith-number/B4DXWRUEXIPKSQF2NLCXMIIZXA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B4DXWRUEXIPKSQF2NLCXMIIZXA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B4DXWRUEXIPKSQF2NLCXMIIZXA/action/storage_attestation","attest_author":"https://pith.science/pith/B4DXWRUEXIPKSQF2NLCXMIIZXA/action/author_attestation","sign_citation":"https://pith.science/pith/B4DXWRUEXIPKSQF2NLCXMIIZXA/action/citation_signature","submit_replication":"https://pith.science/pith/B4DXWRUEXIPKSQF2NLCXMIIZXA/action/replication_record"}},"created_at":"2026-07-17T01:21:58.794132+00:00","updated_at":"2026-07-17T01:21:58.794132+00:00"}