{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:UVIDSD23DHW6PSU2POARCMXS4V","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":"e37562984879a79b781ccffe35189e7d8ea748e8fbb123d4a674ec165f04c125","cross_cats_sorted":["cond-mat.str-el","hep-lat"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-09-03T18:01:22Z","title_canon_sha256":"575a3e3b028e86c75862fa97cb13d60bdf569afa2549ef01d502b9fba92d18a7"},"schema_version":"1.0","source":{"id":"2509.03600","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.03600","created_at":"2026-07-05T12:04:42Z"},{"alias_kind":"arxiv_version","alias_value":"2509.03600v1","created_at":"2026-07-05T12:04:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.03600","created_at":"2026-07-05T12:04:42Z"},{"alias_kind":"pith_short_12","alias_value":"UVIDSD23DHW6","created_at":"2026-07-05T12:04:42Z"},{"alias_kind":"pith_short_16","alias_value":"UVIDSD23DHW6PSU2","created_at":"2026-07-05T12:04:42Z"},{"alias_kind":"pith_short_8","alias_value":"UVIDSD23","created_at":"2026-07-05T12:04:42Z"}],"graph_snapshots":[{"event_id":"sha256:966ceda9e9ea70c9f6f846050edfa44e19c7ee996b68d76e19c6d41808dbfc47","target":"graph","created_at":"2026-07-05T12:04:42Z","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/2509.03600/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Despite recent advances in the lattice representation theory of (generalized) symmetries, many simple quantum spin chains of physical interest are not included in the rigid framework of fusion categories and weak Hopf algebras. We demonstrate that this problem can be overcome by relaxing the requirements on the underlying algebraic structure, and show that general matrix product operator symmetries are described by a pre-bialgebra. As a guiding example, we focus on the anomalous $\\mathbb Z_2$ symmetry of the XX model, which manifests the mixed anomaly between its $U(1)$ momentum and winding sy","authors_text":"Andras Molnar, Frank Verstraete, Kohtaro Kato, Laurens Lootens, Xiao-Qi Sun, Yuhan Liu","cross_cats":["cond-mat.str-el","hep-lat"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-09-03T18:01:22Z","title":"Trading Mathematical for Physical Simplicity: Bialgebraic Structures in Matrix Product Operator Symmetries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.03600","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":"sha256:60fc0409f35aec796f6282b78222df48402cd646e005c035218e332b03d0edc6","target":"record","created_at":"2026-07-05T12:04:42Z","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":"e37562984879a79b781ccffe35189e7d8ea748e8fbb123d4a674ec165f04c125","cross_cats_sorted":["cond-mat.str-el","hep-lat"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-09-03T18:01:22Z","title_canon_sha256":"575a3e3b028e86c75862fa97cb13d60bdf569afa2549ef01d502b9fba92d18a7"},"schema_version":"1.0","source":{"id":"2509.03600","kind":"arxiv","version":1}},"canonical_sha256":"a550390f5b19ede7ca9a7b811132f2e5646f1c2692ce634e9f0b328b30fafb79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a550390f5b19ede7ca9a7b811132f2e5646f1c2692ce634e9f0b328b30fafb79","first_computed_at":"2026-07-05T12:04:42.940359Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:04:42.940359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I5ReX0zoa4fHRxcocbA/iyMZWA+gXZ3LHU6Rod5Z84cKBrEv1oGlj1i3OFBGrGgL9SwhWL+thEAUnhx0kGFZBg==","signature_status":"signed_v1","signed_at":"2026-07-05T12:04:42.940863Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.03600","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60fc0409f35aec796f6282b78222df48402cd646e005c035218e332b03d0edc6","sha256:966ceda9e9ea70c9f6f846050edfa44e19c7ee996b68d76e19c6d41808dbfc47"],"state_sha256":"f8a884a1092a8b00ddb69586fd34f046a3a7918b5b9df10e3d1075e32d84c8d7"}