{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:75PH2SWG3MCPZMNQHKGWOXAV4Z","short_pith_number":"pith:75PH2SWG","schema_version":"1.0","canonical_sha256":"ff5e7d4ac6db04fcb1b03a8d675c15e65d5d9b4680f1e7d57566cc995e454be9","source":{"kind":"arxiv","id":"2603.19189","version":2},"attestation_state":"computed","paper":{"title":"Matrix Product States for Modulated Symmetries: SPT, LSM, and Beyond","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Amogh Anakru, Linhao Li, Sarvesh Srinivasan, Zhen Bi","submitted_at":"2026-03-19T17:44:13Z","abstract_excerpt":"Matrix product states (MPS) provide a powerful framework for characterizing one-dimensional symmetry-protected topological (SPT) phases of matter and for formulating Lieb-Schultz-Mattis (LSM)-type constraints. Here we generalize the MPS formalism to translationally invariant systems with general modulated symmetries. We show that the standard symmetry \"push-through\" condition for conventional global symmetry must be revised to account for symmetry modulation, and we derive the appropriate generalized condition. Using this generalized push-through structure, we classify one-dimensional SPT phas"},"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":"2603.19189","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.str-el","submitted_at":"2026-03-19T17:44:13Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"2ddf3c8655a2ecb1d7d7fc219859287a55054c3b20a116e7da5fc4da98ac8690","abstract_canon_sha256":"1004003cd4a91d0f64429130df26f80ba782e54bf2beb058cfd5c6458e28620f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:09:57.003145Z","signature_b64":"59sUjuS3Z/YyVzupVvrdC3z37k4oc3/3KOU70mHG+2AVnytuUC5L0iNvI3qlkK8nzMqyRcuFjNadpEFdyfP4CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff5e7d4ac6db04fcb1b03a8d675c15e65d5d9b4680f1e7d57566cc995e454be9","last_reissued_at":"2026-06-19T16:09:57.002722Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:09:57.002722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Matrix Product States for Modulated Symmetries: SPT, LSM, and Beyond","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Amogh Anakru, Linhao Li, Sarvesh Srinivasan, Zhen Bi","submitted_at":"2026-03-19T17:44:13Z","abstract_excerpt":"Matrix product states (MPS) provide a powerful framework for characterizing one-dimensional symmetry-protected topological (SPT) phases of matter and for formulating Lieb-Schultz-Mattis (LSM)-type constraints. Here we generalize the MPS formalism to translationally invariant systems with general modulated symmetries. We show that the standard symmetry \"push-through\" condition for conventional global symmetry must be revised to account for symmetry modulation, and we derive the appropriate generalized condition. Using this generalized push-through structure, we classify one-dimensional SPT phas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.19189","kind":"arxiv","version":2},"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/2603.19189/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":"2603.19189","created_at":"2026-06-19T16:09:57.002777+00:00"},{"alias_kind":"arxiv_version","alias_value":"2603.19189v2","created_at":"2026-06-19T16:09:57.002777+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.19189","created_at":"2026-06-19T16:09:57.002777+00:00"},{"alias_kind":"pith_short_12","alias_value":"75PH2SWG3MCP","created_at":"2026-06-19T16:09:57.002777+00:00"},{"alias_kind":"pith_short_16","alias_value":"75PH2SWG3MCPZMNQ","created_at":"2026-06-19T16:09:57.002777+00:00"},{"alias_kind":"pith_short_8","alias_value":"75PH2SWG","created_at":"2026-06-19T16:09:57.002777+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":4,"sample":[{"citing_arxiv_id":"2606.07952","citing_title":"Translationally Covariant Modulated Symmetries: Classification and Goldstone","ref_index":30,"is_internal_anchor":true},{"citing_arxiv_id":"2603.19381","citing_title":"Matrix Product States for Modulated Topological Phases: Crystalline Equivalence Principle and Lieb-Schultz-Mattis Constraints","ref_index":62,"is_internal_anchor":true},{"citing_arxiv_id":"2604.00347","citing_title":"Lieb-Schultz-Mattis Anomalies and Anomaly Matching","ref_index":25,"is_internal_anchor":true},{"citing_arxiv_id":"2604.06741","citing_title":"Projector, Neural, and Tensor-Network Representations of $\\mathbb{Z}_N$ Cluster and Dipolar-cluster SPT States","ref_index":30,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/75PH2SWG3MCPZMNQHKGWOXAV4Z","json":"https://pith.science/pith/75PH2SWG3MCPZMNQHKGWOXAV4Z.json","graph_json":"https://pith.science/api/pith-number/75PH2SWG3MCPZMNQHKGWOXAV4Z/graph.json","events_json":"https://pith.science/api/pith-number/75PH2SWG3MCPZMNQHKGWOXAV4Z/events.json","paper":"https://pith.science/paper/75PH2SWG"},"agent_actions":{"view_html":"https://pith.science/pith/75PH2SWG3MCPZMNQHKGWOXAV4Z","download_json":"https://pith.science/pith/75PH2SWG3MCPZMNQHKGWOXAV4Z.json","view_paper":"https://pith.science/paper/75PH2SWG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2603.19189&json=true","fetch_graph":"https://pith.science/api/pith-number/75PH2SWG3MCPZMNQHKGWOXAV4Z/graph.json","fetch_events":"https://pith.science/api/pith-number/75PH2SWG3MCPZMNQHKGWOXAV4Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/75PH2SWG3MCPZMNQHKGWOXAV4Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/75PH2SWG3MCPZMNQHKGWOXAV4Z/action/storage_attestation","attest_author":"https://pith.science/pith/75PH2SWG3MCPZMNQHKGWOXAV4Z/action/author_attestation","sign_citation":"https://pith.science/pith/75PH2SWG3MCPZMNQHKGWOXAV4Z/action/citation_signature","submit_replication":"https://pith.science/pith/75PH2SWG3MCPZMNQHKGWOXAV4Z/action/replication_record"}},"created_at":"2026-06-19T16:09:57.002777+00:00","updated_at":"2026-06-19T16:09:57.002777+00:00"}