{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:BFDMNHWUB6HV7CTE2P2K6EE4AQ","short_pith_number":"pith:BFDMNHWU","schema_version":"1.0","canonical_sha256":"0946c69ed40f8f5f8a64d3f4af109c041f759352da0b160ff01b407714a0f0d7","source":{"kind":"arxiv","id":"1803.10796","version":3},"attestation_state":"computed","paper":{"title":"On the cobordism classification of symmetry protected topological phases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","math-ph","math.AT","math.MP"],"primary_cat":"hep-th","authors_text":"Kazuya Yonekura","submitted_at":"2018-03-28T18:37:21Z","abstract_excerpt":"In the framework of Atiyah's axioms of topological quantum field theory with unitarity, we give a direct proof of the fact that symmetry protected topological (SPT) phases without Hall effects are classified by cobordism invariants. We first show that the partition functions of those theories are cobordism invariants after a tuning of the Euler term. Conversely, for a given cobordism invariant, we construct a unitary topological field theory whose partition function is given by the cobordism invariant. Two theories having the same cobordism invariant partition functions are isomorphic."},"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":"1803.10796","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-03-28T18:37:21Z","cross_cats_sorted":["cond-mat.str-el","math-ph","math.AT","math.MP"],"title_canon_sha256":"edbfb0120ab75d0ec8148b514854777e0a9173e536e08a790595a50be46dc83f","abstract_canon_sha256":"2e35daa96fe3b9ff72ad0d1bbae3d223a5419abdf1f3bb220890567c9375215f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:18.101006Z","signature_b64":"mxaWp641jZ1+cPmE6TlG7QIjWFcEbXHje3Ftdr4CbromoDuJD/iveIUiuYWVAhdUanNvEprV8n1hAgKeeHZABA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0946c69ed40f8f5f8a64d3f4af109c041f759352da0b160ff01b407714a0f0d7","last_reissued_at":"2026-05-17T23:43:18.100306Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:18.100306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the cobordism classification of symmetry protected topological phases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","math-ph","math.AT","math.MP"],"primary_cat":"hep-th","authors_text":"Kazuya Yonekura","submitted_at":"2018-03-28T18:37:21Z","abstract_excerpt":"In the framework of Atiyah's axioms of topological quantum field theory with unitarity, we give a direct proof of the fact that symmetry protected topological (SPT) phases without Hall effects are classified by cobordism invariants. We first show that the partition functions of those theories are cobordism invariants after a tuning of the Euler term. Conversely, for a given cobordism invariant, we construct a unitary topological field theory whose partition function is given by the cobordism invariant. Two theories having the same cobordism invariant partition functions are isomorphic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10796","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1803.10796","created_at":"2026-05-17T23:43:18.100418+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.10796v3","created_at":"2026-05-17T23:43:18.100418+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10796","created_at":"2026-05-17T23:43:18.100418+00:00"},{"alias_kind":"pith_short_12","alias_value":"BFDMNHWUB6HV","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_16","alias_value":"BFDMNHWUB6HV7CTE","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_8","alias_value":"BFDMNHWU","created_at":"2026-05-18T12:32:16.446611+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2205.09545","citing_title":"Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond","ref_index":259,"is_internal_anchor":true},{"citing_arxiv_id":"2602.11696","citing_title":"Symmetry Spans and Enforced Gaplessness","ref_index":118,"is_internal_anchor":true},{"citing_arxiv_id":"2604.04393","citing_title":"Anomalies in family unification models from bordism classification","ref_index":11,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BFDMNHWUB6HV7CTE2P2K6EE4AQ","json":"https://pith.science/pith/BFDMNHWUB6HV7CTE2P2K6EE4AQ.json","graph_json":"https://pith.science/api/pith-number/BFDMNHWUB6HV7CTE2P2K6EE4AQ/graph.json","events_json":"https://pith.science/api/pith-number/BFDMNHWUB6HV7CTE2P2K6EE4AQ/events.json","paper":"https://pith.science/paper/BFDMNHWU"},"agent_actions":{"view_html":"https://pith.science/pith/BFDMNHWUB6HV7CTE2P2K6EE4AQ","download_json":"https://pith.science/pith/BFDMNHWUB6HV7CTE2P2K6EE4AQ.json","view_paper":"https://pith.science/paper/BFDMNHWU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.10796&json=true","fetch_graph":"https://pith.science/api/pith-number/BFDMNHWUB6HV7CTE2P2K6EE4AQ/graph.json","fetch_events":"https://pith.science/api/pith-number/BFDMNHWUB6HV7CTE2P2K6EE4AQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BFDMNHWUB6HV7CTE2P2K6EE4AQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BFDMNHWUB6HV7CTE2P2K6EE4AQ/action/storage_attestation","attest_author":"https://pith.science/pith/BFDMNHWUB6HV7CTE2P2K6EE4AQ/action/author_attestation","sign_citation":"https://pith.science/pith/BFDMNHWUB6HV7CTE2P2K6EE4AQ/action/citation_signature","submit_replication":"https://pith.science/pith/BFDMNHWUB6HV7CTE2P2K6EE4AQ/action/replication_record"}},"created_at":"2026-05-17T23:43:18.100418+00:00","updated_at":"2026-05-17T23:43:18.100418+00:00"}