{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:QU4WCQBQZ6NMRJKNKCBXJSYPMR","short_pith_number":"pith:QU4WCQBQ","canonical_record":{"source":{"id":"1904.01669","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-04-02T21:09:14Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP","quant-ph"],"title_canon_sha256":"e9e53c5c1f8e5f80101172197e0e0f3d736f15df26abe48d37fb8ac1abc16fd4","abstract_canon_sha256":"bbef135d7f7c7a197f34ef71385cb7b5aa1ad29553f256521d352ff8d2f7d1d3"},"schema_version":"1.0"},"canonical_sha256":"8539614030cf9ac8a54d508374cb0f647751e2d993124672c18a21e30cb77229","source":{"kind":"arxiv","id":"1904.01669","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.01669","created_at":"2026-05-17T23:49:30Z"},{"alias_kind":"arxiv_version","alias_value":"1904.01669v1","created_at":"2026-05-17T23:49:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.01669","created_at":"2026-05-17T23:49:30Z"},{"alias_kind":"pith_short_12","alias_value":"QU4WCQBQZ6NM","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QU4WCQBQZ6NMRJKN","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QU4WCQBQ","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:QU4WCQBQZ6NMRJKNKCBXJSYPMR","target":"record","payload":{"canonical_record":{"source":{"id":"1904.01669","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-04-02T21:09:14Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP","quant-ph"],"title_canon_sha256":"e9e53c5c1f8e5f80101172197e0e0f3d736f15df26abe48d37fb8ac1abc16fd4","abstract_canon_sha256":"bbef135d7f7c7a197f34ef71385cb7b5aa1ad29553f256521d352ff8d2f7d1d3"},"schema_version":"1.0"},"canonical_sha256":"8539614030cf9ac8a54d508374cb0f647751e2d993124672c18a21e30cb77229","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:30.259915Z","signature_b64":"ECa08EHTQZK1x9GO6nhYYX2/VozEo8a/GQNaFth3zbg+P8Mf8GBn89CaEMqwggPG/ptf303VWhakAmvLpFYcCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8539614030cf9ac8a54d508374cb0f647751e2d993124672c18a21e30cb77229","last_reissued_at":"2026-05-17T23:49:30.259336Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:30.259336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.01669","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:49:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v6D6oOW8iwWZAj7bfQMTs5SQ0kvVhUsfw4J4bTWASMkiNYVYTYJsAtDwt6roU1alOw2r4oQRsx/13SjfnqwPCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T12:55:59.659776Z"},"content_sha256":"675b0068c3b30be5836d21a5db0080dee0fbd8c5cdc297c077f61cf4abdfe349","schema_version":"1.0","event_id":"sha256:675b0068c3b30be5836d21a5db0080dee0fbd8c5cdc297c077f61cf4abdfe349"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:QU4WCQBQZ6NMRJKNKCBXJSYPMR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A ${\\mathbb Z}_2$-index of symmetry protected topological phases with reflection symmetry for quantum spin chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Yoshiko Ogata","submitted_at":"2019-04-02T21:09:14Z","abstract_excerpt":"For the classification of SPT phases, defining an index is a central problem. In the famous paper [PTBO1], Pollmann, Tuner, Berg, and Oshikawa introduced ${\\mathbb Z}_2$-indices for injective matrix products states (MPS) which have either ${\\mathbb Z}_2\\times {\\mathbb Z}_2$ dihedral group (of $\\pi$-rotations about $x$, $y$, and $z$-axes) symmetry, time-reversal symmetry, or reflection symmetry. The first two are on-site symmetries. In [O4], an index for on-site symmetries, which generalizes the index in [PTBO1], was introduced for general unique gapped ground state phases in quantum spin chain"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.01669","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:49:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O4Lb/CzvEdRccLreSqGxs+4t4/MdFROJo6g14YzPJ8nuRSEK1kiTKvhRI2cO3f3f2MvrndogGmr0ahFcl2aeDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T12:55:59.660520Z"},"content_sha256":"3cd121e92a853dabdadcdc48870b8890b890c7bf6f12fcf15047635693f0bf3e","schema_version":"1.0","event_id":"sha256:3cd121e92a853dabdadcdc48870b8890b890c7bf6f12fcf15047635693f0bf3e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QU4WCQBQZ6NMRJKNKCBXJSYPMR/bundle.json","state_url":"https://pith.science/pith/QU4WCQBQZ6NMRJKNKCBXJSYPMR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QU4WCQBQZ6NMRJKNKCBXJSYPMR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-24T12:55:59Z","links":{"resolver":"https://pith.science/pith/QU4WCQBQZ6NMRJKNKCBXJSYPMR","bundle":"https://pith.science/pith/QU4WCQBQZ6NMRJKNKCBXJSYPMR/bundle.json","state":"https://pith.science/pith/QU4WCQBQZ6NMRJKNKCBXJSYPMR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QU4WCQBQZ6NMRJKNKCBXJSYPMR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QU4WCQBQZ6NMRJKNKCBXJSYPMR","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":"bbef135d7f7c7a197f34ef71385cb7b5aa1ad29553f256521d352ff8d2f7d1d3","cross_cats_sorted":["cond-mat.stat-mech","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-04-02T21:09:14Z","title_canon_sha256":"e9e53c5c1f8e5f80101172197e0e0f3d736f15df26abe48d37fb8ac1abc16fd4"},"schema_version":"1.0","source":{"id":"1904.01669","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.01669","created_at":"2026-05-17T23:49:30Z"},{"alias_kind":"arxiv_version","alias_value":"1904.01669v1","created_at":"2026-05-17T23:49:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.01669","created_at":"2026-05-17T23:49:30Z"},{"alias_kind":"pith_short_12","alias_value":"QU4WCQBQZ6NM","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QU4WCQBQZ6NMRJKN","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QU4WCQBQ","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:3cd121e92a853dabdadcdc48870b8890b890c7bf6f12fcf15047635693f0bf3e","target":"graph","created_at":"2026-05-17T23:49:30Z","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":"For the classification of SPT phases, defining an index is a central problem. In the famous paper [PTBO1], Pollmann, Tuner, Berg, and Oshikawa introduced ${\\mathbb Z}_2$-indices for injective matrix products states (MPS) which have either ${\\mathbb Z}_2\\times {\\mathbb Z}_2$ dihedral group (of $\\pi$-rotations about $x$, $y$, and $z$-axes) symmetry, time-reversal symmetry, or reflection symmetry. The first two are on-site symmetries. In [O4], an index for on-site symmetries, which generalizes the index in [PTBO1], was introduced for general unique gapped ground state phases in quantum spin chain","authors_text":"Yoshiko Ogata","cross_cats":["cond-mat.stat-mech","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-04-02T21:09:14Z","title":"A ${\\mathbb Z}_2$-index of symmetry protected topological phases with reflection symmetry for quantum spin chains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.01669","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":"sha256:675b0068c3b30be5836d21a5db0080dee0fbd8c5cdc297c077f61cf4abdfe349","target":"record","created_at":"2026-05-17T23:49:30Z","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":"bbef135d7f7c7a197f34ef71385cb7b5aa1ad29553f256521d352ff8d2f7d1d3","cross_cats_sorted":["cond-mat.stat-mech","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-04-02T21:09:14Z","title_canon_sha256":"e9e53c5c1f8e5f80101172197e0e0f3d736f15df26abe48d37fb8ac1abc16fd4"},"schema_version":"1.0","source":{"id":"1904.01669","kind":"arxiv","version":1}},"canonical_sha256":"8539614030cf9ac8a54d508374cb0f647751e2d993124672c18a21e30cb77229","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8539614030cf9ac8a54d508374cb0f647751e2d993124672c18a21e30cb77229","first_computed_at":"2026-05-17T23:49:30.259336Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:30.259336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ECa08EHTQZK1x9GO6nhYYX2/VozEo8a/GQNaFth3zbg+P8Mf8GBn89CaEMqwggPG/ptf303VWhakAmvLpFYcCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:30.259915Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.01669","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:675b0068c3b30be5836d21a5db0080dee0fbd8c5cdc297c077f61cf4abdfe349","sha256:3cd121e92a853dabdadcdc48870b8890b890c7bf6f12fcf15047635693f0bf3e"],"state_sha256":"e166810f13ee21b4a577ea5c978a87711f09209396e08c8b4bce7bf0da7bd8f5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VDnIluCwoEhFl9ZEPRLuuOl4/nL09h0PAZteQtc5uQ2xwy5RlarSAMkgVNfrsynKkq2K7Ua2tdBfKV0zkP+WDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T12:55:59.664432Z","bundle_sha256":"588db093f66f60d20266bde2d27fad520bf50541d7d70131167d6d638a9291a3"}}