{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ZQ6KEJQUHXWINGKZ3AINGRK5IE","short_pith_number":"pith:ZQ6KEJQU","canonical_record":{"source":{"id":"1501.07285","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2015-01-28T21:00:18Z","cross_cats_sorted":["cond-mat.mes-hall","hep-th"],"title_canon_sha256":"a3ca13cdd4db19d9a1e0597dde10a59bce547222bb4e56ed4f1f92f569a05493","abstract_canon_sha256":"6cbb15e2075426f6b3604019ffd6f3f8fb9ee7a2f4b4826e40cc458655ced0d1"},"schema_version":"1.0"},"canonical_sha256":"cc3ca226143dec869959d810d3455d411621bd3e87e33c4b9ccd8c63d18146c6","source":{"kind":"arxiv","id":"1501.07285","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.07285","created_at":"2026-05-18T01:59:37Z"},{"alias_kind":"arxiv_version","alias_value":"1501.07285v3","created_at":"2026-05-18T01:59:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07285","created_at":"2026-05-18T01:59:37Z"},{"alias_kind":"pith_short_12","alias_value":"ZQ6KEJQUHXWI","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZQ6KEJQUHXWINGKZ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZQ6KEJQU","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ZQ6KEJQUHXWINGKZ3AINGRK5IE","target":"record","payload":{"canonical_record":{"source":{"id":"1501.07285","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2015-01-28T21:00:18Z","cross_cats_sorted":["cond-mat.mes-hall","hep-th"],"title_canon_sha256":"a3ca13cdd4db19d9a1e0597dde10a59bce547222bb4e56ed4f1f92f569a05493","abstract_canon_sha256":"6cbb15e2075426f6b3604019ffd6f3f8fb9ee7a2f4b4826e40cc458655ced0d1"},"schema_version":"1.0"},"canonical_sha256":"cc3ca226143dec869959d810d3455d411621bd3e87e33c4b9ccd8c63d18146c6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:37.680951Z","signature_b64":"iI+eG/tDjfiN3gcCo9pdMibg+u1iVwUUfHHQArOGM3pKgkYQraLRxQkBCySxLNv9k1M5kcWA+kYf3X0ykshyAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc3ca226143dec869959d810d3455d411621bd3e87e33c4b9ccd8c63d18146c6","last_reissued_at":"2026-05-18T01:59:37.680181Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:37.680181Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.07285","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:59:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vzRYbA6kmrTUcQTIgZ7c7eyaDzn8n1mzH5dX4gDLsZTQwBZbKa0MiCPOvOviIYwgjTNneiOUSNaNBbPKRFu4AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T20:42:07.709610Z"},"content_sha256":"49e44ac70061af0c74625c4b908be8f0e345925bd8150316ebe726a5cfcc47f9","schema_version":"1.0","event_id":"sha256:49e44ac70061af0c74625c4b908be8f0e345925bd8150316ebe726a5cfcc47f9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ZQ6KEJQUHXWINGKZ3AINGRK5IE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological Phases Protected By Reflection Symmetry and Cross-cap States","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","hep-th"],"primary_cat":"cond-mat.str-el","authors_text":"Chang-Tse Hsieh, Gil Young Cho, Shinsei Ryu, Takahiro Morimoto","submitted_at":"2015-01-28T21:00:18Z","abstract_excerpt":"Twisting symmetries provides an efficient method to diagnose symmetry-protected topological (SPT) phases. In this paper, edge theories of (2+1)-dimensional topological phases protected by reflection as well as other symmetries are studied by twisting reflection symmetry, which effectively puts the edge theories on an unoriented spacetime, such as the Klein bottle. A key technical step taken in this paper is the use of the so-called cross-cap states, which encode entirely the unoriented nature of spacetime, and can be obtained by rearranging the spacetime geometry and exchanging the role of spa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07285","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:59:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"map/5aweUWPdUXtSc4/VwCI7tMsw9zSWi1Twf1JzegRHWquMKHH1Yzg6pH4KPcmAhlTSmdMOduUjaB9THEdoDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T20:42:07.709973Z"},"content_sha256":"f90519b25dfe04653825780b722435369849b7fc2d14ece7b2371031e12691d7","schema_version":"1.0","event_id":"sha256:f90519b25dfe04653825780b722435369849b7fc2d14ece7b2371031e12691d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZQ6KEJQUHXWINGKZ3AINGRK5IE/bundle.json","state_url":"https://pith.science/pith/ZQ6KEJQUHXWINGKZ3AINGRK5IE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZQ6KEJQUHXWINGKZ3AINGRK5IE/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":"2026-06-03T20:42:07Z","links":{"resolver":"https://pith.science/pith/ZQ6KEJQUHXWINGKZ3AINGRK5IE","bundle":"https://pith.science/pith/ZQ6KEJQUHXWINGKZ3AINGRK5IE/bundle.json","state":"https://pith.science/pith/ZQ6KEJQUHXWINGKZ3AINGRK5IE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZQ6KEJQUHXWINGKZ3AINGRK5IE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZQ6KEJQUHXWINGKZ3AINGRK5IE","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":"6cbb15e2075426f6b3604019ffd6f3f8fb9ee7a2f4b4826e40cc458655ced0d1","cross_cats_sorted":["cond-mat.mes-hall","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2015-01-28T21:00:18Z","title_canon_sha256":"a3ca13cdd4db19d9a1e0597dde10a59bce547222bb4e56ed4f1f92f569a05493"},"schema_version":"1.0","source":{"id":"1501.07285","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.07285","created_at":"2026-05-18T01:59:37Z"},{"alias_kind":"arxiv_version","alias_value":"1501.07285v3","created_at":"2026-05-18T01:59:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07285","created_at":"2026-05-18T01:59:37Z"},{"alias_kind":"pith_short_12","alias_value":"ZQ6KEJQUHXWI","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZQ6KEJQUHXWINGKZ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZQ6KEJQU","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:f90519b25dfe04653825780b722435369849b7fc2d14ece7b2371031e12691d7","target":"graph","created_at":"2026-05-18T01:59:37Z","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":"Twisting symmetries provides an efficient method to diagnose symmetry-protected topological (SPT) phases. In this paper, edge theories of (2+1)-dimensional topological phases protected by reflection as well as other symmetries are studied by twisting reflection symmetry, which effectively puts the edge theories on an unoriented spacetime, such as the Klein bottle. A key technical step taken in this paper is the use of the so-called cross-cap states, which encode entirely the unoriented nature of spacetime, and can be obtained by rearranging the spacetime geometry and exchanging the role of spa","authors_text":"Chang-Tse Hsieh, Gil Young Cho, Shinsei Ryu, Takahiro Morimoto","cross_cats":["cond-mat.mes-hall","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2015-01-28T21:00:18Z","title":"Topological Phases Protected By Reflection Symmetry and Cross-cap States"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07285","kind":"arxiv","version":3},"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":"sha256:49e44ac70061af0c74625c4b908be8f0e345925bd8150316ebe726a5cfcc47f9","target":"record","created_at":"2026-05-18T01:59:37Z","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":"6cbb15e2075426f6b3604019ffd6f3f8fb9ee7a2f4b4826e40cc458655ced0d1","cross_cats_sorted":["cond-mat.mes-hall","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2015-01-28T21:00:18Z","title_canon_sha256":"a3ca13cdd4db19d9a1e0597dde10a59bce547222bb4e56ed4f1f92f569a05493"},"schema_version":"1.0","source":{"id":"1501.07285","kind":"arxiv","version":3}},"canonical_sha256":"cc3ca226143dec869959d810d3455d411621bd3e87e33c4b9ccd8c63d18146c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc3ca226143dec869959d810d3455d411621bd3e87e33c4b9ccd8c63d18146c6","first_computed_at":"2026-05-18T01:59:37.680181Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:37.680181Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iI+eG/tDjfiN3gcCo9pdMibg+u1iVwUUfHHQArOGM3pKgkYQraLRxQkBCySxLNv9k1M5kcWA+kYf3X0ykshyAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:37.680951Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.07285","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49e44ac70061af0c74625c4b908be8f0e345925bd8150316ebe726a5cfcc47f9","sha256:f90519b25dfe04653825780b722435369849b7fc2d14ece7b2371031e12691d7"],"state_sha256":"fac56f3a8aceddd16220e1bb58f393dada91598866f088165da95307956e4b14"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ttTtSrhdiqsBOzzB9zcRRjyr75UAgpaBbmybZD70wcsd2Ug4OxfKqTfkOO9L+CAmBw5IfcX8erU29QXNo3PiBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T20:42:07.712520Z","bundle_sha256":"669bd0d245c5b5e4b2e9008b8c7dea88aaf26e36c90581764b5df4c4a8241e19"}}