{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:I7LYEXH6UXTGU7PIEOALBTHHOF","short_pith_number":"pith:I7LYEXH6","canonical_record":{"source":{"id":"1502.02592","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-02-09T18:25:48Z","cross_cats_sorted":["cond-mat.other","math-ph","math.MP"],"title_canon_sha256":"b7d17e75506d51bc9f3b6cee9c9d7c18379a51d89050623013fd7cac4524be95","abstract_canon_sha256":"bcd50eac9c902ea99822e652696fea182f8f595c7eb869c161ace81a636d9046"},"schema_version":"1.0"},"canonical_sha256":"47d7825cfea5e66a7de82380b0cce771474adc037ae09be2df21b97a5d8aaa73","source":{"kind":"arxiv","id":"1502.02592","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02592","created_at":"2026-05-18T01:16:35Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02592v3","created_at":"2026-05-18T01:16:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02592","created_at":"2026-05-18T01:16:35Z"},{"alias_kind":"pith_short_12","alias_value":"I7LYEXH6UXTG","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"I7LYEXH6UXTGU7PI","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"I7LYEXH6","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:I7LYEXH6UXTGU7PIEOALBTHHOF","target":"record","payload":{"canonical_record":{"source":{"id":"1502.02592","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-02-09T18:25:48Z","cross_cats_sorted":["cond-mat.other","math-ph","math.MP"],"title_canon_sha256":"b7d17e75506d51bc9f3b6cee9c9d7c18379a51d89050623013fd7cac4524be95","abstract_canon_sha256":"bcd50eac9c902ea99822e652696fea182f8f595c7eb869c161ace81a636d9046"},"schema_version":"1.0"},"canonical_sha256":"47d7825cfea5e66a7de82380b0cce771474adc037ae09be2df21b97a5d8aaa73","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:35.095410Z","signature_b64":"bzr4Ap30uJQZrL/vNOCnttkveCDgEkJQukasop4Flym0pNudZXAFq9BDl56vSmatASMn8MsLM/RmifYE9B0dCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47d7825cfea5e66a7de82380b0cce771474adc037ae09be2df21b97a5d8aaa73","last_reissued_at":"2026-05-18T01:16:35.094838Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:35.094838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.02592","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":"2026-05-18T01:16:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vTMJEmhOHzL8BfqsUyzqJ9L7P3HJm9L6Jn8h6j5jKdbmMgIF1s0RQvxqBy0atzwUBUx+88ME2+y0qpKtp68tAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T02:09:05.178195Z"},"content_sha256":"fb53e9f6b4996865a7ba159f915a8524ccde933c9e4dabe7fe4e3405bc3dac3a","schema_version":"1.0","event_id":"sha256:fb53e9f6b4996865a7ba159f915a8524ccde933c9e4dabe7fe4e3405bc3dac3a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:I7LYEXH6UXTGU7PIEOALBTHHOF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bulk-edge correspondence of one-dimensional quantum walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.other","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"A. H. Werner, C. Cedzich, C. Stahl, F. A. Gr\\\"unbaum, L. Vel\\'azquez, R. F. Werner","submitted_at":"2015-02-09T18:25:48Z","abstract_excerpt":"We outline a theory of symmetry protected topological phases of one-dimensional quantum walks. We assume spectral gaps around the symmetry-distinguished points +1 and -1, in which only discrete eigenvalues are allowed. The phase classification by integer or binary indices extends the classification known for translation invariant systems in terms of their band structure. However, our theory requires no translation invariance whatsoever, and the indices we define in this general setting are invariant under arbitrary symmetric local perturbations, even those that cannot be continuously contracte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02592","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":"2026-05-18T01:16:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pp+hQQeYLYzqkjtzT5dNnGxwematHsiqNjJ5mg2rZW5TUSJM+nagr4n2/gb6Cp97TtqvNPxgR6rsZ9QwZwtFAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T02:09:05.178751Z"},"content_sha256":"7be22ba2c9a04991e55011dd5d2db90bb651585894474bc7ae88ee257b851ee5","schema_version":"1.0","event_id":"sha256:7be22ba2c9a04991e55011dd5d2db90bb651585894474bc7ae88ee257b851ee5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I7LYEXH6UXTGU7PIEOALBTHHOF/bundle.json","state_url":"https://pith.science/pith/I7LYEXH6UXTGU7PIEOALBTHHOF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I7LYEXH6UXTGU7PIEOALBTHHOF/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":"2026-05-19T02:09:05Z","links":{"resolver":"https://pith.science/pith/I7LYEXH6UXTGU7PIEOALBTHHOF","bundle":"https://pith.science/pith/I7LYEXH6UXTGU7PIEOALBTHHOF/bundle.json","state":"https://pith.science/pith/I7LYEXH6UXTGU7PIEOALBTHHOF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I7LYEXH6UXTGU7PIEOALBTHHOF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:I7LYEXH6UXTGU7PIEOALBTHHOF","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":"bcd50eac9c902ea99822e652696fea182f8f595c7eb869c161ace81a636d9046","cross_cats_sorted":["cond-mat.other","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-02-09T18:25:48Z","title_canon_sha256":"b7d17e75506d51bc9f3b6cee9c9d7c18379a51d89050623013fd7cac4524be95"},"schema_version":"1.0","source":{"id":"1502.02592","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02592","created_at":"2026-05-18T01:16:35Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02592v3","created_at":"2026-05-18T01:16:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02592","created_at":"2026-05-18T01:16:35Z"},{"alias_kind":"pith_short_12","alias_value":"I7LYEXH6UXTG","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"I7LYEXH6UXTGU7PI","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"I7LYEXH6","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:7be22ba2c9a04991e55011dd5d2db90bb651585894474bc7ae88ee257b851ee5","target":"graph","created_at":"2026-05-18T01:16:35Z","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":"We outline a theory of symmetry protected topological phases of one-dimensional quantum walks. We assume spectral gaps around the symmetry-distinguished points +1 and -1, in which only discrete eigenvalues are allowed. The phase classification by integer or binary indices extends the classification known for translation invariant systems in terms of their band structure. However, our theory requires no translation invariance whatsoever, and the indices we define in this general setting are invariant under arbitrary symmetric local perturbations, even those that cannot be continuously contracte","authors_text":"A. H. Werner, C. Cedzich, C. Stahl, F. A. Gr\\\"unbaum, L. Vel\\'azquez, R. F. Werner","cross_cats":["cond-mat.other","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-02-09T18:25:48Z","title":"Bulk-edge correspondence of one-dimensional quantum walks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02592","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:fb53e9f6b4996865a7ba159f915a8524ccde933c9e4dabe7fe4e3405bc3dac3a","target":"record","created_at":"2026-05-18T01:16:35Z","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":"bcd50eac9c902ea99822e652696fea182f8f595c7eb869c161ace81a636d9046","cross_cats_sorted":["cond-mat.other","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-02-09T18:25:48Z","title_canon_sha256":"b7d17e75506d51bc9f3b6cee9c9d7c18379a51d89050623013fd7cac4524be95"},"schema_version":"1.0","source":{"id":"1502.02592","kind":"arxiv","version":3}},"canonical_sha256":"47d7825cfea5e66a7de82380b0cce771474adc037ae09be2df21b97a5d8aaa73","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47d7825cfea5e66a7de82380b0cce771474adc037ae09be2df21b97a5d8aaa73","first_computed_at":"2026-05-18T01:16:35.094838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:35.094838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bzr4Ap30uJQZrL/vNOCnttkveCDgEkJQukasop4Flym0pNudZXAFq9BDl56vSmatASMn8MsLM/RmifYE9B0dCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:35.095410Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.02592","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb53e9f6b4996865a7ba159f915a8524ccde933c9e4dabe7fe4e3405bc3dac3a","sha256:7be22ba2c9a04991e55011dd5d2db90bb651585894474bc7ae88ee257b851ee5"],"state_sha256":"72de1c1441be9f41e2713acdd22ded1313395b77cc0e4daf0de517c75c3811b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vWSvj0IcO1YbdmAv04RT2GGDCcXsNU6jTQb8l5PZqTlZKuv2O3h4WkhQuF9J9LGEF0+btDXEiHZrYFwnJKt1Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T02:09:05.180564Z","bundle_sha256":"b609844586a24258e62aa5e02534fcc0a2c2b9c1ddd1f5d389760c573fe54fb0"}}