{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:4Y5JQIHKHOFT2SZOJRFS5OYQH5","short_pith_number":"pith:4Y5JQIHK","canonical_record":{"source":{"id":"1903.07494","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-03-18T15:00:27Z","cross_cats_sorted":["math.CA","math.CV","math.FA","math.MP","quant-ph"],"title_canon_sha256":"6b2732c7e19dd06f7bb34ed266f7b2428523ae7feea6d5bebb67844c5ea7e4df","abstract_canon_sha256":"f646b9005d78a7b56e048a7682f9a57120de18622c74d11d0f6325d35e4b2cb2"},"schema_version":"1.0"},"canonical_sha256":"e63a9820ea3b8b3d4b2e4c4b2ebb103f58db4346d0407cbbae23b5d435fda887","source":{"kind":"arxiv","id":"1903.07494","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.07494","created_at":"2026-07-05T04:25:07Z"},{"alias_kind":"arxiv_version","alias_value":"1903.07494v2","created_at":"2026-07-05T04:25:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.07494","created_at":"2026-07-05T04:25:07Z"},{"alias_kind":"pith_short_12","alias_value":"4Y5JQIHKHOFT","created_at":"2026-07-05T04:25:07Z"},{"alias_kind":"pith_short_16","alias_value":"4Y5JQIHKHOFT2SZO","created_at":"2026-07-05T04:25:07Z"},{"alias_kind":"pith_short_8","alias_value":"4Y5JQIHK","created_at":"2026-07-05T04:25:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:4Y5JQIHKHOFT2SZOJRFS5OYQH5","target":"record","payload":{"canonical_record":{"source":{"id":"1903.07494","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-03-18T15:00:27Z","cross_cats_sorted":["math.CA","math.CV","math.FA","math.MP","quant-ph"],"title_canon_sha256":"6b2732c7e19dd06f7bb34ed266f7b2428523ae7feea6d5bebb67844c5ea7e4df","abstract_canon_sha256":"f646b9005d78a7b56e048a7682f9a57120de18622c74d11d0f6325d35e4b2cb2"},"schema_version":"1.0"},"canonical_sha256":"e63a9820ea3b8b3d4b2e4c4b2ebb103f58db4346d0407cbbae23b5d435fda887","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:25:07.159008Z","signature_b64":"i/G3yRfkqMxe01wlwf12T1KidD5vHskXFSBVcmlZj6HpqDNOJrwMQ+7ngui/gWd/PAVSMiiHLCOGT/J2JX2PBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e63a9820ea3b8b3d4b2e4c4b2ebb103f58db4346d0407cbbae23b5d435fda887","last_reissued_at":"2026-07-05T04:25:07.158514Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:25:07.158514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.07494","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:25:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"An6Dh8okZaWKgB7UiS9pU5ubbh6OvK76/p4+WASm1KPBlgc7OUDKLDN14irp28qZhS0HGTq2j8RagQf++dt+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T19:29:07.166626Z"},"content_sha256":"afea7565cec6f550a45cfa97159f93249304975125f529e2b07c9ff766fc534c","schema_version":"1.0","event_id":"sha256:afea7565cec6f550a45cfa97159f93249304975125f529e2b07c9ff766fc534c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:4Y5JQIHKHOFT2SZOJRFS5OYQH5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum walks: Schur functions meet symmetry protected topological phases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CV","math.FA","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"A. H. Werner, C. Cedzich, F. A. Gr\\\"unbaum, L. Vel\\'azquez, R. F. Werner, T. Geib","submitted_at":"2019-03-18T15:00:27Z","abstract_excerpt":"This paper uncovers and exploits a link between a central object in harmonic analysis, the so-called Schur functions, and the very hot topic of symmetry protected topological phases of quantum matter. This connection is found in the setting of quantum walks, i.e. quantum analogs of classical random walks. We prove that topological indices classifying symmetry protected topological phases of quantum walks are encoded by matrix Schur functions built out of the walk. This main result of the paper reduces the calculation of these topological indices to a linear algebra problem: calculating symmetr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07494","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/1903.07494/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:25:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4F5CsqHEz+oQA7AKglP8AOaBDztMa5jsicg6hhX7yrYNok8lXwiPZtSlmCgY8vTsnIl9cLH/gl0cKQqHW0oRBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T19:29:07.167156Z"},"content_sha256":"d4ed9eea141ea80a53c04ec6b9960b0b6b2ce32d5ee310a56a197addfa83a004","schema_version":"1.0","event_id":"sha256:d4ed9eea141ea80a53c04ec6b9960b0b6b2ce32d5ee310a56a197addfa83a004"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4Y5JQIHKHOFT2SZOJRFS5OYQH5/bundle.json","state_url":"https://pith.science/pith/4Y5JQIHKHOFT2SZOJRFS5OYQH5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4Y5JQIHKHOFT2SZOJRFS5OYQH5/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":"2026-08-15T19:29:07Z","links":{"resolver":"https://pith.science/pith/4Y5JQIHKHOFT2SZOJRFS5OYQH5","bundle":"https://pith.science/pith/4Y5JQIHKHOFT2SZOJRFS5OYQH5/bundle.json","state":"https://pith.science/pith/4Y5JQIHKHOFT2SZOJRFS5OYQH5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4Y5JQIHKHOFT2SZOJRFS5OYQH5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:4Y5JQIHKHOFT2SZOJRFS5OYQH5","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":"f646b9005d78a7b56e048a7682f9a57120de18622c74d11d0f6325d35e4b2cb2","cross_cats_sorted":["math.CA","math.CV","math.FA","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-03-18T15:00:27Z","title_canon_sha256":"6b2732c7e19dd06f7bb34ed266f7b2428523ae7feea6d5bebb67844c5ea7e4df"},"schema_version":"1.0","source":{"id":"1903.07494","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.07494","created_at":"2026-07-05T04:25:07Z"},{"alias_kind":"arxiv_version","alias_value":"1903.07494v2","created_at":"2026-07-05T04:25:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.07494","created_at":"2026-07-05T04:25:07Z"},{"alias_kind":"pith_short_12","alias_value":"4Y5JQIHKHOFT","created_at":"2026-07-05T04:25:07Z"},{"alias_kind":"pith_short_16","alias_value":"4Y5JQIHKHOFT2SZO","created_at":"2026-07-05T04:25:07Z"},{"alias_kind":"pith_short_8","alias_value":"4Y5JQIHK","created_at":"2026-07-05T04:25:07Z"}],"graph_snapshots":[{"event_id":"sha256:d4ed9eea141ea80a53c04ec6b9960b0b6b2ce32d5ee310a56a197addfa83a004","target":"graph","created_at":"2026-07-05T04:25:07Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1903.07494/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper uncovers and exploits a link between a central object in harmonic analysis, the so-called Schur functions, and the very hot topic of symmetry protected topological phases of quantum matter. This connection is found in the setting of quantum walks, i.e. quantum analogs of classical random walks. We prove that topological indices classifying symmetry protected topological phases of quantum walks are encoded by matrix Schur functions built out of the walk. This main result of the paper reduces the calculation of these topological indices to a linear algebra problem: calculating symmetr","authors_text":"A. H. Werner, C. Cedzich, F. A. Gr\\\"unbaum, L. Vel\\'azquez, R. F. Werner, T. Geib","cross_cats":["math.CA","math.CV","math.FA","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-03-18T15:00:27Z","title":"Quantum walks: Schur functions meet symmetry protected topological phases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07494","kind":"arxiv","version":2},"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:afea7565cec6f550a45cfa97159f93249304975125f529e2b07c9ff766fc534c","target":"record","created_at":"2026-07-05T04:25:07Z","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":"f646b9005d78a7b56e048a7682f9a57120de18622c74d11d0f6325d35e4b2cb2","cross_cats_sorted":["math.CA","math.CV","math.FA","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-03-18T15:00:27Z","title_canon_sha256":"6b2732c7e19dd06f7bb34ed266f7b2428523ae7feea6d5bebb67844c5ea7e4df"},"schema_version":"1.0","source":{"id":"1903.07494","kind":"arxiv","version":2}},"canonical_sha256":"e63a9820ea3b8b3d4b2e4c4b2ebb103f58db4346d0407cbbae23b5d435fda887","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e63a9820ea3b8b3d4b2e4c4b2ebb103f58db4346d0407cbbae23b5d435fda887","first_computed_at":"2026-07-05T04:25:07.158514Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:25:07.158514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i/G3yRfkqMxe01wlwf12T1KidD5vHskXFSBVcmlZj6HpqDNOJrwMQ+7ngui/gWd/PAVSMiiHLCOGT/J2JX2PBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:25:07.159008Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.07494","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:afea7565cec6f550a45cfa97159f93249304975125f529e2b07c9ff766fc534c","sha256:d4ed9eea141ea80a53c04ec6b9960b0b6b2ce32d5ee310a56a197addfa83a004"],"state_sha256":"253fd6aaf98a1d03c89778bdf106bf5cef3ac10b58a123dda0ca463ff2dfb610"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RVJaZR+sgPXNtrvoZS0xSSJiRFsRQUtzgoRyHnCJrjwAtNPRKo0vrXMTZ/IiQBxTfTww5uQABgzAMEI3eLjsBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T19:29:07.172259Z","bundle_sha256":"754acb2b31777239a175548fe7794aa54703215fa95c5cf9645e4007ade77fec"}}