{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:74LGRM33VNI32Y7CAU6DWRXRBD","short_pith_number":"pith:74LGRM33","canonical_record":{"source":{"id":"1301.5639","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2013-01-23T21:00:02Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"7c3c52668586655056216fb4a0d90d8a52fa91e494aca10d895143b84a6d5436","abstract_canon_sha256":"38ff52f6d92e1474cca04c5bd4e88748b4f8f3a6e540f0eababab923263a9ef1"},"schema_version":"1.0"},"canonical_sha256":"ff1668b37bab51bd63e2053c3b46f108e57789214ced794925dbdb6982669454","source":{"kind":"arxiv","id":"1301.5639","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5639","created_at":"2026-05-18T03:26:40Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5639v2","created_at":"2026-05-18T03:26:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5639","created_at":"2026-05-18T03:26:40Z"},{"alias_kind":"pith_short_12","alias_value":"74LGRM33VNI3","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"74LGRM33VNI32Y7C","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"74LGRM33","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:74LGRM33VNI32Y7CAU6DWRXRBD","target":"record","payload":{"canonical_record":{"source":{"id":"1301.5639","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2013-01-23T21:00:02Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"7c3c52668586655056216fb4a0d90d8a52fa91e494aca10d895143b84a6d5436","abstract_canon_sha256":"38ff52f6d92e1474cca04c5bd4e88748b4f8f3a6e540f0eababab923263a9ef1"},"schema_version":"1.0"},"canonical_sha256":"ff1668b37bab51bd63e2053c3b46f108e57789214ced794925dbdb6982669454","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:40.904279Z","signature_b64":"Lhy0rH8Fs+SMBN5J/Vi0rYaXZ1ymnxK+JzRSF6r20I7NAiWwSPeV0QVH1cx5qUnN6pcQoaUTDo3SW5z5nutYBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff1668b37bab51bd63e2053c3b46f108e57789214ced794925dbdb6982669454","last_reissued_at":"2026-05-18T03:26:40.903637Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:40.903637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.5639","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":"2026-05-18T03:26:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fmaCynb+T2XuVt1vmrjYz/i3NdaTLSQDSUULZpJlGQJMzHnimukjSfiC8g5Nh0lko+RLEhBmlx2H2LO6y9HjCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T05:17:38.434056Z"},"content_sha256":"f145b6f07a9f4afdb86d0dff7dad3f36ce119b906244d9a3073406cceead8a17","schema_version":"1.0","event_id":"sha256:f145b6f07a9f4afdb86d0dff7dad3f36ce119b906244d9a3073406cceead8a17"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:74LGRM33VNI32Y7CAU6DWRXRBD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological Zero-Energy Modes in Gapless Commensurate Aubry-Andr\\'e-Harper Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cond-mat.mes-hall","authors_text":"Kai Sun, S. Das Sarma, Sriram Ganeshan","submitted_at":"2013-01-23T21:00:02Z","abstract_excerpt":"The Aubry-Andr\\'e or Harper (AAH) model has been the subject of extensive theoretical research in the context of quantum localization. Recently, it was shown that one-dimensional quasicrystals described by the incommensurate AAH model has a nontrivial topology. In this Letter, we show that the commensurate off-diagonal AAH model is topologically nontrivial in the gapless regime and supports zero-energy edge modes. Unlike the incommensurate case, the nontrivial topology in the off-diagonal AAH model is attributed to the topological properties of the one-dimensional Majorana chain. We discuss th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5639","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":""},"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":"2026-05-18T03:26:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Las1tDPNHKFipw14YLtG/12orZpQbXzMHy2CStVV+q7+Rfrh5zTIhS2N5k2jalnDL0k+x/pq/6w/WV4sDSdtBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T05:17:38.434672Z"},"content_sha256":"c2f2d3e221c5ddf1ef813613803675fadd84f93293652448a1120cfddf0ac16f","schema_version":"1.0","event_id":"sha256:c2f2d3e221c5ddf1ef813613803675fadd84f93293652448a1120cfddf0ac16f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/74LGRM33VNI32Y7CAU6DWRXRBD/bundle.json","state_url":"https://pith.science/pith/74LGRM33VNI32Y7CAU6DWRXRBD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/74LGRM33VNI32Y7CAU6DWRXRBD/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":"2026-06-08T05:17:38Z","links":{"resolver":"https://pith.science/pith/74LGRM33VNI32Y7CAU6DWRXRBD","bundle":"https://pith.science/pith/74LGRM33VNI32Y7CAU6DWRXRBD/bundle.json","state":"https://pith.science/pith/74LGRM33VNI32Y7CAU6DWRXRBD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/74LGRM33VNI32Y7CAU6DWRXRBD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:74LGRM33VNI32Y7CAU6DWRXRBD","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":"38ff52f6d92e1474cca04c5bd4e88748b4f8f3a6e540f0eababab923263a9ef1","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2013-01-23T21:00:02Z","title_canon_sha256":"7c3c52668586655056216fb4a0d90d8a52fa91e494aca10d895143b84a6d5436"},"schema_version":"1.0","source":{"id":"1301.5639","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5639","created_at":"2026-05-18T03:26:40Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5639v2","created_at":"2026-05-18T03:26:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5639","created_at":"2026-05-18T03:26:40Z"},{"alias_kind":"pith_short_12","alias_value":"74LGRM33VNI3","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"74LGRM33VNI32Y7C","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"74LGRM33","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:c2f2d3e221c5ddf1ef813613803675fadd84f93293652448a1120cfddf0ac16f","target":"graph","created_at":"2026-05-18T03:26:40Z","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":"The Aubry-Andr\\'e or Harper (AAH) model has been the subject of extensive theoretical research in the context of quantum localization. Recently, it was shown that one-dimensional quasicrystals described by the incommensurate AAH model has a nontrivial topology. In this Letter, we show that the commensurate off-diagonal AAH model is topologically nontrivial in the gapless regime and supports zero-energy edge modes. Unlike the incommensurate case, the nontrivial topology in the off-diagonal AAH model is attributed to the topological properties of the one-dimensional Majorana chain. We discuss th","authors_text":"Kai Sun, S. Das Sarma, Sriram Ganeshan","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2013-01-23T21:00:02Z","title":"Topological Zero-Energy Modes in Gapless Commensurate Aubry-Andr\\'e-Harper Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5639","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:f145b6f07a9f4afdb86d0dff7dad3f36ce119b906244d9a3073406cceead8a17","target":"record","created_at":"2026-05-18T03:26:40Z","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":"38ff52f6d92e1474cca04c5bd4e88748b4f8f3a6e540f0eababab923263a9ef1","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2013-01-23T21:00:02Z","title_canon_sha256":"7c3c52668586655056216fb4a0d90d8a52fa91e494aca10d895143b84a6d5436"},"schema_version":"1.0","source":{"id":"1301.5639","kind":"arxiv","version":2}},"canonical_sha256":"ff1668b37bab51bd63e2053c3b46f108e57789214ced794925dbdb6982669454","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff1668b37bab51bd63e2053c3b46f108e57789214ced794925dbdb6982669454","first_computed_at":"2026-05-18T03:26:40.903637Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:40.903637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lhy0rH8Fs+SMBN5J/Vi0rYaXZ1ymnxK+JzRSF6r20I7NAiWwSPeV0QVH1cx5qUnN6pcQoaUTDo3SW5z5nutYBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:40.904279Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.5639","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f145b6f07a9f4afdb86d0dff7dad3f36ce119b906244d9a3073406cceead8a17","sha256:c2f2d3e221c5ddf1ef813613803675fadd84f93293652448a1120cfddf0ac16f"],"state_sha256":"6cfc81ad835f88cdff68f5e1d7067f3083d547d58fe28a395b78ca8725927402"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hg7xUF8MsLyvuHv8GYNHGhEcqhbXPnr8X3g06nkM3dQtas6hVtVz4MVWMmg9Pcf67NyOwmFXzjGLQXUk2X89Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T05:17:38.438116Z","bundle_sha256":"651a71764643ef34da71fe96cccb674f7a67d1cb316498c68fbce403951cc5b5"}}