{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:JJU6OUSPVGPBI7IXN5LTBNOTLY","short_pith_number":"pith:JJU6OUSP","canonical_record":{"source":{"id":"1801.09487","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-01-29T13:06:16Z","cross_cats_sorted":["cond-mat.mes-hall","math.MP"],"title_canon_sha256":"fde9fe8cb1d847058f333b3a210d3df84340d18cdf866917092145aa143ef6a9","abstract_canon_sha256":"2346aa1d03fb56f18b67d985ca59b0f77f1f65766c719f48a6c88d819901d2d9"},"schema_version":"1.0"},"canonical_sha256":"4a69e7524fa99e147d176f5730b5d35e26218281d615ec6049a423039d5baf7a","source":{"kind":"arxiv","id":"1801.09487","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09487","created_at":"2026-05-18T00:04:49Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09487v1","created_at":"2026-05-18T00:04:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09487","created_at":"2026-05-18T00:04:49Z"},{"alias_kind":"pith_short_12","alias_value":"JJU6OUSPVGPB","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JJU6OUSPVGPBI7IX","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JJU6OUSP","created_at":"2026-05-18T12:32:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:JJU6OUSPVGPBI7IXN5LTBNOTLY","target":"record","payload":{"canonical_record":{"source":{"id":"1801.09487","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-01-29T13:06:16Z","cross_cats_sorted":["cond-mat.mes-hall","math.MP"],"title_canon_sha256":"fde9fe8cb1d847058f333b3a210d3df84340d18cdf866917092145aa143ef6a9","abstract_canon_sha256":"2346aa1d03fb56f18b67d985ca59b0f77f1f65766c719f48a6c88d819901d2d9"},"schema_version":"1.0"},"canonical_sha256":"4a69e7524fa99e147d176f5730b5d35e26218281d615ec6049a423039d5baf7a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:49.848607Z","signature_b64":"I8iCcb/A8B5Vgwfj7eQsIZtOcLnk+Rh8p70hyblbgWrW0YXPgmFkcQBcvB55AtcfhlK0Bg4rfqwAPOWPu+WFAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a69e7524fa99e147d176f5730b5d35e26218281d615ec6049a423039d5baf7a","last_reissued_at":"2026-05-18T00:04:49.847881Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:49.847881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.09487","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":"2026-05-18T00:04:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GdG2uO5z83YSugWYiGo5HsPqTt6yf8DJk/K1YY+IskOBVQfJ42dVC7InUWvMq+f/RHMXoucJuvqRSj7MAki0BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:10:39.372626Z"},"content_sha256":"aa0375aa267b2e8e5aad6823cb9b4e7605f8847d3d5acabb46a8b109894839cb","schema_version":"1.0","event_id":"sha256:aa0375aa267b2e8e5aad6823cb9b4e7605f8847d3d5acabb46a8b109894839cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:JJU6OUSPVGPBI7IXN5LTBNOTLY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Bulk-Edge Correspondence for Disordered Chiral Chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","math.MP"],"primary_cat":"math-ph","authors_text":"Gian Michele Graf, Jacob Shapiro","submitted_at":"2018-01-29T13:06:16Z","abstract_excerpt":"We study one-dimensional insulators obeying a chiral symmetry in the single-particle picture. The Fermi level is assumed to lie in a mobility gap. Topological indices are defined for infinite (bulk) or half-infinite (edge) systems, and it is shown that for a given Hamiltonian with nearest neighbor hopping the two indices are equal. We also give a new formulation of the index in terms of the Lyapunov exponents of the zero energy Schr\\\"odinger equation, which illustrates the conditions for a topological phase transition occurring in the mobility gap regime."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09487","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":"2026-05-18T00:04:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z4n4wpM0GFjfeZiUxxrNwH6tRWeJCbPSuGscnsHNH2nULk46B/vNPUcscvnZhgiAm2Jd3Qa4i3/WJteBMsHDCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:10:39.373367Z"},"content_sha256":"a07a48792f4f9e6eb328b64bb63dc486dd426977d4713000c11d303454098c35","schema_version":"1.0","event_id":"sha256:a07a48792f4f9e6eb328b64bb63dc486dd426977d4713000c11d303454098c35"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JJU6OUSPVGPBI7IXN5LTBNOTLY/bundle.json","state_url":"https://pith.science/pith/JJU6OUSPVGPBI7IXN5LTBNOTLY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JJU6OUSPVGPBI7IXN5LTBNOTLY/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":"2026-06-09T06:10:39Z","links":{"resolver":"https://pith.science/pith/JJU6OUSPVGPBI7IXN5LTBNOTLY","bundle":"https://pith.science/pith/JJU6OUSPVGPBI7IXN5LTBNOTLY/bundle.json","state":"https://pith.science/pith/JJU6OUSPVGPBI7IXN5LTBNOTLY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JJU6OUSPVGPBI7IXN5LTBNOTLY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:JJU6OUSPVGPBI7IXN5LTBNOTLY","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":"2346aa1d03fb56f18b67d985ca59b0f77f1f65766c719f48a6c88d819901d2d9","cross_cats_sorted":["cond-mat.mes-hall","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-01-29T13:06:16Z","title_canon_sha256":"fde9fe8cb1d847058f333b3a210d3df84340d18cdf866917092145aa143ef6a9"},"schema_version":"1.0","source":{"id":"1801.09487","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09487","created_at":"2026-05-18T00:04:49Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09487v1","created_at":"2026-05-18T00:04:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09487","created_at":"2026-05-18T00:04:49Z"},{"alias_kind":"pith_short_12","alias_value":"JJU6OUSPVGPB","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JJU6OUSPVGPBI7IX","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JJU6OUSP","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:a07a48792f4f9e6eb328b64bb63dc486dd426977d4713000c11d303454098c35","target":"graph","created_at":"2026-05-18T00:04:49Z","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 study one-dimensional insulators obeying a chiral symmetry in the single-particle picture. The Fermi level is assumed to lie in a mobility gap. Topological indices are defined for infinite (bulk) or half-infinite (edge) systems, and it is shown that for a given Hamiltonian with nearest neighbor hopping the two indices are equal. We also give a new formulation of the index in terms of the Lyapunov exponents of the zero energy Schr\\\"odinger equation, which illustrates the conditions for a topological phase transition occurring in the mobility gap regime.","authors_text":"Gian Michele Graf, Jacob Shapiro","cross_cats":["cond-mat.mes-hall","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-01-29T13:06:16Z","title":"The Bulk-Edge Correspondence for Disordered Chiral Chains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09487","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:aa0375aa267b2e8e5aad6823cb9b4e7605f8847d3d5acabb46a8b109894839cb","target":"record","created_at":"2026-05-18T00:04:49Z","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":"2346aa1d03fb56f18b67d985ca59b0f77f1f65766c719f48a6c88d819901d2d9","cross_cats_sorted":["cond-mat.mes-hall","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-01-29T13:06:16Z","title_canon_sha256":"fde9fe8cb1d847058f333b3a210d3df84340d18cdf866917092145aa143ef6a9"},"schema_version":"1.0","source":{"id":"1801.09487","kind":"arxiv","version":1}},"canonical_sha256":"4a69e7524fa99e147d176f5730b5d35e26218281d615ec6049a423039d5baf7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a69e7524fa99e147d176f5730b5d35e26218281d615ec6049a423039d5baf7a","first_computed_at":"2026-05-18T00:04:49.847881Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:49.847881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I8iCcb/A8B5Vgwfj7eQsIZtOcLnk+Rh8p70hyblbgWrW0YXPgmFkcQBcvB55AtcfhlK0Bg4rfqwAPOWPu+WFAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:49.848607Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.09487","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa0375aa267b2e8e5aad6823cb9b4e7605f8847d3d5acabb46a8b109894839cb","sha256:a07a48792f4f9e6eb328b64bb63dc486dd426977d4713000c11d303454098c35"],"state_sha256":"eb6fd44feb6c41630fcd96c3d20c3b60c7525ecc62537cb34f85dba35bf03d88"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HGDt9Jaz3W7qI4XbqV1lxZXEa9ihgmxD/4sM++hHXjhEj9IbVsrZLovkI9bbj4ofDaDfpl8EKKtSYDVd+D1uDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T06:10:39.376614Z","bundle_sha256":"a5f74e0469d590cd9198a8653679093ffb6611fc7e07601987a84a2c4751fda9"}}