{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:5AG7IMOHSHUN7P5H22RLRB5XOK","short_pith_number":"pith:5AG7IMOH","schema_version":"1.0","canonical_sha256":"e80df431c791e8dfbfa7d6a2b887b772a3bb07310aff4733edb83388368653a5","source":{"kind":"arxiv","id":"1212.0322","version":3},"attestation_state":"computed","paper":{"title":"Lyapunov spectra for all symmetry classes of quasi-one-dimensional disordered systems of non-interacting Fermions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.MP"],"primary_cat":"math-ph","authors_text":"Andreas W. W. Ludwig, Hermann Schulz-Baldes, Michael Stolz","submitted_at":"2012-12-03T08:59:22Z","abstract_excerpt":"A random phase property is proposed for products of random matrices drawn from any one of the classical groups associated with the ten Cartan symmetry classes of non-interacting disordered Fermion systems. It allows to calculate the Lyapunov spectrum explicitly in a perturbative regime. These results apply to quasi-one-dimensional random Dirac operators which can be constructed as representatives for each of the ten symmetry classes. For those symmetry classes that correspond to two-dimensional topological insulators or superconductors, the random Dirac operators describing the one-dimensional"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1212.0322","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-12-03T08:59:22Z","cross_cats_sorted":["cond-mat.dis-nn","math.MP"],"title_canon_sha256":"8db9f61f5986e9b04c76b5dc0275abf4ae7267858e3c826d66982b4bcb828487","abstract_canon_sha256":"ee026c3d82d3edf8c1f1ead76ddf9760c516a73cc3f45f19bf68cc8c851a07f4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:09.614944Z","signature_b64":"YM/FTp6DcPLrqX2ha06Vi/D8v0sgKzTmyv00w3kGuvlDThBiW5eQKFhOzKtr0IvPv+VC8gcNfjrekOl8uR3kBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e80df431c791e8dfbfa7d6a2b887b772a3bb07310aff4733edb83388368653a5","last_reissued_at":"2026-05-18T01:01:09.614353Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:09.614353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lyapunov spectra for all symmetry classes of quasi-one-dimensional disordered systems of non-interacting Fermions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.MP"],"primary_cat":"math-ph","authors_text":"Andreas W. W. Ludwig, Hermann Schulz-Baldes, Michael Stolz","submitted_at":"2012-12-03T08:59:22Z","abstract_excerpt":"A random phase property is proposed for products of random matrices drawn from any one of the classical groups associated with the ten Cartan symmetry classes of non-interacting disordered Fermion systems. It allows to calculate the Lyapunov spectrum explicitly in a perturbative regime. These results apply to quasi-one-dimensional random Dirac operators which can be constructed as representatives for each of the ten symmetry classes. For those symmetry classes that correspond to two-dimensional topological insulators or superconductors, the random Dirac operators describing the one-dimensional"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0322","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1212.0322","created_at":"2026-05-18T01:01:09.614466+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.0322v3","created_at":"2026-05-18T01:01:09.614466+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0322","created_at":"2026-05-18T01:01:09.614466+00:00"},{"alias_kind":"pith_short_12","alias_value":"5AG7IMOHSHUN","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"5AG7IMOHSHUN7P5H","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"5AG7IMOH","created_at":"2026-05-18T12:26:53.410803+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5AG7IMOHSHUN7P5H22RLRB5XOK","json":"https://pith.science/pith/5AG7IMOHSHUN7P5H22RLRB5XOK.json","graph_json":"https://pith.science/api/pith-number/5AG7IMOHSHUN7P5H22RLRB5XOK/graph.json","events_json":"https://pith.science/api/pith-number/5AG7IMOHSHUN7P5H22RLRB5XOK/events.json","paper":"https://pith.science/paper/5AG7IMOH"},"agent_actions":{"view_html":"https://pith.science/pith/5AG7IMOHSHUN7P5H22RLRB5XOK","download_json":"https://pith.science/pith/5AG7IMOHSHUN7P5H22RLRB5XOK.json","view_paper":"https://pith.science/paper/5AG7IMOH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.0322&json=true","fetch_graph":"https://pith.science/api/pith-number/5AG7IMOHSHUN7P5H22RLRB5XOK/graph.json","fetch_events":"https://pith.science/api/pith-number/5AG7IMOHSHUN7P5H22RLRB5XOK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5AG7IMOHSHUN7P5H22RLRB5XOK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5AG7IMOHSHUN7P5H22RLRB5XOK/action/storage_attestation","attest_author":"https://pith.science/pith/5AG7IMOHSHUN7P5H22RLRB5XOK/action/author_attestation","sign_citation":"https://pith.science/pith/5AG7IMOHSHUN7P5H22RLRB5XOK/action/citation_signature","submit_replication":"https://pith.science/pith/5AG7IMOHSHUN7P5H22RLRB5XOK/action/replication_record"}},"created_at":"2026-05-18T01:01:09.614466+00:00","updated_at":"2026-05-18T01:01:09.614466+00:00"}