{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:IZIAIFOVK4NI7O2JUVBHDUEBMB","short_pith_number":"pith:IZIAIFOV","canonical_record":{"source":{"id":"1111.5951","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-11-25T11:30:00Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"fd7006bb20f17a1567a16cd8d74a8dfa61b12afac26333cac187999df057339d","abstract_canon_sha256":"8bc517522eebe89071e602c52c88b5b24e42922070828009caafd758984bb4aa"},"schema_version":"1.0"},"canonical_sha256":"46500415d5571a8fbb49a54271d08160459d191728bce3017121bbc529f67f9e","source":{"kind":"arxiv","id":"1111.5951","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.5951","created_at":"2026-05-18T03:55:12Z"},{"alias_kind":"arxiv_version","alias_value":"1111.5951v2","created_at":"2026-05-18T03:55:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5951","created_at":"2026-05-18T03:55:12Z"},{"alias_kind":"pith_short_12","alias_value":"IZIAIFOVK4NI","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"IZIAIFOVK4NI7O2J","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"IZIAIFOV","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:IZIAIFOVK4NI7O2JUVBHDUEBMB","target":"record","payload":{"canonical_record":{"source":{"id":"1111.5951","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-11-25T11:30:00Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"fd7006bb20f17a1567a16cd8d74a8dfa61b12afac26333cac187999df057339d","abstract_canon_sha256":"8bc517522eebe89071e602c52c88b5b24e42922070828009caafd758984bb4aa"},"schema_version":"1.0"},"canonical_sha256":"46500415d5571a8fbb49a54271d08160459d191728bce3017121bbc529f67f9e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:12.187685Z","signature_b64":"oh+SZR+uI/uid7dp0aNoYgi1lyzqJ2YDew20rSXKVeEIjzmjh4yjkzT3NtQ8naWXS5piAuiFmRJN3RsqZRr3CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46500415d5571a8fbb49a54271d08160459d191728bce3017121bbc529f67f9e","last_reissued_at":"2026-05-18T03:55:12.187117Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:12.187117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.5951","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":"2026-05-18T03:55:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GGXb30418RWK4JvIwtBECrlo6LtTLKAk0ram/lQSxiVPs5RKLEk8HlrYEZh1OfwUXfI+I5r7yogjWny4sFP3BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:25:27.978966Z"},"content_sha256":"58d39b2a362798b6dc20dc62abd6fc94838d221be921c364babd07467a1a4f55","schema_version":"1.0","event_id":"sha256:58d39b2a362798b6dc20dc62abd6fc94838d221be921c364babd07467a1a4f55"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:IZIAIFOVK4NI7O2JUVBHDUEBMB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Orthogonal versus covariant Lyapunov vectors for rough hard disk systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"nlin.CD","authors_text":"Hadrien Bosetti, Harald A. Posch","submitted_at":"2011-11-25T11:30:00Z","abstract_excerpt":"The Oseledec splitting of the tangent space into covariant subspaces for a hyperbolic dynamical system is numerically accessible by computing the full set of covariant Lyapunov vectors. In this paper, the covariant Lyapunov vectors, the orthogonal Gram-Schmidt vectors, and the corresponding local (time-dependent) Lyapunov exponents, are analyzed for a planar system of rough hard disks (RHDS). These results are compared to respective results for a smooth-hard-disk system (SHDS). We find that the rotation of the disks deeply affects the Oseledec splitting and the structure of the tangent space. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5951","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":"2026-05-18T03:55:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t0fV8M40nOAZgB1vZ0vRak26qY8RGr45tYQBKn506XFWaRBLvFBTDUZ/yEM4BxlnfVf+CkVypkzvSHhu7Q8UBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:25:27.979467Z"},"content_sha256":"5a2f0484fd637802655735c078806abdee6dd532e2c4f4e3c6856194b96bbcea","schema_version":"1.0","event_id":"sha256:5a2f0484fd637802655735c078806abdee6dd532e2c4f4e3c6856194b96bbcea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IZIAIFOVK4NI7O2JUVBHDUEBMB/bundle.json","state_url":"https://pith.science/pith/IZIAIFOVK4NI7O2JUVBHDUEBMB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IZIAIFOVK4NI7O2JUVBHDUEBMB/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":"2026-05-30T21:25:27Z","links":{"resolver":"https://pith.science/pith/IZIAIFOVK4NI7O2JUVBHDUEBMB","bundle":"https://pith.science/pith/IZIAIFOVK4NI7O2JUVBHDUEBMB/bundle.json","state":"https://pith.science/pith/IZIAIFOVK4NI7O2JUVBHDUEBMB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IZIAIFOVK4NI7O2JUVBHDUEBMB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:IZIAIFOVK4NI7O2JUVBHDUEBMB","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":"8bc517522eebe89071e602c52c88b5b24e42922070828009caafd758984bb4aa","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-11-25T11:30:00Z","title_canon_sha256":"fd7006bb20f17a1567a16cd8d74a8dfa61b12afac26333cac187999df057339d"},"schema_version":"1.0","source":{"id":"1111.5951","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.5951","created_at":"2026-05-18T03:55:12Z"},{"alias_kind":"arxiv_version","alias_value":"1111.5951v2","created_at":"2026-05-18T03:55:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5951","created_at":"2026-05-18T03:55:12Z"},{"alias_kind":"pith_short_12","alias_value":"IZIAIFOVK4NI","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"IZIAIFOVK4NI7O2J","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"IZIAIFOV","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:5a2f0484fd637802655735c078806abdee6dd532e2c4f4e3c6856194b96bbcea","target":"graph","created_at":"2026-05-18T03:55:12Z","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 Oseledec splitting of the tangent space into covariant subspaces for a hyperbolic dynamical system is numerically accessible by computing the full set of covariant Lyapunov vectors. In this paper, the covariant Lyapunov vectors, the orthogonal Gram-Schmidt vectors, and the corresponding local (time-dependent) Lyapunov exponents, are analyzed for a planar system of rough hard disks (RHDS). These results are compared to respective results for a smooth-hard-disk system (SHDS). We find that the rotation of the disks deeply affects the Oseledec splitting and the structure of the tangent space. ","authors_text":"Hadrien Bosetti, Harald A. Posch","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-11-25T11:30:00Z","title":"Orthogonal versus covariant Lyapunov vectors for rough hard disk systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5951","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":"sha256:58d39b2a362798b6dc20dc62abd6fc94838d221be921c364babd07467a1a4f55","target":"record","created_at":"2026-05-18T03:55:12Z","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":"8bc517522eebe89071e602c52c88b5b24e42922070828009caafd758984bb4aa","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2011-11-25T11:30:00Z","title_canon_sha256":"fd7006bb20f17a1567a16cd8d74a8dfa61b12afac26333cac187999df057339d"},"schema_version":"1.0","source":{"id":"1111.5951","kind":"arxiv","version":2}},"canonical_sha256":"46500415d5571a8fbb49a54271d08160459d191728bce3017121bbc529f67f9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46500415d5571a8fbb49a54271d08160459d191728bce3017121bbc529f67f9e","first_computed_at":"2026-05-18T03:55:12.187117Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:12.187117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oh+SZR+uI/uid7dp0aNoYgi1lyzqJ2YDew20rSXKVeEIjzmjh4yjkzT3NtQ8naWXS5piAuiFmRJN3RsqZRr3CA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:12.187685Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.5951","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58d39b2a362798b6dc20dc62abd6fc94838d221be921c364babd07467a1a4f55","sha256:5a2f0484fd637802655735c078806abdee6dd532e2c4f4e3c6856194b96bbcea"],"state_sha256":"4609403356f47cb2eb6fa0d0b96391916161c062e09e7839d604e659237c6376"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Azi7UF5pJlw4xMABSZBV9h6gglKX9153uaqrsBfMUfgVwyM1VRTQ3mXN18CbNpC4qBDRL1Ql90Hz77c/KMZ9Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T21:25:27.982453Z","bundle_sha256":"e3e640701183cafc245a8a6baa91e235904650498a66e121d404fc401d27b9b6"}}