{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:CU7ASWJW62RVGL5D6RDQUDC55J","short_pith_number":"pith:CU7ASWJW","canonical_record":{"source":{"id":"1202.3476","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-02-15T23:57:39Z","cross_cats_sorted":[],"title_canon_sha256":"e61766e129f5c77e12946ef56b3c13c84f4487335c550ecf102ed8317ab943b3","abstract_canon_sha256":"becbc85b7c4e570b072cc04f808839e94c41fd65990e93d4c3df16011f5130d7"},"schema_version":"1.0"},"canonical_sha256":"153e095936f6a3532fa3f4470a0c5dea418c5da387eec8767273bdb977d8e3d2","source":{"kind":"arxiv","id":"1202.3476","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3476","created_at":"2026-05-18T04:01:03Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3476v1","created_at":"2026-05-18T04:01:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3476","created_at":"2026-05-18T04:01:03Z"},{"alias_kind":"pith_short_12","alias_value":"CU7ASWJW62RV","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CU7ASWJW62RVGL5D","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CU7ASWJW","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:CU7ASWJW62RVGL5D6RDQUDC55J","target":"record","payload":{"canonical_record":{"source":{"id":"1202.3476","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-02-15T23:57:39Z","cross_cats_sorted":[],"title_canon_sha256":"e61766e129f5c77e12946ef56b3c13c84f4487335c550ecf102ed8317ab943b3","abstract_canon_sha256":"becbc85b7c4e570b072cc04f808839e94c41fd65990e93d4c3df16011f5130d7"},"schema_version":"1.0"},"canonical_sha256":"153e095936f6a3532fa3f4470a0c5dea418c5da387eec8767273bdb977d8e3d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:01:03.524995Z","signature_b64":"ZncP73Q+qx9BbEChae5RIIFFijrsmlM1I2fP8z97n1IkzT/jkk/MCiOjV4i19vZ5Uu7bJrpGMtL+48LLrdeQDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"153e095936f6a3532fa3f4470a0c5dea418c5da387eec8767273bdb977d8e3d2","last_reissued_at":"2026-05-18T04:01:03.524390Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:01:03.524390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.3476","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":"2026-05-18T04:01:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lBAWecMljPwD0NROiRD2PFnHHupafpEax1zjFPUN11EWfEhhI85o9QYOxmEGebJyOWA1jPCryMjizEJGs1ORDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:12:10.627579Z"},"content_sha256":"2634e43a7d9b905d340d18ed357edbe3e546a2165937f3b2618a6cd9b86e7c3a","schema_version":"1.0","event_id":"sha256:2634e43a7d9b905d340d18ed357edbe3e546a2165937f3b2618a6cd9b86e7c3a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:CU7ASWJW62RVGL5D6RDQUDC55J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Covariant hydrodynamic Lyapunov modes and strong stochasticity threshold in Hamiltonian lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Diego Paz\\'o, Juan M. L\\'opez, M. Romero-Bastida","submitted_at":"2012-02-15T23:57:39Z","abstract_excerpt":"We scrutinize the reliability of covariant and Gram-Schmidt Lyapunov vectors for capturing hydrodynamic Lyapunov modes (HLMs) in one-dimensional Hamiltonian lattices. We show that,in contrast with previous claims, HLMs do exist for any energy density, so that strong chaos is not essential for the appearance of genuine (covariant) HLMs. In contrast, Gram-Schmidt Lyapunov vectors lead to misleading results concerning the existence of HLMs in the case of weak chaos."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3476","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":"2026-05-18T04:01:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4YbEgeOjNX5rLa0upvi35z2hV+CU2fpuc+kSb/X+7VqvltD70kpzSmTf5u9lspEZCLLN0gGkuqYsRv7xiodrDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:12:10.627920Z"},"content_sha256":"e741ab36e3a67816250bd86c840163089a888c07d4b51282ca05240c44456ee1","schema_version":"1.0","event_id":"sha256:e741ab36e3a67816250bd86c840163089a888c07d4b51282ca05240c44456ee1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CU7ASWJW62RVGL5D6RDQUDC55J/bundle.json","state_url":"https://pith.science/pith/CU7ASWJW62RVGL5D6RDQUDC55J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CU7ASWJW62RVGL5D6RDQUDC55J/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":"2026-06-23T14:12:10Z","links":{"resolver":"https://pith.science/pith/CU7ASWJW62RVGL5D6RDQUDC55J","bundle":"https://pith.science/pith/CU7ASWJW62RVGL5D6RDQUDC55J/bundle.json","state":"https://pith.science/pith/CU7ASWJW62RVGL5D6RDQUDC55J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CU7ASWJW62RVGL5D6RDQUDC55J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CU7ASWJW62RVGL5D6RDQUDC55J","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":"becbc85b7c4e570b072cc04f808839e94c41fd65990e93d4c3df16011f5130d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-02-15T23:57:39Z","title_canon_sha256":"e61766e129f5c77e12946ef56b3c13c84f4487335c550ecf102ed8317ab943b3"},"schema_version":"1.0","source":{"id":"1202.3476","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3476","created_at":"2026-05-18T04:01:03Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3476v1","created_at":"2026-05-18T04:01:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3476","created_at":"2026-05-18T04:01:03Z"},{"alias_kind":"pith_short_12","alias_value":"CU7ASWJW62RV","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CU7ASWJW62RVGL5D","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CU7ASWJW","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:e741ab36e3a67816250bd86c840163089a888c07d4b51282ca05240c44456ee1","target":"graph","created_at":"2026-05-18T04:01:03Z","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 scrutinize the reliability of covariant and Gram-Schmidt Lyapunov vectors for capturing hydrodynamic Lyapunov modes (HLMs) in one-dimensional Hamiltonian lattices. We show that,in contrast with previous claims, HLMs do exist for any energy density, so that strong chaos is not essential for the appearance of genuine (covariant) HLMs. In contrast, Gram-Schmidt Lyapunov vectors lead to misleading results concerning the existence of HLMs in the case of weak chaos.","authors_text":"Diego Paz\\'o, Juan M. L\\'opez, M. Romero-Bastida","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-02-15T23:57:39Z","title":"Covariant hydrodynamic Lyapunov modes and strong stochasticity threshold in Hamiltonian lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3476","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":"sha256:2634e43a7d9b905d340d18ed357edbe3e546a2165937f3b2618a6cd9b86e7c3a","target":"record","created_at":"2026-05-18T04:01:03Z","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":"becbc85b7c4e570b072cc04f808839e94c41fd65990e93d4c3df16011f5130d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-02-15T23:57:39Z","title_canon_sha256":"e61766e129f5c77e12946ef56b3c13c84f4487335c550ecf102ed8317ab943b3"},"schema_version":"1.0","source":{"id":"1202.3476","kind":"arxiv","version":1}},"canonical_sha256":"153e095936f6a3532fa3f4470a0c5dea418c5da387eec8767273bdb977d8e3d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"153e095936f6a3532fa3f4470a0c5dea418c5da387eec8767273bdb977d8e3d2","first_computed_at":"2026-05-18T04:01:03.524390Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:03.524390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZncP73Q+qx9BbEChae5RIIFFijrsmlM1I2fP8z97n1IkzT/jkk/MCiOjV4i19vZ5Uu7bJrpGMtL+48LLrdeQDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:03.524995Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.3476","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2634e43a7d9b905d340d18ed357edbe3e546a2165937f3b2618a6cd9b86e7c3a","sha256:e741ab36e3a67816250bd86c840163089a888c07d4b51282ca05240c44456ee1"],"state_sha256":"fb99368770d3a6546ac6800926895c45b83db341a568b7c822e0d03fab4a73ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0UZx2XubmsbEmkDoLriYg04dqS/8JAcZeAqH1+RGmzkrsWCfbrC5wUrezpkoTJNp8rzP9rON+SDe7qQSJ4QJCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T14:12:10.629797Z","bundle_sha256":"b519d4c282aee2697c7d3b0d4a45b8f01e23d79736c617db53b7f05b1bd58a25"}}