{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JPH4F4JEOJEKZLUCGHR5MEXLO7","short_pith_number":"pith:JPH4F4JE","canonical_record":{"source":{"id":"1308.4901","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-22T15:33:55Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"title_canon_sha256":"4a4062ae25e35a60025fe3731eb2221691bdfffc6a240c03391932ceeb410d20","abstract_canon_sha256":"091de3c09459e105542b10dd1b053bc87c3cb3a8478362907a013ad11fc22fe9"},"schema_version":"1.0"},"canonical_sha256":"4bcfc2f1247248acae8231e3d612eb77c6f2d2db1363150ddd4f79cd3d9af9ef","source":{"kind":"arxiv","id":"1308.4901","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4901","created_at":"2026-05-18T01:48:04Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4901v2","created_at":"2026-05-18T01:48:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4901","created_at":"2026-05-18T01:48:04Z"},{"alias_kind":"pith_short_12","alias_value":"JPH4F4JEOJEK","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JPH4F4JEOJEKZLUC","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JPH4F4JE","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JPH4F4JEOJEKZLUCGHR5MEXLO7","target":"record","payload":{"canonical_record":{"source":{"id":"1308.4901","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-22T15:33:55Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"title_canon_sha256":"4a4062ae25e35a60025fe3731eb2221691bdfffc6a240c03391932ceeb410d20","abstract_canon_sha256":"091de3c09459e105542b10dd1b053bc87c3cb3a8478362907a013ad11fc22fe9"},"schema_version":"1.0"},"canonical_sha256":"4bcfc2f1247248acae8231e3d612eb77c6f2d2db1363150ddd4f79cd3d9af9ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:48:04.615476Z","signature_b64":"awyg7zT7I3fZMDgM4La1gW/sfzAAwhVGlqhboHmbIQOR5Wshr72yz+nssu3fO6YJxljy3kn3+y1YL3y1WG/cBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bcfc2f1247248acae8231e3d612eb77c6f2d2db1363150ddd4f79cd3d9af9ef","last_reissued_at":"2026-05-18T01:48:04.614906Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:48:04.614906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.4901","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":"2026-05-18T01:48:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2H4T17KZmNgnWCgiVq0PUQ1gDDGyBeTXUIOq+83ESywxwTdc2gJV58xpacvhtpj4Mac1H6A9rLiZo/+93qsBBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T08:01:02.926435Z"},"content_sha256":"f5f4f5028bb23705bea34218ebce526697eee433fce23e166140e2a40201ada3","schema_version":"1.0","event_id":"sha256:f5f4f5028bb23705bea34218ebce526697eee433fce23e166140e2a40201ada3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JPH4F4JEOJEKZLUCGHR5MEXLO7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Thermalization in harmonic particle chains with velocity flips","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"Jani Lukkarinen","submitted_at":"2013-08-22T15:33:55Z","abstract_excerpt":"We propose a new mathematical tool for the study of transport properties of models for lattice vibrations in crystalline solids. By replication of dynamical degrees of freedom, we aim at a new dynamical system where the \"local\" dynamics can be isolated and solved independently from the \"global\" evolution. The replication procedure is very generic but not unique as it depends on how the original dynamics are split between the local and global dynamics. As an explicit example, we apply the scheme to study thermalization of the pinned harmonic chain with velocity flips. We improve on the previous"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4901","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":"2026-05-18T01:48:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BRZ0GzdgU1XrzqTXWfH80yOald6D+8InWS4hoWTwIsDi6Ms1TOf5c15GKWdB62OYFHKkGUtIoAJtXcYrfVJnDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T08:01:02.926777Z"},"content_sha256":"3186f1784765a37f8a1f580462e50e4f82e7aaec0a3e81fec4c21b2e31eeea51","schema_version":"1.0","event_id":"sha256:3186f1784765a37f8a1f580462e50e4f82e7aaec0a3e81fec4c21b2e31eeea51"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JPH4F4JEOJEKZLUCGHR5MEXLO7/bundle.json","state_url":"https://pith.science/pith/JPH4F4JEOJEKZLUCGHR5MEXLO7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JPH4F4JEOJEKZLUCGHR5MEXLO7/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":"2026-06-20T08:01:02Z","links":{"resolver":"https://pith.science/pith/JPH4F4JEOJEKZLUCGHR5MEXLO7","bundle":"https://pith.science/pith/JPH4F4JEOJEKZLUCGHR5MEXLO7/bundle.json","state":"https://pith.science/pith/JPH4F4JEOJEKZLUCGHR5MEXLO7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JPH4F4JEOJEKZLUCGHR5MEXLO7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JPH4F4JEOJEKZLUCGHR5MEXLO7","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":"091de3c09459e105542b10dd1b053bc87c3cb3a8478362907a013ad11fc22fe9","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-22T15:33:55Z","title_canon_sha256":"4a4062ae25e35a60025fe3731eb2221691bdfffc6a240c03391932ceeb410d20"},"schema_version":"1.0","source":{"id":"1308.4901","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4901","created_at":"2026-05-18T01:48:04Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4901v2","created_at":"2026-05-18T01:48:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4901","created_at":"2026-05-18T01:48:04Z"},{"alias_kind":"pith_short_12","alias_value":"JPH4F4JEOJEK","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JPH4F4JEOJEKZLUC","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JPH4F4JE","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:3186f1784765a37f8a1f580462e50e4f82e7aaec0a3e81fec4c21b2e31eeea51","target":"graph","created_at":"2026-05-18T01:48:04Z","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 propose a new mathematical tool for the study of transport properties of models for lattice vibrations in crystalline solids. By replication of dynamical degrees of freedom, we aim at a new dynamical system where the \"local\" dynamics can be isolated and solved independently from the \"global\" evolution. The replication procedure is very generic but not unique as it depends on how the original dynamics are split between the local and global dynamics. As an explicit example, we apply the scheme to study thermalization of the pinned harmonic chain with velocity flips. We improve on the previous","authors_text":"Jani Lukkarinen","cross_cats":["cond-mat.stat-mech","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-22T15:33:55Z","title":"Thermalization in harmonic particle chains with velocity flips"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4901","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:f5f4f5028bb23705bea34218ebce526697eee433fce23e166140e2a40201ada3","target":"record","created_at":"2026-05-18T01:48:04Z","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":"091de3c09459e105542b10dd1b053bc87c3cb3a8478362907a013ad11fc22fe9","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-22T15:33:55Z","title_canon_sha256":"4a4062ae25e35a60025fe3731eb2221691bdfffc6a240c03391932ceeb410d20"},"schema_version":"1.0","source":{"id":"1308.4901","kind":"arxiv","version":2}},"canonical_sha256":"4bcfc2f1247248acae8231e3d612eb77c6f2d2db1363150ddd4f79cd3d9af9ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4bcfc2f1247248acae8231e3d612eb77c6f2d2db1363150ddd4f79cd3d9af9ef","first_computed_at":"2026-05-18T01:48:04.614906Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:48:04.614906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"awyg7zT7I3fZMDgM4La1gW/sfzAAwhVGlqhboHmbIQOR5Wshr72yz+nssu3fO6YJxljy3kn3+y1YL3y1WG/cBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:48:04.615476Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.4901","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5f4f5028bb23705bea34218ebce526697eee433fce23e166140e2a40201ada3","sha256:3186f1784765a37f8a1f580462e50e4f82e7aaec0a3e81fec4c21b2e31eeea51"],"state_sha256":"39270463c85d992bc39a60c253668b52d3aacca6cdc9b6a3a9918053cc57385a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qh5K8dG45/3SbX5vYqg6JkmrIBZJGIMd3rgk0HaW9unRTBJmo4ZNC50WusXhep4RkFj7vwIUl5TfXjRfgXC4AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T08:01:02.929060Z","bundle_sha256":"942a9f8639564bf3e618ca27e59d9f8455631526569798a89aafc70ce53fb312"}}