{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:27WB6WK22U5V2ZB6I365YS66CE","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":"6990ed03bc1d7918051e835075268d6129b8a34b81335e7a56b0281050bb67f2","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-31T23:00:38Z","title_canon_sha256":"2adf893f31edd6780fa3db283c23a2539f467cb0c3f3b29d46b5f33e20889c46"},"schema_version":"1.0","source":{"id":"1401.0230","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0230","created_at":"2026-05-18T01:45:34Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0230v2","created_at":"2026-05-18T01:45:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0230","created_at":"2026-05-18T01:45:34Z"},{"alias_kind":"pith_short_12","alias_value":"27WB6WK22U5V","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"27WB6WK22U5V2ZB6","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"27WB6WK2","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:f9396494ab81dd159c752930d873d7d12861e0ece0f122b706c21ffd7840848d","target":"graph","created_at":"2026-05-18T01:45:34Z","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":"Using a Lagrangian mechanics approach, we construct a framework to study the dissipative properties of systems composed of two components one of which is highly lossy and the other is lossless. We have shown in our previous work that for such a composite system the modes split into two distinct classes, high-loss and low-loss, according to their dissipative behavior. A principal result of this paper is that for any such dissipative Lagrangian system, with losses accounted by a Rayleigh dissipative function, a rather universal phenomenon occurs, namely, selective overdamping: The high-loss mode","authors_text":"Aaron Welters, Alex Figotin","cross_cats":["math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-31T23:00:38Z","title":"Lagrangian Framework for Systems Composed of High-Loss and Lossless Components"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0230","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":"sha256:0f1283f0bd67c0a769f692cd197bab9c203b7fd3ee07b2eaeeb637cfc740a895","target":"record","created_at":"2026-05-18T01:45:34Z","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":"6990ed03bc1d7918051e835075268d6129b8a34b81335e7a56b0281050bb67f2","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-31T23:00:38Z","title_canon_sha256":"2adf893f31edd6780fa3db283c23a2539f467cb0c3f3b29d46b5f33e20889c46"},"schema_version":"1.0","source":{"id":"1401.0230","kind":"arxiv","version":2}},"canonical_sha256":"d7ec1f595ad53b5d643e46fddc4bde1135aff0dffb7e5935227dbb7ab03e4c52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7ec1f595ad53b5d643e46fddc4bde1135aff0dffb7e5935227dbb7ab03e4c52","first_computed_at":"2026-05-18T01:45:34.792884Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:45:34.792884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+UlaSZeeNjhN/4RObhQr6DpYJHg/J7X5i0fuqe4C+9Z7FXWbsZeGdYtz8MBVPuC61UTJ3+LVkJcNiSpSbFvQCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:45:34.793362Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0230","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f1283f0bd67c0a769f692cd197bab9c203b7fd3ee07b2eaeeb637cfc740a895","sha256:f9396494ab81dd159c752930d873d7d12861e0ece0f122b706c21ffd7840848d"],"state_sha256":"efd5005bef0380dfd98c206cd47bab5bc2a3af7e7ba4dfc99b3009be06acea06"}