{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:RUS6XB4F65NHNKMFGPZD4ANV6M","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":"01eac5b42fd395c09f3b201492a8d0e0f578d12323e2e37c07cb05cca357634e","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math-ph","submitted_at":"2008-03-16T02:13:32Z","title_canon_sha256":"87afdfc599c3ac0b128eaa112d7b00e0b3fa11e1636a0c3fee073eb748d4a8ff"},"schema_version":"1.0","source":{"id":"0803.2330","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0803.2330","created_at":"2026-05-18T04:34:10Z"},{"alias_kind":"arxiv_version","alias_value":"0803.2330v4","created_at":"2026-05-18T04:34:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.2330","created_at":"2026-05-18T04:34:10Z"},{"alias_kind":"pith_short_12","alias_value":"RUS6XB4F65NH","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"RUS6XB4F65NHNKMF","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"RUS6XB4F","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:cb76d7dd1c9d1eb6f78f23f6d895c10131e0d8e45ab99f73092e849cf5d2844e","target":"graph","created_at":"2026-05-18T04:34:10Z","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":"In this paper we proposed a proposition: for any nonconservative classical mechanical system and any initial condition, there exists a conservative one; the two systems share one and only one common phase curve; the Hamiltonian of the conservative system is the sum of the total energy of the nonconservative system on the aforementioned phase curve and a constant depending on the initial condition. Hence, this approach entails substituting an infinite number of conservative systems for a dissipative mechanical system corresponding to varied initial conditions. One key way we use to demonstrate ","authors_text":"Tianshu Luo, Yimu Guo","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math-ph","submitted_at":"2008-03-16T02:13:32Z","title":"A Sort of Relation among a Dissipative Mechanical System and Conservative Ones"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.2330","kind":"arxiv","version":4},"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":"sha256:882f17773ff6587dafee1aaa25846454bc021b2a79b890d94f5ed8f00609b99e","target":"record","created_at":"2026-05-18T04:34:10Z","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":"01eac5b42fd395c09f3b201492a8d0e0f578d12323e2e37c07cb05cca357634e","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math-ph","submitted_at":"2008-03-16T02:13:32Z","title_canon_sha256":"87afdfc599c3ac0b128eaa112d7b00e0b3fa11e1636a0c3fee073eb748d4a8ff"},"schema_version":"1.0","source":{"id":"0803.2330","kind":"arxiv","version":4}},"canonical_sha256":"8d25eb8785f75a76a98533f23e01b5f33e5a8c7c09b4f6925a1b1e73b627590b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d25eb8785f75a76a98533f23e01b5f33e5a8c7c09b4f6925a1b1e73b627590b","first_computed_at":"2026-05-18T04:34:10.258971Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:10.258971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F2isZ6q8wlPOozvpRrbgWdfUAeSVzHLK0rugMbb6whTYoKljLfbow882MMGsBJ4vel7dCPAsjOsHErOK9IGBDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:10.259446Z","signed_message":"canonical_sha256_bytes"},"source_id":"0803.2330","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:882f17773ff6587dafee1aaa25846454bc021b2a79b890d94f5ed8f00609b99e","sha256:cb76d7dd1c9d1eb6f78f23f6d895c10131e0d8e45ab99f73092e849cf5d2844e"],"state_sha256":"1d2ebeadd47d4fb4173b65c6f0e0dac649314e101b8fcd6ce9e710d39dc3e59b"}