{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:I7JVKPYJR27O5T7PTU62MU66LW","short_pith_number":"pith:I7JVKPYJ","canonical_record":{"source":{"id":"1007.2709","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math-ph","submitted_at":"2010-07-16T07:32:20Z","cross_cats_sorted":["math.MP","math.SG","physics.comp-ph"],"title_canon_sha256":"3350a9cef5f5473939dcae094135db5bffe0494d0ce7d881c6a50ceb23a03db3","abstract_canon_sha256":"41e6c1cc68bfe1c1a8da8de89cfb7cf6aad28e705b1c4b2a4e4bcc23fcef98f1"},"schema_version":"1.0"},"canonical_sha256":"47d3553f098ebeeecfef9d3da653de5db9f542641dae887f295d64b28391036b","source":{"kind":"arxiv","id":"1007.2709","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.2709","created_at":"2026-05-18T04:42:35Z"},{"alias_kind":"arxiv_version","alias_value":"1007.2709v1","created_at":"2026-05-18T04:42:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.2709","created_at":"2026-05-18T04:42:35Z"},{"alias_kind":"pith_short_12","alias_value":"I7JVKPYJR27O","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"I7JVKPYJR27O5T7P","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"I7JVKPYJ","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:I7JVKPYJR27O5T7PTU62MU66LW","target":"record","payload":{"canonical_record":{"source":{"id":"1007.2709","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math-ph","submitted_at":"2010-07-16T07:32:20Z","cross_cats_sorted":["math.MP","math.SG","physics.comp-ph"],"title_canon_sha256":"3350a9cef5f5473939dcae094135db5bffe0494d0ce7d881c6a50ceb23a03db3","abstract_canon_sha256":"41e6c1cc68bfe1c1a8da8de89cfb7cf6aad28e705b1c4b2a4e4bcc23fcef98f1"},"schema_version":"1.0"},"canonical_sha256":"47d3553f098ebeeecfef9d3da653de5db9f542641dae887f295d64b28391036b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:35.129124Z","signature_b64":"HL3H55fNNNHqmo2b+iAZgAvj+/GQU42vjSVEg7j/ta10AOm7TWIBFVDAokMbCBZqZnxnHzLPBQwjDzXbEeEoCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47d3553f098ebeeecfef9d3da653de5db9f542641dae887f295d64b28391036b","last_reissued_at":"2026-05-18T04:42:35.128715Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:35.128715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.2709","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":"2026-05-18T04:42:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P4lHcbGyG0W2wEfqyqY8yJGY6oQc8JMbsYSGcCtgP1odW/DPGrPj2AWu2cTpte6Xoze9MKriemxef7/9fJFPDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:22:38.481676Z"},"content_sha256":"167437571c7c805111266d142c2a7bc792d79bae90455876115e992dd154bce7","schema_version":"1.0","event_id":"sha256:167437571c7c805111266d142c2a7bc792d79bae90455876115e992dd154bce7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:I7JVKPYJR27O5T7PTU62MU66LW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Examination of the Time-Centered Difference Scheme for Dissipative Mechanical Systems from a Hamiltonian Perspective","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.MP","math.SG","physics.comp-ph"],"primary_cat":"math-ph","authors_text":"Tianshu Luo, Yimu Guo","submitted_at":"2010-07-16T07:32:20Z","abstract_excerpt":"On this paper, we have proposed an approach to observe the time-centered difference scheme for dissipative mechanical systems from a Hamiltonian perspective and to introduce the idea of symplectic algorithm to dissipative systems. The dissipative mechanical systems discussed in this paper are finite dimensional.This approach is based upon 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.2709","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":"2026-05-18T04:42:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"umGn7bMEV7qNTgZ++jYp05VZCVBJTIDQ4yaTZ5+KEBmTdeix0Zu79SF1Y0Naj8Ps1Dqkv8PsGG+coxO/NirICA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:22:38.482018Z"},"content_sha256":"1669df1430bb23f77976f7b513ecbcb2caa08f232061e2e4de253ed90a4209b8","schema_version":"1.0","event_id":"sha256:1669df1430bb23f77976f7b513ecbcb2caa08f232061e2e4de253ed90a4209b8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I7JVKPYJR27O5T7PTU62MU66LW/bundle.json","state_url":"https://pith.science/pith/I7JVKPYJR27O5T7PTU62MU66LW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I7JVKPYJR27O5T7PTU62MU66LW/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":"2026-06-25T11:22:38Z","links":{"resolver":"https://pith.science/pith/I7JVKPYJR27O5T7PTU62MU66LW","bundle":"https://pith.science/pith/I7JVKPYJR27O5T7PTU62MU66LW/bundle.json","state":"https://pith.science/pith/I7JVKPYJR27O5T7PTU62MU66LW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I7JVKPYJR27O5T7PTU62MU66LW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:I7JVKPYJR27O5T7PTU62MU66LW","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":"41e6c1cc68bfe1c1a8da8de89cfb7cf6aad28e705b1c4b2a4e4bcc23fcef98f1","cross_cats_sorted":["math.MP","math.SG","physics.comp-ph"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math-ph","submitted_at":"2010-07-16T07:32:20Z","title_canon_sha256":"3350a9cef5f5473939dcae094135db5bffe0494d0ce7d881c6a50ceb23a03db3"},"schema_version":"1.0","source":{"id":"1007.2709","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.2709","created_at":"2026-05-18T04:42:35Z"},{"alias_kind":"arxiv_version","alias_value":"1007.2709v1","created_at":"2026-05-18T04:42:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.2709","created_at":"2026-05-18T04:42:35Z"},{"alias_kind":"pith_short_12","alias_value":"I7JVKPYJR27O","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"I7JVKPYJR27O5T7P","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"I7JVKPYJ","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:1669df1430bb23f77976f7b513ecbcb2caa08f232061e2e4de253ed90a4209b8","target":"graph","created_at":"2026-05-18T04:42:35Z","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":"On this paper, we have proposed an approach to observe the time-centered difference scheme for dissipative mechanical systems from a Hamiltonian perspective and to introduce the idea of symplectic algorithm to dissipative systems. The dissipative mechanical systems discussed in this paper are finite dimensional.This approach is based upon 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","authors_text":"Tianshu Luo, Yimu Guo","cross_cats":["math.MP","math.SG","physics.comp-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math-ph","submitted_at":"2010-07-16T07:32:20Z","title":"An Examination of the Time-Centered Difference Scheme for Dissipative Mechanical Systems from a Hamiltonian Perspective"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.2709","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":"sha256:167437571c7c805111266d142c2a7bc792d79bae90455876115e992dd154bce7","target":"record","created_at":"2026-05-18T04:42:35Z","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":"41e6c1cc68bfe1c1a8da8de89cfb7cf6aad28e705b1c4b2a4e4bcc23fcef98f1","cross_cats_sorted":["math.MP","math.SG","physics.comp-ph"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math-ph","submitted_at":"2010-07-16T07:32:20Z","title_canon_sha256":"3350a9cef5f5473939dcae094135db5bffe0494d0ce7d881c6a50ceb23a03db3"},"schema_version":"1.0","source":{"id":"1007.2709","kind":"arxiv","version":1}},"canonical_sha256":"47d3553f098ebeeecfef9d3da653de5db9f542641dae887f295d64b28391036b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47d3553f098ebeeecfef9d3da653de5db9f542641dae887f295d64b28391036b","first_computed_at":"2026-05-18T04:42:35.128715Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:35.128715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HL3H55fNNNHqmo2b+iAZgAvj+/GQU42vjSVEg7j/ta10AOm7TWIBFVDAokMbCBZqZnxnHzLPBQwjDzXbEeEoCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:35.129124Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.2709","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:167437571c7c805111266d142c2a7bc792d79bae90455876115e992dd154bce7","sha256:1669df1430bb23f77976f7b513ecbcb2caa08f232061e2e4de253ed90a4209b8"],"state_sha256":"8a8fa0a3a7c3b33046e8080ca90f6d343c7ff67746c85c8c609c38c86ae28e3b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/6RNQj6bvVgdBFOrvL+iwbJmRtVwEDHfSshWaBQCKtkWYcFAXObo0SH4rsSZzzcjNgLOWtKXOyq+UefsKi79CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T11:22:38.483883Z","bundle_sha256":"75e783b17b6fb5a8bf17c1e17ae3e9672c5363152f4ff392d5e2ac5d4d8df4e7"}}