{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:NGIC4XLP6QOJ4O6VZRSVTYO4OV","short_pith_number":"pith:NGIC4XLP","canonical_record":{"source":{"id":"math-ph/0210030","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2002-10-15T12:49:38Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"79e50f8300733df69928410ed262b201fa5b467870e2c9813c2ad9032ffa216d","abstract_canon_sha256":"ed9c18a8c6c30994ac8ddedc99c5a62391509ec7e21d3db8324b5afcc1865cdb"},"schema_version":"1.0"},"canonical_sha256":"69902e5d6ff41c9e3bd5cc6559e1dc75474164af9b4b2e4e3b3c7313442af99e","source":{"kind":"arxiv","id":"math-ph/0210030","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0210030","created_at":"2026-07-04T16:35:11Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0210030v1","created_at":"2026-07-04T16:35:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0210030","created_at":"2026-07-04T16:35:11Z"},{"alias_kind":"pith_short_12","alias_value":"NGIC4XLP6QOJ","created_at":"2026-07-04T16:35:11Z"},{"alias_kind":"pith_short_16","alias_value":"NGIC4XLP6QOJ4O6V","created_at":"2026-07-04T16:35:11Z"},{"alias_kind":"pith_short_8","alias_value":"NGIC4XLP","created_at":"2026-07-04T16:35:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:NGIC4XLP6QOJ4O6VZRSVTYO4OV","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0210030","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2002-10-15T12:49:38Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"79e50f8300733df69928410ed262b201fa5b467870e2c9813c2ad9032ffa216d","abstract_canon_sha256":"ed9c18a8c6c30994ac8ddedc99c5a62391509ec7e21d3db8324b5afcc1865cdb"},"schema_version":"1.0"},"canonical_sha256":"69902e5d6ff41c9e3bd5cc6559e1dc75474164af9b4b2e4e3b3c7313442af99e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:35:11.806087Z","signature_b64":"gZoFYmbhkb+d2epk+yJISPAE8Jdhd2YMvKpjeGEq6OV0zRWZBxgMEY6+VckDez3csTEp5K/rqZU6G7r6jQdGAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69902e5d6ff41c9e3bd5cc6559e1dc75474164af9b4b2e4e3b3c7313442af99e","last_reissued_at":"2026-07-04T16:35:11.805654Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:35:11.805654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0210030","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":"2026-07-04T16:35:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xSKDpyp0+73Krpgc8pQKUYNLokWzUYqoAqv/KFBD+5EOXCdIUoPGp+1Q11Q52w1CCO2MVBer19K+g/EGsl42DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T19:05:50.079544Z"},"content_sha256":"009e24be260bf7c22008edfee518f6bfdc871a5b87b1401c3be59572ce50519b","schema_version":"1.0","event_id":"sha256:009e24be260bf7c22008edfee518f6bfdc871a5b87b1401c3be59572ce50519b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:NGIC4XLP6QOJ4O6VZRSVTYO4OV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The algebraic entropy of classical mechanics","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Brett Ryland, Robert I McLachlan","submitted_at":"2002-10-15T12:49:38Z","abstract_excerpt":"We describe the `Lie algebra of classical mechanics', modelled on the Lie algebra generated by kinetic and potential energy of a simple mechanical system with respect to the canonical Poisson bracket. It is a polynomially graded Lie algebra, a class we introduce. We describe these Lie algebras, give an algorithm to calculate the dimensions $c_n$ of the homogeneous subspaces of the Lie algebra of classical mechanics, and determine the value of its entropy $\\lim_{n\\to\\infty} c_n^{1/n}$. It is $1.82542377420108...$, a fundamental constant associated to classical mechanics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0210030","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math-ph/0210030/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T16:35:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nUvQMP5LxIjRSFRieVJjnMnX/NsSN38WedMBH+SN5VWS1Q9puo/DXbGXmJjxbKNTqmcagr4jBNtggoMHKhm4Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T19:05:50.080072Z"},"content_sha256":"91ed16181b3f64d5b2694d202a4c089c7a7a5b0603550468dcb50acc336ba61c","schema_version":"1.0","event_id":"sha256:91ed16181b3f64d5b2694d202a4c089c7a7a5b0603550468dcb50acc336ba61c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NGIC4XLP6QOJ4O6VZRSVTYO4OV/bundle.json","state_url":"https://pith.science/pith/NGIC4XLP6QOJ4O6VZRSVTYO4OV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NGIC4XLP6QOJ4O6VZRSVTYO4OV/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":"2026-08-04T19:05:50Z","links":{"resolver":"https://pith.science/pith/NGIC4XLP6QOJ4O6VZRSVTYO4OV","bundle":"https://pith.science/pith/NGIC4XLP6QOJ4O6VZRSVTYO4OV/bundle.json","state":"https://pith.science/pith/NGIC4XLP6QOJ4O6VZRSVTYO4OV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NGIC4XLP6QOJ4O6VZRSVTYO4OV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:NGIC4XLP6QOJ4O6VZRSVTYO4OV","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":"ed9c18a8c6c30994ac8ddedc99c5a62391509ec7e21d3db8324b5afcc1865cdb","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2002-10-15T12:49:38Z","title_canon_sha256":"79e50f8300733df69928410ed262b201fa5b467870e2c9813c2ad9032ffa216d"},"schema_version":"1.0","source":{"id":"math-ph/0210030","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0210030","created_at":"2026-07-04T16:35:11Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0210030v1","created_at":"2026-07-04T16:35:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0210030","created_at":"2026-07-04T16:35:11Z"},{"alias_kind":"pith_short_12","alias_value":"NGIC4XLP6QOJ","created_at":"2026-07-04T16:35:11Z"},{"alias_kind":"pith_short_16","alias_value":"NGIC4XLP6QOJ4O6V","created_at":"2026-07-04T16:35:11Z"},{"alias_kind":"pith_short_8","alias_value":"NGIC4XLP","created_at":"2026-07-04T16:35:11Z"}],"graph_snapshots":[{"event_id":"sha256:91ed16181b3f64d5b2694d202a4c089c7a7a5b0603550468dcb50acc336ba61c","target":"graph","created_at":"2026-07-04T16:35:11Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math-ph/0210030/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We describe the `Lie algebra of classical mechanics', modelled on the Lie algebra generated by kinetic and potential energy of a simple mechanical system with respect to the canonical Poisson bracket. It is a polynomially graded Lie algebra, a class we introduce. We describe these Lie algebras, give an algorithm to calculate the dimensions $c_n$ of the homogeneous subspaces of the Lie algebra of classical mechanics, and determine the value of its entropy $\\lim_{n\\to\\infty} c_n^{1/n}$. It is $1.82542377420108...$, a fundamental constant associated to classical mechanics.","authors_text":"Brett Ryland, Robert I McLachlan","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2002-10-15T12:49:38Z","title":"The algebraic entropy of classical mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0210030","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":"sha256:009e24be260bf7c22008edfee518f6bfdc871a5b87b1401c3be59572ce50519b","target":"record","created_at":"2026-07-04T16:35:11Z","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":"ed9c18a8c6c30994ac8ddedc99c5a62391509ec7e21d3db8324b5afcc1865cdb","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2002-10-15T12:49:38Z","title_canon_sha256":"79e50f8300733df69928410ed262b201fa5b467870e2c9813c2ad9032ffa216d"},"schema_version":"1.0","source":{"id":"math-ph/0210030","kind":"arxiv","version":1}},"canonical_sha256":"69902e5d6ff41c9e3bd5cc6559e1dc75474164af9b4b2e4e3b3c7313442af99e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69902e5d6ff41c9e3bd5cc6559e1dc75474164af9b4b2e4e3b3c7313442af99e","first_computed_at":"2026-07-04T16:35:11.805654Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:35:11.805654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gZoFYmbhkb+d2epk+yJISPAE8Jdhd2YMvKpjeGEq6OV0zRWZBxgMEY6+VckDez3csTEp5K/rqZU6G7r6jQdGAw==","signature_status":"signed_v1","signed_at":"2026-07-04T16:35:11.806087Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0210030","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:009e24be260bf7c22008edfee518f6bfdc871a5b87b1401c3be59572ce50519b","sha256:91ed16181b3f64d5b2694d202a4c089c7a7a5b0603550468dcb50acc336ba61c"],"state_sha256":"12eb661c108c234c86bec52e3d8cde0fd409cda696e2ae51582f83a4cbd5a366"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HwdPOzKbSCPSpEaca5djkMQA+ZewVWl2mHE7HdCJ49AXtHZ7++YCWY/qo/ccMJ/u8DOdjCG4jsPlhffagqUiAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T19:05:50.083907Z","bundle_sha256":"3a5b9225fd1b4f702a605025e72de2296bd6c0262e5ebaa6373b2aaac73e89c8"}}