{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:MXIA6AS4ZGI3TDDHTPRGXFXU3S","short_pith_number":"pith:MXIA6AS4","schema_version":"1.0","canonical_sha256":"65d00f025cc991b98c679be26b96f4dc9fc47b03e0e024a800b1a9b51b74283d","source":{"kind":"arxiv","id":"2607.24825","version":1},"attestation_state":"computed","paper":{"title":"The D'Alembert-Lagrange Principle and Lagrange Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.HO","authors_text":"Oleg Zubelevich","submitted_at":"2026-07-20T10:05:31Z","abstract_excerpt":"This expository article serves as a methodical guide, presenting a rigorous mathematical formulation of the D'Alembert-Lagrange principle and the derivation of the Lagrange equations for mechanical systems subject to ideal constraints. Designed for educational purposes, the paper establishes a clear geometric framework for the extended phase space, defining the space of virtual displacements and constraint reactions independently of their specific analytical representations. A central focus of this instructional text is the transition from the general equation of dynamics to the Lagrange equat"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.24825","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2026-07-20T10:05:31Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d8fb15f16a304edfd14f2dad95076fb97924f0dd9eb37f6b9db68bfe8a390e5b","abstract_canon_sha256":"3e879a372a23e36d1133539b2b79aba69639d8882c33baa29860f4b05ef15c4f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-29T00:24:46.621151Z","signature_b64":"NzW6L4HffDyiQbRE6f/ybYCOtShlIRUPqXnT+CWPv9JOAOb3JLBozhqVHLpSFH5trAsb0jVhM+G9ZJtgUcOrDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65d00f025cc991b98c679be26b96f4dc9fc47b03e0e024a800b1a9b51b74283d","last_reissued_at":"2026-07-29T00:24:46.620269Z","signature_status":"signed_v1","first_computed_at":"2026-07-29T00:24:46.620269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The D'Alembert-Lagrange Principle and Lagrange Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.HO","authors_text":"Oleg Zubelevich","submitted_at":"2026-07-20T10:05:31Z","abstract_excerpt":"This expository article serves as a methodical guide, presenting a rigorous mathematical formulation of the D'Alembert-Lagrange principle and the derivation of the Lagrange equations for mechanical systems subject to ideal constraints. Designed for educational purposes, the paper establishes a clear geometric framework for the extended phase space, defining the space of virtual displacements and constraint reactions independently of their specific analytical representations. A central focus of this instructional text is the transition from the general equation of dynamics to the Lagrange equat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24825","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/2607.24825/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.24825","created_at":"2026-07-29T00:24:46.620728+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.24825v1","created_at":"2026-07-29T00:24:46.620728+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.24825","created_at":"2026-07-29T00:24:46.620728+00:00"},{"alias_kind":"pith_short_12","alias_value":"MXIA6AS4ZGI3","created_at":"2026-07-29T00:24:46.620728+00:00"},{"alias_kind":"pith_short_16","alias_value":"MXIA6AS4ZGI3TDDH","created_at":"2026-07-29T00:24:46.620728+00:00"},{"alias_kind":"pith_short_8","alias_value":"MXIA6AS4","created_at":"2026-07-29T00:24:46.620728+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MXIA6AS4ZGI3TDDHTPRGXFXU3S","json":"https://pith.science/pith/MXIA6AS4ZGI3TDDHTPRGXFXU3S.json","graph_json":"https://pith.science/api/pith-number/MXIA6AS4ZGI3TDDHTPRGXFXU3S/graph.json","events_json":"https://pith.science/api/pith-number/MXIA6AS4ZGI3TDDHTPRGXFXU3S/events.json","paper":"https://pith.science/paper/MXIA6AS4"},"agent_actions":{"view_html":"https://pith.science/pith/MXIA6AS4ZGI3TDDHTPRGXFXU3S","download_json":"https://pith.science/pith/MXIA6AS4ZGI3TDDHTPRGXFXU3S.json","view_paper":"https://pith.science/paper/MXIA6AS4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.24825&json=true","fetch_graph":"https://pith.science/api/pith-number/MXIA6AS4ZGI3TDDHTPRGXFXU3S/graph.json","fetch_events":"https://pith.science/api/pith-number/MXIA6AS4ZGI3TDDHTPRGXFXU3S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MXIA6AS4ZGI3TDDHTPRGXFXU3S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MXIA6AS4ZGI3TDDHTPRGXFXU3S/action/storage_attestation","attest_author":"https://pith.science/pith/MXIA6AS4ZGI3TDDHTPRGXFXU3S/action/author_attestation","sign_citation":"https://pith.science/pith/MXIA6AS4ZGI3TDDHTPRGXFXU3S/action/citation_signature","submit_replication":"https://pith.science/pith/MXIA6AS4ZGI3TDDHTPRGXFXU3S/action/replication_record"}},"created_at":"2026-07-29T00:24:46.620728+00:00","updated_at":"2026-07-29T00:24:46.620728+00:00"}