{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:SLVTSWR4NB5HNJKRN42WZIBVP2","short_pith_number":"pith:SLVTSWR4","schema_version":"1.0","canonical_sha256":"92eb395a3c687a76a5516f356ca0357eaf79717fbb0c1ff052e253af403437c5","source":{"kind":"arxiv","id":"1502.03560","version":4},"attestation_state":"computed","paper":{"title":"On the multiplicative form of the Lagrangian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Kittikun Surawuttinack, Monsit Tanasittikosol, Sikarin Yoo-Kong","submitted_at":"2015-02-12T08:23:22Z","abstract_excerpt":"An alternative class of the Lagrangian called the multiplicative form is suc- cessfully derived for a system with one degree of freedom for both non-relativistic and relativistic cases. This new Lagrangian can be considered as a 1-parameter: {\\lambda} extended class from the standard additive form of the Lagrangian since both yield the same equation of motion. Remarkably, the multiplicative form of the Lagrangian could be treated as a generating function to produce an infinite hierar- chy of Lagrangians which give the same equation of motion. This nontrivial set of Lagrangians confirms that in"},"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":"1502.03560","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-02-12T08:23:22Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"030174ddba6207be10f8222062e80e3ab61f5fb8091b438efa5b2eb9f0bc2b89","abstract_canon_sha256":"4b61059bdcead0f34833945bd82850304351804c139116aa4e14c26129bd1377"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:52.426146Z","signature_b64":"JhOcj7fyoae24nKZYjAoeErOuapHkdmZO1Gfab2ECy11vq9w+FR903JGqDfgsN23ppkGCyhDN4ImJfRuOXmHAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92eb395a3c687a76a5516f356ca0357eaf79717fbb0c1ff052e253af403437c5","last_reissued_at":"2026-05-18T00:51:52.425663Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:52.425663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the multiplicative form of the Lagrangian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Kittikun Surawuttinack, Monsit Tanasittikosol, Sikarin Yoo-Kong","submitted_at":"2015-02-12T08:23:22Z","abstract_excerpt":"An alternative class of the Lagrangian called the multiplicative form is suc- cessfully derived for a system with one degree of freedom for both non-relativistic and relativistic cases. This new Lagrangian can be considered as a 1-parameter: {\\lambda} extended class from the standard additive form of the Lagrangian since both yield the same equation of motion. Remarkably, the multiplicative form of the Lagrangian could be treated as a generating function to produce an infinite hierar- chy of Lagrangians which give the same equation of motion. This nontrivial set of Lagrangians confirms that in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03560","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1502.03560","created_at":"2026-05-18T00:51:52.425745+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.03560v4","created_at":"2026-05-18T00:51:52.425745+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.03560","created_at":"2026-05-18T00:51:52.425745+00:00"},{"alias_kind":"pith_short_12","alias_value":"SLVTSWR4NB5H","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"SLVTSWR4NB5HNJKR","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"SLVTSWR4","created_at":"2026-05-18T12:29:42.218222+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/SLVTSWR4NB5HNJKRN42WZIBVP2","json":"https://pith.science/pith/SLVTSWR4NB5HNJKRN42WZIBVP2.json","graph_json":"https://pith.science/api/pith-number/SLVTSWR4NB5HNJKRN42WZIBVP2/graph.json","events_json":"https://pith.science/api/pith-number/SLVTSWR4NB5HNJKRN42WZIBVP2/events.json","paper":"https://pith.science/paper/SLVTSWR4"},"agent_actions":{"view_html":"https://pith.science/pith/SLVTSWR4NB5HNJKRN42WZIBVP2","download_json":"https://pith.science/pith/SLVTSWR4NB5HNJKRN42WZIBVP2.json","view_paper":"https://pith.science/paper/SLVTSWR4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.03560&json=true","fetch_graph":"https://pith.science/api/pith-number/SLVTSWR4NB5HNJKRN42WZIBVP2/graph.json","fetch_events":"https://pith.science/api/pith-number/SLVTSWR4NB5HNJKRN42WZIBVP2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SLVTSWR4NB5HNJKRN42WZIBVP2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SLVTSWR4NB5HNJKRN42WZIBVP2/action/storage_attestation","attest_author":"https://pith.science/pith/SLVTSWR4NB5HNJKRN42WZIBVP2/action/author_attestation","sign_citation":"https://pith.science/pith/SLVTSWR4NB5HNJKRN42WZIBVP2/action/citation_signature","submit_replication":"https://pith.science/pith/SLVTSWR4NB5HNJKRN42WZIBVP2/action/replication_record"}},"created_at":"2026-05-18T00:51:52.425745+00:00","updated_at":"2026-05-18T00:51:52.425745+00:00"}