{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:73ZJYESR6QOHNTXDALK3J42GE3","short_pith_number":"pith:73ZJYESR","schema_version":"1.0","canonical_sha256":"fef29c1251f41c76cee302d5b4f34626d8b1618d2afd2a1abf3b9d465d27eed0","source":{"kind":"arxiv","id":"1604.06663","version":1},"attestation_state":"computed","paper":{"title":"Small oscillations of the pendulum, Euler's method, and adequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.LO","math.MP"],"primary_cat":"math.HO","authors_text":"Karin U. Katz, Mikhail G. Katz, Tahl Nowik, Vladimir Kanovei","submitted_at":"2016-04-13T16:06:52Z","abstract_excerpt":"Small oscillations evolved a great deal from Klein to Robinson. We propose a concept of solution of differential equation based on Euler's method with infinitesimal mesh, with well-posedness based on a relation of adequality following Fermat and Leibniz. The result is that the period of infinitesimal oscillations is independent of their amplitude.\n  Keywords: harmonic motion; infinitesimal; pendulum; small oscillations"},"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":"1604.06663","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2016-04-13T16:06:52Z","cross_cats_sorted":["math-ph","math.LO","math.MP"],"title_canon_sha256":"f2f2f0f3adbdc48423a1cb8c0ef7c860e8c164cbc883305fddc73cee0f425ee3","abstract_canon_sha256":"04130b9f17baa464c5ce6a35c349d404a55894a4527a1eaf1d61c1e1fe2bd352"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:34.582135Z","signature_b64":"SlhQ7Zwyc9xSdkJ9pcqWbbC6lMguyRIX30uQ209TumlBiU0wV8jFPqr0XTPAfwlnD40F6iEk+Hnn2XkoXi3aAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fef29c1251f41c76cee302d5b4f34626d8b1618d2afd2a1abf3b9d465d27eed0","last_reissued_at":"2026-05-18T00:49:34.581502Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:34.581502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Small oscillations of the pendulum, Euler's method, and adequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.LO","math.MP"],"primary_cat":"math.HO","authors_text":"Karin U. Katz, Mikhail G. Katz, Tahl Nowik, Vladimir Kanovei","submitted_at":"2016-04-13T16:06:52Z","abstract_excerpt":"Small oscillations evolved a great deal from Klein to Robinson. We propose a concept of solution of differential equation based on Euler's method with infinitesimal mesh, with well-posedness based on a relation of adequality following Fermat and Leibniz. The result is that the period of infinitesimal oscillations is independent of their amplitude.\n  Keywords: harmonic motion; infinitesimal; pendulum; small oscillations"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06663","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1604.06663","created_at":"2026-05-18T00:49:34.581601+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.06663v1","created_at":"2026-05-18T00:49:34.581601+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06663","created_at":"2026-05-18T00:49:34.581601+00:00"},{"alias_kind":"pith_short_12","alias_value":"73ZJYESR6QOH","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_16","alias_value":"73ZJYESR6QOHNTXD","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_8","alias_value":"73ZJYESR","created_at":"2026-05-18T12:30:04.600751+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/73ZJYESR6QOHNTXDALK3J42GE3","json":"https://pith.science/pith/73ZJYESR6QOHNTXDALK3J42GE3.json","graph_json":"https://pith.science/api/pith-number/73ZJYESR6QOHNTXDALK3J42GE3/graph.json","events_json":"https://pith.science/api/pith-number/73ZJYESR6QOHNTXDALK3J42GE3/events.json","paper":"https://pith.science/paper/73ZJYESR"},"agent_actions":{"view_html":"https://pith.science/pith/73ZJYESR6QOHNTXDALK3J42GE3","download_json":"https://pith.science/pith/73ZJYESR6QOHNTXDALK3J42GE3.json","view_paper":"https://pith.science/paper/73ZJYESR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.06663&json=true","fetch_graph":"https://pith.science/api/pith-number/73ZJYESR6QOHNTXDALK3J42GE3/graph.json","fetch_events":"https://pith.science/api/pith-number/73ZJYESR6QOHNTXDALK3J42GE3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/73ZJYESR6QOHNTXDALK3J42GE3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/73ZJYESR6QOHNTXDALK3J42GE3/action/storage_attestation","attest_author":"https://pith.science/pith/73ZJYESR6QOHNTXDALK3J42GE3/action/author_attestation","sign_citation":"https://pith.science/pith/73ZJYESR6QOHNTXDALK3J42GE3/action/citation_signature","submit_replication":"https://pith.science/pith/73ZJYESR6QOHNTXDALK3J42GE3/action/replication_record"}},"created_at":"2026-05-18T00:49:34.581601+00:00","updated_at":"2026-05-18T00:49:34.581601+00:00"}