{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:IA6DKMYBANOZ674E3F4FG2HASK","short_pith_number":"pith:IA6DKMYB","schema_version":"1.0","canonical_sha256":"403c353301035d9f7f84d9785368e092983571b8011417b8958ba663fda434ce","source":{"kind":"arxiv","id":"1207.3848","version":1},"attestation_state":"computed","paper":{"title":"On a bounded version of Holder's Theorem and an application to the permutability equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Jean-Claude Falmagne","submitted_at":"2012-07-16T23:50:17Z","abstract_excerpt":"The permutability equation G(G(x,y),z) = G(G(x,z),y) is satisfied by many scientific and geometric laws. A few examples among many are: The Lorentz-FitzGerald Contraction, Beer's Law, the Pythagorean Theorem, and the formula for computing the volume of a cylinder. We prove here a representation theorem for the permutability equation, which generalizes a well-known result. The proof is based on a bounded version of Holder's Theorem."},"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":"1207.3848","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-07-16T23:50:17Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"6a8da7d0153d5dc4f2970a21bef894252f7bdc5a213bdf42e6ad649d2381bd0c","abstract_canon_sha256":"e320323372e3cd0decea1a93c480b020a85aeb0dd1cd40422cc9cc8ff6f8442a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:49.829159Z","signature_b64":"UP+jNOEf04j9Oi2SJ9DVxxQIPHRDd/46ZH9FQdI09uP95xYTMR5BZiJcIR1uXLG3+teSA8/1H9+8OCTwVSZZCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"403c353301035d9f7f84d9785368e092983571b8011417b8958ba663fda434ce","last_reissued_at":"2026-05-18T03:50:49.828538Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:49.828538Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a bounded version of Holder's Theorem and an application to the permutability equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Jean-Claude Falmagne","submitted_at":"2012-07-16T23:50:17Z","abstract_excerpt":"The permutability equation G(G(x,y),z) = G(G(x,z),y) is satisfied by many scientific and geometric laws. A few examples among many are: The Lorentz-FitzGerald Contraction, Beer's Law, the Pythagorean Theorem, and the formula for computing the volume of a cylinder. We prove here a representation theorem for the permutability equation, which generalizes a well-known result. The proof is based on a bounded version of Holder's Theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3848","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":"1207.3848","created_at":"2026-05-18T03:50:49.828628+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.3848v1","created_at":"2026-05-18T03:50:49.828628+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3848","created_at":"2026-05-18T03:50:49.828628+00:00"},{"alias_kind":"pith_short_12","alias_value":"IA6DKMYBANOZ","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_16","alias_value":"IA6DKMYBANOZ674E","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_8","alias_value":"IA6DKMYB","created_at":"2026-05-18T12:27:09.501522+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/IA6DKMYBANOZ674E3F4FG2HASK","json":"https://pith.science/pith/IA6DKMYBANOZ674E3F4FG2HASK.json","graph_json":"https://pith.science/api/pith-number/IA6DKMYBANOZ674E3F4FG2HASK/graph.json","events_json":"https://pith.science/api/pith-number/IA6DKMYBANOZ674E3F4FG2HASK/events.json","paper":"https://pith.science/paper/IA6DKMYB"},"agent_actions":{"view_html":"https://pith.science/pith/IA6DKMYBANOZ674E3F4FG2HASK","download_json":"https://pith.science/pith/IA6DKMYBANOZ674E3F4FG2HASK.json","view_paper":"https://pith.science/paper/IA6DKMYB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.3848&json=true","fetch_graph":"https://pith.science/api/pith-number/IA6DKMYBANOZ674E3F4FG2HASK/graph.json","fetch_events":"https://pith.science/api/pith-number/IA6DKMYBANOZ674E3F4FG2HASK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IA6DKMYBANOZ674E3F4FG2HASK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IA6DKMYBANOZ674E3F4FG2HASK/action/storage_attestation","attest_author":"https://pith.science/pith/IA6DKMYBANOZ674E3F4FG2HASK/action/author_attestation","sign_citation":"https://pith.science/pith/IA6DKMYBANOZ674E3F4FG2HASK/action/citation_signature","submit_replication":"https://pith.science/pith/IA6DKMYBANOZ674E3F4FG2HASK/action/replication_record"}},"created_at":"2026-05-18T03:50:49.828628+00:00","updated_at":"2026-05-18T03:50:49.828628+00:00"}