{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:IA6DKMYBANOZ674E3F4FG2HASK","short_pith_number":"pith:IA6DKMYB","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"},"canonical_sha256":"403c353301035d9f7f84d9785368e092983571b8011417b8958ba663fda434ce","source":{"kind":"arxiv","id":"1207.3848","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3848","created_at":"2026-05-18T03:50:49Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3848v1","created_at":"2026-05-18T03:50:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3848","created_at":"2026-05-18T03:50:49Z"},{"alias_kind":"pith_short_12","alias_value":"IA6DKMYBANOZ","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IA6DKMYBANOZ674E","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IA6DKMYB","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:IA6DKMYBANOZ674E3F4FG2HASK","target":"record","payload":{"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"},"canonical_sha256":"403c353301035d9f7f84d9785368e092983571b8011417b8958ba663fda434ce","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"},"source_kind":"arxiv","source_id":"1207.3848","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":"2026-05-18T03:50:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WQKBNNd1CODhInysRDJnFc2O8AGZ3wHs8RwnQoq+gyspdxuDiPam3leReGyqDVjT4XutIaUGIEAEPZO2fXuWAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T13:06:52.891071Z"},"content_sha256":"257da7fa010249147bae778c9d0253c27167441f0c478f764e76ee84c581fe91","schema_version":"1.0","event_id":"sha256:257da7fa010249147bae778c9d0253c27167441f0c478f764e76ee84c581fe91"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:IA6DKMYBANOZ674E3F4FG2HASK","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:50:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hPCOk1PF6ay8r2lgz4TVbpe+631YwJvd3TNQ6MN3X79aCaFiCO+vW96KPtRNThwQkWa7/6ft1Jh120BP1E1BAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T13:06:52.891424Z"},"content_sha256":"57d3dac8d1a4e6e853dc804faa4cfb3de41d793a7e41063bcd0d571e50d73fec","schema_version":"1.0","event_id":"sha256:57d3dac8d1a4e6e853dc804faa4cfb3de41d793a7e41063bcd0d571e50d73fec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IA6DKMYBANOZ674E3F4FG2HASK/bundle.json","state_url":"https://pith.science/pith/IA6DKMYBANOZ674E3F4FG2HASK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IA6DKMYBANOZ674E3F4FG2HASK/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":"2026-06-30T13:06:52Z","links":{"resolver":"https://pith.science/pith/IA6DKMYBANOZ674E3F4FG2HASK","bundle":"https://pith.science/pith/IA6DKMYBANOZ674E3F4FG2HASK/bundle.json","state":"https://pith.science/pith/IA6DKMYBANOZ674E3F4FG2HASK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IA6DKMYBANOZ674E3F4FG2HASK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:IA6DKMYBANOZ674E3F4FG2HASK","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":"e320323372e3cd0decea1a93c480b020a85aeb0dd1cd40422cc9cc8ff6f8442a","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-07-16T23:50:17Z","title_canon_sha256":"6a8da7d0153d5dc4f2970a21bef894252f7bdc5a213bdf42e6ad649d2381bd0c"},"schema_version":"1.0","source":{"id":"1207.3848","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3848","created_at":"2026-05-18T03:50:49Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3848v1","created_at":"2026-05-18T03:50:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3848","created_at":"2026-05-18T03:50:49Z"},{"alias_kind":"pith_short_12","alias_value":"IA6DKMYBANOZ","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IA6DKMYBANOZ674E","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IA6DKMYB","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:57d3dac8d1a4e6e853dc804faa4cfb3de41d793a7e41063bcd0d571e50d73fec","target":"graph","created_at":"2026-05-18T03:50:49Z","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"},"paper":{"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.","authors_text":"Jean-Claude Falmagne","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-07-16T23:50:17Z","title":"On a bounded version of Holder's Theorem and an application to the permutability equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3848","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":"sha256:257da7fa010249147bae778c9d0253c27167441f0c478f764e76ee84c581fe91","target":"record","created_at":"2026-05-18T03:50:49Z","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":"e320323372e3cd0decea1a93c480b020a85aeb0dd1cd40422cc9cc8ff6f8442a","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-07-16T23:50:17Z","title_canon_sha256":"6a8da7d0153d5dc4f2970a21bef894252f7bdc5a213bdf42e6ad649d2381bd0c"},"schema_version":"1.0","source":{"id":"1207.3848","kind":"arxiv","version":1}},"canonical_sha256":"403c353301035d9f7f84d9785368e092983571b8011417b8958ba663fda434ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"403c353301035d9f7f84d9785368e092983571b8011417b8958ba663fda434ce","first_computed_at":"2026-05-18T03:50:49.828538Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:49.828538Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UP+jNOEf04j9Oi2SJ9DVxxQIPHRDd/46ZH9FQdI09uP95xYTMR5BZiJcIR1uXLG3+teSA8/1H9+8OCTwVSZZCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:49.829159Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.3848","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:257da7fa010249147bae778c9d0253c27167441f0c478f764e76ee84c581fe91","sha256:57d3dac8d1a4e6e853dc804faa4cfb3de41d793a7e41063bcd0d571e50d73fec"],"state_sha256":"5666ba1b8308b72d8cfb5b125ed001cf062b14858587a41cac2a5a3b4af76bb4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hNvXeBX6nmnrB6VT/UAWVwLrLWTozLuL5al3zKLyA+sgT4HewaHJaJehL+vKeeB67RWSC7nJZN9ZoxWK6Oi5DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T13:06:52.893270Z","bundle_sha256":"c6fa1a80710046f191ae92f47c349cbced6e2fa9cdfff560be1ff505ac61e42c"}}