{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:MHT55JO2ZHLYAIKJCOEHXKL3SK","short_pith_number":"pith:MHT55JO2","canonical_record":{"source":{"id":"math/0607072","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2006-07-04T08:06:20Z","cross_cats_sorted":[],"title_canon_sha256":"2e96066347e3829ae62410b70674fcf202505d4998f13dc88557e120b1e17bea","abstract_canon_sha256":"79b895bf9306e890ccdf526de14215db9db510da8e66489bedd78da804da41f7"},"schema_version":"1.0"},"canonical_sha256":"61e7dea5dac9d780214913887ba97b92a38461b1fe7696abd305deecdfa021fb","source":{"kind":"arxiv","id":"math/0607072","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0607072","created_at":"2026-05-18T01:27:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0607072v3","created_at":"2026-05-18T01:27:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0607072","created_at":"2026-05-18T01:27:29Z"},{"alias_kind":"pith_short_12","alias_value":"MHT55JO2ZHLY","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"MHT55JO2ZHLYAIKJ","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"MHT55JO2","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:MHT55JO2ZHLYAIKJCOEHXKL3SK","target":"record","payload":{"canonical_record":{"source":{"id":"math/0607072","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2006-07-04T08:06:20Z","cross_cats_sorted":[],"title_canon_sha256":"2e96066347e3829ae62410b70674fcf202505d4998f13dc88557e120b1e17bea","abstract_canon_sha256":"79b895bf9306e890ccdf526de14215db9db510da8e66489bedd78da804da41f7"},"schema_version":"1.0"},"canonical_sha256":"61e7dea5dac9d780214913887ba97b92a38461b1fe7696abd305deecdfa021fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:29.186203Z","signature_b64":"CobyXrAJdoxmjllKMgxmVxtYAKuEfEquoa5s0K3Hy9B4KvULgytqq84/Uoz0XTodXxM9O46QVGeDp4Ah6BUHDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61e7dea5dac9d780214913887ba97b92a38461b1fe7696abd305deecdfa021fb","last_reissued_at":"2026-05-18T01:27:29.185601Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:29.185601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0607072","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:27:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L3pTRN9dsTS1jWcUIFjl2lQfgqHe1iw9imH3rR11NHDde41RtbY361ccyr/f2Qu5ACcrYznjMpffVgpqyUEECA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:13:56.896162Z"},"content_sha256":"4f2dd6f618d920f500d22d50b8873305acaece5d26bfe60d5462826f46001f28","schema_version":"1.0","event_id":"sha256:4f2dd6f618d920f500d22d50b8873305acaece5d26bfe60d5462826f46001f28"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:MHT55JO2ZHLYAIKJCOEHXKL3SK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on the paper by Bugeaud and Laurent \"Minoration effective de la distance p-adique entre puissances de nombres alg\\'ebriques\"","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Tomohiro Yamada","submitted_at":"2006-07-04T08:06:20Z","abstract_excerpt":"We shall make a slight improvement to a result of p-adic logarithms which gives a nontrivial upper bound for the exponent of p dividing the Fermat quotient x^{p-1}-1."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0607072","kind":"arxiv","version":3},"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":"2026-05-18T01:27:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Fx3s2gqdQKewtaIgAuxi6uy4bXVHxiA5io9eI0oHOcqTo3Wwa27xn2eNFL+62CqAtNVZJWgSootqlZcqdBcCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:13:56.896705Z"},"content_sha256":"4c42fd2ad174819675ab1c8c9aeab8366324c6f649f573d6d4aaaa0afce01f92","schema_version":"1.0","event_id":"sha256:4c42fd2ad174819675ab1c8c9aeab8366324c6f649f573d6d4aaaa0afce01f92"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MHT55JO2ZHLYAIKJCOEHXKL3SK/bundle.json","state_url":"https://pith.science/pith/MHT55JO2ZHLYAIKJCOEHXKL3SK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MHT55JO2ZHLYAIKJCOEHXKL3SK/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":"2026-05-28T22:13:56Z","links":{"resolver":"https://pith.science/pith/MHT55JO2ZHLYAIKJCOEHXKL3SK","bundle":"https://pith.science/pith/MHT55JO2ZHLYAIKJCOEHXKL3SK/bundle.json","state":"https://pith.science/pith/MHT55JO2ZHLYAIKJCOEHXKL3SK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MHT55JO2ZHLYAIKJCOEHXKL3SK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:MHT55JO2ZHLYAIKJCOEHXKL3SK","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":"79b895bf9306e890ccdf526de14215db9db510da8e66489bedd78da804da41f7","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2006-07-04T08:06:20Z","title_canon_sha256":"2e96066347e3829ae62410b70674fcf202505d4998f13dc88557e120b1e17bea"},"schema_version":"1.0","source":{"id":"math/0607072","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0607072","created_at":"2026-05-18T01:27:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0607072v3","created_at":"2026-05-18T01:27:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0607072","created_at":"2026-05-18T01:27:29Z"},{"alias_kind":"pith_short_12","alias_value":"MHT55JO2ZHLY","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"MHT55JO2ZHLYAIKJ","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"MHT55JO2","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:4c42fd2ad174819675ab1c8c9aeab8366324c6f649f573d6d4aaaa0afce01f92","target":"graph","created_at":"2026-05-18T01:27:29Z","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":"We shall make a slight improvement to a result of p-adic logarithms which gives a nontrivial upper bound for the exponent of p dividing the Fermat quotient x^{p-1}-1.","authors_text":"Tomohiro Yamada","cross_cats":[],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2006-07-04T08:06:20Z","title":"A note on the paper by Bugeaud and Laurent \"Minoration effective de la distance p-adique entre puissances de nombres alg\\'ebriques\""},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0607072","kind":"arxiv","version":3},"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":"sha256:4f2dd6f618d920f500d22d50b8873305acaece5d26bfe60d5462826f46001f28","target":"record","created_at":"2026-05-18T01:27:29Z","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":"79b895bf9306e890ccdf526de14215db9db510da8e66489bedd78da804da41f7","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2006-07-04T08:06:20Z","title_canon_sha256":"2e96066347e3829ae62410b70674fcf202505d4998f13dc88557e120b1e17bea"},"schema_version":"1.0","source":{"id":"math/0607072","kind":"arxiv","version":3}},"canonical_sha256":"61e7dea5dac9d780214913887ba97b92a38461b1fe7696abd305deecdfa021fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61e7dea5dac9d780214913887ba97b92a38461b1fe7696abd305deecdfa021fb","first_computed_at":"2026-05-18T01:27:29.185601Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:29.185601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CobyXrAJdoxmjllKMgxmVxtYAKuEfEquoa5s0K3Hy9B4KvULgytqq84/Uoz0XTodXxM9O46QVGeDp4Ah6BUHDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:29.186203Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0607072","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f2dd6f618d920f500d22d50b8873305acaece5d26bfe60d5462826f46001f28","sha256:4c42fd2ad174819675ab1c8c9aeab8366324c6f649f573d6d4aaaa0afce01f92"],"state_sha256":"365b1208365f1ecc00a1a15f3b62c792290fa0452a7097a4bc57bb38c29aa2c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+srNqJOb1btaGFHLTqjWIEdwfgvLAujQAhp4r+5Wv/MdhlTUUQDpaR4VOG2LwBjfA3p6B+Y5MRN3IGJxlYOIBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T22:13:56.899943Z","bundle_sha256":"321c44a600edd24388650c3fe3bed14a8cccbcfb02a0bcfdfdf61b93871e978d"}}