{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ULKZVSLIZZCP5GUGGV5JCZT7RX","short_pith_number":"pith:ULKZVSLI","canonical_record":{"source":{"id":"1310.6605","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-24T13:19:03Z","cross_cats_sorted":[],"title_canon_sha256":"a633f5af026600305c113f4bd9dd766b46fe73d5f705fdd490f2e9c4a91ba6d4","abstract_canon_sha256":"a1a7eb145c5055d9bdf04a50c53a135c341a703e437abbf129b0504a17f486a8"},"schema_version":"1.0"},"canonical_sha256":"a2d59ac968ce44fe9a86357a91667f8ddf5f44940e576f4e5d003df8c39f2c97","source":{"kind":"arxiv","id":"1310.6605","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.6605","created_at":"2026-05-18T03:09:08Z"},{"alias_kind":"arxiv_version","alias_value":"1310.6605v1","created_at":"2026-05-18T03:09:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6605","created_at":"2026-05-18T03:09:08Z"},{"alias_kind":"pith_short_12","alias_value":"ULKZVSLIZZCP","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"ULKZVSLIZZCP5GUG","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"ULKZVSLI","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ULKZVSLIZZCP5GUGGV5JCZT7RX","target":"record","payload":{"canonical_record":{"source":{"id":"1310.6605","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-24T13:19:03Z","cross_cats_sorted":[],"title_canon_sha256":"a633f5af026600305c113f4bd9dd766b46fe73d5f705fdd490f2e9c4a91ba6d4","abstract_canon_sha256":"a1a7eb145c5055d9bdf04a50c53a135c341a703e437abbf129b0504a17f486a8"},"schema_version":"1.0"},"canonical_sha256":"a2d59ac968ce44fe9a86357a91667f8ddf5f44940e576f4e5d003df8c39f2c97","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:08.963579Z","signature_b64":"cTp3RHbGrBNMpeuJK5O+95Qgu52YqJ4VpdAku/gig//jw13hs0WjanlKLzZ769H6JOmRF5lU6PhEpMpNMDxuBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2d59ac968ce44fe9a86357a91667f8ddf5f44940e576f4e5d003df8c39f2c97","last_reissued_at":"2026-05-18T03:09:08.962673Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:08.962673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.6605","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":"2026-05-18T03:09:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pycvxfqSdS+3bQU6er2exfjblWsAn0ASKHugqr0V9aBIKZdNiPlFieBj3a9eC/LAKsBvZie3S46hD2X7ZMckAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:13:32.978977Z"},"content_sha256":"44505c3bdba460bdfb25f20a48de087fe003eec514a96a550d642b89cce92d95","schema_version":"1.0","event_id":"sha256:44505c3bdba460bdfb25f20a48de087fe003eec514a96a550d642b89cce92d95"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ULKZVSLIZZCP5GUGGV5JCZT7RX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Euler, Goldbach, and \"Fermat's Theorem\"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Franz Lemmermeyer","submitted_at":"2013-10-24T13:19:03Z","abstract_excerpt":"While preparing the correspondence between Leonhard Euler and Christian Goldbach for publication, Martin Mattmueller asked whether the lemma given in the postscript of Euler's letter dated July 26, 1749, was enough for completing the proof of Fermat's Four Squares Theorem. In this article we will show that Euler's result can in fact be used for proving this result via induction."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6605","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":"2026-05-18T03:09:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bJHANT5pe0d8rHINi7xEo13z6K0Ib0QuLnaGhNWC5r2jOHHei2J0MygYpJzaSyL9Ke+kZek0fYkzfs6tZHQ0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:13:32.979715Z"},"content_sha256":"01740e1beedb8e34e07e9605d95957162c7df69ab217eb95d4408a029fae906a","schema_version":"1.0","event_id":"sha256:01740e1beedb8e34e07e9605d95957162c7df69ab217eb95d4408a029fae906a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ULKZVSLIZZCP5GUGGV5JCZT7RX/bundle.json","state_url":"https://pith.science/pith/ULKZVSLIZZCP5GUGGV5JCZT7RX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ULKZVSLIZZCP5GUGGV5JCZT7RX/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":"2026-06-11T21:13:32Z","links":{"resolver":"https://pith.science/pith/ULKZVSLIZZCP5GUGGV5JCZT7RX","bundle":"https://pith.science/pith/ULKZVSLIZZCP5GUGGV5JCZT7RX/bundle.json","state":"https://pith.science/pith/ULKZVSLIZZCP5GUGGV5JCZT7RX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ULKZVSLIZZCP5GUGGV5JCZT7RX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ULKZVSLIZZCP5GUGGV5JCZT7RX","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":"a1a7eb145c5055d9bdf04a50c53a135c341a703e437abbf129b0504a17f486a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-24T13:19:03Z","title_canon_sha256":"a633f5af026600305c113f4bd9dd766b46fe73d5f705fdd490f2e9c4a91ba6d4"},"schema_version":"1.0","source":{"id":"1310.6605","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.6605","created_at":"2026-05-18T03:09:08Z"},{"alias_kind":"arxiv_version","alias_value":"1310.6605v1","created_at":"2026-05-18T03:09:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6605","created_at":"2026-05-18T03:09:08Z"},{"alias_kind":"pith_short_12","alias_value":"ULKZVSLIZZCP","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"ULKZVSLIZZCP5GUG","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"ULKZVSLI","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:01740e1beedb8e34e07e9605d95957162c7df69ab217eb95d4408a029fae906a","target":"graph","created_at":"2026-05-18T03:09:08Z","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":"While preparing the correspondence between Leonhard Euler and Christian Goldbach for publication, Martin Mattmueller asked whether the lemma given in the postscript of Euler's letter dated July 26, 1749, was enough for completing the proof of Fermat's Four Squares Theorem. In this article we will show that Euler's result can in fact be used for proving this result via induction.","authors_text":"Franz Lemmermeyer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-24T13:19:03Z","title":"Euler, Goldbach, and \"Fermat's Theorem\""},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6605","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":"sha256:44505c3bdba460bdfb25f20a48de087fe003eec514a96a550d642b89cce92d95","target":"record","created_at":"2026-05-18T03:09:08Z","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":"a1a7eb145c5055d9bdf04a50c53a135c341a703e437abbf129b0504a17f486a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-24T13:19:03Z","title_canon_sha256":"a633f5af026600305c113f4bd9dd766b46fe73d5f705fdd490f2e9c4a91ba6d4"},"schema_version":"1.0","source":{"id":"1310.6605","kind":"arxiv","version":1}},"canonical_sha256":"a2d59ac968ce44fe9a86357a91667f8ddf5f44940e576f4e5d003df8c39f2c97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2d59ac968ce44fe9a86357a91667f8ddf5f44940e576f4e5d003df8c39f2c97","first_computed_at":"2026-05-18T03:09:08.962673Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:08.962673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cTp3RHbGrBNMpeuJK5O+95Qgu52YqJ4VpdAku/gig//jw13hs0WjanlKLzZ769H6JOmRF5lU6PhEpMpNMDxuBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:08.963579Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.6605","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44505c3bdba460bdfb25f20a48de087fe003eec514a96a550d642b89cce92d95","sha256:01740e1beedb8e34e07e9605d95957162c7df69ab217eb95d4408a029fae906a"],"state_sha256":"51f36fdd09e7fea6c607c7f25714e408072291dc9908c6949615034a645a8476"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QG5aTySZrYLLCyj7fFDKsvFb0Gm1mXoeMAlpZdBGjAhkTFyJl7cMkAoO+MCygkpHDSr7194dYlIUCbs1htkZBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T21:13:32.983689Z","bundle_sha256":"fe0009f4fb10efd0e545924dd2ae8201f8288bb58b709772b9520e8cf356977e"}}