{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GUVRRJX5PJJCC2GDUJDSWU4ECE","short_pith_number":"pith:GUVRRJX5","canonical_record":{"source":{"id":"1609.06986","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-22T13:54:51Z","cross_cats_sorted":[],"title_canon_sha256":"40f86dda8985eefeaeecdf6714945147485d72db9a7a784d91ccd159884c86db","abstract_canon_sha256":"b0c933f5d428f3d13ae91e1a6b3e79df2af862184000c46b494470d1bb0ff828"},"schema_version":"1.0"},"canonical_sha256":"352b18a6fd7a522168c3a2472b5384113fa9ab2a80765aab8131fb7655a18a88","source":{"kind":"arxiv","id":"1609.06986","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.06986","created_at":"2026-05-18T00:36:09Z"},{"alias_kind":"arxiv_version","alias_value":"1609.06986v1","created_at":"2026-05-18T00:36:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06986","created_at":"2026-05-18T00:36:09Z"},{"alias_kind":"pith_short_12","alias_value":"GUVRRJX5PJJC","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GUVRRJX5PJJCC2GD","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GUVRRJX5","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GUVRRJX5PJJCC2GDUJDSWU4ECE","target":"record","payload":{"canonical_record":{"source":{"id":"1609.06986","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-22T13:54:51Z","cross_cats_sorted":[],"title_canon_sha256":"40f86dda8985eefeaeecdf6714945147485d72db9a7a784d91ccd159884c86db","abstract_canon_sha256":"b0c933f5d428f3d13ae91e1a6b3e79df2af862184000c46b494470d1bb0ff828"},"schema_version":"1.0"},"canonical_sha256":"352b18a6fd7a522168c3a2472b5384113fa9ab2a80765aab8131fb7655a18a88","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:09.574445Z","signature_b64":"Uh+YsJV8WA6Ugd+fYOiOnSZSbg3nL8mEeer3Dm+GLgUbw4+Dng0xrNF4D2FQ3K6f/jhcvFsuLd18t9vaRQb4AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"352b18a6fd7a522168c3a2472b5384113fa9ab2a80765aab8131fb7655a18a88","last_reissued_at":"2026-05-18T00:36:09.573889Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:09.573889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.06986","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":"2026-05-18T00:36:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k62f391emfo9SPrZsiI7xHHj72K3Ng+dlA3EMXSSMkLox6Egw5iRE5QPeWJLYOr/ZvCNmqD0NuvL0DLZJJdMAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:33:33.851971Z"},"content_sha256":"be5c83eb994985335d75d69a90a774bbc11082093125c4cf91d02c86893c9abf","schema_version":"1.0","event_id":"sha256:be5c83eb994985335d75d69a90a774bbc11082093125c4cf91d02c86893c9abf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GUVRRJX5PJJCC2GDUJDSWU4ECE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"More on Diophantine sextuples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrej Dujella, Matija Kazalicki","submitted_at":"2016-09-22T13:54:51Z","abstract_excerpt":"A rational Diophantine m-tuple is a set of m nonzero rationals such that the product of any two of them increased by 1 is a perfect square. The first rational Diophantine quadruple was found by Diophantus, while Euler proved that there are infinitely many rational Diophantine quintuples. In 1999, Gibbs found the first example of a rational Diophantine sextuple, and Dujella, Kazalicki, Mikic and Szikszai recently proved that there exist infinitely many rational Diophantine sextuples.\n  In this paper, generalizing the work of Piezas, we describe a method for generating new parametric formulas fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06986","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":"2026-05-18T00:36:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uxgGCR1jOsGBkbQ83LCRevxh32AIMj1BiFT/6Ix6rblA6KokuDzEVNq4x1A8xI1ooAs2xQ5cZAqiacVsVYIRAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:33:33.852331Z"},"content_sha256":"3c772d25551bf068851e57d2afbd7a0b51ea039e4e6d26e43e3c1fb72752afa3","schema_version":"1.0","event_id":"sha256:3c772d25551bf068851e57d2afbd7a0b51ea039e4e6d26e43e3c1fb72752afa3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GUVRRJX5PJJCC2GDUJDSWU4ECE/bundle.json","state_url":"https://pith.science/pith/GUVRRJX5PJJCC2GDUJDSWU4ECE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GUVRRJX5PJJCC2GDUJDSWU4ECE/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":"2026-06-02T17:33:33Z","links":{"resolver":"https://pith.science/pith/GUVRRJX5PJJCC2GDUJDSWU4ECE","bundle":"https://pith.science/pith/GUVRRJX5PJJCC2GDUJDSWU4ECE/bundle.json","state":"https://pith.science/pith/GUVRRJX5PJJCC2GDUJDSWU4ECE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GUVRRJX5PJJCC2GDUJDSWU4ECE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GUVRRJX5PJJCC2GDUJDSWU4ECE","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":"b0c933f5d428f3d13ae91e1a6b3e79df2af862184000c46b494470d1bb0ff828","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-22T13:54:51Z","title_canon_sha256":"40f86dda8985eefeaeecdf6714945147485d72db9a7a784d91ccd159884c86db"},"schema_version":"1.0","source":{"id":"1609.06986","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.06986","created_at":"2026-05-18T00:36:09Z"},{"alias_kind":"arxiv_version","alias_value":"1609.06986v1","created_at":"2026-05-18T00:36:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06986","created_at":"2026-05-18T00:36:09Z"},{"alias_kind":"pith_short_12","alias_value":"GUVRRJX5PJJC","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GUVRRJX5PJJCC2GD","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GUVRRJX5","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:3c772d25551bf068851e57d2afbd7a0b51ea039e4e6d26e43e3c1fb72752afa3","target":"graph","created_at":"2026-05-18T00:36:09Z","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":"A rational Diophantine m-tuple is a set of m nonzero rationals such that the product of any two of them increased by 1 is a perfect square. The first rational Diophantine quadruple was found by Diophantus, while Euler proved that there are infinitely many rational Diophantine quintuples. In 1999, Gibbs found the first example of a rational Diophantine sextuple, and Dujella, Kazalicki, Mikic and Szikszai recently proved that there exist infinitely many rational Diophantine sextuples.\n  In this paper, generalizing the work of Piezas, we describe a method for generating new parametric formulas fo","authors_text":"Andrej Dujella, Matija Kazalicki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-22T13:54:51Z","title":"More on Diophantine sextuples"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06986","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:be5c83eb994985335d75d69a90a774bbc11082093125c4cf91d02c86893c9abf","target":"record","created_at":"2026-05-18T00:36:09Z","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":"b0c933f5d428f3d13ae91e1a6b3e79df2af862184000c46b494470d1bb0ff828","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-22T13:54:51Z","title_canon_sha256":"40f86dda8985eefeaeecdf6714945147485d72db9a7a784d91ccd159884c86db"},"schema_version":"1.0","source":{"id":"1609.06986","kind":"arxiv","version":1}},"canonical_sha256":"352b18a6fd7a522168c3a2472b5384113fa9ab2a80765aab8131fb7655a18a88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"352b18a6fd7a522168c3a2472b5384113fa9ab2a80765aab8131fb7655a18a88","first_computed_at":"2026-05-18T00:36:09.573889Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:09.573889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Uh+YsJV8WA6Ugd+fYOiOnSZSbg3nL8mEeer3Dm+GLgUbw4+Dng0xrNF4D2FQ3K6f/jhcvFsuLd18t9vaRQb4AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:09.574445Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.06986","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be5c83eb994985335d75d69a90a774bbc11082093125c4cf91d02c86893c9abf","sha256:3c772d25551bf068851e57d2afbd7a0b51ea039e4e6d26e43e3c1fb72752afa3"],"state_sha256":"7b70334b5d9b022b3ee7baebf2e2db3d650d4251b64e8e78680f4d624c496e26"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HAWEbHx7mdZbt0iu63k3X4ZZ8MjYgFELexn0nnyIRrF6TtV++CfZW+s/ZRGWg2dR6ViCQ0fB57FirbkSGvR8BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T17:33:33.854398Z","bundle_sha256":"c9435d47d8eaf73c06ae6074919eb91352ec3bfcea5fe5b497ae8e8751b450c5"}}