{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:VXODBUIGI5B63DJ2CHJ245ASDZ","short_pith_number":"pith:VXODBUIG","canonical_record":{"source":{"id":"2011.09401","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-11-18T16:58:38Z","cross_cats_sorted":[],"title_canon_sha256":"f555893ee3700f06871c1f5309c485f01d4249852f04cb0b3dba846438d14b4a","abstract_canon_sha256":"c21a9be23c32fac8d78b621dfffbb987022bf3f4e7cc22d5ab23308f6b18ea5f"},"schema_version":"1.0"},"canonical_sha256":"addc30d1064743ed8d3a11d3ae74121e7a2a3a88a804876ce3a185e4c078650c","source":{"kind":"arxiv","id":"2011.09401","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.09401","created_at":"2026-07-05T01:52:43Z"},{"alias_kind":"arxiv_version","alias_value":"2011.09401v1","created_at":"2026-07-05T01:52:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.09401","created_at":"2026-07-05T01:52:43Z"},{"alias_kind":"pith_short_12","alias_value":"VXODBUIGI5B6","created_at":"2026-07-05T01:52:43Z"},{"alias_kind":"pith_short_16","alias_value":"VXODBUIGI5B63DJ2","created_at":"2026-07-05T01:52:43Z"},{"alias_kind":"pith_short_8","alias_value":"VXODBUIG","created_at":"2026-07-05T01:52:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:VXODBUIGI5B63DJ2CHJ245ASDZ","target":"record","payload":{"canonical_record":{"source":{"id":"2011.09401","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-11-18T16:58:38Z","cross_cats_sorted":[],"title_canon_sha256":"f555893ee3700f06871c1f5309c485f01d4249852f04cb0b3dba846438d14b4a","abstract_canon_sha256":"c21a9be23c32fac8d78b621dfffbb987022bf3f4e7cc22d5ab23308f6b18ea5f"},"schema_version":"1.0"},"canonical_sha256":"addc30d1064743ed8d3a11d3ae74121e7a2a3a88a804876ce3a185e4c078650c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:52:43.637533Z","signature_b64":"8XuCvWtl3upFtJyxQdhYhvgis+HCwEXvYxVBzqRvdDC3avBfKS3HCiJnr+hDaeh++y9x9FclqO51f07fxLrxBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"addc30d1064743ed8d3a11d3ae74121e7a2a3a88a804876ce3a185e4c078650c","last_reissued_at":"2026-07-05T01:52:43.637111Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:52:43.637111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2011.09401","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":"2026-07-05T01:52:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HgogN0i05f3TaOW4yGLef8byNOlYj56x0qA9lblD6FrKHCndZeR5UzMEaE8WePNuPwBNm6g7OoM+E1q7bXVtAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T06:26:56.870707Z"},"content_sha256":"79e47511cc5f1588ef3263cf3f67d36d5aa20372cb26d75798a6377d21be9edc","schema_version":"1.0","event_id":"sha256:79e47511cc5f1588ef3263cf3f67d36d5aa20372cb26d75798a6377d21be9edc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:VXODBUIGI5B63DJ2CHJ245ASDZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bounds on the largest prime factor of a negative discriminant with one class per genus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"John Armitage","submitted_at":"2020-11-18T16:58:38Z","abstract_excerpt":"It was conjectured by Gauss that any negative discriminant with at least 32 genera has at least two classes of binary quadratic forms in each genus. We prove that such a discriminant cannot have a particularly large prime factor, by an argument similar to that of Baker's solution to Gauss' class number one problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.09401","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2011.09401/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:52:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SLSmQqBQzprGGMBkj9WtU4CMj1UCFs77tpbqNWtUpNqEV7WdiseA8pGx5cw3IjzdpID+4XJ+Djy8ZWMnMHQ+Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T06:26:56.871269Z"},"content_sha256":"41746bebc2acd079ea0a7ce175a8be535c3c1cb0564b4169089285ac64c1369d","schema_version":"1.0","event_id":"sha256:41746bebc2acd079ea0a7ce175a8be535c3c1cb0564b4169089285ac64c1369d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VXODBUIGI5B63DJ2CHJ245ASDZ/bundle.json","state_url":"https://pith.science/pith/VXODBUIGI5B63DJ2CHJ245ASDZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VXODBUIGI5B63DJ2CHJ245ASDZ/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":"2026-08-14T06:26:56Z","links":{"resolver":"https://pith.science/pith/VXODBUIGI5B63DJ2CHJ245ASDZ","bundle":"https://pith.science/pith/VXODBUIGI5B63DJ2CHJ245ASDZ/bundle.json","state":"https://pith.science/pith/VXODBUIGI5B63DJ2CHJ245ASDZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VXODBUIGI5B63DJ2CHJ245ASDZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:VXODBUIGI5B63DJ2CHJ245ASDZ","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":"c21a9be23c32fac8d78b621dfffbb987022bf3f4e7cc22d5ab23308f6b18ea5f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-11-18T16:58:38Z","title_canon_sha256":"f555893ee3700f06871c1f5309c485f01d4249852f04cb0b3dba846438d14b4a"},"schema_version":"1.0","source":{"id":"2011.09401","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.09401","created_at":"2026-07-05T01:52:43Z"},{"alias_kind":"arxiv_version","alias_value":"2011.09401v1","created_at":"2026-07-05T01:52:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.09401","created_at":"2026-07-05T01:52:43Z"},{"alias_kind":"pith_short_12","alias_value":"VXODBUIGI5B6","created_at":"2026-07-05T01:52:43Z"},{"alias_kind":"pith_short_16","alias_value":"VXODBUIGI5B63DJ2","created_at":"2026-07-05T01:52:43Z"},{"alias_kind":"pith_short_8","alias_value":"VXODBUIG","created_at":"2026-07-05T01:52:43Z"}],"graph_snapshots":[{"event_id":"sha256:41746bebc2acd079ea0a7ce175a8be535c3c1cb0564b4169089285ac64c1369d","target":"graph","created_at":"2026-07-05T01:52:43Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2011.09401/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It was conjectured by Gauss that any negative discriminant with at least 32 genera has at least two classes of binary quadratic forms in each genus. We prove that such a discriminant cannot have a particularly large prime factor, by an argument similar to that of Baker's solution to Gauss' class number one problem.","authors_text":"John Armitage","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-11-18T16:58:38Z","title":"Bounds on the largest prime factor of a negative discriminant with one class per genus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.09401","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":"sha256:79e47511cc5f1588ef3263cf3f67d36d5aa20372cb26d75798a6377d21be9edc","target":"record","created_at":"2026-07-05T01:52:43Z","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":"c21a9be23c32fac8d78b621dfffbb987022bf3f4e7cc22d5ab23308f6b18ea5f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-11-18T16:58:38Z","title_canon_sha256":"f555893ee3700f06871c1f5309c485f01d4249852f04cb0b3dba846438d14b4a"},"schema_version":"1.0","source":{"id":"2011.09401","kind":"arxiv","version":1}},"canonical_sha256":"addc30d1064743ed8d3a11d3ae74121e7a2a3a88a804876ce3a185e4c078650c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"addc30d1064743ed8d3a11d3ae74121e7a2a3a88a804876ce3a185e4c078650c","first_computed_at":"2026-07-05T01:52:43.637111Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:52:43.637111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8XuCvWtl3upFtJyxQdhYhvgis+HCwEXvYxVBzqRvdDC3avBfKS3HCiJnr+hDaeh++y9x9FclqO51f07fxLrxBw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:52:43.637533Z","signed_message":"canonical_sha256_bytes"},"source_id":"2011.09401","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79e47511cc5f1588ef3263cf3f67d36d5aa20372cb26d75798a6377d21be9edc","sha256:41746bebc2acd079ea0a7ce175a8be535c3c1cb0564b4169089285ac64c1369d"],"state_sha256":"08eaad6afad827c4ce053671d3e74d5ddc5143599b8f0eac5183401b04f3d72c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eZ+hx5GJ+pzrL/LBXlbkF/sPNishhiGMiQ6snoMerLTVh2DV/6rpurinFnao7rVgDv0j+Kr1e1eZHKQxx5xRBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T06:26:56.875282Z","bundle_sha256":"6f9fcba159954fa8923aaee85557b383c69552ca5d65dcfbb3d16ed8a104e107"}}