{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:CQBWO4LAJCOG7NMZXY6GZTEKYT","short_pith_number":"pith:CQBWO4LA","canonical_record":{"source":{"id":"1903.04606","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-03-11T21:06:09Z","cross_cats_sorted":[],"title_canon_sha256":"48de0a0ad65cb3775ff1763f6c358d861fccc5ef9e5d8af3c181f829e198eceb","abstract_canon_sha256":"861088c9d5a616a1a0dba75773319d6f7fe3bc37d5d28e21a61aeab0cc6c9f02"},"schema_version":"1.0"},"canonical_sha256":"1403677160489c6fb599be3c6ccc8ac4d93ebee41646b444c96f3f302421b299","source":{"kind":"arxiv","id":"1903.04606","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.04606","created_at":"2026-05-17T23:51:29Z"},{"alias_kind":"arxiv_version","alias_value":"1903.04606v1","created_at":"2026-05-17T23:51:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.04606","created_at":"2026-05-17T23:51:29Z"},{"alias_kind":"pith_short_12","alias_value":"CQBWO4LAJCOG","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"CQBWO4LAJCOG7NMZ","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"CQBWO4LA","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:CQBWO4LAJCOG7NMZXY6GZTEKYT","target":"record","payload":{"canonical_record":{"source":{"id":"1903.04606","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-03-11T21:06:09Z","cross_cats_sorted":[],"title_canon_sha256":"48de0a0ad65cb3775ff1763f6c358d861fccc5ef9e5d8af3c181f829e198eceb","abstract_canon_sha256":"861088c9d5a616a1a0dba75773319d6f7fe3bc37d5d28e21a61aeab0cc6c9f02"},"schema_version":"1.0"},"canonical_sha256":"1403677160489c6fb599be3c6ccc8ac4d93ebee41646b444c96f3f302421b299","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:29.160225Z","signature_b64":"YOyejvGG8fBRB8ojENp6mAewHTdP4Oo8l61/BXUwKMEshBWkxTfnTzNO+Viwqzt0U1pAYzTjg0cui7NCZxyMCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1403677160489c6fb599be3c6ccc8ac4d93ebee41646b444c96f3f302421b299","last_reissued_at":"2026-05-17T23:51:29.159843Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:29.159843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.04606","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":"2026-05-17T23:51:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SZ6+dkgWNEJgLosVLgbTHrr/nQcdIem5NoATbThNoXLF+civ/fTeZROoDGZmnzkDKBm695IDbxqfXQIIQJucCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T06:53:00.699523Z"},"content_sha256":"c5bd0b95719b2258082e120bf924a40186c6117ae81b830ccac92f6f5a32a96f","schema_version":"1.0","event_id":"sha256:c5bd0b95719b2258082e120bf924a40186c6117ae81b830ccac92f6f5a32a96f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:CQBWO4LAJCOG7NMZXY6GZTEKYT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"So what is class number 2?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Scott T. Chapman","submitted_at":"2019-03-11T21:06:09Z","abstract_excerpt":"Using factorization properties, we give several characterizations for an algebraic number ring to have class number 2."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.04606","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":"2026-05-17T23:51:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wFq9oYf0Z+pSzsSBnxE1QATS35UVCVd6tKlMc3Hbvfz5Emv5ZPQlUHIsn+WxxEYDV4lgqgmXTqTAko4A91KKDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T06:53:00.699854Z"},"content_sha256":"158798fe09231a3dcb741883814a7eb2766455a87529e67cef4da26228a62cd2","schema_version":"1.0","event_id":"sha256:158798fe09231a3dcb741883814a7eb2766455a87529e67cef4da26228a62cd2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CQBWO4LAJCOG7NMZXY6GZTEKYT/bundle.json","state_url":"https://pith.science/pith/CQBWO4LAJCOG7NMZXY6GZTEKYT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CQBWO4LAJCOG7NMZXY6GZTEKYT/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":"2026-06-27T06:53:00Z","links":{"resolver":"https://pith.science/pith/CQBWO4LAJCOG7NMZXY6GZTEKYT","bundle":"https://pith.science/pith/CQBWO4LAJCOG7NMZXY6GZTEKYT/bundle.json","state":"https://pith.science/pith/CQBWO4LAJCOG7NMZXY6GZTEKYT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CQBWO4LAJCOG7NMZXY6GZTEKYT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:CQBWO4LAJCOG7NMZXY6GZTEKYT","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":"861088c9d5a616a1a0dba75773319d6f7fe3bc37d5d28e21a61aeab0cc6c9f02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-03-11T21:06:09Z","title_canon_sha256":"48de0a0ad65cb3775ff1763f6c358d861fccc5ef9e5d8af3c181f829e198eceb"},"schema_version":"1.0","source":{"id":"1903.04606","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.04606","created_at":"2026-05-17T23:51:29Z"},{"alias_kind":"arxiv_version","alias_value":"1903.04606v1","created_at":"2026-05-17T23:51:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.04606","created_at":"2026-05-17T23:51:29Z"},{"alias_kind":"pith_short_12","alias_value":"CQBWO4LAJCOG","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"CQBWO4LAJCOG7NMZ","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"CQBWO4LA","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:158798fe09231a3dcb741883814a7eb2766455a87529e67cef4da26228a62cd2","target":"graph","created_at":"2026-05-17T23:51:29Z","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":"Using factorization properties, we give several characterizations for an algebraic number ring to have class number 2.","authors_text":"Scott T. Chapman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-03-11T21:06:09Z","title":"So what is class number 2?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.04606","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:c5bd0b95719b2258082e120bf924a40186c6117ae81b830ccac92f6f5a32a96f","target":"record","created_at":"2026-05-17T23:51:29Z","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":"861088c9d5a616a1a0dba75773319d6f7fe3bc37d5d28e21a61aeab0cc6c9f02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-03-11T21:06:09Z","title_canon_sha256":"48de0a0ad65cb3775ff1763f6c358d861fccc5ef9e5d8af3c181f829e198eceb"},"schema_version":"1.0","source":{"id":"1903.04606","kind":"arxiv","version":1}},"canonical_sha256":"1403677160489c6fb599be3c6ccc8ac4d93ebee41646b444c96f3f302421b299","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1403677160489c6fb599be3c6ccc8ac4d93ebee41646b444c96f3f302421b299","first_computed_at":"2026-05-17T23:51:29.159843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:29.159843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YOyejvGG8fBRB8ojENp6mAewHTdP4Oo8l61/BXUwKMEshBWkxTfnTzNO+Viwqzt0U1pAYzTjg0cui7NCZxyMCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:29.160225Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.04606","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5bd0b95719b2258082e120bf924a40186c6117ae81b830ccac92f6f5a32a96f","sha256:158798fe09231a3dcb741883814a7eb2766455a87529e67cef4da26228a62cd2"],"state_sha256":"c1205799fdc6fb77214a93106666a92f02548021036ea57cfe203b6aef9e83c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M0f8uGzBGwtR+JwTGPB53Ls5t5I0TwKn4MFgZAnnbJdWXZxYRlkGuPbQ5Nb3L+iaoSwrTDEgLjny6E3/qBhaAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T06:53:00.701682Z","bundle_sha256":"5a692a5f776291a44b93cf96811d467942f6456dde7aef0bd1edb2ae59c8fae2"}}