{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MOUVG2J3OZDS5LLG5ZP74YDXH2","short_pith_number":"pith:MOUVG2J3","canonical_record":{"source":{"id":"1810.06197","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-10-15T06:36:24Z","cross_cats_sorted":[],"title_canon_sha256":"38028cea8d532a1faa2658536c00bbebb5a5c55b9db5ee0b90982aaada8a5ca5","abstract_canon_sha256":"edc69a5a3d789af90a3626bd188058db2d5f00679e1548fc156109f6e14cf01c"},"schema_version":"1.0"},"canonical_sha256":"63a953693b76472ead66ee5ffe60773ebdafe46811d6def8209db7c0127ee7f4","source":{"kind":"arxiv","id":"1810.06197","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.06197","created_at":"2026-05-18T00:03:21Z"},{"alias_kind":"arxiv_version","alias_value":"1810.06197v1","created_at":"2026-05-18T00:03:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.06197","created_at":"2026-05-18T00:03:21Z"},{"alias_kind":"pith_short_12","alias_value":"MOUVG2J3OZDS","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MOUVG2J3OZDS5LLG","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MOUVG2J3","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MOUVG2J3OZDS5LLG5ZP74YDXH2","target":"record","payload":{"canonical_record":{"source":{"id":"1810.06197","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-10-15T06:36:24Z","cross_cats_sorted":[],"title_canon_sha256":"38028cea8d532a1faa2658536c00bbebb5a5c55b9db5ee0b90982aaada8a5ca5","abstract_canon_sha256":"edc69a5a3d789af90a3626bd188058db2d5f00679e1548fc156109f6e14cf01c"},"schema_version":"1.0"},"canonical_sha256":"63a953693b76472ead66ee5ffe60773ebdafe46811d6def8209db7c0127ee7f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:21.167309Z","signature_b64":"nK3yzw5oNK/2YtNpAc2bggD7O6MlO7heRyessu4RHorHCEKpkz7hwxzlvFadwEu3mn1rn6wZpZWF6WHJlYLrAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63a953693b76472ead66ee5ffe60773ebdafe46811d6def8209db7c0127ee7f4","last_reissued_at":"2026-05-18T00:03:21.166863Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:21.166863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.06197","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":"2026-05-18T00:03:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0iSgs2FYgnjMdFHPM24GFrhOZEfj6DR8JSxLtHnDIFGlL+UPTEGA8Pgw9gVsXrmxkOrWyjhk8WgX6lFtk9SpBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:02:30.790611Z"},"content_sha256":"ccb8d08e1702568f77d2d07f04f9ac627d5aadff48157ddc0dfca3a1201f239b","schema_version":"1.0","event_id":"sha256:ccb8d08e1702568f77d2d07f04f9ac627d5aadff48157ddc0dfca3a1201f239b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MOUVG2J3OZDS5LLG5ZP74YDXH2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On some extension of Gauss' work and applications (II)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dong Hwa Shin, Ho Yun Jung, Ick Sun Eum, Ja Kyung Koo","submitted_at":"2018-10-15T06:36:24Z","abstract_excerpt":"Let $K$ be an imaginary quadratic field of discriminant $d_K$, and let $\\mathfrak{n}$ be a nontrivial integral ideal of $K$ in which $N$ is the smallest positive integer. Let $\\mathcal{Q}_N(d_K)$ be the set of primitive positive definite binary quadratic forms of discriminant $d_K$ whose leading coefficients are relatively prime to $N$. We adopt an equivalence relation $\\sim_\\mathfrak{n}$ on $\\mathcal{Q}_N(d_K)$ so that the set of equivalence classes $\\mathcal{Q}_N(d_K)/\\sim_\\mathfrak{n}$ can be regarded as a group isomorphic to the ray class group of $K$ modulo $\\mathfrak{n}$. We further pres"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06197","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":"2026-05-18T00:03:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tKHV4sScf+sn+aM8PUMlf5tZzQTRLGJLjUpgDn4xFrDgZmZg8P5nRiuTCRlJolMVVojbdUzY0cHHC/g2dcsbDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:02:30.791285Z"},"content_sha256":"38d4eb58d6c2499998e870bd6dc121f6c33d546b93a18e890e8daa184a03e2f6","schema_version":"1.0","event_id":"sha256:38d4eb58d6c2499998e870bd6dc121f6c33d546b93a18e890e8daa184a03e2f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MOUVG2J3OZDS5LLG5ZP74YDXH2/bundle.json","state_url":"https://pith.science/pith/MOUVG2J3OZDS5LLG5ZP74YDXH2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MOUVG2J3OZDS5LLG5ZP74YDXH2/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":"2026-06-11T00:02:30Z","links":{"resolver":"https://pith.science/pith/MOUVG2J3OZDS5LLG5ZP74YDXH2","bundle":"https://pith.science/pith/MOUVG2J3OZDS5LLG5ZP74YDXH2/bundle.json","state":"https://pith.science/pith/MOUVG2J3OZDS5LLG5ZP74YDXH2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MOUVG2J3OZDS5LLG5ZP74YDXH2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MOUVG2J3OZDS5LLG5ZP74YDXH2","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":"edc69a5a3d789af90a3626bd188058db2d5f00679e1548fc156109f6e14cf01c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-10-15T06:36:24Z","title_canon_sha256":"38028cea8d532a1faa2658536c00bbebb5a5c55b9db5ee0b90982aaada8a5ca5"},"schema_version":"1.0","source":{"id":"1810.06197","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.06197","created_at":"2026-05-18T00:03:21Z"},{"alias_kind":"arxiv_version","alias_value":"1810.06197v1","created_at":"2026-05-18T00:03:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.06197","created_at":"2026-05-18T00:03:21Z"},{"alias_kind":"pith_short_12","alias_value":"MOUVG2J3OZDS","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MOUVG2J3OZDS5LLG","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MOUVG2J3","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:38d4eb58d6c2499998e870bd6dc121f6c33d546b93a18e890e8daa184a03e2f6","target":"graph","created_at":"2026-05-18T00:03:21Z","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":"Let $K$ be an imaginary quadratic field of discriminant $d_K$, and let $\\mathfrak{n}$ be a nontrivial integral ideal of $K$ in which $N$ is the smallest positive integer. Let $\\mathcal{Q}_N(d_K)$ be the set of primitive positive definite binary quadratic forms of discriminant $d_K$ whose leading coefficients are relatively prime to $N$. We adopt an equivalence relation $\\sim_\\mathfrak{n}$ on $\\mathcal{Q}_N(d_K)$ so that the set of equivalence classes $\\mathcal{Q}_N(d_K)/\\sim_\\mathfrak{n}$ can be regarded as a group isomorphic to the ray class group of $K$ modulo $\\mathfrak{n}$. We further pres","authors_text":"Dong Hwa Shin, Ho Yun Jung, Ick Sun Eum, Ja Kyung Koo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-10-15T06:36:24Z","title":"On some extension of Gauss' work and applications (II)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06197","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:ccb8d08e1702568f77d2d07f04f9ac627d5aadff48157ddc0dfca3a1201f239b","target":"record","created_at":"2026-05-18T00:03:21Z","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":"edc69a5a3d789af90a3626bd188058db2d5f00679e1548fc156109f6e14cf01c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-10-15T06:36:24Z","title_canon_sha256":"38028cea8d532a1faa2658536c00bbebb5a5c55b9db5ee0b90982aaada8a5ca5"},"schema_version":"1.0","source":{"id":"1810.06197","kind":"arxiv","version":1}},"canonical_sha256":"63a953693b76472ead66ee5ffe60773ebdafe46811d6def8209db7c0127ee7f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63a953693b76472ead66ee5ffe60773ebdafe46811d6def8209db7c0127ee7f4","first_computed_at":"2026-05-18T00:03:21.166863Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:21.166863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nK3yzw5oNK/2YtNpAc2bggD7O6MlO7heRyessu4RHorHCEKpkz7hwxzlvFadwEu3mn1rn6wZpZWF6WHJlYLrAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:21.167309Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.06197","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ccb8d08e1702568f77d2d07f04f9ac627d5aadff48157ddc0dfca3a1201f239b","sha256:38d4eb58d6c2499998e870bd6dc121f6c33d546b93a18e890e8daa184a03e2f6"],"state_sha256":"a19b55689daaf4a91c75589147a368dd980437526bbae597ec84e9b4d4797a7c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W4RXZdonDXMMNkK3QqCag+vNCX0zCGWpUiqt9BJdEt7Z1yGMhDqZ3EVdrR1Wb/LIAHTVQw+8usQ0TBD+UTVCCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T00:02:30.795840Z","bundle_sha256":"e7b92667fac33927218f679e9065fcc70f6ed4fcf4a41b53c6b0c28cdcee939d"}}