{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:N7MO4FJB7EGFTDB57PMELUCEVU","short_pith_number":"pith:N7MO4FJB","canonical_record":{"source":{"id":"1109.6278","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-09-28T17:31:58Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"5cf1b11c787fa82e2818579a6f68f4b581330646464269002b1bb7ba4e933acb","abstract_canon_sha256":"072cc66036a6850696bef87905cb8d4c78da82d3c42ae5567790443fd4a660cf"},"schema_version":"1.0"},"canonical_sha256":"6fd8ee1521f90c598c3dfbd845d044ad00c3392e7f8e2f560e5fa18c9f5d7b40","source":{"kind":"arxiv","id":"1109.6278","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6278","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6278v4","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6278","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"pith_short_12","alias_value":"N7MO4FJB7EGF","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"N7MO4FJB7EGFTDB5","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"N7MO4FJB","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:N7MO4FJB7EGFTDB57PMELUCEVU","target":"record","payload":{"canonical_record":{"source":{"id":"1109.6278","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-09-28T17:31:58Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"5cf1b11c787fa82e2818579a6f68f4b581330646464269002b1bb7ba4e933acb","abstract_canon_sha256":"072cc66036a6850696bef87905cb8d4c78da82d3c42ae5567790443fd4a660cf"},"schema_version":"1.0"},"canonical_sha256":"6fd8ee1521f90c598c3dfbd845d044ad00c3392e7f8e2f560e5fa18c9f5d7b40","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:45.144948Z","signature_b64":"letwRVWy3AK1ZdbmiNKq2XiQBVIqLL2Zl9AEl9lwT3nMMYY0pcfhGMho//84JP38h9BzSUbsrQ/8G6I558JWAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fd8ee1521f90c598c3dfbd845d044ad00c3392e7f8e2f560e5fa18c9f5d7b40","last_reissued_at":"2026-05-18T02:57:45.144545Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:45.144545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.6278","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:57:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ov//Ic5qROayY1wWNXUOWs5iRysKQmqAWkYoZ/I9pJqZukkse3z5Tgv8DETMlHgbeSYkIDH5QVAfLX918UBzAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:20:36.016181Z"},"content_sha256":"b26026d1ae2055c3c6cf1e1229c2c3fb33fc60371df2016c0bcda6916e63b0f7","schema_version":"1.0","event_id":"sha256:b26026d1ae2055c3c6cf1e1229c2c3fb33fc60371df2016c0bcda6916e63b0f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:N7MO4FJB7EGFTDB57PMELUCEVU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the number of elliptic curves with prescribed isogeny or torsion group over number fields of prime degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Filip Najman","submitted_at":"2011-09-28T17:31:58Z","abstract_excerpt":"Let $p$ be a prime and $K$ a number field of degree $p$. We count the number of elliptic curves, up to $\\bar{K}$-isomorphism, having a prescribed property, where this property is either that the curve contains a fixed torsion group as a subgroup, or that it has an isogeny of prescribed degree."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6278","kind":"arxiv","version":4},"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":"2026-05-18T02:57:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jOEzDQvuZenPE13cf0WfMrzm+PQp84f8/V552lMALCAIatunI6BlC2TCtynC0kJbAeFtcV9MxSD/xViIwz0xBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:20:36.016803Z"},"content_sha256":"e8fea1b180292d9f437fadb3af83ca7dc433fe041a0e0a070ce29657bb2a295d","schema_version":"1.0","event_id":"sha256:e8fea1b180292d9f437fadb3af83ca7dc433fe041a0e0a070ce29657bb2a295d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N7MO4FJB7EGFTDB57PMELUCEVU/bundle.json","state_url":"https://pith.science/pith/N7MO4FJB7EGFTDB57PMELUCEVU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N7MO4FJB7EGFTDB57PMELUCEVU/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":"2026-05-27T15:20:36Z","links":{"resolver":"https://pith.science/pith/N7MO4FJB7EGFTDB57PMELUCEVU","bundle":"https://pith.science/pith/N7MO4FJB7EGFTDB57PMELUCEVU/bundle.json","state":"https://pith.science/pith/N7MO4FJB7EGFTDB57PMELUCEVU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N7MO4FJB7EGFTDB57PMELUCEVU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:N7MO4FJB7EGFTDB57PMELUCEVU","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":"072cc66036a6850696bef87905cb8d4c78da82d3c42ae5567790443fd4a660cf","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-09-28T17:31:58Z","title_canon_sha256":"5cf1b11c787fa82e2818579a6f68f4b581330646464269002b1bb7ba4e933acb"},"schema_version":"1.0","source":{"id":"1109.6278","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6278","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6278v4","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6278","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"pith_short_12","alias_value":"N7MO4FJB7EGF","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"N7MO4FJB7EGFTDB5","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"N7MO4FJB","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:e8fea1b180292d9f437fadb3af83ca7dc433fe041a0e0a070ce29657bb2a295d","target":"graph","created_at":"2026-05-18T02:57:45Z","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 $p$ be a prime and $K$ a number field of degree $p$. We count the number of elliptic curves, up to $\\bar{K}$-isomorphism, having a prescribed property, where this property is either that the curve contains a fixed torsion group as a subgroup, or that it has an isogeny of prescribed degree.","authors_text":"Filip Najman","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-09-28T17:31:58Z","title":"On the number of elliptic curves with prescribed isogeny or torsion group over number fields of prime degree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6278","kind":"arxiv","version":4},"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:b26026d1ae2055c3c6cf1e1229c2c3fb33fc60371df2016c0bcda6916e63b0f7","target":"record","created_at":"2026-05-18T02:57:45Z","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":"072cc66036a6850696bef87905cb8d4c78da82d3c42ae5567790443fd4a660cf","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-09-28T17:31:58Z","title_canon_sha256":"5cf1b11c787fa82e2818579a6f68f4b581330646464269002b1bb7ba4e933acb"},"schema_version":"1.0","source":{"id":"1109.6278","kind":"arxiv","version":4}},"canonical_sha256":"6fd8ee1521f90c598c3dfbd845d044ad00c3392e7f8e2f560e5fa18c9f5d7b40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fd8ee1521f90c598c3dfbd845d044ad00c3392e7f8e2f560e5fa18c9f5d7b40","first_computed_at":"2026-05-18T02:57:45.144545Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:45.144545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"letwRVWy3AK1ZdbmiNKq2XiQBVIqLL2Zl9AEl9lwT3nMMYY0pcfhGMho//84JP38h9BzSUbsrQ/8G6I558JWAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:45.144948Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.6278","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b26026d1ae2055c3c6cf1e1229c2c3fb33fc60371df2016c0bcda6916e63b0f7","sha256:e8fea1b180292d9f437fadb3af83ca7dc433fe041a0e0a070ce29657bb2a295d"],"state_sha256":"8128621e3d452147e1cfaea1e670e2a23a4eb41b18f9f18972794a01fd4d13af"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gSYT/zTJfWr8xvvsdzt14SDbGd0wfvcsQoeUnxEsipzM8p3+Na47WwgOISyglaRpPen34SOHXdGSYB2TCHHEAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T15:20:36.019415Z","bundle_sha256":"5ecab7500381addc2746f3f57f6a17dedf9413ec10b929897eedd657d4a6d998"}}