{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:WWUENZPBLBLTU445JNHNU25RP2","short_pith_number":"pith:WWUENZPB","canonical_record":{"source":{"id":"1207.2273","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-10T09:25:17Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"fc932fcaece43bdef168764dcf1b64bdff256f05a7b160de5559ad831ae95b49","abstract_canon_sha256":"b5447a552a8cda3495f3bad3cf3a8213dc48369a01c3f2411ffc4433fce15086"},"schema_version":"1.0"},"canonical_sha256":"b5a846e5e158573a739d4b4eda6bb17e80e733e33842c58e80493f106fc7a55d","source":{"kind":"arxiv","id":"1207.2273","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.2273","created_at":"2026-05-18T03:26:23Z"},{"alias_kind":"arxiv_version","alias_value":"1207.2273v2","created_at":"2026-05-18T03:26:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2273","created_at":"2026-05-18T03:26:23Z"},{"alias_kind":"pith_short_12","alias_value":"WWUENZPBLBLT","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"WWUENZPBLBLTU445","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"WWUENZPB","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:WWUENZPBLBLTU445JNHNU25RP2","target":"record","payload":{"canonical_record":{"source":{"id":"1207.2273","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-10T09:25:17Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"fc932fcaece43bdef168764dcf1b64bdff256f05a7b160de5559ad831ae95b49","abstract_canon_sha256":"b5447a552a8cda3495f3bad3cf3a8213dc48369a01c3f2411ffc4433fce15086"},"schema_version":"1.0"},"canonical_sha256":"b5a846e5e158573a739d4b4eda6bb17e80e733e33842c58e80493f106fc7a55d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:23.152403Z","signature_b64":"LwkzF5/wUoDySdvkL0QNB3kwbuJ8abqdtfteFSzbuS0fy9A3cVelcSXkSkPYMVRN8tEuu6H0cPpVmCvxxTkmBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5a846e5e158573a739d4b4eda6bb17e80e733e33842c58e80493f106fc7a55d","last_reissued_at":"2026-05-18T03:26:23.151636Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:23.151636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.2273","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:26:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YqpBk3AFnFoH5aeEY/3yjlEd7cPolq4zI6XXWonI40JY9b+FweyQMwNpnYha0RBmL4q+hj4tV680omAimx41DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T18:17:00.280265Z"},"content_sha256":"cdb41d24288065e9e1857d115b00b936a5cda810afeca5c558839ec3a49064e2","schema_version":"1.0","event_id":"sha256:cdb41d24288065e9e1857d115b00b936a5cda810afeca5c558839ec3a49064e2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:WWUENZPBLBLTU445JNHNU25RP2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bielliptic and Hyperelliptic modular curves X(N) and the group Aut(X(N))","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Aristides Kontogeorgis, Francesc Bars, Xavier Xarles","submitted_at":"2012-07-10T09:25:17Z","abstract_excerpt":"We determine all modular curves X(N) (with $N\\geq 7$) which are hyperelliptic or bielliptic. We make available a proof that the automorphism group of X(N) coincides with the normalizer of $\\Gamma(N)$ in $\\operatorname{PSL}_2(\\mathbb{R})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2273","kind":"arxiv","version":2},"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":"2026-05-18T03:26:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tdC6YA7hy3/tEOYJwi3/BYfMWiG/aNTsM6LPYNNZzLaJMGBXt4LwzocVcCC40TwJMn0Hp+F4iYcEQpgzW/ciDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T18:17:00.280958Z"},"content_sha256":"92ce667d6d8cf2db0f1ee53a948d1316bdd940c0167bac1f25549d479f92916c","schema_version":"1.0","event_id":"sha256:92ce667d6d8cf2db0f1ee53a948d1316bdd940c0167bac1f25549d479f92916c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WWUENZPBLBLTU445JNHNU25RP2/bundle.json","state_url":"https://pith.science/pith/WWUENZPBLBLTU445JNHNU25RP2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WWUENZPBLBLTU445JNHNU25RP2/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":"2026-05-30T18:17:00Z","links":{"resolver":"https://pith.science/pith/WWUENZPBLBLTU445JNHNU25RP2","bundle":"https://pith.science/pith/WWUENZPBLBLTU445JNHNU25RP2/bundle.json","state":"https://pith.science/pith/WWUENZPBLBLTU445JNHNU25RP2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WWUENZPBLBLTU445JNHNU25RP2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:WWUENZPBLBLTU445JNHNU25RP2","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":"b5447a552a8cda3495f3bad3cf3a8213dc48369a01c3f2411ffc4433fce15086","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-10T09:25:17Z","title_canon_sha256":"fc932fcaece43bdef168764dcf1b64bdff256f05a7b160de5559ad831ae95b49"},"schema_version":"1.0","source":{"id":"1207.2273","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.2273","created_at":"2026-05-18T03:26:23Z"},{"alias_kind":"arxiv_version","alias_value":"1207.2273v2","created_at":"2026-05-18T03:26:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2273","created_at":"2026-05-18T03:26:23Z"},{"alias_kind":"pith_short_12","alias_value":"WWUENZPBLBLT","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"WWUENZPBLBLTU445","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"WWUENZPB","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:92ce667d6d8cf2db0f1ee53a948d1316bdd940c0167bac1f25549d479f92916c","target":"graph","created_at":"2026-05-18T03:26:23Z","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":"We determine all modular curves X(N) (with $N\\geq 7$) which are hyperelliptic or bielliptic. We make available a proof that the automorphism group of X(N) coincides with the normalizer of $\\Gamma(N)$ in $\\operatorname{PSL}_2(\\mathbb{R})$.","authors_text":"Aristides Kontogeorgis, Francesc Bars, Xavier Xarles","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-10T09:25:17Z","title":"Bielliptic and Hyperelliptic modular curves X(N) and the group Aut(X(N))"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2273","kind":"arxiv","version":2},"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:cdb41d24288065e9e1857d115b00b936a5cda810afeca5c558839ec3a49064e2","target":"record","created_at":"2026-05-18T03:26:23Z","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":"b5447a552a8cda3495f3bad3cf3a8213dc48369a01c3f2411ffc4433fce15086","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-10T09:25:17Z","title_canon_sha256":"fc932fcaece43bdef168764dcf1b64bdff256f05a7b160de5559ad831ae95b49"},"schema_version":"1.0","source":{"id":"1207.2273","kind":"arxiv","version":2}},"canonical_sha256":"b5a846e5e158573a739d4b4eda6bb17e80e733e33842c58e80493f106fc7a55d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5a846e5e158573a739d4b4eda6bb17e80e733e33842c58e80493f106fc7a55d","first_computed_at":"2026-05-18T03:26:23.151636Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:23.151636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LwkzF5/wUoDySdvkL0QNB3kwbuJ8abqdtfteFSzbuS0fy9A3cVelcSXkSkPYMVRN8tEuu6H0cPpVmCvxxTkmBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:23.152403Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.2273","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cdb41d24288065e9e1857d115b00b936a5cda810afeca5c558839ec3a49064e2","sha256:92ce667d6d8cf2db0f1ee53a948d1316bdd940c0167bac1f25549d479f92916c"],"state_sha256":"df6244f19ea1e9f050aa2cdb160205562ee2294f8990c306c1bc665bb622b6d1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kWyNhXhy3X922rwG8qDqSUH0AIKOubIfdk4p4TwqOfJf6R/rU3M1rsUc9tSpEInMP2tO4k3/QbvLoVV37/foBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T18:17:00.284824Z","bundle_sha256":"0e9d3a7aa8a93e11bfbf5c00d47c09cd032ef119fe90da3d989f27c931db2b03"}}