{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:FGECWVPY575PO7T5SLQEFGPBA7","short_pith_number":"pith:FGECWVPY","canonical_record":{"source":{"id":"1708.00044","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-31T19:29:32Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"b09591f3e9b03aae6c4adce35efe37bd77bc7a7e9f54ef7180fd6e33fdce8297","abstract_canon_sha256":"4e17db491fb10fbe0fdbaef79c66db5e412a6ddf629386600098bf01a67c0380"},"schema_version":"1.0"},"canonical_sha256":"29882b55f8effaf77e7d92e04299e107f057e00a46b95ed7870b4a1840a6382b","source":{"kind":"arxiv","id":"1708.00044","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.00044","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"arxiv_version","alias_value":"1708.00044v3","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00044","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"pith_short_12","alias_value":"FGECWVPY575P","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FGECWVPY575PO7T5","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FGECWVPY","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:FGECWVPY575PO7T5SLQEFGPBA7","target":"record","payload":{"canonical_record":{"source":{"id":"1708.00044","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-31T19:29:32Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"b09591f3e9b03aae6c4adce35efe37bd77bc7a7e9f54ef7180fd6e33fdce8297","abstract_canon_sha256":"4e17db491fb10fbe0fdbaef79c66db5e412a6ddf629386600098bf01a67c0380"},"schema_version":"1.0"},"canonical_sha256":"29882b55f8effaf77e7d92e04299e107f057e00a46b95ed7870b4a1840a6382b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:01.457372Z","signature_b64":"gLjbm8Y/sNmII8WL1Rw65ljJ3qu5jKC3EJ/Wz2tE+unOtXVPscSKMrsBYdFTdZo6q1peSrUfgj3jxC6wcKBwCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29882b55f8effaf77e7d92e04299e107f057e00a46b95ed7870b4a1840a6382b","last_reissued_at":"2026-05-17T23:53:01.456724Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:01.456724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.00044","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KvrTBDYTwcxsGqkdDDjFVy55l7xRwA3EGCsQ05ddYa9rkA6MH1g8wVoQSEjX1qaJKURDBnm3IlVBO5bnFJkFCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:51:57.460709Z"},"content_sha256":"369e73d86d93e5d3e80b64179a67618f103f6519f35173a67b78d43769a8e8a0","schema_version":"1.0","event_id":"sha256:369e73d86d93e5d3e80b64179a67618f103f6519f35173a67b78d43769a8e8a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:FGECWVPY575PO7T5SLQEFGPBA7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The distribution of $G$-Weyl CM fields and the Colmez conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Adrian Barquero-Sanchez, Frank Thorne, Riad Masri","submitted_at":"2017-07-31T19:29:32Z","abstract_excerpt":"Let $G$ be a transitive subgroup of $S_d$ and $E$ be a CM field of degree $2d$ with a maximal totally real $G$-field. If the Galois group of the Galois closure of $E$ is isomorphic to the wreath product of $C_2$ and $G$, then we say that $E$ is a $G$-Weyl CM field.\n  Let $N_{2d}^{\\textrm{Weyl}}(X,G)$ count the $G$-Weyl CM fields $E$ of degree $2d$ with discriminant $|d_E| \\leq X$ and define \\begin{align*} N_{2d}^{\\textrm{Weyl}}(X):=\\sum_{G \\leq S_d}N_{2d}^{\\textrm{Weyl}}(X,G). \\end{align*} Further, let $N_{2d}^{\\textrm{cm}}(X)$ count the CM fields $E$ of degree $2d$ with discriminant $|d_E| \\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00044","kind":"arxiv","version":3},"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":"2026-05-17T23:53:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H8rIqlhnUeF7S/4midZ69dUNt0tKaP2UtmFvV0Oy28gjBy6ECCcrjWgu5oeGft6yfSky3bwxJ0X5z/QZHrsZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:51:57.461059Z"},"content_sha256":"be4b8cdd3a635be394ffc039c823a404d4dcbaf18453a00b4183cfaeab0199de","schema_version":"1.0","event_id":"sha256:be4b8cdd3a635be394ffc039c823a404d4dcbaf18453a00b4183cfaeab0199de"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FGECWVPY575PO7T5SLQEFGPBA7/bundle.json","state_url":"https://pith.science/pith/FGECWVPY575PO7T5SLQEFGPBA7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FGECWVPY575PO7T5SLQEFGPBA7/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":"2026-06-06T18:51:57Z","links":{"resolver":"https://pith.science/pith/FGECWVPY575PO7T5SLQEFGPBA7","bundle":"https://pith.science/pith/FGECWVPY575PO7T5SLQEFGPBA7/bundle.json","state":"https://pith.science/pith/FGECWVPY575PO7T5SLQEFGPBA7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FGECWVPY575PO7T5SLQEFGPBA7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FGECWVPY575PO7T5SLQEFGPBA7","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":"4e17db491fb10fbe0fdbaef79c66db5e412a6ddf629386600098bf01a67c0380","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-31T19:29:32Z","title_canon_sha256":"b09591f3e9b03aae6c4adce35efe37bd77bc7a7e9f54ef7180fd6e33fdce8297"},"schema_version":"1.0","source":{"id":"1708.00044","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.00044","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"arxiv_version","alias_value":"1708.00044v3","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00044","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"pith_short_12","alias_value":"FGECWVPY575P","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FGECWVPY575PO7T5","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FGECWVPY","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:be4b8cdd3a635be394ffc039c823a404d4dcbaf18453a00b4183cfaeab0199de","target":"graph","created_at":"2026-05-17T23:53:01Z","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 $G$ be a transitive subgroup of $S_d$ and $E$ be a CM field of degree $2d$ with a maximal totally real $G$-field. If the Galois group of the Galois closure of $E$ is isomorphic to the wreath product of $C_2$ and $G$, then we say that $E$ is a $G$-Weyl CM field.\n  Let $N_{2d}^{\\textrm{Weyl}}(X,G)$ count the $G$-Weyl CM fields $E$ of degree $2d$ with discriminant $|d_E| \\leq X$ and define \\begin{align*} N_{2d}^{\\textrm{Weyl}}(X):=\\sum_{G \\leq S_d}N_{2d}^{\\textrm{Weyl}}(X,G). \\end{align*} Further, let $N_{2d}^{\\textrm{cm}}(X)$ count the CM fields $E$ of degree $2d$ with discriminant $|d_E| \\l","authors_text":"Adrian Barquero-Sanchez, Frank Thorne, Riad Masri","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-31T19:29:32Z","title":"The distribution of $G$-Weyl CM fields and the Colmez conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00044","kind":"arxiv","version":3},"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":"sha256:369e73d86d93e5d3e80b64179a67618f103f6519f35173a67b78d43769a8e8a0","target":"record","created_at":"2026-05-17T23:53:01Z","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":"4e17db491fb10fbe0fdbaef79c66db5e412a6ddf629386600098bf01a67c0380","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-31T19:29:32Z","title_canon_sha256":"b09591f3e9b03aae6c4adce35efe37bd77bc7a7e9f54ef7180fd6e33fdce8297"},"schema_version":"1.0","source":{"id":"1708.00044","kind":"arxiv","version":3}},"canonical_sha256":"29882b55f8effaf77e7d92e04299e107f057e00a46b95ed7870b4a1840a6382b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29882b55f8effaf77e7d92e04299e107f057e00a46b95ed7870b4a1840a6382b","first_computed_at":"2026-05-17T23:53:01.456724Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:01.456724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gLjbm8Y/sNmII8WL1Rw65ljJ3qu5jKC3EJ/Wz2tE+unOtXVPscSKMrsBYdFTdZo6q1peSrUfgj3jxC6wcKBwCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:01.457372Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.00044","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:369e73d86d93e5d3e80b64179a67618f103f6519f35173a67b78d43769a8e8a0","sha256:be4b8cdd3a635be394ffc039c823a404d4dcbaf18453a00b4183cfaeab0199de"],"state_sha256":"8467783d8b83c3ba5e652879a2c49b6d27dfe0bdd03bec2d645c98406d11bf7d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qUooLtt1a51VfWpNU0heg0xr54CdFjhzRCCGNu/VcUTi+hBmKdtGbaUg9uDnE6opNEHirKYcbg1xBTXc3E4WBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T18:51:57.463235Z","bundle_sha256":"9f0e7dc0a82d6006e88b131b619cd30c4b10e24c1c761d99a375e955eaee50bc"}}