{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:GIFHG46KM3V4UFB7AAXDFM6F52","short_pith_number":"pith:GIFHG46K","canonical_record":{"source":{"id":"1710.10681","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-29T19:59:06Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"c1be712c5ea4f408c2d1650d8be3f79951e08364457e0132ff70f02677b9edf7","abstract_canon_sha256":"7aa81fd47746ed38800f7f7bc128900c351467266c9124d43518cd8a940aa19c"},"schema_version":"1.0"},"canonical_sha256":"320a7373ca66ebca143f002e32b3c5eea371377c3c51844386a53d84f534c769","source":{"kind":"arxiv","id":"1710.10681","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10681","created_at":"2026-05-18T00:31:46Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10681v1","created_at":"2026-05-18T00:31:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10681","created_at":"2026-05-18T00:31:46Z"},{"alias_kind":"pith_short_12","alias_value":"GIFHG46KM3V4","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GIFHG46KM3V4UFB7","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GIFHG46K","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:GIFHG46KM3V4UFB7AAXDFM6F52","target":"record","payload":{"canonical_record":{"source":{"id":"1710.10681","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-29T19:59:06Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"c1be712c5ea4f408c2d1650d8be3f79951e08364457e0132ff70f02677b9edf7","abstract_canon_sha256":"7aa81fd47746ed38800f7f7bc128900c351467266c9124d43518cd8a940aa19c"},"schema_version":"1.0"},"canonical_sha256":"320a7373ca66ebca143f002e32b3c5eea371377c3c51844386a53d84f534c769","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:46.773761Z","signature_b64":"EGGF0ySCHtp5TbbcooRGEi6lZbuaNPlI0BTdyU8HlafVNwzIlr6SynF1WOzD+OcjJrEezjMDuIPdOJVsYhWJBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"320a7373ca66ebca143f002e32b3c5eea371377c3c51844386a53d84f534c769","last_reissued_at":"2026-05-18T00:31:46.773036Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:46.773036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.10681","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":"2026-05-18T00:31:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ulp/oQ3L5e5WUkgC8Gz2AmKoud3GQnyTdUNXBwa6eWyN2zQ+60RjysALDTdllLwI3rmaJyz3X+kztgyeUYtJAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T02:20:42.563641Z"},"content_sha256":"3d0a8b8e274802b39133b7a5eac81046d9b886748e6b3077ba095d11105da29f","schema_version":"1.0","event_id":"sha256:3d0a8b8e274802b39133b7a5eac81046d9b886748e6b3077ba095d11105da29f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:GIFHG46KM3V4UFB7AAXDFM6F52","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The $2$-Class Tower of $\\mathbb{Q}(\\sqrt{-5460})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.NT","authors_text":"Jiuya Wang, Nigel Boston","submitted_at":"2017-10-29T19:59:06Z","abstract_excerpt":"The seminal papers in the field of root-discriminant bounds are those of Odlyzko and Martinet. Both papers include the question of whether the field $\\mathbb{Q}(\\sqrt{-5460})$ has finite or infinite $2$-class tower. This is a critical case that will either substantially lower the best known upper bound for lim inf of root-discriminants (if infinite) or else give a counter-example to what is often termed Martinet's conjecture or question (if finite). Using extensive computation and introducing some new techniques, we give strong evidence that the tower is in fact finite, establishing other prop"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10681","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":"2026-05-18T00:31:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EjWuoS6xj//tLXkV3Bb56ObLpA3aIaHuoeoYHLbXzjw6VJRYWNHDADGDKTm57DNffwiBEuW0MUxKKoh2NJDACw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T02:20:42.564013Z"},"content_sha256":"0210d02cf9cfb1789474f0367d6ba91bcaf0be0bc0b1139b30d3eb7e2d7b9ad3","schema_version":"1.0","event_id":"sha256:0210d02cf9cfb1789474f0367d6ba91bcaf0be0bc0b1139b30d3eb7e2d7b9ad3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GIFHG46KM3V4UFB7AAXDFM6F52/bundle.json","state_url":"https://pith.science/pith/GIFHG46KM3V4UFB7AAXDFM6F52/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GIFHG46KM3V4UFB7AAXDFM6F52/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":"2026-05-19T02:20:42Z","links":{"resolver":"https://pith.science/pith/GIFHG46KM3V4UFB7AAXDFM6F52","bundle":"https://pith.science/pith/GIFHG46KM3V4UFB7AAXDFM6F52/bundle.json","state":"https://pith.science/pith/GIFHG46KM3V4UFB7AAXDFM6F52/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GIFHG46KM3V4UFB7AAXDFM6F52/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GIFHG46KM3V4UFB7AAXDFM6F52","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":"7aa81fd47746ed38800f7f7bc128900c351467266c9124d43518cd8a940aa19c","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-29T19:59:06Z","title_canon_sha256":"c1be712c5ea4f408c2d1650d8be3f79951e08364457e0132ff70f02677b9edf7"},"schema_version":"1.0","source":{"id":"1710.10681","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10681","created_at":"2026-05-18T00:31:46Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10681v1","created_at":"2026-05-18T00:31:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10681","created_at":"2026-05-18T00:31:46Z"},{"alias_kind":"pith_short_12","alias_value":"GIFHG46KM3V4","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GIFHG46KM3V4UFB7","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GIFHG46K","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:0210d02cf9cfb1789474f0367d6ba91bcaf0be0bc0b1139b30d3eb7e2d7b9ad3","target":"graph","created_at":"2026-05-18T00:31:46Z","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":"The seminal papers in the field of root-discriminant bounds are those of Odlyzko and Martinet. Both papers include the question of whether the field $\\mathbb{Q}(\\sqrt{-5460})$ has finite or infinite $2$-class tower. This is a critical case that will either substantially lower the best known upper bound for lim inf of root-discriminants (if infinite) or else give a counter-example to what is often termed Martinet's conjecture or question (if finite). Using extensive computation and introducing some new techniques, we give strong evidence that the tower is in fact finite, establishing other prop","authors_text":"Jiuya Wang, Nigel Boston","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-29T19:59:06Z","title":"The $2$-Class Tower of $\\mathbb{Q}(\\sqrt{-5460})$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10681","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":"sha256:3d0a8b8e274802b39133b7a5eac81046d9b886748e6b3077ba095d11105da29f","target":"record","created_at":"2026-05-18T00:31:46Z","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":"7aa81fd47746ed38800f7f7bc128900c351467266c9124d43518cd8a940aa19c","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-29T19:59:06Z","title_canon_sha256":"c1be712c5ea4f408c2d1650d8be3f79951e08364457e0132ff70f02677b9edf7"},"schema_version":"1.0","source":{"id":"1710.10681","kind":"arxiv","version":1}},"canonical_sha256":"320a7373ca66ebca143f002e32b3c5eea371377c3c51844386a53d84f534c769","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"320a7373ca66ebca143f002e32b3c5eea371377c3c51844386a53d84f534c769","first_computed_at":"2026-05-18T00:31:46.773036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:46.773036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EGGF0ySCHtp5TbbcooRGEi6lZbuaNPlI0BTdyU8HlafVNwzIlr6SynF1WOzD+OcjJrEezjMDuIPdOJVsYhWJBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:46.773761Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.10681","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d0a8b8e274802b39133b7a5eac81046d9b886748e6b3077ba095d11105da29f","sha256:0210d02cf9cfb1789474f0367d6ba91bcaf0be0bc0b1139b30d3eb7e2d7b9ad3"],"state_sha256":"f642f65aff8d6db8514445774239ffc52f89c45dfdce79cae0069bda660f6f90"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f63TYBvliHl5dcFR9QmDJQnpxAmxLxJ/8x/TUsrphGxb9ZC0dn3hs5Ev8/uj1ctAdVoE52ZBYyipLjqJVpG8BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T02:20:42.565202Z","bundle_sha256":"2bcd7b3a45d413300fef6a1022b93a63636df3283d098d8cc8e85c4beb88a409"}}