{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:6YW7DB5DUO3N2ITVGTT464RGWW","short_pith_number":"pith:6YW7DB5D","schema_version":"1.0","canonical_sha256":"f62df187a3a3b6dd227534e7cf7226b5b305804e62cb1a097db16e33c68638cb","source":{"kind":"arxiv","id":"1112.2820","version":1},"attestation_state":"computed","paper":{"title":"Index formulae for Stark units and their solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Xavier-Fran\\c{c}ois Roblot","submitted_at":"2011-12-13T08:39:58Z","abstract_excerpt":"Let $K/k$ be an abelian extension of number fields with a distinguished place of $k$ that splits totally in $K$. In that situation, the abelian rank one Stark conjecture predicts the existence of a unit in $K$, called the Stark unit, constructed from the values of the $L$-functions attached to the extension. In this paper, assuming the Stark unit exists, we prove index formulae for it. In a second part, we study the solutions of the index formulae and prove that they admit solutions unconditionally for quadratic, quartic and sextic (with some additional conditions) cyclic extensions. As a resu"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1112.2820","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-12-13T08:39:58Z","cross_cats_sorted":[],"title_canon_sha256":"810ab252a3845ff1df1c30d0191b798353b242d7c3e198cb8e8c77ef85c26745","abstract_canon_sha256":"e8d408f7d42e9a2a2fd4c4d1c4047234e520419ae787811bcba359f1a95f8133"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:32.352640Z","signature_b64":"FxF0VqK+LAv1hWSFh4P5RvmI8wvN54eXju3jNwwriXCRaPmTwDlzqsVFJC0hsW91sOhWVyv4V2++m9VZ39q5Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f62df187a3a3b6dd227534e7cf7226b5b305804e62cb1a097db16e33c68638cb","last_reissued_at":"2026-05-18T04:06:32.352042Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:32.352042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Index formulae for Stark units and their solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Xavier-Fran\\c{c}ois Roblot","submitted_at":"2011-12-13T08:39:58Z","abstract_excerpt":"Let $K/k$ be an abelian extension of number fields with a distinguished place of $k$ that splits totally in $K$. In that situation, the abelian rank one Stark conjecture predicts the existence of a unit in $K$, called the Stark unit, constructed from the values of the $L$-functions attached to the extension. In this paper, assuming the Stark unit exists, we prove index formulae for it. In a second part, we study the solutions of the index formulae and prove that they admit solutions unconditionally for quadratic, quartic and sextic (with some additional conditions) cyclic extensions. As a resu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2820","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1112.2820","created_at":"2026-05-18T04:06:32.352142+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.2820v1","created_at":"2026-05-18T04:06:32.352142+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2820","created_at":"2026-05-18T04:06:32.352142+00:00"},{"alias_kind":"pith_short_12","alias_value":"6YW7DB5DUO3N","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"6YW7DB5DUO3N2ITV","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"6YW7DB5D","created_at":"2026-05-18T12:26:22.705136+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6YW7DB5DUO3N2ITVGTT464RGWW","json":"https://pith.science/pith/6YW7DB5DUO3N2ITVGTT464RGWW.json","graph_json":"https://pith.science/api/pith-number/6YW7DB5DUO3N2ITVGTT464RGWW/graph.json","events_json":"https://pith.science/api/pith-number/6YW7DB5DUO3N2ITVGTT464RGWW/events.json","paper":"https://pith.science/paper/6YW7DB5D"},"agent_actions":{"view_html":"https://pith.science/pith/6YW7DB5DUO3N2ITVGTT464RGWW","download_json":"https://pith.science/pith/6YW7DB5DUO3N2ITVGTT464RGWW.json","view_paper":"https://pith.science/paper/6YW7DB5D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.2820&json=true","fetch_graph":"https://pith.science/api/pith-number/6YW7DB5DUO3N2ITVGTT464RGWW/graph.json","fetch_events":"https://pith.science/api/pith-number/6YW7DB5DUO3N2ITVGTT464RGWW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6YW7DB5DUO3N2ITVGTT464RGWW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6YW7DB5DUO3N2ITVGTT464RGWW/action/storage_attestation","attest_author":"https://pith.science/pith/6YW7DB5DUO3N2ITVGTT464RGWW/action/author_attestation","sign_citation":"https://pith.science/pith/6YW7DB5DUO3N2ITVGTT464RGWW/action/citation_signature","submit_replication":"https://pith.science/pith/6YW7DB5DUO3N2ITVGTT464RGWW/action/replication_record"}},"created_at":"2026-05-18T04:06:32.352142+00:00","updated_at":"2026-05-18T04:06:32.352142+00:00"}