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Let $B/\\mathbb{F}_q$ be finite \\'etale cubic, $\\operatorname{char}\\mathbb{F}_q\\ne2,3$, and let $T_B=\\ker(\\operatorname{N}_{B/\\mathbb{F}_q}:\\operatorname{Res}_{B/\\mathbb{F}_q}\\mathbb{G}_m\\to\\mathbb{G}_m)$. For every subgroup $H\\subset T_B(\\mathbb{F}_q)$ of index $m$, every coset $gH$, every $\\gamma\\in B^\\times$, and every smooth fiber $\\operatorname{Tr}(\\gamma h)=s$, $s^3\\ne27\\operatorname{N}(\\gamma)$, we prove $N_{gH,B"},"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":"2605.21939","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-05-21T03:18:50Z","cross_cats_sorted":[],"title_canon_sha256":"2826731f4a747609f788f2ff18e22bbade5b7d8bd89de0c3e3f0bdd3b97a49ae","abstract_canon_sha256":"2305b9652a132b9df8b7b3b04c08488c07b38848986c605387d74cb558ab9a27"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T01:04:15.902134Z","signature_b64":"ZvE9fVHUBgGS4n16huiWWQUL5ncFRdyv+W6PQmZVE+Zy/ftFTNcXdgApUv0VbI3cGJRfP852Z2tYiemLP7H7BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4119bb74435dbf094f60baaf6a29e026fbf6dc7dc2cbd18a5f2a4796801af0a4","last_reissued_at":"2026-05-22T01:04:15.901422Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T01:04:15.901422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coset-refined trace statistics, nodal characters, and affine branches in cubic norm tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Henry Shin","submitted_at":"2026-05-21T03:18:50Z","abstract_excerpt":"Prescribed trace/norm estimates and Soto-Andrade-type sums control whole fibers or related global character sums. We prove a coset-refined trace theorem for cubic norm-one tori. Let $B/\\mathbb{F}_q$ be finite \\'etale cubic, $\\operatorname{char}\\mathbb{F}_q\\ne2,3$, and let $T_B=\\ker(\\operatorname{N}_{B/\\mathbb{F}_q}:\\operatorname{Res}_{B/\\mathbb{F}_q}\\mathbb{G}_m\\to\\mathbb{G}_m)$. For every subgroup $H\\subset T_B(\\mathbb{F}_q)$ of index $m$, every coset $gH$, every $\\gamma\\in B^\\times$, and every smooth fiber $\\operatorname{Tr}(\\gamma h)=s$, $s^3\\ne27\\operatorname{N}(\\gamma)$, we prove $N_{gH,B"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21939","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.21939/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2605.21939","created_at":"2026-05-22T01:04:15.901530+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.21939v1","created_at":"2026-05-22T01:04:15.901530+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.21939","created_at":"2026-05-22T01:04:15.901530+00:00"},{"alias_kind":"pith_short_12","alias_value":"IEM3W5CDLW7Q","created_at":"2026-05-22T01:04:15.901530+00:00"},{"alias_kind":"pith_short_16","alias_value":"IEM3W5CDLW7QST3A","created_at":"2026-05-22T01:04:15.901530+00:00"},{"alias_kind":"pith_short_8","alias_value":"IEM3W5CD","created_at":"2026-05-22T01:04:15.901530+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/IEM3W5CDLW7QST3AXKXWUKPAE3","json":"https://pith.science/pith/IEM3W5CDLW7QST3AXKXWUKPAE3.json","graph_json":"https://pith.science/api/pith-number/IEM3W5CDLW7QST3AXKXWUKPAE3/graph.json","events_json":"https://pith.science/api/pith-number/IEM3W5CDLW7QST3AXKXWUKPAE3/events.json","paper":"https://pith.science/paper/IEM3W5CD"},"agent_actions":{"view_html":"https://pith.science/pith/IEM3W5CDLW7QST3AXKXWUKPAE3","download_json":"https://pith.science/pith/IEM3W5CDLW7QST3AXKXWUKPAE3.json","view_paper":"https://pith.science/paper/IEM3W5CD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.21939&json=true","fetch_graph":"https://pith.science/api/pith-number/IEM3W5CDLW7QST3AXKXWUKPAE3/graph.json","fetch_events":"https://pith.science/api/pith-number/IEM3W5CDLW7QST3AXKXWUKPAE3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IEM3W5CDLW7QST3AXKXWUKPAE3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IEM3W5CDLW7QST3AXKXWUKPAE3/action/storage_attestation","attest_author":"https://pith.science/pith/IEM3W5CDLW7QST3AXKXWUKPAE3/action/author_attestation","sign_citation":"https://pith.science/pith/IEM3W5CDLW7QST3AXKXWUKPAE3/action/citation_signature","submit_replication":"https://pith.science/pith/IEM3W5CDLW7QST3AXKXWUKPAE3/action/replication_record"}},"created_at":"2026-05-22T01:04:15.901530+00:00","updated_at":"2026-05-22T01:04:15.901530+00:00"}