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Given $s \\in F,$ we give an explicit formula for $\\| \\sigma(s)\\|$ and $\\sum_{i<j} \\sigma_i(s)\\sigma_j(s),$ where $\\| \\sigma(s)\\|=\\sqrt{\\sum_{i=1}^r(\\sigma_i(s))^2}.$ Let $\\mathfrak{M}$ be a fractional ideal in $F$ and $\\min\\left( \\mathfrak{M}\\right):=\\min\\{\\|\\sigma(s)\\| \\, | \\, s \\in \\mathfrak{M}, s\\neq 0 \\}.$ The set of shortest nonzero lattice points for $\\mathfrak{M}$ is given by $\\{s\\in \\mathfrak{M} : \\| \\sigma(s)\\|=\\min(\\mathfrak{M}) \\}.$ We provide shortest nonzero latti"},"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":"2411.02575","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-11-04T20:16:00Z","cross_cats_sorted":[],"title_canon_sha256":"e678ee582f720fa9d7b6324dadff0aadf0973d5e82816d9ee14942338663d22d","abstract_canon_sha256":"4f77ce05fb215da664eda726e0ad8dfa7980f13bfcbf2456df10d26facac5b24"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:04:37.577104Z","signature_b64":"acUNcJylfwao1yXDdpSjC08Fp+XLYIN5sZBPQSaXOCOSel0xLeerd4F1y3iRhoOiEk7o5Zhfa7JIW0NEleVFDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adc89083faa0bfc6047ea6ce4700df340c55f4b3abc7f4c04b09ebeb4fe576ac","last_reissued_at":"2026-06-09T01:04:37.576671Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:04:37.576671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Shortest nonzero lattice points in a totally real multi-quadratic number field and applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jishu Das","submitted_at":"2024-11-04T20:16:00Z","abstract_excerpt":"Let $F$ be a multi-quadratic totally real number field. Let $\\sigma_1,\\dots, \\sigma_r$ denote its distinct embeddings. Given $s \\in F,$ we give an explicit formula for $\\| \\sigma(s)\\|$ and $\\sum_{i<j} \\sigma_i(s)\\sigma_j(s),$ where $\\| \\sigma(s)\\|=\\sqrt{\\sum_{i=1}^r(\\sigma_i(s))^2}.$ Let $\\mathfrak{M}$ be a fractional ideal in $F$ and $\\min\\left( \\mathfrak{M}\\right):=\\min\\{\\|\\sigma(s)\\| \\, | \\, s \\in \\mathfrak{M}, s\\neq 0 \\}.$ The set of shortest nonzero lattice points for $\\mathfrak{M}$ is given by $\\{s\\in \\mathfrak{M} : \\| \\sigma(s)\\|=\\min(\\mathfrak{M}) \\}.$ We provide shortest nonzero latti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.02575","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/2411.02575/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":"2411.02575","created_at":"2026-06-09T01:04:37.576731+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.02575v1","created_at":"2026-06-09T01:04:37.576731+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.02575","created_at":"2026-06-09T01:04:37.576731+00:00"},{"alias_kind":"pith_short_12","alias_value":"VXEJBA72UC74","created_at":"2026-06-09T01:04:37.576731+00:00"},{"alias_kind":"pith_short_16","alias_value":"VXEJBA72UC74MBD6","created_at":"2026-06-09T01:04:37.576731+00:00"},{"alias_kind":"pith_short_8","alias_value":"VXEJBA72","created_at":"2026-06-09T01:04:37.576731+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/VXEJBA72UC74MBD6U3HEOAG7GQ","json":"https://pith.science/pith/VXEJBA72UC74MBD6U3HEOAG7GQ.json","graph_json":"https://pith.science/api/pith-number/VXEJBA72UC74MBD6U3HEOAG7GQ/graph.json","events_json":"https://pith.science/api/pith-number/VXEJBA72UC74MBD6U3HEOAG7GQ/events.json","paper":"https://pith.science/paper/VXEJBA72"},"agent_actions":{"view_html":"https://pith.science/pith/VXEJBA72UC74MBD6U3HEOAG7GQ","download_json":"https://pith.science/pith/VXEJBA72UC74MBD6U3HEOAG7GQ.json","view_paper":"https://pith.science/paper/VXEJBA72","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.02575&json=true","fetch_graph":"https://pith.science/api/pith-number/VXEJBA72UC74MBD6U3HEOAG7GQ/graph.json","fetch_events":"https://pith.science/api/pith-number/VXEJBA72UC74MBD6U3HEOAG7GQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VXEJBA72UC74MBD6U3HEOAG7GQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VXEJBA72UC74MBD6U3HEOAG7GQ/action/storage_attestation","attest_author":"https://pith.science/pith/VXEJBA72UC74MBD6U3HEOAG7GQ/action/author_attestation","sign_citation":"https://pith.science/pith/VXEJBA72UC74MBD6U3HEOAG7GQ/action/citation_signature","submit_replication":"https://pith.science/pith/VXEJBA72UC74MBD6U3HEOAG7GQ/action/replication_record"}},"created_at":"2026-06-09T01:04:37.576731+00:00","updated_at":"2026-06-09T01:04:37.576731+00:00"}