{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:NUXA5JDKFYUQG5KGBAPEARR6YH","short_pith_number":"pith:NUXA5JDK","schema_version":"1.0","canonical_sha256":"6d2e0ea46a2e29037546081e40463ec1e1dab35d3881b560cae90f98dfe1c6e0","source":{"kind":"arxiv","id":"1903.07089","version":1},"attestation_state":"computed","paper":{"title":"Twisters and signed fundamental domains for number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Eduardo Friedman, Milton Espinoza","submitted_at":"2019-03-17T13:59:20Z","abstract_excerpt":"We give a signed fundamental domain for the action on $\\mathbb{R}^{r_1}_+\\times{\\mathbb{C}^*}^{r_2}$ of the totally positive units $E_+$ of a number field $k$ of degree $n=r_1+2r_2$ which we assume is not totally complex. Here $r_1$ and $r_2$ denote the number of real and complex places of $k$ and $\\mathbb{R}_+$ denotes the positive real numbers. The signed fundamental domain consists of $n$-dimensional $k$-rational cones $C_\\alpha$, each equipped with a sign $\\mu_\\alpha=\\pm1$, with the property that the net number of intersections of the cones with any $E_+$-orbit is 1.\n  The cones $C_\\alpha$"},"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":"1903.07089","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-03-17T13:59:20Z","cross_cats_sorted":[],"title_canon_sha256":"6ea73351bebf4bcf6aa2d960ace9fd016fbbf97f5e864b98815ef938ce590bfa","abstract_canon_sha256":"c9d70f44b552ef0109a7c29095f1a7f05c0e2006fe2542ff7eb758706f65325f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:04.272159Z","signature_b64":"rnXt4quc0+7cG04iEs0gjoq+LkKKv8T1DAXY50BNu9HBN20e+7Lt7ncSkT3PbxhM2YhtmFoRFvCQzJapku/GCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d2e0ea46a2e29037546081e40463ec1e1dab35d3881b560cae90f98dfe1c6e0","last_reissued_at":"2026-05-17T23:51:04.271498Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:04.271498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Twisters and signed fundamental domains for number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Eduardo Friedman, Milton Espinoza","submitted_at":"2019-03-17T13:59:20Z","abstract_excerpt":"We give a signed fundamental domain for the action on $\\mathbb{R}^{r_1}_+\\times{\\mathbb{C}^*}^{r_2}$ of the totally positive units $E_+$ of a number field $k$ of degree $n=r_1+2r_2$ which we assume is not totally complex. Here $r_1$ and $r_2$ denote the number of real and complex places of $k$ and $\\mathbb{R}_+$ denotes the positive real numbers. The signed fundamental domain consists of $n$-dimensional $k$-rational cones $C_\\alpha$, each equipped with a sign $\\mu_\\alpha=\\pm1$, with the property that the net number of intersections of the cones with any $E_+$-orbit is 1.\n  The cones $C_\\alpha$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07089","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":"1903.07089","created_at":"2026-05-17T23:51:04.271602+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.07089v1","created_at":"2026-05-17T23:51:04.271602+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.07089","created_at":"2026-05-17T23:51:04.271602+00:00"},{"alias_kind":"pith_short_12","alias_value":"NUXA5JDKFYUQ","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"NUXA5JDKFYUQG5KG","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"NUXA5JDK","created_at":"2026-05-18T12:33:24.271573+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/NUXA5JDKFYUQG5KGBAPEARR6YH","json":"https://pith.science/pith/NUXA5JDKFYUQG5KGBAPEARR6YH.json","graph_json":"https://pith.science/api/pith-number/NUXA5JDKFYUQG5KGBAPEARR6YH/graph.json","events_json":"https://pith.science/api/pith-number/NUXA5JDKFYUQG5KGBAPEARR6YH/events.json","paper":"https://pith.science/paper/NUXA5JDK"},"agent_actions":{"view_html":"https://pith.science/pith/NUXA5JDKFYUQG5KGBAPEARR6YH","download_json":"https://pith.science/pith/NUXA5JDKFYUQG5KGBAPEARR6YH.json","view_paper":"https://pith.science/paper/NUXA5JDK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.07089&json=true","fetch_graph":"https://pith.science/api/pith-number/NUXA5JDKFYUQG5KGBAPEARR6YH/graph.json","fetch_events":"https://pith.science/api/pith-number/NUXA5JDKFYUQG5KGBAPEARR6YH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NUXA5JDKFYUQG5KGBAPEARR6YH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NUXA5JDKFYUQG5KGBAPEARR6YH/action/storage_attestation","attest_author":"https://pith.science/pith/NUXA5JDKFYUQG5KGBAPEARR6YH/action/author_attestation","sign_citation":"https://pith.science/pith/NUXA5JDKFYUQG5KGBAPEARR6YH/action/citation_signature","submit_replication":"https://pith.science/pith/NUXA5JDKFYUQG5KGBAPEARR6YH/action/replication_record"}},"created_at":"2026-05-17T23:51:04.271602+00:00","updated_at":"2026-05-17T23:51:04.271602+00:00"}