{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:PQUBYB26S7YODYKNVDUVUICBPQ","short_pith_number":"pith:PQUBYB26","schema_version":"1.0","canonical_sha256":"7c281c075e97f0e1e14da8e95a20417c193c1f6a2cf89a437da625c722a06b17","source":{"kind":"arxiv","id":"1108.1444","version":1},"attestation_state":"computed","paper":{"title":"Analytic varieties with finite volume amoebas are algebraic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Farid Madani, Mounir Nisse","submitted_at":"2011-08-06T03:30:44Z","abstract_excerpt":"In this paper, we study the amoeba volume of a given $k-$dimensional generic analytic variety $V$ of the complex algebraic torus $(\\C^*)^n$. When $n\\geq 2k$, we show that $V$ is algebraic if and only if the volume of its amoeba is finite. In this precise case, we establish a comparison theorem for the volume of the amoeba and the coamoeba. Examples and applications to the $k-$linear spaces will be given."},"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":"1108.1444","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-06T03:30:44Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"32baae7534d7844576f822ca440b6b7c0ccedae1bb3fa0ea1b5eb1b2656faf5b","abstract_canon_sha256":"4a71ced27f16250b2527eb2ee3077a55fe25ebf611ed7bca831b8c22d96f74c6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:01.040300Z","signature_b64":"/P9H4JAYNTp9z2tesB99V3EjtEjPe2j9860+Q0u3/lXquvCOTdpG2+FIaSyDbEnjjUbyidToszlGNmHR0BvECw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c281c075e97f0e1e14da8e95a20417c193c1f6a2cf89a437da625c722a06b17","last_reissued_at":"2026-05-18T04:16:01.039572Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:01.039572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analytic varieties with finite volume amoebas are algebraic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Farid Madani, Mounir Nisse","submitted_at":"2011-08-06T03:30:44Z","abstract_excerpt":"In this paper, we study the amoeba volume of a given $k-$dimensional generic analytic variety $V$ of the complex algebraic torus $(\\C^*)^n$. When $n\\geq 2k$, we show that $V$ is algebraic if and only if the volume of its amoeba is finite. In this precise case, we establish a comparison theorem for the volume of the amoeba and the coamoeba. Examples and applications to the $k-$linear spaces will be given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1444","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":"1108.1444","created_at":"2026-05-18T04:16:01.039691+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.1444v1","created_at":"2026-05-18T04:16:01.039691+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.1444","created_at":"2026-05-18T04:16:01.039691+00:00"},{"alias_kind":"pith_short_12","alias_value":"PQUBYB26S7YO","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"PQUBYB26S7YODYKN","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"PQUBYB26","created_at":"2026-05-18T12:26:39.201973+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/PQUBYB26S7YODYKNVDUVUICBPQ","json":"https://pith.science/pith/PQUBYB26S7YODYKNVDUVUICBPQ.json","graph_json":"https://pith.science/api/pith-number/PQUBYB26S7YODYKNVDUVUICBPQ/graph.json","events_json":"https://pith.science/api/pith-number/PQUBYB26S7YODYKNVDUVUICBPQ/events.json","paper":"https://pith.science/paper/PQUBYB26"},"agent_actions":{"view_html":"https://pith.science/pith/PQUBYB26S7YODYKNVDUVUICBPQ","download_json":"https://pith.science/pith/PQUBYB26S7YODYKNVDUVUICBPQ.json","view_paper":"https://pith.science/paper/PQUBYB26","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.1444&json=true","fetch_graph":"https://pith.science/api/pith-number/PQUBYB26S7YODYKNVDUVUICBPQ/graph.json","fetch_events":"https://pith.science/api/pith-number/PQUBYB26S7YODYKNVDUVUICBPQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PQUBYB26S7YODYKNVDUVUICBPQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PQUBYB26S7YODYKNVDUVUICBPQ/action/storage_attestation","attest_author":"https://pith.science/pith/PQUBYB26S7YODYKNVDUVUICBPQ/action/author_attestation","sign_citation":"https://pith.science/pith/PQUBYB26S7YODYKNVDUVUICBPQ/action/citation_signature","submit_replication":"https://pith.science/pith/PQUBYB26S7YODYKNVDUVUICBPQ/action/replication_record"}},"created_at":"2026-05-18T04:16:01.039691+00:00","updated_at":"2026-05-18T04:16:01.039691+00:00"}