{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:K4KAW6GG5W24IBKK7RWJU4ZCZJ","short_pith_number":"pith:K4KAW6GG","schema_version":"1.0","canonical_sha256":"57140b78c6edb5c4054afc6c9a7322ca7b154d9ab0965ecb8d7f635082863315","source":{"kind":"arxiv","id":"1107.1162","version":1},"attestation_state":"computed","paper":{"title":"Multivariate ultrametric root counting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Ashraf Ibrahim, Martin Avendano","submitted_at":"2011-07-06T15:37:43Z","abstract_excerpt":"Let $K$ be a field, complete with respect to a discrete non-archimedian valuation and let $k$ be the residue field. Consider a system $F$ of $n$ polynomial equations in $K\\vars$. Our first result is a reformulation of the classical Hensel's Lemma in the language of tropical geometry: we show sufficient conditions (semiregularity at $w$) that guarantee that the first digit map $\\delta:(K^\\ast)^n\\to(k^\\ast)^n$ is a one to one correspondence between the solutions of $F$ in $(K^\\ast)^n$ with valuation $w$ and the solutions in $(k^\\ast)^n$ of the initial form system ${\\rm in}_w(F)$. Using this 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":"1107.1162","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-06T15:37:43Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"44c8cb75b51fb4f92cb9bccc5caec28633bc3162be2a99069b304db923a3297a","abstract_canon_sha256":"bf1104b1e5a73693195a9e6813cef835dfdb3d518c343a4e30e6d3dad3e3a287"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:45.452023Z","signature_b64":"icxYNpFeiRE9GNO82Ww7MM2lBZ1KYX+vmWRPyezP89YcfWHlCj76gM4X06IGg3e2sjTPVMvnvtHIVtq+jlHDAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57140b78c6edb5c4054afc6c9a7322ca7b154d9ab0965ecb8d7f635082863315","last_reissued_at":"2026-05-18T04:18:45.451564Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:45.451564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multivariate ultrametric root counting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Ashraf Ibrahim, Martin Avendano","submitted_at":"2011-07-06T15:37:43Z","abstract_excerpt":"Let $K$ be a field, complete with respect to a discrete non-archimedian valuation and let $k$ be the residue field. Consider a system $F$ of $n$ polynomial equations in $K\\vars$. Our first result is a reformulation of the classical Hensel's Lemma in the language of tropical geometry: we show sufficient conditions (semiregularity at $w$) that guarantee that the first digit map $\\delta:(K^\\ast)^n\\to(k^\\ast)^n$ is a one to one correspondence between the solutions of $F$ in $(K^\\ast)^n$ with valuation $w$ and the solutions in $(k^\\ast)^n$ of the initial form system ${\\rm in}_w(F)$. Using this resu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1162","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":"1107.1162","created_at":"2026-05-18T04:18:45.451636+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.1162v1","created_at":"2026-05-18T04:18:45.451636+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1162","created_at":"2026-05-18T04:18:45.451636+00:00"},{"alias_kind":"pith_short_12","alias_value":"K4KAW6GG5W24","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"K4KAW6GG5W24IBKK","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"K4KAW6GG","created_at":"2026-05-18T12:26:32.869790+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/K4KAW6GG5W24IBKK7RWJU4ZCZJ","json":"https://pith.science/pith/K4KAW6GG5W24IBKK7RWJU4ZCZJ.json","graph_json":"https://pith.science/api/pith-number/K4KAW6GG5W24IBKK7RWJU4ZCZJ/graph.json","events_json":"https://pith.science/api/pith-number/K4KAW6GG5W24IBKK7RWJU4ZCZJ/events.json","paper":"https://pith.science/paper/K4KAW6GG"},"agent_actions":{"view_html":"https://pith.science/pith/K4KAW6GG5W24IBKK7RWJU4ZCZJ","download_json":"https://pith.science/pith/K4KAW6GG5W24IBKK7RWJU4ZCZJ.json","view_paper":"https://pith.science/paper/K4KAW6GG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.1162&json=true","fetch_graph":"https://pith.science/api/pith-number/K4KAW6GG5W24IBKK7RWJU4ZCZJ/graph.json","fetch_events":"https://pith.science/api/pith-number/K4KAW6GG5W24IBKK7RWJU4ZCZJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K4KAW6GG5W24IBKK7RWJU4ZCZJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K4KAW6GG5W24IBKK7RWJU4ZCZJ/action/storage_attestation","attest_author":"https://pith.science/pith/K4KAW6GG5W24IBKK7RWJU4ZCZJ/action/author_attestation","sign_citation":"https://pith.science/pith/K4KAW6GG5W24IBKK7RWJU4ZCZJ/action/citation_signature","submit_replication":"https://pith.science/pith/K4KAW6GG5W24IBKK7RWJU4ZCZJ/action/replication_record"}},"created_at":"2026-05-18T04:18:45.451636+00:00","updated_at":"2026-05-18T04:18:45.451636+00:00"}