{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:PFEWBSV6GQTRZIVDBYSN5MF2GF","short_pith_number":"pith:PFEWBSV6","schema_version":"1.0","canonical_sha256":"794960cabe34271ca2a30e24deb0ba316cd2bb964a4c4647a1b43b5b89e6aa5a","source":{"kind":"arxiv","id":"1112.6071","version":1},"attestation_state":"computed","paper":{"title":"Tame automorphisms with multidegrees in the form of arithmetic progressions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Jiantao Li, Xiankun Du","submitted_at":"2011-12-28T06:56:33Z","abstract_excerpt":"Let $(a,a+d,a+2d)$ be an arithmetic progression of positive integers. The following statements are proved:\n  (1) If $a\\mid 2d$, then $(a, a+d, a+2d)\\in\\mdeg(\\Tame(\\mathbb{C}^3))$.\n  (2) If $a\\nmid 2d$, then, except for arithmetic progressions of the form $(4i,4i+ij,4i+2ij)$ with $i,j \\in\\mathbb{N}$ and $j$ is an odd number, $(a, a+d, a+2d)\\notin\\mdeg(\\Tame(\\mathbb{C}^3))$. We also related the exceptional unknown case to a conjecture of Jie-tai Yu, which concerns with the lower bound of the degree of the Poisson bracket of two polynomials."},"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":"1112.6071","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-28T06:56:33Z","cross_cats_sorted":[],"title_canon_sha256":"ab4fe4fc60b2fe9a923cecb2a162574de777e3474a4ce9151b7d7555d977d7e5","abstract_canon_sha256":"ccfa71e9a27fa20a0bd30877eab73fd68ae5dfc07ae549c0803c26d29321fc27"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:36.910382Z","signature_b64":"DFm0b6qrlcIr2OGfP3gGL4o+EWj8AxdX/rH5LNRgQHibvnuJMzB9YBxgjY0yTGyseamH0XEzQzq3T6uE9G0LBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"794960cabe34271ca2a30e24deb0ba316cd2bb964a4c4647a1b43b5b89e6aa5a","last_reissued_at":"2026-05-18T04:05:36.909634Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:36.909634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tame automorphisms with multidegrees in the form of arithmetic progressions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Jiantao Li, Xiankun Du","submitted_at":"2011-12-28T06:56:33Z","abstract_excerpt":"Let $(a,a+d,a+2d)$ be an arithmetic progression of positive integers. The following statements are proved:\n  (1) If $a\\mid 2d$, then $(a, a+d, a+2d)\\in\\mdeg(\\Tame(\\mathbb{C}^3))$.\n  (2) If $a\\nmid 2d$, then, except for arithmetic progressions of the form $(4i,4i+ij,4i+2ij)$ with $i,j \\in\\mathbb{N}$ and $j$ is an odd number, $(a, a+d, a+2d)\\notin\\mdeg(\\Tame(\\mathbb{C}^3))$. We also related the exceptional unknown case to a conjecture of Jie-tai Yu, which concerns with the lower bound of the degree of the Poisson bracket of two polynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.6071","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":"1112.6071","created_at":"2026-05-18T04:05:36.909770+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.6071v1","created_at":"2026-05-18T04:05:36.909770+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.6071","created_at":"2026-05-18T04:05:36.909770+00:00"},{"alias_kind":"pith_short_12","alias_value":"PFEWBSV6GQTR","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"PFEWBSV6GQTRZIVD","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"PFEWBSV6","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/PFEWBSV6GQTRZIVDBYSN5MF2GF","json":"https://pith.science/pith/PFEWBSV6GQTRZIVDBYSN5MF2GF.json","graph_json":"https://pith.science/api/pith-number/PFEWBSV6GQTRZIVDBYSN5MF2GF/graph.json","events_json":"https://pith.science/api/pith-number/PFEWBSV6GQTRZIVDBYSN5MF2GF/events.json","paper":"https://pith.science/paper/PFEWBSV6"},"agent_actions":{"view_html":"https://pith.science/pith/PFEWBSV6GQTRZIVDBYSN5MF2GF","download_json":"https://pith.science/pith/PFEWBSV6GQTRZIVDBYSN5MF2GF.json","view_paper":"https://pith.science/paper/PFEWBSV6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.6071&json=true","fetch_graph":"https://pith.science/api/pith-number/PFEWBSV6GQTRZIVDBYSN5MF2GF/graph.json","fetch_events":"https://pith.science/api/pith-number/PFEWBSV6GQTRZIVDBYSN5MF2GF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PFEWBSV6GQTRZIVDBYSN5MF2GF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PFEWBSV6GQTRZIVDBYSN5MF2GF/action/storage_attestation","attest_author":"https://pith.science/pith/PFEWBSV6GQTRZIVDBYSN5MF2GF/action/author_attestation","sign_citation":"https://pith.science/pith/PFEWBSV6GQTRZIVDBYSN5MF2GF/action/citation_signature","submit_replication":"https://pith.science/pith/PFEWBSV6GQTRZIVDBYSN5MF2GF/action/replication_record"}},"created_at":"2026-05-18T04:05:36.909770+00:00","updated_at":"2026-05-18T04:05:36.909770+00:00"}