{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PFEWBSV6GQTRZIVDBYSN5MF2GF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ccfa71e9a27fa20a0bd30877eab73fd68ae5dfc07ae549c0803c26d29321fc27","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-28T06:56:33Z","title_canon_sha256":"ab4fe4fc60b2fe9a923cecb2a162574de777e3474a4ce9151b7d7555d977d7e5"},"schema_version":"1.0","source":{"id":"1112.6071","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.6071","created_at":"2026-05-18T04:05:36Z"},{"alias_kind":"arxiv_version","alias_value":"1112.6071v1","created_at":"2026-05-18T04:05:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.6071","created_at":"2026-05-18T04:05:36Z"},{"alias_kind":"pith_short_12","alias_value":"PFEWBSV6GQTR","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PFEWBSV6GQTRZIVD","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PFEWBSV6","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:99af2240f0f27f90891fa1da749743a4c62314ee9cf3a2f1c50f9490a6ef22c2","target":"graph","created_at":"2026-05-18T04:05:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Jiantao Li, Xiankun Du","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-28T06:56:33Z","title":"Tame automorphisms with multidegrees in the form of arithmetic progressions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.6071","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4809020512fc1e1aa7aad0aaebcf2a44d3a6da32c8610d02a918e77a19ec2cf4","target":"record","created_at":"2026-05-18T04:05:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ccfa71e9a27fa20a0bd30877eab73fd68ae5dfc07ae549c0803c26d29321fc27","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-28T06:56:33Z","title_canon_sha256":"ab4fe4fc60b2fe9a923cecb2a162574de777e3474a4ce9151b7d7555d977d7e5"},"schema_version":"1.0","source":{"id":"1112.6071","kind":"arxiv","version":1}},"canonical_sha256":"794960cabe34271ca2a30e24deb0ba316cd2bb964a4c4647a1b43b5b89e6aa5a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"794960cabe34271ca2a30e24deb0ba316cd2bb964a4c4647a1b43b5b89e6aa5a","first_computed_at":"2026-05-18T04:05:36.909634Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:36.909634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DFm0b6qrlcIr2OGfP3gGL4o+EWj8AxdX/rH5LNRgQHibvnuJMzB9YBxgjY0yTGyseamH0XEzQzq3T6uE9G0LBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:36.910382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.6071","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4809020512fc1e1aa7aad0aaebcf2a44d3a6da32c8610d02a918e77a19ec2cf4","sha256:99af2240f0f27f90891fa1da749743a4c62314ee9cf3a2f1c50f9490a6ef22c2"],"state_sha256":"1720d3ebb2040674cbf52f724cee3b519b868f43f1fbaec1adb65a03e007347a"}