{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:WQ7TQTUJNT646XSZHUBTKWVVTK","short_pith_number":"pith:WQ7TQTUJ","canonical_record":{"source":{"id":"1604.01551","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-04-06T09:20:40Z","cross_cats_sorted":["math.AG","math.GR"],"title_canon_sha256":"4e4fc5840c7b9df622740ede65a71a14ea8c19f0c20781d2b637134560927723","abstract_canon_sha256":"b6ad925016d1dfb5923aa36c11b6403777adb7cd52ec430f7d4fffe09f80b382"},"schema_version":"1.0"},"canonical_sha256":"b43f384e896cfdcf5e593d03355ab59a8d2b6d2145fe8b12622f55143150c8d1","source":{"kind":"arxiv","id":"1604.01551","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.01551","created_at":"2026-05-18T01:17:36Z"},{"alias_kind":"arxiv_version","alias_value":"1604.01551v1","created_at":"2026-05-18T01:17:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.01551","created_at":"2026-05-18T01:17:36Z"},{"alias_kind":"pith_short_12","alias_value":"WQ7TQTUJNT64","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"WQ7TQTUJNT646XSZ","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"WQ7TQTUJ","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:WQ7TQTUJNT646XSZHUBTKWVVTK","target":"record","payload":{"canonical_record":{"source":{"id":"1604.01551","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-04-06T09:20:40Z","cross_cats_sorted":["math.AG","math.GR"],"title_canon_sha256":"4e4fc5840c7b9df622740ede65a71a14ea8c19f0c20781d2b637134560927723","abstract_canon_sha256":"b6ad925016d1dfb5923aa36c11b6403777adb7cd52ec430f7d4fffe09f80b382"},"schema_version":"1.0"},"canonical_sha256":"b43f384e896cfdcf5e593d03355ab59a8d2b6d2145fe8b12622f55143150c8d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:36.133711Z","signature_b64":"fF/JEkQ2ZgEf4z2HAzagGRV7Uk+0qPTU9oM957muJVd6tVLA8beW8jA61XUDvQiV8DvV3024TY+cbY7pD+2dDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b43f384e896cfdcf5e593d03355ab59a8d2b6d2145fe8b12622f55143150c8d1","last_reissued_at":"2026-05-18T01:17:36.133120Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:36.133120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.01551","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:17:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2Jwz4PEuWjrZweUd7cNcU18UZBoOXriFGKUFD5JWrWwT86onbrL8+VL8vQEPTcq/5vqkTzEckUtrSJeirfC8Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T17:51:43.624934Z"},"content_sha256":"a957a9ee0ca953019ecc459dff56b7cad3d4ebdc6aab5506f4ca287cfff6a49d","schema_version":"1.0","event_id":"sha256:a957a9ee0ca953019ecc459dff56b7cad3d4ebdc6aab5506f4ca287cfff6a49d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:WQ7TQTUJNT646XSZHUBTKWVVTK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stably co-tame polynomial automorphisms over commutative rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.GR"],"primary_cat":"math.AC","authors_text":"Shigeru Kuroda","submitted_at":"2016-04-06T09:20:40Z","abstract_excerpt":"We say that a polynomial automorphism $\\phi $ in $n$ variables is stably co-tame if the tame subgroup in $n$ variables is contained in the subgroup generated by $\\phi $ and affine automorphisms in $n+1$ variables. In this paper, we give conditions for stably co-tameness of polynomial automorphisms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01551","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:17:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QX3o2yX3uFcnp93aa/YaD2f1+2OFdUzlOkbnLA/Sl/xDq472ielhgQkyDnb+JqTINrrG4W3nPk369h75AuSwAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T17:51:43.625373Z"},"content_sha256":"8333a4d6183fad0efcaa3206e72a92678b8130dac3d2ab5d09d0341aca7544e7","schema_version":"1.0","event_id":"sha256:8333a4d6183fad0efcaa3206e72a92678b8130dac3d2ab5d09d0341aca7544e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WQ7TQTUJNT646XSZHUBTKWVVTK/bundle.json","state_url":"https://pith.science/pith/WQ7TQTUJNT646XSZHUBTKWVVTK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WQ7TQTUJNT646XSZHUBTKWVVTK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T17:51:43Z","links":{"resolver":"https://pith.science/pith/WQ7TQTUJNT646XSZHUBTKWVVTK","bundle":"https://pith.science/pith/WQ7TQTUJNT646XSZHUBTKWVVTK/bundle.json","state":"https://pith.science/pith/WQ7TQTUJNT646XSZHUBTKWVVTK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WQ7TQTUJNT646XSZHUBTKWVVTK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WQ7TQTUJNT646XSZHUBTKWVVTK","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":"b6ad925016d1dfb5923aa36c11b6403777adb7cd52ec430f7d4fffe09f80b382","cross_cats_sorted":["math.AG","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-04-06T09:20:40Z","title_canon_sha256":"4e4fc5840c7b9df622740ede65a71a14ea8c19f0c20781d2b637134560927723"},"schema_version":"1.0","source":{"id":"1604.01551","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.01551","created_at":"2026-05-18T01:17:36Z"},{"alias_kind":"arxiv_version","alias_value":"1604.01551v1","created_at":"2026-05-18T01:17:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.01551","created_at":"2026-05-18T01:17:36Z"},{"alias_kind":"pith_short_12","alias_value":"WQ7TQTUJNT64","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"WQ7TQTUJNT646XSZ","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"WQ7TQTUJ","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:8333a4d6183fad0efcaa3206e72a92678b8130dac3d2ab5d09d0341aca7544e7","target":"graph","created_at":"2026-05-18T01:17:36Z","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":"We say that a polynomial automorphism $\\phi $ in $n$ variables is stably co-tame if the tame subgroup in $n$ variables is contained in the subgroup generated by $\\phi $ and affine automorphisms in $n+1$ variables. In this paper, we give conditions for stably co-tameness of polynomial automorphisms.","authors_text":"Shigeru Kuroda","cross_cats":["math.AG","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-04-06T09:20:40Z","title":"Stably co-tame polynomial automorphisms over commutative rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01551","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:a957a9ee0ca953019ecc459dff56b7cad3d4ebdc6aab5506f4ca287cfff6a49d","target":"record","created_at":"2026-05-18T01:17:36Z","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":"b6ad925016d1dfb5923aa36c11b6403777adb7cd52ec430f7d4fffe09f80b382","cross_cats_sorted":["math.AG","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-04-06T09:20:40Z","title_canon_sha256":"4e4fc5840c7b9df622740ede65a71a14ea8c19f0c20781d2b637134560927723"},"schema_version":"1.0","source":{"id":"1604.01551","kind":"arxiv","version":1}},"canonical_sha256":"b43f384e896cfdcf5e593d03355ab59a8d2b6d2145fe8b12622f55143150c8d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b43f384e896cfdcf5e593d03355ab59a8d2b6d2145fe8b12622f55143150c8d1","first_computed_at":"2026-05-18T01:17:36.133120Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:36.133120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fF/JEkQ2ZgEf4z2HAzagGRV7Uk+0qPTU9oM957muJVd6tVLA8beW8jA61XUDvQiV8DvV3024TY+cbY7pD+2dDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:36.133711Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.01551","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a957a9ee0ca953019ecc459dff56b7cad3d4ebdc6aab5506f4ca287cfff6a49d","sha256:8333a4d6183fad0efcaa3206e72a92678b8130dac3d2ab5d09d0341aca7544e7"],"state_sha256":"cc47f329a5d8ef2b0563b9da8c482a398f19ec59efb0745190a6130971197756"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nV+kcAc5u+daa1EQ7KYo/DZpzmOBdHMgIsxCCTt1u9nuG+qIBZZyWh0tZpIU1/eiGMajutAs87ywdnNoTzOoDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T17:51:43.628662Z","bundle_sha256":"89da78eaefa058f52ddaf619016e67721743bcd9593c32c74d788a360b584f65"}}