{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:4IUDYB56VMW3MHG2XX6TKH6VL7","short_pith_number":"pith:4IUDYB56","canonical_record":{"source":{"id":"0903.4839","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-03-27T16:16:02Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"80b94635a12ffbcd607b06e301de1e11554a4e7378b3724c80095672905eff22","abstract_canon_sha256":"09847746a9f73ca579ce487129da67bb3eec1b266562c0acefa4c08d04bf03c7"},"schema_version":"1.0"},"canonical_sha256":"e2283c07beab2db61cdabdfd351fd55ff7cda6334c06422c95066a3d79a633e7","source":{"kind":"arxiv","id":"0903.4839","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.4839","created_at":"2026-05-18T00:29:06Z"},{"alias_kind":"arxiv_version","alias_value":"0903.4839v1","created_at":"2026-05-18T00:29:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.4839","created_at":"2026-05-18T00:29:06Z"},{"alias_kind":"pith_short_12","alias_value":"4IUDYB56VMW3","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"4IUDYB56VMW3MHG2","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"4IUDYB56","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:4IUDYB56VMW3MHG2XX6TKH6VL7","target":"record","payload":{"canonical_record":{"source":{"id":"0903.4839","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-03-27T16:16:02Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"80b94635a12ffbcd607b06e301de1e11554a4e7378b3724c80095672905eff22","abstract_canon_sha256":"09847746a9f73ca579ce487129da67bb3eec1b266562c0acefa4c08d04bf03c7"},"schema_version":"1.0"},"canonical_sha256":"e2283c07beab2db61cdabdfd351fd55ff7cda6334c06422c95066a3d79a633e7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:06.184387Z","signature_b64":"ly0nDz2qwYxKm1LvEPSLyk5eYo41xIoJaSBhf0dGb1fbIRUQXJMcoxfjXnxvEhO7bdKR4zxpuJ9cwS0TqtwFDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2283c07beab2db61cdabdfd351fd55ff7cda6334c06422c95066a3d79a633e7","last_reissued_at":"2026-05-18T00:29:06.183915Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:06.183915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0903.4839","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":"2026-05-18T00:29:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GG7bovE9EA2V6kHhPzK2VDeuYaNEQwhc09cr6LZHJKOxWiPgr+LEllbndBhFEiuWjFk5ztZIFiGqZxE1g/9RCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T14:54:49.774206Z"},"content_sha256":"0d6a55b2d828beafe0325e165ac97af14e0cfaed84066b921b8f623ea3e303c1","schema_version":"1.0","event_id":"sha256:0d6a55b2d828beafe0325e165ac97af14e0cfaed84066b921b8f623ea3e303c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:4IUDYB56VMW3MHG2XX6TKH6VL7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Automorphisms of the endomorphism semigroup of a free commutative algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.RA","authors_text":"A. Belov-Kanel, R. Lipyanski","submitted_at":"2009-03-27T16:16:02Z","abstract_excerpt":"We describe the automorphism group of the endomorphism semigroup $\\End(K[x_1,...,x_n])$ of ring $K[x_1,...,x_n]$ of polynomials over an {\\it arbitrary} field $K$. A similar result is obtained for automorphism group of the category of finitely generated free commutative-associative algebras of the variety $\\mathcal{CA}$ commutative algebras. This solves two problems posed by B. Plotkin (\\cite{24}, Problems 12 and 15).\n  More precisely, we prove that if $\\varphi\\in \\Aut\\End(K[x_1,...,x_n])$ then there exists a semi-linear automorphism $s:K[x_1,...,x_n]\\to K[x_1,...,x_n]$ such that $\\varphi(g)=s\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.4839","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":"2026-05-18T00:29:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bf4loWWUWcZJ8aUnTzdwQ51R2gTCIb7WHyLqeTULuLIwe5PsgTF+h72950aAJiiuxpmg63g1udRx//LCK9chCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T14:54:49.774889Z"},"content_sha256":"c8b3faecede613d09ff93a354bf36dc31d708b0cc9097f75225c330f4b28e4ec","schema_version":"1.0","event_id":"sha256:c8b3faecede613d09ff93a354bf36dc31d708b0cc9097f75225c330f4b28e4ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4IUDYB56VMW3MHG2XX6TKH6VL7/bundle.json","state_url":"https://pith.science/pith/4IUDYB56VMW3MHG2XX6TKH6VL7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4IUDYB56VMW3MHG2XX6TKH6VL7/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":"2026-06-01T14:54:49Z","links":{"resolver":"https://pith.science/pith/4IUDYB56VMW3MHG2XX6TKH6VL7","bundle":"https://pith.science/pith/4IUDYB56VMW3MHG2XX6TKH6VL7/bundle.json","state":"https://pith.science/pith/4IUDYB56VMW3MHG2XX6TKH6VL7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4IUDYB56VMW3MHG2XX6TKH6VL7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:4IUDYB56VMW3MHG2XX6TKH6VL7","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":"09847746a9f73ca579ce487129da67bb3eec1b266562c0acefa4c08d04bf03c7","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-03-27T16:16:02Z","title_canon_sha256":"80b94635a12ffbcd607b06e301de1e11554a4e7378b3724c80095672905eff22"},"schema_version":"1.0","source":{"id":"0903.4839","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.4839","created_at":"2026-05-18T00:29:06Z"},{"alias_kind":"arxiv_version","alias_value":"0903.4839v1","created_at":"2026-05-18T00:29:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.4839","created_at":"2026-05-18T00:29:06Z"},{"alias_kind":"pith_short_12","alias_value":"4IUDYB56VMW3","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"4IUDYB56VMW3MHG2","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"4IUDYB56","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:c8b3faecede613d09ff93a354bf36dc31d708b0cc9097f75225c330f4b28e4ec","target":"graph","created_at":"2026-05-18T00:29:06Z","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 describe the automorphism group of the endomorphism semigroup $\\End(K[x_1,...,x_n])$ of ring $K[x_1,...,x_n]$ of polynomials over an {\\it arbitrary} field $K$. A similar result is obtained for automorphism group of the category of finitely generated free commutative-associative algebras of the variety $\\mathcal{CA}$ commutative algebras. This solves two problems posed by B. Plotkin (\\cite{24}, Problems 12 and 15).\n  More precisely, we prove that if $\\varphi\\in \\Aut\\End(K[x_1,...,x_n])$ then there exists a semi-linear automorphism $s:K[x_1,...,x_n]\\to K[x_1,...,x_n]$ such that $\\varphi(g)=s\\","authors_text":"A. Belov-Kanel, R. Lipyanski","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-03-27T16:16:02Z","title":"Automorphisms of the endomorphism semigroup of a free commutative algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.4839","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":"sha256:0d6a55b2d828beafe0325e165ac97af14e0cfaed84066b921b8f623ea3e303c1","target":"record","created_at":"2026-05-18T00:29:06Z","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":"09847746a9f73ca579ce487129da67bb3eec1b266562c0acefa4c08d04bf03c7","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-03-27T16:16:02Z","title_canon_sha256":"80b94635a12ffbcd607b06e301de1e11554a4e7378b3724c80095672905eff22"},"schema_version":"1.0","source":{"id":"0903.4839","kind":"arxiv","version":1}},"canonical_sha256":"e2283c07beab2db61cdabdfd351fd55ff7cda6334c06422c95066a3d79a633e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2283c07beab2db61cdabdfd351fd55ff7cda6334c06422c95066a3d79a633e7","first_computed_at":"2026-05-18T00:29:06.183915Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:06.183915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ly0nDz2qwYxKm1LvEPSLyk5eYo41xIoJaSBhf0dGb1fbIRUQXJMcoxfjXnxvEhO7bdKR4zxpuJ9cwS0TqtwFDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:06.184387Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.4839","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d6a55b2d828beafe0325e165ac97af14e0cfaed84066b921b8f623ea3e303c1","sha256:c8b3faecede613d09ff93a354bf36dc31d708b0cc9097f75225c330f4b28e4ec"],"state_sha256":"fecfb2628fefef90493bc65438af2090db679e760c1643e2e3d41387f027783e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YeIJ0Pg2n4qKcMLEwmccI2IrtCDbSDIG3yoWdMbq9kNqejvOG2HlOFU/i6dgDpsCBnQiFLX23wBnYdWysOLsBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T14:54:49.777843Z","bundle_sha256":"1163d9a03ee03d636ad558c01208c94be444b7a4a0d6c8202e35f9ce99c5565a"}}