{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:2PIN3QMK44X47ZOS5VRC27KWWO","short_pith_number":"pith:2PIN3QMK","canonical_record":{"source":{"id":"1601.01210","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-06T15:30:08Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"a7ce862f5eb548d5df370749442056358861fd760ae1a72b5e217e5ef0a035b3","abstract_canon_sha256":"a065ca47364abfd1e2c3f6dda6834ec023273180be833505efbc916b35b8daab"},"schema_version":"1.0"},"canonical_sha256":"d3d0ddc18ae72fcfe5d2ed622d7d56b3b805f496e29219341f208cce319179d3","source":{"kind":"arxiv","id":"1601.01210","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.01210","created_at":"2026-05-18T01:23:17Z"},{"alias_kind":"arxiv_version","alias_value":"1601.01210v1","created_at":"2026-05-18T01:23:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01210","created_at":"2026-05-18T01:23:17Z"},{"alias_kind":"pith_short_12","alias_value":"2PIN3QMK44X4","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2PIN3QMK44X47ZOS","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2PIN3QMK","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:2PIN3QMK44X47ZOS5VRC27KWWO","target":"record","payload":{"canonical_record":{"source":{"id":"1601.01210","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-06T15:30:08Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"a7ce862f5eb548d5df370749442056358861fd760ae1a72b5e217e5ef0a035b3","abstract_canon_sha256":"a065ca47364abfd1e2c3f6dda6834ec023273180be833505efbc916b35b8daab"},"schema_version":"1.0"},"canonical_sha256":"d3d0ddc18ae72fcfe5d2ed622d7d56b3b805f496e29219341f208cce319179d3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:17.560726Z","signature_b64":"LQJ4zLsA0BDAKTBhIjDcIgGvCKmZ8+htRdQLwMGSUg+G17g5GVDQxd6xBZuMvTGHBLBuczVlNPeA/NrFt/fXBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3d0ddc18ae72fcfe5d2ed622d7d56b3b805f496e29219341f208cce319179d3","last_reissued_at":"2026-05-18T01:23:17.560059Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:17.560059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.01210","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":"2026-05-18T01:23:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NazOHCss/Z0HLYtocQSfXAaxRRYrGpv0JtiTsWcRq7VP8X/ysRzAOsf8mf4vqiYZ3wntk9AdgOQX8xP1C+ImAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:20:49.246802Z"},"content_sha256":"db2c8541d771ef1efbfa9bbab59d24534c150a803733c60374091614121255cf","schema_version":"1.0","event_id":"sha256:db2c8541d771ef1efbfa9bbab59d24534c150a803733c60374091614121255cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:2PIN3QMK44X47ZOS5VRC27KWWO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On some nice polynomial automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Elzbieta Adamus, Pawel Bogdan, Teresa Crespo, Zbigniew Hajto","submitted_at":"2016-01-06T15:30:08Z","abstract_excerpt":"Given a polynomial endomorphism F of the n-dimensional affine space over a field K, we define a sequence of polynomial endomorphisms of the affine space associated to F. We call F nice if there exists an integer m such that the m-th term of the sequence vanishes. Then F is invertible and its inverse may be computed in terms of the endomorphisms in the sequence. In this paper we study the class of nice polynomial automorphisms and obtain that this class is large and includes triangulable automorphisms and all linear cubic homogeneous polynomial automorphisms of nilpotence index up to 3. We prov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01210","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":"2026-05-18T01:23:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XVzSXocl+8s22VcqfC98y47kcVfMzL1BvgJ1T+T+WrayVpZFjkcHpPb0GpjL3pnWeezoY0vX/OAH4f53kSwIBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:20:49.247154Z"},"content_sha256":"2a4f4e23e7ea2922aaa4be09ebfa4455ba7980ab943ce1405b4651e579eeb031","schema_version":"1.0","event_id":"sha256:2a4f4e23e7ea2922aaa4be09ebfa4455ba7980ab943ce1405b4651e579eeb031"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2PIN3QMK44X47ZOS5VRC27KWWO/bundle.json","state_url":"https://pith.science/pith/2PIN3QMK44X47ZOS5VRC27KWWO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2PIN3QMK44X47ZOS5VRC27KWWO/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":"2026-06-03T14:20:49Z","links":{"resolver":"https://pith.science/pith/2PIN3QMK44X47ZOS5VRC27KWWO","bundle":"https://pith.science/pith/2PIN3QMK44X47ZOS5VRC27KWWO/bundle.json","state":"https://pith.science/pith/2PIN3QMK44X47ZOS5VRC27KWWO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2PIN3QMK44X47ZOS5VRC27KWWO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2PIN3QMK44X47ZOS5VRC27KWWO","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":"a065ca47364abfd1e2c3f6dda6834ec023273180be833505efbc916b35b8daab","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-06T15:30:08Z","title_canon_sha256":"a7ce862f5eb548d5df370749442056358861fd760ae1a72b5e217e5ef0a035b3"},"schema_version":"1.0","source":{"id":"1601.01210","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.01210","created_at":"2026-05-18T01:23:17Z"},{"alias_kind":"arxiv_version","alias_value":"1601.01210v1","created_at":"2026-05-18T01:23:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01210","created_at":"2026-05-18T01:23:17Z"},{"alias_kind":"pith_short_12","alias_value":"2PIN3QMK44X4","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2PIN3QMK44X47ZOS","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2PIN3QMK","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:2a4f4e23e7ea2922aaa4be09ebfa4455ba7980ab943ce1405b4651e579eeb031","target":"graph","created_at":"2026-05-18T01:23:17Z","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":"Given a polynomial endomorphism F of the n-dimensional affine space over a field K, we define a sequence of polynomial endomorphisms of the affine space associated to F. We call F nice if there exists an integer m such that the m-th term of the sequence vanishes. Then F is invertible and its inverse may be computed in terms of the endomorphisms in the sequence. In this paper we study the class of nice polynomial automorphisms and obtain that this class is large and includes triangulable automorphisms and all linear cubic homogeneous polynomial automorphisms of nilpotence index up to 3. We prov","authors_text":"Elzbieta Adamus, Pawel Bogdan, Teresa Crespo, Zbigniew Hajto","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-06T15:30:08Z","title":"On some nice polynomial automorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01210","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:db2c8541d771ef1efbfa9bbab59d24534c150a803733c60374091614121255cf","target":"record","created_at":"2026-05-18T01:23:17Z","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":"a065ca47364abfd1e2c3f6dda6834ec023273180be833505efbc916b35b8daab","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-06T15:30:08Z","title_canon_sha256":"a7ce862f5eb548d5df370749442056358861fd760ae1a72b5e217e5ef0a035b3"},"schema_version":"1.0","source":{"id":"1601.01210","kind":"arxiv","version":1}},"canonical_sha256":"d3d0ddc18ae72fcfe5d2ed622d7d56b3b805f496e29219341f208cce319179d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3d0ddc18ae72fcfe5d2ed622d7d56b3b805f496e29219341f208cce319179d3","first_computed_at":"2026-05-18T01:23:17.560059Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:17.560059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LQJ4zLsA0BDAKTBhIjDcIgGvCKmZ8+htRdQLwMGSUg+G17g5GVDQxd6xBZuMvTGHBLBuczVlNPeA/NrFt/fXBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:17.560726Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.01210","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db2c8541d771ef1efbfa9bbab59d24534c150a803733c60374091614121255cf","sha256:2a4f4e23e7ea2922aaa4be09ebfa4455ba7980ab943ce1405b4651e579eeb031"],"state_sha256":"6e7a9824f79e7d5c1e715b60d89fda938f8acb0ecb3d5d7fa8b9be417e5b2872"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qW4i7kFogFCjHsYYZImIdLUaQ3vFQ+rl1c7umgYuOZJrNnYKmxuMkI+Qr/xkoUdAmQ+PAdaSjMNM+PO0bcl5Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T14:20:49.249173Z","bundle_sha256":"0d2b50078f1f58f233f11b01dc312da5d619238ece2091b5ce31af723b2ed0e6"}}