{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5VGVWHYCAJX4F3JHTONBJMHVGJ","short_pith_number":"pith:5VGVWHYC","canonical_record":{"source":{"id":"1506.00164","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-05-30T20:57:56Z","cross_cats_sorted":[],"title_canon_sha256":"09dcce82224e409080f776edab2e901fa79b3c3cc281ec857bcef22d431262d6","abstract_canon_sha256":"a95a071793535e56691a418dbcfeea42cc7d40d731b28d3e35b6cefc84cfdb8c"},"schema_version":"1.0"},"canonical_sha256":"ed4d5b1f02026fc2ed279b9a14b0f532400108618b19b7cb471a808343291304","source":{"kind":"arxiv","id":"1506.00164","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.00164","created_at":"2026-05-18T00:43:21Z"},{"alias_kind":"arxiv_version","alias_value":"1506.00164v1","created_at":"2026-05-18T00:43:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.00164","created_at":"2026-05-18T00:43:21Z"},{"alias_kind":"pith_short_12","alias_value":"5VGVWHYCAJX4","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"5VGVWHYCAJX4F3JH","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"5VGVWHYC","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5VGVWHYCAJX4F3JHTONBJMHVGJ","target":"record","payload":{"canonical_record":{"source":{"id":"1506.00164","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-05-30T20:57:56Z","cross_cats_sorted":[],"title_canon_sha256":"09dcce82224e409080f776edab2e901fa79b3c3cc281ec857bcef22d431262d6","abstract_canon_sha256":"a95a071793535e56691a418dbcfeea42cc7d40d731b28d3e35b6cefc84cfdb8c"},"schema_version":"1.0"},"canonical_sha256":"ed4d5b1f02026fc2ed279b9a14b0f532400108618b19b7cb471a808343291304","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:21.353681Z","signature_b64":"6rg7ILUyxi/c9XHH1tQ+/j00bCO28nakHunD1hhwA1+xQk6vOLzvWE9Ok3+QW2K6EC3cIgrulxj8019BGUYHCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed4d5b1f02026fc2ed279b9a14b0f532400108618b19b7cb471a808343291304","last_reissued_at":"2026-05-18T00:43:21.352951Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:21.352951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.00164","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":"2026-05-18T00:43:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mf8+6rApFutSChFaIp+whbQbdPKPzLjzhnENZS3gQWiGJ/b3yA30aC7/v6ZyL0680ZxLkF2snW0xGwrfo7vwAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T20:23:42.386599Z"},"content_sha256":"72a9213d2edbcd4a9b92a1f9a7215343175b1ab7938cb48a3e32c9fd7456711e","schema_version":"1.0","event_id":"sha256:72a9213d2edbcd4a9b92a1f9a7215343175b1ab7938cb48a3e32c9fd7456711e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5VGVWHYCAJX4F3JHTONBJMHVGJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Locally nilpotent derivations and automorphism groups of certain Danielewski surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Angelo Calil Bianchi, Marcelo Oliveira Veloso","submitted_at":"2015-05-30T20:57:56Z","abstract_excerpt":"We describe the set of all locally nilpotent derivations of the quotient ring $\\mathbb{K}[X,Y,Z]/(f(X)Y - \\varphi(X,Z))$ constructed from the defining equation $f(X)Y = \\varphi(X,Z)$ of a generalized Danielewski surface in $\\mathbb K^3$ for a specific choice of polynomials $f$ and $\\varphi$, with $\\mathbb K$ an algebraically closed field of characteristic zero. As a consequence of this description we calculate the $ML$-invariant and the Derksen invariant of this ring. We also determine a set of generators for the group of $\\mathbb K$-automorphisms of $\\mathbb K[X,Y,Z]/(f(X)Y - \\varphi(Z))$ als"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00164","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":"2026-05-18T00:43:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VKxQuqIWQgjaufwwjofL0xWQXxzC/nWFiRWFKyCzGeSKGmAlXAgXPZQf57zWfK4C2fwZzZ/xSAd7r4W2hhonAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T20:23:42.386940Z"},"content_sha256":"903e7f6c6569346a8d1e72a5d3346a12884898d6e27926e110549d96c1a9922c","schema_version":"1.0","event_id":"sha256:903e7f6c6569346a8d1e72a5d3346a12884898d6e27926e110549d96c1a9922c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5VGVWHYCAJX4F3JHTONBJMHVGJ/bundle.json","state_url":"https://pith.science/pith/5VGVWHYCAJX4F3JHTONBJMHVGJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5VGVWHYCAJX4F3JHTONBJMHVGJ/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":"2026-06-28T20:23:42Z","links":{"resolver":"https://pith.science/pith/5VGVWHYCAJX4F3JHTONBJMHVGJ","bundle":"https://pith.science/pith/5VGVWHYCAJX4F3JHTONBJMHVGJ/bundle.json","state":"https://pith.science/pith/5VGVWHYCAJX4F3JHTONBJMHVGJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5VGVWHYCAJX4F3JHTONBJMHVGJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5VGVWHYCAJX4F3JHTONBJMHVGJ","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":"a95a071793535e56691a418dbcfeea42cc7d40d731b28d3e35b6cefc84cfdb8c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-05-30T20:57:56Z","title_canon_sha256":"09dcce82224e409080f776edab2e901fa79b3c3cc281ec857bcef22d431262d6"},"schema_version":"1.0","source":{"id":"1506.00164","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.00164","created_at":"2026-05-18T00:43:21Z"},{"alias_kind":"arxiv_version","alias_value":"1506.00164v1","created_at":"2026-05-18T00:43:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.00164","created_at":"2026-05-18T00:43:21Z"},{"alias_kind":"pith_short_12","alias_value":"5VGVWHYCAJX4","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"5VGVWHYCAJX4F3JH","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"5VGVWHYC","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:903e7f6c6569346a8d1e72a5d3346a12884898d6e27926e110549d96c1a9922c","target":"graph","created_at":"2026-05-18T00:43:21Z","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 set of all locally nilpotent derivations of the quotient ring $\\mathbb{K}[X,Y,Z]/(f(X)Y - \\varphi(X,Z))$ constructed from the defining equation $f(X)Y = \\varphi(X,Z)$ of a generalized Danielewski surface in $\\mathbb K^3$ for a specific choice of polynomials $f$ and $\\varphi$, with $\\mathbb K$ an algebraically closed field of characteristic zero. As a consequence of this description we calculate the $ML$-invariant and the Derksen invariant of this ring. We also determine a set of generators for the group of $\\mathbb K$-automorphisms of $\\mathbb K[X,Y,Z]/(f(X)Y - \\varphi(Z))$ als","authors_text":"Angelo Calil Bianchi, Marcelo Oliveira Veloso","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-05-30T20:57:56Z","title":"Locally nilpotent derivations and automorphism groups of certain Danielewski surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00164","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":"sha256:72a9213d2edbcd4a9b92a1f9a7215343175b1ab7938cb48a3e32c9fd7456711e","target":"record","created_at":"2026-05-18T00:43:21Z","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":"a95a071793535e56691a418dbcfeea42cc7d40d731b28d3e35b6cefc84cfdb8c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-05-30T20:57:56Z","title_canon_sha256":"09dcce82224e409080f776edab2e901fa79b3c3cc281ec857bcef22d431262d6"},"schema_version":"1.0","source":{"id":"1506.00164","kind":"arxiv","version":1}},"canonical_sha256":"ed4d5b1f02026fc2ed279b9a14b0f532400108618b19b7cb471a808343291304","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed4d5b1f02026fc2ed279b9a14b0f532400108618b19b7cb471a808343291304","first_computed_at":"2026-05-18T00:43:21.352951Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:21.352951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6rg7ILUyxi/c9XHH1tQ+/j00bCO28nakHunD1hhwA1+xQk6vOLzvWE9Ok3+QW2K6EC3cIgrulxj8019BGUYHCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:21.353681Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.00164","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72a9213d2edbcd4a9b92a1f9a7215343175b1ab7938cb48a3e32c9fd7456711e","sha256:903e7f6c6569346a8d1e72a5d3346a12884898d6e27926e110549d96c1a9922c"],"state_sha256":"75116ec5a62c07d402b227d601834c3b0f94c1c221bbc12795f9c71c0bb0855e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UoO69UEhPklKwZM8KFUtpai02jPyn2tHCRlOzifL0wsA4fSXdtThWl/Wo8rUJd1bH/u32dCyDEhVRPmlircUCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T20:23:42.388850Z","bundle_sha256":"d86901a2022bbdf2470b88e7811eee00ea164828316167bed732c1e210bd7088"}}