{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:UEIOV7WZNL4PQMFE27WERY35F7","short_pith_number":"pith:UEIOV7WZ","canonical_record":{"source":{"id":"1606.04531","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-06-14T19:59:52Z","cross_cats_sorted":[],"title_canon_sha256":"b728f79927ff69e95dceec20b2eb2ddfe23a95de35d1604658c08a17fc7dc4ee","abstract_canon_sha256":"f8ba40d0fabee4cb0ec7515956923e3571cb8930d7555bc36d6878c32c4b9a14"},"schema_version":"1.0"},"canonical_sha256":"a110eafed96af8f830a4d7ec48e37d2fd53e3decc942d4db3a37b808afb6ce46","source":{"kind":"arxiv","id":"1606.04531","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.04531","created_at":"2026-05-18T01:12:22Z"},{"alias_kind":"arxiv_version","alias_value":"1606.04531v2","created_at":"2026-05-18T01:12:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.04531","created_at":"2026-05-18T01:12:22Z"},{"alias_kind":"pith_short_12","alias_value":"UEIOV7WZNL4P","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UEIOV7WZNL4PQMFE","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UEIOV7WZ","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:UEIOV7WZNL4PQMFE27WERY35F7","target":"record","payload":{"canonical_record":{"source":{"id":"1606.04531","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-06-14T19:59:52Z","cross_cats_sorted":[],"title_canon_sha256":"b728f79927ff69e95dceec20b2eb2ddfe23a95de35d1604658c08a17fc7dc4ee","abstract_canon_sha256":"f8ba40d0fabee4cb0ec7515956923e3571cb8930d7555bc36d6878c32c4b9a14"},"schema_version":"1.0"},"canonical_sha256":"a110eafed96af8f830a4d7ec48e37d2fd53e3decc942d4db3a37b808afb6ce46","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:22.339757Z","signature_b64":"hvvlF778DZziqJ73wThKZrrKg4oewnmJPhKCgY8X2DOduNxmgt4tXKaiYrGteAKKbgXTySVh4hPOe1GfUbUrDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a110eafed96af8f830a4d7ec48e37d2fd53e3decc942d4db3a37b808afb6ce46","last_reissued_at":"2026-05-18T01:12:22.339431Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:22.339431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.04531","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nAy5FH30pMBwDRZfoxRrps74osYE0nuOiQTpZpNIbxDq80VPV+V50L8nO7KQpu+CZfPwEZq11Ntqq+Mqy0wnDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T15:53:35.772964Z"},"content_sha256":"f25dfc1a6f9539609ec6cf7b4c1b29ddb942c4341d5c41e486f4b8ef098e27af","schema_version":"1.0","event_id":"sha256:f25dfc1a6f9539609ec6cf7b4c1b29ddb942c4341d5c41e486f4b8ef098e27af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:UEIOV7WZNL4PQMFE27WERY35F7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The two-dimensional Jacobian Conjecture and unique factorization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Vered Moskowicz","submitted_at":"2016-06-14T19:59:52Z","abstract_excerpt":"The two-dimensional Jacobian Conjecture says that a $\\mathbb{C}$-algebra endomorphism $F:\\mathbb{C}[x,y] \\to \\mathbb{C}[x,y]$ that has an invertible Jacobian is an automorphism. We show that if a $\\mathbb{C}$-algebra endomorphism $F:\\mathbb{C}[x,y] \\to \\mathbb{C}[x,y]$ has an invertible Jacobian and if $v \\in \\mathbb{C}[F(x),F(y),x]$ is a product of prime elements of $\\mathbb{C}[F(x),F(y),x]$, then $F$ is an automorphism, where $v$ is such that $y = u/v$, where $u \\in \\mathbb{C}[F(x),F(y),x]$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04531","kind":"arxiv","version":2},"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":"2026-05-18T01:12:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y873KmwLg5iS01gG5hk843dlvTsWACZNDxx5CJ7nrNXu15zyjrtKXhSRfN634QTGhhoBNLOXUEV1B9j3tVKQDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T15:53:35.773307Z"},"content_sha256":"9e1cc8a276a26a96bb0880abd7862e7a519f5a9de34ed87581e54ae375cdd376","schema_version":"1.0","event_id":"sha256:9e1cc8a276a26a96bb0880abd7862e7a519f5a9de34ed87581e54ae375cdd376"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UEIOV7WZNL4PQMFE27WERY35F7/bundle.json","state_url":"https://pith.science/pith/UEIOV7WZNL4PQMFE27WERY35F7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UEIOV7WZNL4PQMFE27WERY35F7/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":"2026-06-26T15:53:35Z","links":{"resolver":"https://pith.science/pith/UEIOV7WZNL4PQMFE27WERY35F7","bundle":"https://pith.science/pith/UEIOV7WZNL4PQMFE27WERY35F7/bundle.json","state":"https://pith.science/pith/UEIOV7WZNL4PQMFE27WERY35F7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UEIOV7WZNL4PQMFE27WERY35F7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UEIOV7WZNL4PQMFE27WERY35F7","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":"f8ba40d0fabee4cb0ec7515956923e3571cb8930d7555bc36d6878c32c4b9a14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-06-14T19:59:52Z","title_canon_sha256":"b728f79927ff69e95dceec20b2eb2ddfe23a95de35d1604658c08a17fc7dc4ee"},"schema_version":"1.0","source":{"id":"1606.04531","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.04531","created_at":"2026-05-18T01:12:22Z"},{"alias_kind":"arxiv_version","alias_value":"1606.04531v2","created_at":"2026-05-18T01:12:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.04531","created_at":"2026-05-18T01:12:22Z"},{"alias_kind":"pith_short_12","alias_value":"UEIOV7WZNL4P","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UEIOV7WZNL4PQMFE","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UEIOV7WZ","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:9e1cc8a276a26a96bb0880abd7862e7a519f5a9de34ed87581e54ae375cdd376","target":"graph","created_at":"2026-05-18T01:12:22Z","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":"The two-dimensional Jacobian Conjecture says that a $\\mathbb{C}$-algebra endomorphism $F:\\mathbb{C}[x,y] \\to \\mathbb{C}[x,y]$ that has an invertible Jacobian is an automorphism. We show that if a $\\mathbb{C}$-algebra endomorphism $F:\\mathbb{C}[x,y] \\to \\mathbb{C}[x,y]$ has an invertible Jacobian and if $v \\in \\mathbb{C}[F(x),F(y),x]$ is a product of prime elements of $\\mathbb{C}[F(x),F(y),x]$, then $F$ is an automorphism, where $v$ is such that $y = u/v$, where $u \\in \\mathbb{C}[F(x),F(y),x]$.","authors_text":"Vered Moskowicz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-06-14T19:59:52Z","title":"The two-dimensional Jacobian Conjecture and unique factorization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04531","kind":"arxiv","version":2},"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:f25dfc1a6f9539609ec6cf7b4c1b29ddb942c4341d5c41e486f4b8ef098e27af","target":"record","created_at":"2026-05-18T01:12:22Z","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":"f8ba40d0fabee4cb0ec7515956923e3571cb8930d7555bc36d6878c32c4b9a14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-06-14T19:59:52Z","title_canon_sha256":"b728f79927ff69e95dceec20b2eb2ddfe23a95de35d1604658c08a17fc7dc4ee"},"schema_version":"1.0","source":{"id":"1606.04531","kind":"arxiv","version":2}},"canonical_sha256":"a110eafed96af8f830a4d7ec48e37d2fd53e3decc942d4db3a37b808afb6ce46","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a110eafed96af8f830a4d7ec48e37d2fd53e3decc942d4db3a37b808afb6ce46","first_computed_at":"2026-05-18T01:12:22.339431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:22.339431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hvvlF778DZziqJ73wThKZrrKg4oewnmJPhKCgY8X2DOduNxmgt4tXKaiYrGteAKKbgXTySVh4hPOe1GfUbUrDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:22.339757Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.04531","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f25dfc1a6f9539609ec6cf7b4c1b29ddb942c4341d5c41e486f4b8ef098e27af","sha256:9e1cc8a276a26a96bb0880abd7862e7a519f5a9de34ed87581e54ae375cdd376"],"state_sha256":"0a878171f927abd744fdf4ef6aa715848913df0b5fd8cdfce7ccac74d0aa289f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fZQLV2WQ9T1gs8gzCkJx1yC/KT9gJD+K9xhD1sWDAvI+MLNkMQOU0Y6giGYS+hunCuy4MazCikPdeufsFPbjBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T15:53:35.775561Z","bundle_sha256":"b4b376c65fc4c0def3fc1dd698ed393a3993531b7f1647093531935473b4565e"}}