{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OKQG6P55GWGIUP55Z6VQWLMPMH","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":"7af0c1be18efa8ffdd0c9ebaa19137e4396146a5c5e9a579563602f33d7f177c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-10-16T16:00:53Z","title_canon_sha256":"dfec63c797a67e46861377c9edc434b90f1a408e9e68769bdec603de80fdb72c"},"schema_version":"1.0","source":{"id":"1210.4465","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4465","created_at":"2026-05-18T03:43:05Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4465v1","created_at":"2026-05-18T03:43:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4465","created_at":"2026-05-18T03:43:05Z"},{"alias_kind":"pith_short_12","alias_value":"OKQG6P55GWGI","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OKQG6P55GWGIUP55","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OKQG6P55","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:42bc1e92c089d44fa9e6e86cef2741fc30dce415ad5806aa14fdbac898e613f7","target":"graph","created_at":"2026-05-18T03:43:05Z","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 hope to be able (in the future) to carefully analyze this structure and to tie the Jacobian Conjecture in dimension two to certain Zeta functions, thereby invoking a powerful arithmetic machinery to handle the two dimensional Jacobian Conjecture. Let us denote by ${\\rm et}(\\mathbb{C}^2)$ the semigroup of two dimensional Keller mappings. We would like to prove something like the following: a) That there exists an infinite index set $I$, and a family of mappings indexed by $I$, $\\{F_i\\,|\\,i\\in I\\} \\subset {\\rm et}(\\mathbb{C}^2)$ such that $$ {\\rm et}(\\mathbb{C}^2)={\\rm Aut}(\\mathbb{C}^2)\\cup\\","authors_text":"Ronen Peretz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-10-16T16:00:53Z","title":"On the structure of the semigroup of entire \\'etale mappings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4465","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":"sha256:33f9dc1565ff531ad9b1e2273fbf0264ba145f1c4cd33e50ffbf875b9a4704bb","target":"record","created_at":"2026-05-18T03:43:05Z","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":"7af0c1be18efa8ffdd0c9ebaa19137e4396146a5c5e9a579563602f33d7f177c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-10-16T16:00:53Z","title_canon_sha256":"dfec63c797a67e46861377c9edc434b90f1a408e9e68769bdec603de80fdb72c"},"schema_version":"1.0","source":{"id":"1210.4465","kind":"arxiv","version":1}},"canonical_sha256":"72a06f3fbd358c8a3fbdcfab0b2d8f61dc543862696a915039a89ddafdea7b66","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72a06f3fbd358c8a3fbdcfab0b2d8f61dc543862696a915039a89ddafdea7b66","first_computed_at":"2026-05-18T03:43:05.863403Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:05.863403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5mrEAM25cPq3G9GfHevGd7UFhDS9lVmsWN2OJi5+TxDE9CnHt2iwGOLas4tpcWMzG5eU5B4IvGs8IPe2ntnIAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:05.864051Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.4465","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33f9dc1565ff531ad9b1e2273fbf0264ba145f1c4cd33e50ffbf875b9a4704bb","sha256:42bc1e92c089d44fa9e6e86cef2741fc30dce415ad5806aa14fdbac898e613f7"],"state_sha256":"a1eb286921b64495dc2599f76280176fab1a9441c409a7281f557157fa973d5d"}