{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:GAQGSAWBASXTRHBSDORPJBDNBF","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":"119805ef2b6107ec501d512b531581bd1186f5a20ad527d27a662fa5b095f745","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-02-10T20:27:32Z","title_canon_sha256":"99ca540b56bfc71488b54740e7491ae72bf590cc6b0cf45be5dc077984f5c607"},"schema_version":"1.0","source":{"id":"1902.03665","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.03665","created_at":"2026-05-17T23:54:19Z"},{"alias_kind":"arxiv_version","alias_value":"1902.03665v1","created_at":"2026-05-17T23:54:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03665","created_at":"2026-05-17T23:54:19Z"},{"alias_kind":"pith_short_12","alias_value":"GAQGSAWBASXT","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"GAQGSAWBASXTRHBS","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"GAQGSAWB","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:29a533232ae4f5931fa98c5640d8e91360d2a1ae132800b9ff841d62aa046c29","target":"graph","created_at":"2026-05-17T23:54:19Z","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":"A notion of one-dimensional formal ring is presented. It consists of a triple $(A,\\Phi,\\Psi)$ where $A$ is a unital ring and $\\Phi$ and $\\Psi$ are two formal power series in $2$ variables ${\\Phi(x,y),\\Psi(x,y)\\in A\\llbracket x,y\\rrbracket}$, the first one defining a one-dimensional formal group law over $A$ and the second one providing a second composition law satisfying axiomatic properties of compatibility with the first one. For a characteristic-zero ring $A$, a large class of one-dimensional formal rings can be obtained by constructing a new composition law, defined in terms of the group l","authors_text":"Jos\\'e Carrasco, Piergiulio Tempesta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-02-10T20:27:32Z","title":"Formal Rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03665","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:bcf0207b018068f286213be90796d5b19ffb12412273636bcb18c126a21cc484","target":"record","created_at":"2026-05-17T23:54:19Z","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":"119805ef2b6107ec501d512b531581bd1186f5a20ad527d27a662fa5b095f745","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-02-10T20:27:32Z","title_canon_sha256":"99ca540b56bfc71488b54740e7491ae72bf590cc6b0cf45be5dc077984f5c607"},"schema_version":"1.0","source":{"id":"1902.03665","kind":"arxiv","version":1}},"canonical_sha256":"30206902c104af389c321ba2f4846d09706379d92f602ce490416383ff88bb79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30206902c104af389c321ba2f4846d09706379d92f602ce490416383ff88bb79","first_computed_at":"2026-05-17T23:54:19.976520Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:19.976520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"udnvBfgSPiSg2YomXQD43mJq7kJSQahWkWzagzSka3HZcqJzR+pfgJrsRVqvVYU8AXV9LlbMNmnEa4uMtfgbBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:19.977237Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.03665","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bcf0207b018068f286213be90796d5b19ffb12412273636bcb18c126a21cc484","sha256:29a533232ae4f5931fa98c5640d8e91360d2a1ae132800b9ff841d62aa046c29"],"state_sha256":"ca59434ac6bbc1a384ba4cccb9e04fe2dd8fd6d23d189a525a80fe63385b1113"}