{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BGWJIJZ24RZ5AWY7GECGDSJZHJ","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":"53519826ac1afa30e919285074701f2cd43e957eba94d57978124c7e90793296","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2013-02-11T11:14:56Z","title_canon_sha256":"f9a72a17fe3d79c36df40375a6cabc7b3cb3c45ad07fee14ab4d321fcdd6a7f9"},"schema_version":"1.0","source":{"id":"1302.3111","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3111","created_at":"2026-05-18T03:33:48Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3111v1","created_at":"2026-05-18T03:33:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3111","created_at":"2026-05-18T03:33:48Z"},{"alias_kind":"pith_short_12","alias_value":"BGWJIJZ24RZ5","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BGWJIJZ24RZ5AWY7","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BGWJIJZ2","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:dc18b8cb03e788c2bc1145ee65c89f47ab70433bda34154c9f84f7ca16fe4021","target":"graph","created_at":"2026-05-18T03:33:48Z","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":"Some basic properties of the ring of integers $\\mathbb{Z}$ are extended to entire rings. In particular, arithmetic in entire principal rings is very similar than arithmetic in the ring of integers $\\mathbb{Z}$. These arithmetic properties are derived from a $\\star$-ring extension of the considered entire ring (ring extension with conjugation) equipped with a real function which is a multiplicative structure-preserving map between two algebras. The algebra of this ring extension is studied in detail. Some examples of such ring extension are given.","authors_text":"Alexandre Laugier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2013-02-11T11:14:56Z","title":"Ring extension of entire ring with conjugation; arithmetic in entire rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3111","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:fd49411a234677333079a3c0fd52e647f241a04e3dd00311fb23f88ff7ff9360","target":"record","created_at":"2026-05-18T03:33:48Z","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":"53519826ac1afa30e919285074701f2cd43e957eba94d57978124c7e90793296","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2013-02-11T11:14:56Z","title_canon_sha256":"f9a72a17fe3d79c36df40375a6cabc7b3cb3c45ad07fee14ab4d321fcdd6a7f9"},"schema_version":"1.0","source":{"id":"1302.3111","kind":"arxiv","version":1}},"canonical_sha256":"09ac94273ae473d05b1f310461c9393a4c8968d40524eee45cba4a33a53ee333","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"09ac94273ae473d05b1f310461c9393a4c8968d40524eee45cba4a33a53ee333","first_computed_at":"2026-05-18T03:33:48.700010Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:48.700010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dsHRVIbQhjefXUz0tLA1T2i1VS2ttVjewwc4k0xcbdmNPEaMWMmr7oQHyFBuSpeKA3Weyg8LLxRqBHyw59zGAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:48.700620Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.3111","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd49411a234677333079a3c0fd52e647f241a04e3dd00311fb23f88ff7ff9360","sha256:dc18b8cb03e788c2bc1145ee65c89f47ab70433bda34154c9f84f7ca16fe4021"],"state_sha256":"35b2d4528dcbbe1f59ea336f1695c27814b5f26cf3b7e2d2e539101e7fc15230"}