{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:QZZSTNODSFU6CS2U65PUCIOB3L","short_pith_number":"pith:QZZSTNOD","canonical_record":{"source":{"id":"1705.04157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-05-11T13:17:09Z","cross_cats_sorted":[],"title_canon_sha256":"4f7e2c41522fb67d0a6c6f35e8804e96ab0b4a3d0c0ac6036752973c321b0a77","abstract_canon_sha256":"17d01ffb5452fc2aea213d27420a22f6dfe39ef3457fa40f5da92784a6642d99"},"schema_version":"1.0"},"canonical_sha256":"867329b5c39169e14b54f75f4121c1daeba5394ead39e44a5218294f6ad28c33","source":{"kind":"arxiv","id":"1705.04157","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.04157","created_at":"2026-05-17T23:56:55Z"},{"alias_kind":"arxiv_version","alias_value":"1705.04157v1","created_at":"2026-05-17T23:56:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04157","created_at":"2026-05-17T23:56:55Z"},{"alias_kind":"pith_short_12","alias_value":"QZZSTNODSFU6","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QZZSTNODSFU6CS2U","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QZZSTNOD","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:QZZSTNODSFU6CS2U65PUCIOB3L","target":"record","payload":{"canonical_record":{"source":{"id":"1705.04157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-05-11T13:17:09Z","cross_cats_sorted":[],"title_canon_sha256":"4f7e2c41522fb67d0a6c6f35e8804e96ab0b4a3d0c0ac6036752973c321b0a77","abstract_canon_sha256":"17d01ffb5452fc2aea213d27420a22f6dfe39ef3457fa40f5da92784a6642d99"},"schema_version":"1.0"},"canonical_sha256":"867329b5c39169e14b54f75f4121c1daeba5394ead39e44a5218294f6ad28c33","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:55.950613Z","signature_b64":"3L2QsGjNrxL6wdlK/CEyl20esPC53Izq8CqfIlhMBOeNXuhRd9+QaoaBmA/KIKpUksDn+hplAzgnhJ2vVdPnAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"867329b5c39169e14b54f75f4121c1daeba5394ead39e44a5218294f6ad28c33","last_reissued_at":"2026-05-17T23:56:55.949619Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:55.949619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.04157","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":"2026-05-17T23:56:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XpV817/McjRxKmq9LTlmQFjp85Jo1+MHzrdRZfg/hdcDqYW4bIw1+jAP+PTc1BTta3qP0zOJqBY/1/1TCeZWBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:22:07.040825Z"},"content_sha256":"e4eb08ec97be338a6d6cca59b1b8ea22a3ff4eea7840df4502121b517fe07b3f","schema_version":"1.0","event_id":"sha256:e4eb08ec97be338a6d6cca59b1b8ea22a3ff4eea7840df4502121b517fe07b3f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:QZZSTNODSFU6CS2U65PUCIOB3L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic computation of genetic patterns related to three-dimensional evolution algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Juan N\\'u\\~nez, \\'Oscar J. Falc\\'on, Ra\\'ul M. Falc\\'on","submitted_at":"2017-05-11T13:17:09Z","abstract_excerpt":"The mitosis process of an eukaryotic cell can be represented by the structure constants of an evolution algebra. Any isotopism of the latter corresponds to a mutation of genotypes of the former. This paper uses Computational Algebraic Geometry to determine the distribution of three-dimensional evolution algebras over any field into isotopism classes and hence, to describe the spectrum of genetic patterns of three distinct genotypes during a mitosis process. Their distribution into isomorphism classes is also determined in case of dealing with algebras having a one-dimensional annihilator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04157","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":"2026-05-17T23:56:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m0OmvncGrU/Q5pjv/k7TAFRBF1qkD/IdhV2RHqBLmWscW45EdQRcr+d7OPfdtM3WRVmynWr6TmqrFL7eBac1Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:22:07.041174Z"},"content_sha256":"77f3c8af13384527e7fdf7cfb67e9419e269fd401f79c06c544a3892ad671758","schema_version":"1.0","event_id":"sha256:77f3c8af13384527e7fdf7cfb67e9419e269fd401f79c06c544a3892ad671758"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QZZSTNODSFU6CS2U65PUCIOB3L/bundle.json","state_url":"https://pith.science/pith/QZZSTNODSFU6CS2U65PUCIOB3L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QZZSTNODSFU6CS2U65PUCIOB3L/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":"2026-06-24T20:22:07Z","links":{"resolver":"https://pith.science/pith/QZZSTNODSFU6CS2U65PUCIOB3L","bundle":"https://pith.science/pith/QZZSTNODSFU6CS2U65PUCIOB3L/bundle.json","state":"https://pith.science/pith/QZZSTNODSFU6CS2U65PUCIOB3L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QZZSTNODSFU6CS2U65PUCIOB3L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QZZSTNODSFU6CS2U65PUCIOB3L","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":"17d01ffb5452fc2aea213d27420a22f6dfe39ef3457fa40f5da92784a6642d99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-05-11T13:17:09Z","title_canon_sha256":"4f7e2c41522fb67d0a6c6f35e8804e96ab0b4a3d0c0ac6036752973c321b0a77"},"schema_version":"1.0","source":{"id":"1705.04157","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.04157","created_at":"2026-05-17T23:56:55Z"},{"alias_kind":"arxiv_version","alias_value":"1705.04157v1","created_at":"2026-05-17T23:56:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04157","created_at":"2026-05-17T23:56:55Z"},{"alias_kind":"pith_short_12","alias_value":"QZZSTNODSFU6","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QZZSTNODSFU6CS2U","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QZZSTNOD","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:77f3c8af13384527e7fdf7cfb67e9419e269fd401f79c06c544a3892ad671758","target":"graph","created_at":"2026-05-17T23:56:55Z","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 mitosis process of an eukaryotic cell can be represented by the structure constants of an evolution algebra. Any isotopism of the latter corresponds to a mutation of genotypes of the former. This paper uses Computational Algebraic Geometry to determine the distribution of three-dimensional evolution algebras over any field into isotopism classes and hence, to describe the spectrum of genetic patterns of three distinct genotypes during a mitosis process. Their distribution into isomorphism classes is also determined in case of dealing with algebras having a one-dimensional annihilator.","authors_text":"Juan N\\'u\\~nez, \\'Oscar J. Falc\\'on, Ra\\'ul M. Falc\\'on","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-05-11T13:17:09Z","title":"Algebraic computation of genetic patterns related to three-dimensional evolution algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04157","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:e4eb08ec97be338a6d6cca59b1b8ea22a3ff4eea7840df4502121b517fe07b3f","target":"record","created_at":"2026-05-17T23:56:55Z","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":"17d01ffb5452fc2aea213d27420a22f6dfe39ef3457fa40f5da92784a6642d99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-05-11T13:17:09Z","title_canon_sha256":"4f7e2c41522fb67d0a6c6f35e8804e96ab0b4a3d0c0ac6036752973c321b0a77"},"schema_version":"1.0","source":{"id":"1705.04157","kind":"arxiv","version":1}},"canonical_sha256":"867329b5c39169e14b54f75f4121c1daeba5394ead39e44a5218294f6ad28c33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"867329b5c39169e14b54f75f4121c1daeba5394ead39e44a5218294f6ad28c33","first_computed_at":"2026-05-17T23:56:55.949619Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:55.949619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3L2QsGjNrxL6wdlK/CEyl20esPC53Izq8CqfIlhMBOeNXuhRd9+QaoaBmA/KIKpUksDn+hplAzgnhJ2vVdPnAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:55.950613Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.04157","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4eb08ec97be338a6d6cca59b1b8ea22a3ff4eea7840df4502121b517fe07b3f","sha256:77f3c8af13384527e7fdf7cfb67e9419e269fd401f79c06c544a3892ad671758"],"state_sha256":"830a59ccabc2adf923b3fbe168d7e8f04e348d8910c3da3c91954a8361f81151"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UZD7wnaTWyQbn6RyKysKVnVE5uM05Hsuum9WXt/W6xFF/8j8q+2RHmzx6qK+xQHfB7iV7YC7YMSB+yJQtEhzCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T20:22:07.043257Z","bundle_sha256":"601ed5d0f3d797de79ae87f33b8477b403f7fac67c59c09af90c8dec69bc2e1b"}}