{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:R7S6NXAWAJWQZ57QKTWDXMJ3WJ","short_pith_number":"pith:R7S6NXAW","schema_version":"1.0","canonical_sha256":"8fe5e6dc16026d0cf7f054ec3bb13bb270cb11392081ac45c79c065338e83fff","source":{"kind":"arxiv","id":"1212.2171","version":1},"attestation_state":"computed","paper":{"title":"Binary modules and their endomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Hans Schoutens","submitted_at":"2012-12-10T19:20:57Z","abstract_excerpt":"Based upon properties of ordinal length, we introduce a new class of modules, the binary modules, and study their endomorphism ring. The nilpotent endomorphisms form a two-sided ideal, and after factoring this out, we get a commutative ring. In particular, any binary module without embedded primes is isomorphic to an ideal in a reduced ring."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1212.2171","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-12-10T19:20:57Z","cross_cats_sorted":[],"title_canon_sha256":"c2c92f737f3de21d718458df06effdf6be0b05ce0da420c99459a3f9e85294ac","abstract_canon_sha256":"9bf5cd66bbd16fe7d065b94384bd68ddbe1fc0f9d06af6e8639bd3def703e146"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:46.833675Z","signature_b64":"w/73sAd5z55v9XRFCVnsPUDEQjsUY528xKZU+NFTVOUIe7R6mqM3RHBBnKdAfjpXNtYTHUI2FE/DooUEu0EuAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8fe5e6dc16026d0cf7f054ec3bb13bb270cb11392081ac45c79c065338e83fff","last_reissued_at":"2026-05-18T03:38:46.832909Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:46.832909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Binary modules and their endomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Hans Schoutens","submitted_at":"2012-12-10T19:20:57Z","abstract_excerpt":"Based upon properties of ordinal length, we introduce a new class of modules, the binary modules, and study their endomorphism ring. The nilpotent endomorphisms form a two-sided ideal, and after factoring this out, we get a commutative ring. In particular, any binary module without embedded primes is isomorphic to an ideal in a reduced ring."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2171","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1212.2171","created_at":"2026-05-18T03:38:46.833022+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.2171v1","created_at":"2026-05-18T03:38:46.833022+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.2171","created_at":"2026-05-18T03:38:46.833022+00:00"},{"alias_kind":"pith_short_12","alias_value":"R7S6NXAWAJWQ","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_16","alias_value":"R7S6NXAWAJWQZ57Q","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_8","alias_value":"R7S6NXAW","created_at":"2026-05-18T12:27:20.899486+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/R7S6NXAWAJWQZ57QKTWDXMJ3WJ","json":"https://pith.science/pith/R7S6NXAWAJWQZ57QKTWDXMJ3WJ.json","graph_json":"https://pith.science/api/pith-number/R7S6NXAWAJWQZ57QKTWDXMJ3WJ/graph.json","events_json":"https://pith.science/api/pith-number/R7S6NXAWAJWQZ57QKTWDXMJ3WJ/events.json","paper":"https://pith.science/paper/R7S6NXAW"},"agent_actions":{"view_html":"https://pith.science/pith/R7S6NXAWAJWQZ57QKTWDXMJ3WJ","download_json":"https://pith.science/pith/R7S6NXAWAJWQZ57QKTWDXMJ3WJ.json","view_paper":"https://pith.science/paper/R7S6NXAW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.2171&json=true","fetch_graph":"https://pith.science/api/pith-number/R7S6NXAWAJWQZ57QKTWDXMJ3WJ/graph.json","fetch_events":"https://pith.science/api/pith-number/R7S6NXAWAJWQZ57QKTWDXMJ3WJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R7S6NXAWAJWQZ57QKTWDXMJ3WJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R7S6NXAWAJWQZ57QKTWDXMJ3WJ/action/storage_attestation","attest_author":"https://pith.science/pith/R7S6NXAWAJWQZ57QKTWDXMJ3WJ/action/author_attestation","sign_citation":"https://pith.science/pith/R7S6NXAWAJWQZ57QKTWDXMJ3WJ/action/citation_signature","submit_replication":"https://pith.science/pith/R7S6NXAWAJWQZ57QKTWDXMJ3WJ/action/replication_record"}},"created_at":"2026-05-18T03:38:46.833022+00:00","updated_at":"2026-05-18T03:38:46.833022+00:00"}