{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:FDBRQARDMBG4MPKFK2UXN3U2ZS","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":"caa2b00a816742e095ea1024c53006d83935d5b462e7c3b2a151502d21130dac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-02-28T07:53:55Z","title_canon_sha256":"b9e378549f24617ff6d60989f6a3879162b42928aa9e7f5be95db8fa6db8adb8"},"schema_version":"1.0","source":{"id":"1902.10939","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.10939","created_at":"2026-05-17T23:52:26Z"},{"alias_kind":"arxiv_version","alias_value":"1902.10939v1","created_at":"2026-05-17T23:52:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.10939","created_at":"2026-05-17T23:52:26Z"},{"alias_kind":"pith_short_12","alias_value":"FDBRQARDMBG4","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"FDBRQARDMBG4MPKF","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"FDBRQARD","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:9aa48a8f1e74643096cccff8be033675dcaf5632e485da1c0f7b8f47060ab9d6","target":"graph","created_at":"2026-05-17T23:52:26Z","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":"In this article, using generalized derivations, we obtain a simple idea to prove the non-commutative Newton binomial formula in unital algebras and then, we extend that formula to non-unital algebras. Additionally, we establish the non-commutative Newton binomial formula with a negative power.","authors_text":"A. Hosseini, M. Mohammadzadeh Karizaki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-02-28T07:53:55Z","title":"On the non-commutative Newton binomial formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10939","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":"sha256:7a5b6ccbaf74439808bab4a6ce69c3a4447a9406f5f82d672f91ac0a8cf23069","target":"record","created_at":"2026-05-17T23:52:26Z","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":"caa2b00a816742e095ea1024c53006d83935d5b462e7c3b2a151502d21130dac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-02-28T07:53:55Z","title_canon_sha256":"b9e378549f24617ff6d60989f6a3879162b42928aa9e7f5be95db8fa6db8adb8"},"schema_version":"1.0","source":{"id":"1902.10939","kind":"arxiv","version":1}},"canonical_sha256":"28c3180223604dc63d4556a976ee9acca1c8a74e9db0eb5a9058737c367aa398","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28c3180223604dc63d4556a976ee9acca1c8a74e9db0eb5a9058737c367aa398","first_computed_at":"2026-05-17T23:52:26.311227Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:26.311227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mMLzhtZ6NZReB8GkMH7eAaSLqWwBFKayGCFMtDuVGpYtvzprMJB5fVQYfHYLDitiwxhpxEVg+Cn5QXBuGLawCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:26.311822Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.10939","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a5b6ccbaf74439808bab4a6ce69c3a4447a9406f5f82d672f91ac0a8cf23069","sha256:9aa48a8f1e74643096cccff8be033675dcaf5632e485da1c0f7b8f47060ab9d6"],"state_sha256":"015d8174249853d08a0c2aff3cc8822b1f576a48e10e6bd0c118173b7942402a"}