{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:6ZKOPODJ6NOC2CT3JG6URPJL2G","short_pith_number":"pith:6ZKOPODJ","canonical_record":{"source":{"id":"1903.04773","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-03-12T08:18:53Z","cross_cats_sorted":[],"title_canon_sha256":"55be33cda8e795acaaf27480af2d7c2bedff7cf79426f7bb0f1f56ac067cc6f1","abstract_canon_sha256":"d2c9e62806711037843f2c08c1c7d5b1ac51cc2f1e7b7d266f745077b913fa22"},"schema_version":"1.0"},"canonical_sha256":"f654e7b869f35c2d0a7b49bd48bd2bd1b77b1722e6c17cf3815c514f30a46db4","source":{"kind":"arxiv","id":"1903.04773","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.04773","created_at":"2026-05-17T23:51:28Z"},{"alias_kind":"arxiv_version","alias_value":"1903.04773v1","created_at":"2026-05-17T23:51:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.04773","created_at":"2026-05-17T23:51:28Z"},{"alias_kind":"pith_short_12","alias_value":"6ZKOPODJ6NOC","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"6ZKOPODJ6NOC2CT3","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"6ZKOPODJ","created_at":"2026-05-18T12:33:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:6ZKOPODJ6NOC2CT3JG6URPJL2G","target":"record","payload":{"canonical_record":{"source":{"id":"1903.04773","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-03-12T08:18:53Z","cross_cats_sorted":[],"title_canon_sha256":"55be33cda8e795acaaf27480af2d7c2bedff7cf79426f7bb0f1f56ac067cc6f1","abstract_canon_sha256":"d2c9e62806711037843f2c08c1c7d5b1ac51cc2f1e7b7d266f745077b913fa22"},"schema_version":"1.0"},"canonical_sha256":"f654e7b869f35c2d0a7b49bd48bd2bd1b77b1722e6c17cf3815c514f30a46db4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:28.744778Z","signature_b64":"UdtFzHhKWb1XeN/hJevOqKxRZW/HB1FdNfhJMANPodU1lE1GeTKOO+LdOYtErbUKX6gWbpl4rt59WbbYV+8TDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f654e7b869f35c2d0a7b49bd48bd2bd1b77b1722e6c17cf3815c514f30a46db4","last_reissued_at":"2026-05-17T23:51:28.744322Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:28.744322Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.04773","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":"2026-05-17T23:51:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LDmlqLltJvbvR8ddlJdiodl5qr/m8a7w/JZwCo1VQEh6bKnrdSLcN8nzfAixrVgtYwXp7gqJAVkKTnfAZEtqAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T03:17:09.787889Z"},"content_sha256":"d4523b62eb28d264c0c68e1ab39b11f10214058d11b1edfe41246d7daeeee6ca","schema_version":"1.0","event_id":"sha256:d4523b62eb28d264c0c68e1ab39b11f10214058d11b1edfe41246d7daeeee6ca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:6ZKOPODJ6NOC2CT3JG6URPJL2G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multiplicative derivations on rank-$s$ matrices for relatively small $s$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Baochuan Xie, Xiaowei Xu, Yanhua Wang, Zhibing Zhao","submitted_at":"2019-03-12T08:18:53Z","abstract_excerpt":"Let $n$ and $s$ be fixed integers such that $n\\geq 2$ and $1\\leq s\\leq \\frac{n}{2}$. Let $M_n(\\mathbb{K})$ be the ring of all $n\\times n$ matrices over a field $\\mathbb{K}$. If a map $\\delta:M_n(\\mathbb{K})\\rightarrow M_n(\\mathbb{K})$ satisfies that $\\delta(xy)=\\delta(x)y+x\\delta(y)$ for any two rank-$s$ matrices $x,y\\in M_n(\\mathbb{K})$, then there exists a derivation $D$ of $M_n(\\mathbb{K})$ such that $\\delta(x)=D(x)$ holds for each rank-$k$ matrix $x\\in M_n(\\mathbb{K})$ with $0\\leq k\\leq s$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.04773","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":"2026-05-17T23:51:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FlMZtbf5UrJ4Nz4guqGUw2DgFmQYlGgLMCve2UhQtQ/dzgo/0TPidvB1BvS5ZGsiZEZwemPIY8gdIa1sWVdFBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T03:17:09.788643Z"},"content_sha256":"27b24a464cef4e01d1538c148d3c4f122fef0b5b6d825d37ff6559cd760a3e3e","schema_version":"1.0","event_id":"sha256:27b24a464cef4e01d1538c148d3c4f122fef0b5b6d825d37ff6559cd760a3e3e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6ZKOPODJ6NOC2CT3JG6URPJL2G/bundle.json","state_url":"https://pith.science/pith/6ZKOPODJ6NOC2CT3JG6URPJL2G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6ZKOPODJ6NOC2CT3JG6URPJL2G/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":"2026-05-23T03:17:09Z","links":{"resolver":"https://pith.science/pith/6ZKOPODJ6NOC2CT3JG6URPJL2G","bundle":"https://pith.science/pith/6ZKOPODJ6NOC2CT3JG6URPJL2G/bundle.json","state":"https://pith.science/pith/6ZKOPODJ6NOC2CT3JG6URPJL2G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6ZKOPODJ6NOC2CT3JG6URPJL2G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:6ZKOPODJ6NOC2CT3JG6URPJL2G","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":"d2c9e62806711037843f2c08c1c7d5b1ac51cc2f1e7b7d266f745077b913fa22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-03-12T08:18:53Z","title_canon_sha256":"55be33cda8e795acaaf27480af2d7c2bedff7cf79426f7bb0f1f56ac067cc6f1"},"schema_version":"1.0","source":{"id":"1903.04773","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.04773","created_at":"2026-05-17T23:51:28Z"},{"alias_kind":"arxiv_version","alias_value":"1903.04773v1","created_at":"2026-05-17T23:51:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.04773","created_at":"2026-05-17T23:51:28Z"},{"alias_kind":"pith_short_12","alias_value":"6ZKOPODJ6NOC","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"6ZKOPODJ6NOC2CT3","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"6ZKOPODJ","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:27b24a464cef4e01d1538c148d3c4f122fef0b5b6d825d37ff6559cd760a3e3e","target":"graph","created_at":"2026-05-17T23:51:28Z","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":"Let $n$ and $s$ be fixed integers such that $n\\geq 2$ and $1\\leq s\\leq \\frac{n}{2}$. Let $M_n(\\mathbb{K})$ be the ring of all $n\\times n$ matrices over a field $\\mathbb{K}$. If a map $\\delta:M_n(\\mathbb{K})\\rightarrow M_n(\\mathbb{K})$ satisfies that $\\delta(xy)=\\delta(x)y+x\\delta(y)$ for any two rank-$s$ matrices $x,y\\in M_n(\\mathbb{K})$, then there exists a derivation $D$ of $M_n(\\mathbb{K})$ such that $\\delta(x)=D(x)$ holds for each rank-$k$ matrix $x\\in M_n(\\mathbb{K})$ with $0\\leq k\\leq s$.","authors_text":"Baochuan Xie, Xiaowei Xu, Yanhua Wang, Zhibing Zhao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-03-12T08:18:53Z","title":"Multiplicative derivations on rank-$s$ matrices for relatively small $s$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.04773","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:d4523b62eb28d264c0c68e1ab39b11f10214058d11b1edfe41246d7daeeee6ca","target":"record","created_at":"2026-05-17T23:51:28Z","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":"d2c9e62806711037843f2c08c1c7d5b1ac51cc2f1e7b7d266f745077b913fa22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-03-12T08:18:53Z","title_canon_sha256":"55be33cda8e795acaaf27480af2d7c2bedff7cf79426f7bb0f1f56ac067cc6f1"},"schema_version":"1.0","source":{"id":"1903.04773","kind":"arxiv","version":1}},"canonical_sha256":"f654e7b869f35c2d0a7b49bd48bd2bd1b77b1722e6c17cf3815c514f30a46db4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f654e7b869f35c2d0a7b49bd48bd2bd1b77b1722e6c17cf3815c514f30a46db4","first_computed_at":"2026-05-17T23:51:28.744322Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:28.744322Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UdtFzHhKWb1XeN/hJevOqKxRZW/HB1FdNfhJMANPodU1lE1GeTKOO+LdOYtErbUKX6gWbpl4rt59WbbYV+8TDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:28.744778Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.04773","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d4523b62eb28d264c0c68e1ab39b11f10214058d11b1edfe41246d7daeeee6ca","sha256:27b24a464cef4e01d1538c148d3c4f122fef0b5b6d825d37ff6559cd760a3e3e"],"state_sha256":"70d90b7a7037b5c09d7a7ea094e659e7d3fa78792891098605f5e397d089a0ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yu42h3KzuxelqDBNbJzys9/X7AMyIpWVUQr42jI9IneQs19GJPJNHn5jTlrqktMd3t3y0tl2b8NTdqxzNYafCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T03:17:09.792550Z","bundle_sha256":"bdb03264949b9930cc564e3e5e953a3463493fafe1c4c8edf2b9f95110411487"}}