{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:6KQF7BBDO36JE4GO2BA2NWRWCZ","short_pith_number":"pith:6KQF7BBD","canonical_record":{"source":{"id":"1511.06331","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-11-19T19:59:13Z","cross_cats_sorted":[],"title_canon_sha256":"ed3c8594fd4a86fc77dda6d2d4ab3e161abf22e63bfecaebf29c70c0fddf8545","abstract_canon_sha256":"99bc537c73ca78936fc532ee7127132a4cdcd9815ba5ebc2bf407b89a9aba5f8"},"schema_version":"1.0"},"canonical_sha256":"f2a05f842376fc9270ced041a6da36165439ced66fd35d588569e1dbe8ed5163","source":{"kind":"arxiv","id":"1511.06331","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.06331","created_at":"2026-05-18T01:26:25Z"},{"alias_kind":"arxiv_version","alias_value":"1511.06331v1","created_at":"2026-05-18T01:26:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.06331","created_at":"2026-05-18T01:26:25Z"},{"alias_kind":"pith_short_12","alias_value":"6KQF7BBDO36J","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6KQF7BBDO36JE4GO","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6KQF7BBD","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:6KQF7BBDO36JE4GO2BA2NWRWCZ","target":"record","payload":{"canonical_record":{"source":{"id":"1511.06331","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-11-19T19:59:13Z","cross_cats_sorted":[],"title_canon_sha256":"ed3c8594fd4a86fc77dda6d2d4ab3e161abf22e63bfecaebf29c70c0fddf8545","abstract_canon_sha256":"99bc537c73ca78936fc532ee7127132a4cdcd9815ba5ebc2bf407b89a9aba5f8"},"schema_version":"1.0"},"canonical_sha256":"f2a05f842376fc9270ced041a6da36165439ced66fd35d588569e1dbe8ed5163","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:25.903815Z","signature_b64":"XPr43MbZKV5HzMHH/HS/Zuiz8lO7AAmXKAN8pNKPLSnkTgx46TGudndq30bL9pUIqIbq5mabyj4d5qVJwwl6AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2a05f842376fc9270ced041a6da36165439ced66fd35d588569e1dbe8ed5163","last_reissued_at":"2026-05-18T01:26:25.903355Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:25.903355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.06331","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":"2026-05-18T01:26:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KTzg9y9E9Fw2bfhpJ6VTvK9k3oMtIQULL17R1/iypIMiBiwOp1r97qCvM+19BWSWY5lKcv8tavlTL2GcL2vvAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:38:17.223640Z"},"content_sha256":"972b854b553857d27daf83bc02e642fd7c8d3338df0872e243cb60c4bb48584e","schema_version":"1.0","event_id":"sha256:972b854b553857d27daf83bc02e642fd7c8d3338df0872e243cb60c4bb48584e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:6KQF7BBDO36JE4GO2BA2NWRWCZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Multilinear Polynomials In Four Variables Evaluated On Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"David Buzinski, Robin Winstanley","submitted_at":"2015-11-19T19:59:13Z","abstract_excerpt":"Let $K$ be an algebraically closed field of characteristic $0$ and let $M_n(K)$, $n \\ge 3$, be the matrix ring over $K$. We will show that the image of any multilinear polynomial in four variables evaluated on $M_n(K)$ contains all matrices of trace $0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06331","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":"2026-05-18T01:26:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6pQOu5BIoaTvcNyRIZMjf06r8YY7mo3gZ9zV/g69578CoCEeBOGO6evR37R4+TWE2/lv2zcmDIA+TDpqE0hqCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:38:17.224287Z"},"content_sha256":"c207669298713dcefaef71640ec967e7d4e2bb4536065382c73c63d2bfcaa20b","schema_version":"1.0","event_id":"sha256:c207669298713dcefaef71640ec967e7d4e2bb4536065382c73c63d2bfcaa20b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6KQF7BBDO36JE4GO2BA2NWRWCZ/bundle.json","state_url":"https://pith.science/pith/6KQF7BBDO36JE4GO2BA2NWRWCZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6KQF7BBDO36JE4GO2BA2NWRWCZ/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":"2026-06-11T02:38:17Z","links":{"resolver":"https://pith.science/pith/6KQF7BBDO36JE4GO2BA2NWRWCZ","bundle":"https://pith.science/pith/6KQF7BBDO36JE4GO2BA2NWRWCZ/bundle.json","state":"https://pith.science/pith/6KQF7BBDO36JE4GO2BA2NWRWCZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6KQF7BBDO36JE4GO2BA2NWRWCZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6KQF7BBDO36JE4GO2BA2NWRWCZ","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":"99bc537c73ca78936fc532ee7127132a4cdcd9815ba5ebc2bf407b89a9aba5f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-11-19T19:59:13Z","title_canon_sha256":"ed3c8594fd4a86fc77dda6d2d4ab3e161abf22e63bfecaebf29c70c0fddf8545"},"schema_version":"1.0","source":{"id":"1511.06331","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.06331","created_at":"2026-05-18T01:26:25Z"},{"alias_kind":"arxiv_version","alias_value":"1511.06331v1","created_at":"2026-05-18T01:26:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.06331","created_at":"2026-05-18T01:26:25Z"},{"alias_kind":"pith_short_12","alias_value":"6KQF7BBDO36J","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6KQF7BBDO36JE4GO","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6KQF7BBD","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:c207669298713dcefaef71640ec967e7d4e2bb4536065382c73c63d2bfcaa20b","target":"graph","created_at":"2026-05-18T01:26:25Z","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 $K$ be an algebraically closed field of characteristic $0$ and let $M_n(K)$, $n \\ge 3$, be the matrix ring over $K$. We will show that the image of any multilinear polynomial in four variables evaluated on $M_n(K)$ contains all matrices of trace $0$.","authors_text":"David Buzinski, Robin Winstanley","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-11-19T19:59:13Z","title":"On Multilinear Polynomials In Four Variables Evaluated On Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06331","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":"sha256:972b854b553857d27daf83bc02e642fd7c8d3338df0872e243cb60c4bb48584e","target":"record","created_at":"2026-05-18T01:26:25Z","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":"99bc537c73ca78936fc532ee7127132a4cdcd9815ba5ebc2bf407b89a9aba5f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-11-19T19:59:13Z","title_canon_sha256":"ed3c8594fd4a86fc77dda6d2d4ab3e161abf22e63bfecaebf29c70c0fddf8545"},"schema_version":"1.0","source":{"id":"1511.06331","kind":"arxiv","version":1}},"canonical_sha256":"f2a05f842376fc9270ced041a6da36165439ced66fd35d588569e1dbe8ed5163","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2a05f842376fc9270ced041a6da36165439ced66fd35d588569e1dbe8ed5163","first_computed_at":"2026-05-18T01:26:25.903355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:25.903355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XPr43MbZKV5HzMHH/HS/Zuiz8lO7AAmXKAN8pNKPLSnkTgx46TGudndq30bL9pUIqIbq5mabyj4d5qVJwwl6AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:25.903815Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.06331","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:972b854b553857d27daf83bc02e642fd7c8d3338df0872e243cb60c4bb48584e","sha256:c207669298713dcefaef71640ec967e7d4e2bb4536065382c73c63d2bfcaa20b"],"state_sha256":"fcc8135ab1d38f9a207952cec6b76bf59d95b96c21ae4b15f00319fec314a651"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NmaB46USg9CByoEXq3xVWIvtAnyCFQ4ajsj0IeWMlb/FBRKYWOFpvbpUbQ0SL09SAXzc9Xdbf8OpuUHRTnTACg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T02:38:17.227849Z","bundle_sha256":"c92eec158317aa25a1be2e4e0f7fc6c28f23707f65936cdc923d95189438c814"}}