{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:K5GT6IOZL3EAKW3WD4AYUYXKPG","short_pith_number":"pith:K5GT6IOZ","canonical_record":{"source":{"id":"1901.02686","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-01-09T11:45:10Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"e864d2c2004442616c14d64f4dbbcf828a4461296d23a171594ffeca4d19d453","abstract_canon_sha256":"d6772e1766d4c4c787a0e57a8f10967f7b7a2964099c8c5a65abb38d11b3e166"},"schema_version":"1.0"},"canonical_sha256":"574d3f21d95ec8055b761f018a62ea79903f486e4f26f3d51c7555b18e757fe8","source":{"kind":"arxiv","id":"1901.02686","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.02686","created_at":"2026-05-17T23:56:39Z"},{"alias_kind":"arxiv_version","alias_value":"1901.02686v1","created_at":"2026-05-17T23:56:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.02686","created_at":"2026-05-17T23:56:39Z"},{"alias_kind":"pith_short_12","alias_value":"K5GT6IOZL3EA","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"K5GT6IOZL3EAKW3W","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"K5GT6IOZ","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:K5GT6IOZL3EAKW3WD4AYUYXKPG","target":"record","payload":{"canonical_record":{"source":{"id":"1901.02686","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-01-09T11:45:10Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"e864d2c2004442616c14d64f4dbbcf828a4461296d23a171594ffeca4d19d453","abstract_canon_sha256":"d6772e1766d4c4c787a0e57a8f10967f7b7a2964099c8c5a65abb38d11b3e166"},"schema_version":"1.0"},"canonical_sha256":"574d3f21d95ec8055b761f018a62ea79903f486e4f26f3d51c7555b18e757fe8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:39.816656Z","signature_b64":"oOQec+h9HzsauG8m9o8VR9Zu3DwBMO5GYbTt6orlY8ulC0hT2JsgGgxD5FgUiD2jgxoitpGQO3ReAb7yOSG3Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"574d3f21d95ec8055b761f018a62ea79903f486e4f26f3d51c7555b18e757fe8","last_reissued_at":"2026-05-17T23:56:39.815868Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:39.815868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.02686","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":"2026-05-17T23:56:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D3Pk6VjXOip5eUXi2f2uLgkOQ4qruTlRZ+xclKbJUWEalEMo5oWG1oIYSjoKGk8aFoAtzqCCy02x4iwqZIWeCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T18:34:32.800348Z"},"content_sha256":"7c2e83a8053077f0754db98ebe157179d739031b42004c089e75d164fa9ff26c","schema_version":"1.0","event_id":"sha256:7c2e83a8053077f0754db98ebe157179d739031b42004c089e75d164fa9ff26c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:K5GT6IOZL3EAKW3WD4AYUYXKPG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hasse--Schmidt Derivations and Cayley--Hamilton Theorem for Exterior Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Inna Scherbak, Letterio Gatto","submitted_at":"2019-01-09T11:45:10Z","abstract_excerpt":"Using the natural notion of {\\em Hasse--Schmidt derivations on an exterior algebra}, we relate two classical and seemingly unrelated subjects. The first is the celebrated Cayley--Hamilton theorem of linear algebra, \"{\\em each endomorphism of a finite-dimensional vector space is a root of its own characteristic polynomial}\", and the second concerns the expression of the bosonic vertex operators occurring in the representation theory of the (infinite-dimensional) Heinsenberg algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02686","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":"2026-05-17T23:56:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KCg0lD1ZoFHOx1k5vL0rTMMrOyXYJ9Lp0OKneuunh28ceHtYfuTH1jQo3Qx70gvjxQkRNFdkzUFZS8MGROdTDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T18:34:32.800687Z"},"content_sha256":"190c38aa45f507755badd1359e8b91815be3fb56b2962549a6e3ed2350b43999","schema_version":"1.0","event_id":"sha256:190c38aa45f507755badd1359e8b91815be3fb56b2962549a6e3ed2350b43999"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K5GT6IOZL3EAKW3WD4AYUYXKPG/bundle.json","state_url":"https://pith.science/pith/K5GT6IOZL3EAKW3WD4AYUYXKPG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K5GT6IOZL3EAKW3WD4AYUYXKPG/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":"2026-06-28T18:34:32Z","links":{"resolver":"https://pith.science/pith/K5GT6IOZL3EAKW3WD4AYUYXKPG","bundle":"https://pith.science/pith/K5GT6IOZL3EAKW3WD4AYUYXKPG/bundle.json","state":"https://pith.science/pith/K5GT6IOZL3EAKW3WD4AYUYXKPG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K5GT6IOZL3EAKW3WD4AYUYXKPG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:K5GT6IOZL3EAKW3WD4AYUYXKPG","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":"d6772e1766d4c4c787a0e57a8f10967f7b7a2964099c8c5a65abb38d11b3e166","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-01-09T11:45:10Z","title_canon_sha256":"e864d2c2004442616c14d64f4dbbcf828a4461296d23a171594ffeca4d19d453"},"schema_version":"1.0","source":{"id":"1901.02686","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.02686","created_at":"2026-05-17T23:56:39Z"},{"alias_kind":"arxiv_version","alias_value":"1901.02686v1","created_at":"2026-05-17T23:56:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.02686","created_at":"2026-05-17T23:56:39Z"},{"alias_kind":"pith_short_12","alias_value":"K5GT6IOZL3EA","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"K5GT6IOZL3EAKW3W","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"K5GT6IOZ","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:190c38aa45f507755badd1359e8b91815be3fb56b2962549a6e3ed2350b43999","target":"graph","created_at":"2026-05-17T23:56:39Z","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":"Using the natural notion of {\\em Hasse--Schmidt derivations on an exterior algebra}, we relate two classical and seemingly unrelated subjects. The first is the celebrated Cayley--Hamilton theorem of linear algebra, \"{\\em each endomorphism of a finite-dimensional vector space is a root of its own characteristic polynomial}\", and the second concerns the expression of the bosonic vertex operators occurring in the representation theory of the (infinite-dimensional) Heinsenberg algebra.","authors_text":"Inna Scherbak, Letterio Gatto","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-01-09T11:45:10Z","title":"Hasse--Schmidt Derivations and Cayley--Hamilton Theorem for Exterior Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02686","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":"sha256:7c2e83a8053077f0754db98ebe157179d739031b42004c089e75d164fa9ff26c","target":"record","created_at":"2026-05-17T23:56:39Z","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":"d6772e1766d4c4c787a0e57a8f10967f7b7a2964099c8c5a65abb38d11b3e166","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-01-09T11:45:10Z","title_canon_sha256":"e864d2c2004442616c14d64f4dbbcf828a4461296d23a171594ffeca4d19d453"},"schema_version":"1.0","source":{"id":"1901.02686","kind":"arxiv","version":1}},"canonical_sha256":"574d3f21d95ec8055b761f018a62ea79903f486e4f26f3d51c7555b18e757fe8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"574d3f21d95ec8055b761f018a62ea79903f486e4f26f3d51c7555b18e757fe8","first_computed_at":"2026-05-17T23:56:39.815868Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:39.815868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oOQec+h9HzsauG8m9o8VR9Zu3DwBMO5GYbTt6orlY8ulC0hT2JsgGgxD5FgUiD2jgxoitpGQO3ReAb7yOSG3Dg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:39.816656Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.02686","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c2e83a8053077f0754db98ebe157179d739031b42004c089e75d164fa9ff26c","sha256:190c38aa45f507755badd1359e8b91815be3fb56b2962549a6e3ed2350b43999"],"state_sha256":"1888e595a4d8ee9a9c0bbce841ecd4702860ff0a6fd4902e54fe8504170306b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EE7CrA+EDrAm2lhbjkY2xoPQ2siNLV6vEKraSArAq9ke2jhAFrCqFjOEfdT261Lm6RurVay7KOW0VlzYxZJ/Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T18:34:32.802523Z","bundle_sha256":"a79740b32abe2d5a7e69e83299069e6670062df78c82320245ff3d3b60fde3af"}}