{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:QKGXJKEQP4JTL5TLRZU5WEBHSO","short_pith_number":"pith:QKGXJKEQ","canonical_record":{"source":{"id":"1110.6620","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-10-30T16:33:50Z","cross_cats_sorted":[],"title_canon_sha256":"d297b5bb77a5dc408e4f0f3d7c37e8ca566c1064ec928c14a0db6580b0560d5f","abstract_canon_sha256":"a144c2f9d79ea4cc1bf2b1402b54578d5091f39726399b836cc861ab81095ac4"},"schema_version":"1.0"},"canonical_sha256":"828d74a8907f1335f66b8e69db102793b5ade9652a232a638a29c29d73f63acc","source":{"kind":"arxiv","id":"1110.6620","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6620","created_at":"2026-05-18T02:41:17Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6620v4","created_at":"2026-05-18T02:41:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6620","created_at":"2026-05-18T02:41:17Z"},{"alias_kind":"pith_short_12","alias_value":"QKGXJKEQP4JT","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QKGXJKEQP4JTL5TL","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QKGXJKEQ","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:QKGXJKEQP4JTL5TLRZU5WEBHSO","target":"record","payload":{"canonical_record":{"source":{"id":"1110.6620","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-10-30T16:33:50Z","cross_cats_sorted":[],"title_canon_sha256":"d297b5bb77a5dc408e4f0f3d7c37e8ca566c1064ec928c14a0db6580b0560d5f","abstract_canon_sha256":"a144c2f9d79ea4cc1bf2b1402b54578d5091f39726399b836cc861ab81095ac4"},"schema_version":"1.0"},"canonical_sha256":"828d74a8907f1335f66b8e69db102793b5ade9652a232a638a29c29d73f63acc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:17.365914Z","signature_b64":"rCn3kQRfShs8cj7v8Uku9NE25MYPqnGOtbJ5+ykvZbsUg2ZTMem1+NKAkY0hJURh4N3K73N6T2+rIr4BzByACA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"828d74a8907f1335f66b8e69db102793b5ade9652a232a638a29c29d73f63acc","last_reissued_at":"2026-05-18T02:41:17.365425Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:17.365425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.6620","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:41:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WO8oAxevfSvhKSLiClinnu7aqe42p3O/Xo2ZU8iAQ7uMwCdRm3eSM6dlHBaJduPHODGPRC4iJ6XtGjuuy4eEBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T03:10:51.829197Z"},"content_sha256":"52424794ddc0330a2e3a3b0c382ee2fa0c4c42d7099b2e0796178f52ebc9cee0","schema_version":"1.0","event_id":"sha256:52424794ddc0330a2e3a3b0c382ee2fa0c4c42d7099b2e0796178f52ebc9cee0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:QKGXJKEQP4JTL5TLRZU5WEBHSO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the characteristic polynomial of Cartan matrices and Chebyshev polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Pantelis A. Damianou","submitted_at":"2011-10-30T16:33:50Z","abstract_excerpt":"We explore some interesting features of the characteristic polynomial of the Cartan matrix of a simple Lie algebra. The characteristic polynomial is closely related with the Chebyshev polynomials of first and second kind. In addition, we give explicit formulas for the characteristic polynomial of the Coxeter adjacency matrix, we compute the associated polynomials and use them to derive the Coxeter polynomial of the underlying graph. We determine the expression of the Coxeter and associated polynomials as a product of cyclotomic factors. We use this data to propose an algorithm for factoring Ch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6620","kind":"arxiv","version":4},"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":"2026-05-18T02:41:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HGkxtSl51+0D9XFaKKDtq1oeMyuifT1vPEaDhp1kzSI0RK86tMhcTOy26da8aq1jlzfTIl6KMPDLEhwyqYXvCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T03:10:51.829711Z"},"content_sha256":"fe388b97d2991b991aaac53adb1802a9ef7c09f3a5d1f7b9f95272550f6d04da","schema_version":"1.0","event_id":"sha256:fe388b97d2991b991aaac53adb1802a9ef7c09f3a5d1f7b9f95272550f6d04da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QKGXJKEQP4JTL5TLRZU5WEBHSO/bundle.json","state_url":"https://pith.science/pith/QKGXJKEQP4JTL5TLRZU5WEBHSO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QKGXJKEQP4JTL5TLRZU5WEBHSO/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":"2026-05-22T03:10:51Z","links":{"resolver":"https://pith.science/pith/QKGXJKEQP4JTL5TLRZU5WEBHSO","bundle":"https://pith.science/pith/QKGXJKEQP4JTL5TLRZU5WEBHSO/bundle.json","state":"https://pith.science/pith/QKGXJKEQP4JTL5TLRZU5WEBHSO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QKGXJKEQP4JTL5TLRZU5WEBHSO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QKGXJKEQP4JTL5TLRZU5WEBHSO","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":"a144c2f9d79ea4cc1bf2b1402b54578d5091f39726399b836cc861ab81095ac4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-10-30T16:33:50Z","title_canon_sha256":"d297b5bb77a5dc408e4f0f3d7c37e8ca566c1064ec928c14a0db6580b0560d5f"},"schema_version":"1.0","source":{"id":"1110.6620","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6620","created_at":"2026-05-18T02:41:17Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6620v4","created_at":"2026-05-18T02:41:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6620","created_at":"2026-05-18T02:41:17Z"},{"alias_kind":"pith_short_12","alias_value":"QKGXJKEQP4JT","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QKGXJKEQP4JTL5TL","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QKGXJKEQ","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:fe388b97d2991b991aaac53adb1802a9ef7c09f3a5d1f7b9f95272550f6d04da","target":"graph","created_at":"2026-05-18T02:41:17Z","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":"We explore some interesting features of the characteristic polynomial of the Cartan matrix of a simple Lie algebra. The characteristic polynomial is closely related with the Chebyshev polynomials of first and second kind. In addition, we give explicit formulas for the characteristic polynomial of the Coxeter adjacency matrix, we compute the associated polynomials and use them to derive the Coxeter polynomial of the underlying graph. We determine the expression of the Coxeter and associated polynomials as a product of cyclotomic factors. We use this data to propose an algorithm for factoring Ch","authors_text":"Pantelis A. Damianou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-10-30T16:33:50Z","title":"On the characteristic polynomial of Cartan matrices and Chebyshev polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6620","kind":"arxiv","version":4},"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":"sha256:52424794ddc0330a2e3a3b0c382ee2fa0c4c42d7099b2e0796178f52ebc9cee0","target":"record","created_at":"2026-05-18T02:41:17Z","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":"a144c2f9d79ea4cc1bf2b1402b54578d5091f39726399b836cc861ab81095ac4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-10-30T16:33:50Z","title_canon_sha256":"d297b5bb77a5dc408e4f0f3d7c37e8ca566c1064ec928c14a0db6580b0560d5f"},"schema_version":"1.0","source":{"id":"1110.6620","kind":"arxiv","version":4}},"canonical_sha256":"828d74a8907f1335f66b8e69db102793b5ade9652a232a638a29c29d73f63acc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"828d74a8907f1335f66b8e69db102793b5ade9652a232a638a29c29d73f63acc","first_computed_at":"2026-05-18T02:41:17.365425Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:17.365425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rCn3kQRfShs8cj7v8Uku9NE25MYPqnGOtbJ5+ykvZbsUg2ZTMem1+NKAkY0hJURh4N3K73N6T2+rIr4BzByACA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:17.365914Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.6620","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52424794ddc0330a2e3a3b0c382ee2fa0c4c42d7099b2e0796178f52ebc9cee0","sha256:fe388b97d2991b991aaac53adb1802a9ef7c09f3a5d1f7b9f95272550f6d04da"],"state_sha256":"2cc6db860a7e2fabda3bd1750cdc507cbf92851c71dd8d9f6803e7107c5c0217"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W7EtCRHPAlOWBqqbjILcwnBO4x9qTS8w/RBFU7iDgMsZQQwzlpcTu78tPMmEhd13EuE5KczE3fDy0jp1gVoACg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T03:10:51.832361Z","bundle_sha256":"600cb8a159094d84df0e2b6e36e7fa130c162d98814a269c96dab86b90cce104"}}