{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:PH3N7C7EZUM3PSMIPB4TFL5BHK","short_pith_number":"pith:PH3N7C7E","canonical_record":{"source":{"id":"1506.06352","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-06-21T11:37:34Z","cross_cats_sorted":[],"title_canon_sha256":"af7fbf4367996cf52bc71cc80cca47b9ec0556e4f253c396484d0f01e638a667","abstract_canon_sha256":"c8f1e16c037347c3832a0d2da2fffa727b224bc0094388c0daf71e0c9bea0f58"},"schema_version":"1.0"},"canonical_sha256":"79f6df8be4cd19b7c988787932afa13aa910166fc0f74800c16e03fd2c4a078d","source":{"kind":"arxiv","id":"1506.06352","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06352","created_at":"2026-05-18T00:57:42Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06352v2","created_at":"2026-05-18T00:57:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06352","created_at":"2026-05-18T00:57:42Z"},{"alias_kind":"pith_short_12","alias_value":"PH3N7C7EZUM3","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PH3N7C7EZUM3PSMI","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PH3N7C7E","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:PH3N7C7EZUM3PSMIPB4TFL5BHK","target":"record","payload":{"canonical_record":{"source":{"id":"1506.06352","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-06-21T11:37:34Z","cross_cats_sorted":[],"title_canon_sha256":"af7fbf4367996cf52bc71cc80cca47b9ec0556e4f253c396484d0f01e638a667","abstract_canon_sha256":"c8f1e16c037347c3832a0d2da2fffa727b224bc0094388c0daf71e0c9bea0f58"},"schema_version":"1.0"},"canonical_sha256":"79f6df8be4cd19b7c988787932afa13aa910166fc0f74800c16e03fd2c4a078d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:42.765349Z","signature_b64":"cDbte2HYKeyO1oSStLBdxwUEB2Lu/OJrsysgFjqMYNMEcjlm5FMTfg4ANja3CUoxT5c47gxfxB8HxDjsPqtYCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79f6df8be4cd19b7c988787932afa13aa910166fc0f74800c16e03fd2c4a078d","last_reissued_at":"2026-05-18T00:57:42.764720Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:42.764720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.06352","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:57:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UxV2NzMpk5w0cOjotaGchJBa6MNzGbC0WJrrDYYvxthjPOJYhID7woX09BfS8uEnSjSwKc3Hle6320Ivcq2rAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:41:29.219809Z"},"content_sha256":"3c22b68b79981b03acc0c70d24065d151823588cb6cbfff3c57700af9d9fbce4","schema_version":"1.0","event_id":"sha256:3c22b68b79981b03acc0c70d24065d151823588cb6cbfff3c57700af9d9fbce4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:PH3N7C7EZUM3PSMIPB4TFL5BHK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Schur-Weyl duality and the free Lie algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"J. Matthew Douglass, Stephen Doty","submitted_at":"2015-06-21T11:37:34Z","abstract_excerpt":"We prove an analogue of Schur-Weyl duality for the space of homogeneous Lie polynomials of degree r in n variables."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06352","kind":"arxiv","version":2},"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":"2026-05-18T00:57:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"asP2ORKqlugStSK58/1JbG6SA6vogX7na6UD3k752w+T00gSytPh1DXpUjSxzeXv5JDkoIfrZsBECize/oNGBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:41:29.220147Z"},"content_sha256":"ff92560eaafb5982dafe94e9a82e8502fa0eab28ecc3f000fda7ce50c7232d03","schema_version":"1.0","event_id":"sha256:ff92560eaafb5982dafe94e9a82e8502fa0eab28ecc3f000fda7ce50c7232d03"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PH3N7C7EZUM3PSMIPB4TFL5BHK/bundle.json","state_url":"https://pith.science/pith/PH3N7C7EZUM3PSMIPB4TFL5BHK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PH3N7C7EZUM3PSMIPB4TFL5BHK/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":"2026-05-28T08:41:29Z","links":{"resolver":"https://pith.science/pith/PH3N7C7EZUM3PSMIPB4TFL5BHK","bundle":"https://pith.science/pith/PH3N7C7EZUM3PSMIPB4TFL5BHK/bundle.json","state":"https://pith.science/pith/PH3N7C7EZUM3PSMIPB4TFL5BHK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PH3N7C7EZUM3PSMIPB4TFL5BHK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PH3N7C7EZUM3PSMIPB4TFL5BHK","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":"c8f1e16c037347c3832a0d2da2fffa727b224bc0094388c0daf71e0c9bea0f58","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-06-21T11:37:34Z","title_canon_sha256":"af7fbf4367996cf52bc71cc80cca47b9ec0556e4f253c396484d0f01e638a667"},"schema_version":"1.0","source":{"id":"1506.06352","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06352","created_at":"2026-05-18T00:57:42Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06352v2","created_at":"2026-05-18T00:57:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06352","created_at":"2026-05-18T00:57:42Z"},{"alias_kind":"pith_short_12","alias_value":"PH3N7C7EZUM3","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PH3N7C7EZUM3PSMI","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PH3N7C7E","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:ff92560eaafb5982dafe94e9a82e8502fa0eab28ecc3f000fda7ce50c7232d03","target":"graph","created_at":"2026-05-18T00:57:42Z","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 prove an analogue of Schur-Weyl duality for the space of homogeneous Lie polynomials of degree r in n variables.","authors_text":"J. Matthew Douglass, Stephen Doty","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-06-21T11:37:34Z","title":"Schur-Weyl duality and the free Lie algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06352","kind":"arxiv","version":2},"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":"sha256:3c22b68b79981b03acc0c70d24065d151823588cb6cbfff3c57700af9d9fbce4","target":"record","created_at":"2026-05-18T00:57:42Z","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":"c8f1e16c037347c3832a0d2da2fffa727b224bc0094388c0daf71e0c9bea0f58","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-06-21T11:37:34Z","title_canon_sha256":"af7fbf4367996cf52bc71cc80cca47b9ec0556e4f253c396484d0f01e638a667"},"schema_version":"1.0","source":{"id":"1506.06352","kind":"arxiv","version":2}},"canonical_sha256":"79f6df8be4cd19b7c988787932afa13aa910166fc0f74800c16e03fd2c4a078d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79f6df8be4cd19b7c988787932afa13aa910166fc0f74800c16e03fd2c4a078d","first_computed_at":"2026-05-18T00:57:42.764720Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:42.764720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cDbte2HYKeyO1oSStLBdxwUEB2Lu/OJrsysgFjqMYNMEcjlm5FMTfg4ANja3CUoxT5c47gxfxB8HxDjsPqtYCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:42.765349Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.06352","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c22b68b79981b03acc0c70d24065d151823588cb6cbfff3c57700af9d9fbce4","sha256:ff92560eaafb5982dafe94e9a82e8502fa0eab28ecc3f000fda7ce50c7232d03"],"state_sha256":"28271d9086cd90d8bed7bd9d4a92d2f3016b8294f44a9ece119f58783123131d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"epy++jfwAaeXeZbGsjagyy0l440WcVku4Z8KefLcSWja37kL+DfvyNnIEWnwDsuceqMOucCdawXTEPvQhVaCDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T08:41:29.222144Z","bundle_sha256":"b920c8311285856ad0dcd30604ed2863f52ff52e71b71320567e9c1817240f7a"}}