{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:KPZZQZNK2SX6XRFGQ7IXIMVRVZ","short_pith_number":"pith:KPZZQZNK","canonical_record":{"source":{"id":"0912.0184","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-12-01T15:23:07Z","cross_cats_sorted":[],"title_canon_sha256":"cb413d8fcb8f8e682f038b351f8e8076b6cc8146faa2f905d09702bd23a0d7a1","abstract_canon_sha256":"1bebf95f26e9629bb734f3f12402574233b4509ab0789ab51eaec8f27ec80d85"},"schema_version":"1.0"},"canonical_sha256":"53f39865aad4afebc4a687d17432b1ae7a0d1ff61863dba2a177703f8108e1fe","source":{"kind":"arxiv","id":"0912.0184","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.0184","created_at":"2026-05-18T03:34:03Z"},{"alias_kind":"arxiv_version","alias_value":"0912.0184v2","created_at":"2026-05-18T03:34:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0184","created_at":"2026-05-18T03:34:03Z"},{"alias_kind":"pith_short_12","alias_value":"KPZZQZNK2SX6","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"KPZZQZNK2SX6XRFG","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"KPZZQZNK","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:KPZZQZNK2SX6XRFGQ7IXIMVRVZ","target":"record","payload":{"canonical_record":{"source":{"id":"0912.0184","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-12-01T15:23:07Z","cross_cats_sorted":[],"title_canon_sha256":"cb413d8fcb8f8e682f038b351f8e8076b6cc8146faa2f905d09702bd23a0d7a1","abstract_canon_sha256":"1bebf95f26e9629bb734f3f12402574233b4509ab0789ab51eaec8f27ec80d85"},"schema_version":"1.0"},"canonical_sha256":"53f39865aad4afebc4a687d17432b1ae7a0d1ff61863dba2a177703f8108e1fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:03.781762Z","signature_b64":"Cuw4NL5OOZwtqYz4G6vsc6vu7MHrFgtS3txRrQOyCQxOCbNlyz03fUGgAGjU0uhnJSUkyYLXxUQeoxN/NJ2cDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53f39865aad4afebc4a687d17432b1ae7a0d1ff61863dba2a177703f8108e1fe","last_reissued_at":"2026-05-18T03:34:03.781031Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:03.781031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0912.0184","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":"2026-05-18T03:34:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zGb/QArY/puEzQc+yuMgjy8mSm4l4jMwx97dPfh6M9iaq8bXagDydmJ0Ehz1e9wy0Rvbg52QwpMxkjcKEJm3BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T15:09:21.708920Z"},"content_sha256":"f3bc849266246ab77daf823ce9d2da44dbc06744ba1fe0eeb9b2231fb6f16e90","schema_version":"1.0","event_id":"sha256:f3bc849266246ab77daf823ce9d2da44dbc06744ba1fe0eeb9b2231fb6f16e90"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:KPZZQZNK2SX6XRFGQ7IXIMVRVZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The (1-E)-transform in combinatorial Hopf algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"F. Hivert, J.-C. Novelli, J.-G. Luque, J.-Y. Thibon","submitted_at":"2009-12-01T15:23:07Z","abstract_excerpt":"We extend to several combinatorial Hopf algebras the endomorphism of symmetric functions sending the first power-sum to zero and leaving the other ones invariant. As a transformation of alphabets, this is the (1-E)-transform, where E is the exponential alphabet, whose elementary symmetric functions are e_n=1/n!. In the case of noncommutative symmetric functions, we recover Schocker's idempotents for derangement numbers [Discr. Math. 269 (2003), 239].\n  From these idempotents, we construct subalgebras of the descent algebras analogous to the peak algebras and study their representation theory. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0184","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":"2026-05-18T03:34:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WLsubdCB0IqMJ0rCC+w8i9VIBJe4pA/XERFOKPLCoaFBTK0wadZyyPyCuKxzdroEhIaOIPL2mWiggSdfaQ6EAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T15:09:21.709563Z"},"content_sha256":"203862509f950c114181738f1d8227c5754ff90f94c8d4f650e027a6e9d231ee","schema_version":"1.0","event_id":"sha256:203862509f950c114181738f1d8227c5754ff90f94c8d4f650e027a6e9d231ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KPZZQZNK2SX6XRFGQ7IXIMVRVZ/bundle.json","state_url":"https://pith.science/pith/KPZZQZNK2SX6XRFGQ7IXIMVRVZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KPZZQZNK2SX6XRFGQ7IXIMVRVZ/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":"2026-05-29T15:09:21Z","links":{"resolver":"https://pith.science/pith/KPZZQZNK2SX6XRFGQ7IXIMVRVZ","bundle":"https://pith.science/pith/KPZZQZNK2SX6XRFGQ7IXIMVRVZ/bundle.json","state":"https://pith.science/pith/KPZZQZNK2SX6XRFGQ7IXIMVRVZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KPZZQZNK2SX6XRFGQ7IXIMVRVZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:KPZZQZNK2SX6XRFGQ7IXIMVRVZ","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":"1bebf95f26e9629bb734f3f12402574233b4509ab0789ab51eaec8f27ec80d85","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-12-01T15:23:07Z","title_canon_sha256":"cb413d8fcb8f8e682f038b351f8e8076b6cc8146faa2f905d09702bd23a0d7a1"},"schema_version":"1.0","source":{"id":"0912.0184","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.0184","created_at":"2026-05-18T03:34:03Z"},{"alias_kind":"arxiv_version","alias_value":"0912.0184v2","created_at":"2026-05-18T03:34:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0184","created_at":"2026-05-18T03:34:03Z"},{"alias_kind":"pith_short_12","alias_value":"KPZZQZNK2SX6","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"KPZZQZNK2SX6XRFG","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"KPZZQZNK","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:203862509f950c114181738f1d8227c5754ff90f94c8d4f650e027a6e9d231ee","target":"graph","created_at":"2026-05-18T03:34:03Z","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 extend to several combinatorial Hopf algebras the endomorphism of symmetric functions sending the first power-sum to zero and leaving the other ones invariant. As a transformation of alphabets, this is the (1-E)-transform, where E is the exponential alphabet, whose elementary symmetric functions are e_n=1/n!. In the case of noncommutative symmetric functions, we recover Schocker's idempotents for derangement numbers [Discr. Math. 269 (2003), 239].\n  From these idempotents, we construct subalgebras of the descent algebras analogous to the peak algebras and study their representation theory. ","authors_text":"F. Hivert, J.-C. Novelli, J.-G. Luque, J.-Y. Thibon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-12-01T15:23:07Z","title":"The (1-E)-transform in combinatorial Hopf algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0184","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:f3bc849266246ab77daf823ce9d2da44dbc06744ba1fe0eeb9b2231fb6f16e90","target":"record","created_at":"2026-05-18T03:34:03Z","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":"1bebf95f26e9629bb734f3f12402574233b4509ab0789ab51eaec8f27ec80d85","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-12-01T15:23:07Z","title_canon_sha256":"cb413d8fcb8f8e682f038b351f8e8076b6cc8146faa2f905d09702bd23a0d7a1"},"schema_version":"1.0","source":{"id":"0912.0184","kind":"arxiv","version":2}},"canonical_sha256":"53f39865aad4afebc4a687d17432b1ae7a0d1ff61863dba2a177703f8108e1fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53f39865aad4afebc4a687d17432b1ae7a0d1ff61863dba2a177703f8108e1fe","first_computed_at":"2026-05-18T03:34:03.781031Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:03.781031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cuw4NL5OOZwtqYz4G6vsc6vu7MHrFgtS3txRrQOyCQxOCbNlyz03fUGgAGjU0uhnJSUkyYLXxUQeoxN/NJ2cDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:03.781762Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.0184","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3bc849266246ab77daf823ce9d2da44dbc06744ba1fe0eeb9b2231fb6f16e90","sha256:203862509f950c114181738f1d8227c5754ff90f94c8d4f650e027a6e9d231ee"],"state_sha256":"8781b7a44a960c7e8203a138c2140f8bd6fa7072d9196774ecd2f63e22ee0d30"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"swoYWTzuL8mnWqHGkYnPNTOdfMSICtb2HIkmbXJHuW8oq2EAdpPelK+modUAx9PsXqHV3EpYl+uxl5Qlx/pzBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T15:09:21.712908Z","bundle_sha256":"79bc92ac23492d1ef78ee19b9317e4ccdcf09b522ae13be2b49e8e479b19524a"}}