{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:T7SO3HVADAFNBROL4ECT6C3226","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":"34020d86cafdfabf51b2fece8ad1050e656276694983cfa8a20835a936aac19e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-17T14:06:40Z","title_canon_sha256":"49aea912d504b642e769bf82cb086e6682956eb644ea78be67be8268048826ff"},"schema_version":"1.0","source":{"id":"1902.06264","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.06264","created_at":"2026-05-17T23:52:50Z"},{"alias_kind":"arxiv_version","alias_value":"1902.06264v2","created_at":"2026-05-17T23:52:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.06264","created_at":"2026-05-17T23:52:50Z"},{"alias_kind":"pith_short_12","alias_value":"T7SO3HVADAFN","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"T7SO3HVADAFNBROL","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"T7SO3HVA","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:29b53a5060b868c17860466c8d4b5ad7a680e1c27834275b71b89f755ab458ef","target":"graph","created_at":"2026-05-17T23:52:50Z","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":"Certain classical generating functions for elements of reflection groups can be expressed using fundamental invariants called exponents. We give new analogues of such generating functions that accommodate orbits of reflecting hyperplanes using similar invariants we call reflexponents. Our verifications are case-by-case.","authors_text":"Nathan Williams","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-17T14:06:40Z","title":"Reflexponents"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.06264","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:ddce6903ad7a506c3d0efff96c0440ab67346f7dee9a04e7eafced43eff546db","target":"record","created_at":"2026-05-17T23:52:50Z","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":"34020d86cafdfabf51b2fece8ad1050e656276694983cfa8a20835a936aac19e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-17T14:06:40Z","title_canon_sha256":"49aea912d504b642e769bf82cb086e6682956eb644ea78be67be8268048826ff"},"schema_version":"1.0","source":{"id":"1902.06264","kind":"arxiv","version":2}},"canonical_sha256":"9fe4ed9ea0180ad0c5cbe1053f0b7ad79d1a7673bb339b696f16b0c2323e9cdc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fe4ed9ea0180ad0c5cbe1053f0b7ad79d1a7673bb339b696f16b0c2323e9cdc","first_computed_at":"2026-05-17T23:52:50.805053Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:50.805053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b0LEfnu6j2VIMOmf32tidgPaIG6E711zF2lUJqnEufHGGF+qnxQyA/r0o8t6OuPdPuQmQLHZV/PFXE7YG1ywBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:50.805701Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.06264","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ddce6903ad7a506c3d0efff96c0440ab67346f7dee9a04e7eafced43eff546db","sha256:29b53a5060b868c17860466c8d4b5ad7a680e1c27834275b71b89f755ab458ef"],"state_sha256":"2346926d7597b6ad5a8dd9c542997f3d3d42a614f2252530740c19ff16aadde2"}