{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:5XN6J3BHPN2IN3OFY2FUR64J7M","short_pith_number":"pith:5XN6J3BH","canonical_record":{"source":{"id":"1311.7294","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-11-28T12:06:24Z","cross_cats_sorted":[],"title_canon_sha256":"5b3002b2fe9315d0dcadf9bc5ef21675aa3aa1c0186b9e323f7caaf012c023fe","abstract_canon_sha256":"393306479c495ef987e7a4dcd8988ef37892ec921240730fa1611cf7ed4c5aba"},"schema_version":"1.0"},"canonical_sha256":"eddbe4ec277b7486edc5c68b48fb89fb36cb22fda006133e897a24dee619a746","source":{"kind":"arxiv","id":"1311.7294","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.7294","created_at":"2026-05-18T03:04:58Z"},{"alias_kind":"arxiv_version","alias_value":"1311.7294v2","created_at":"2026-05-18T03:04:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7294","created_at":"2026-05-18T03:04:58Z"},{"alias_kind":"pith_short_12","alias_value":"5XN6J3BHPN2I","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5XN6J3BHPN2IN3OF","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5XN6J3BH","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:5XN6J3BHPN2IN3OFY2FUR64J7M","target":"record","payload":{"canonical_record":{"source":{"id":"1311.7294","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-11-28T12:06:24Z","cross_cats_sorted":[],"title_canon_sha256":"5b3002b2fe9315d0dcadf9bc5ef21675aa3aa1c0186b9e323f7caaf012c023fe","abstract_canon_sha256":"393306479c495ef987e7a4dcd8988ef37892ec921240730fa1611cf7ed4c5aba"},"schema_version":"1.0"},"canonical_sha256":"eddbe4ec277b7486edc5c68b48fb89fb36cb22fda006133e897a24dee619a746","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:58.959959Z","signature_b64":"ASH9uxOr2D3M4LtX2ZdCYCk41ZI7uc4M1GTPRIzTGcvf3KbsfL9l2vESLaQhtyRZaY6c9Ygx00SnaIAmHPEgCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eddbe4ec277b7486edc5c68b48fb89fb36cb22fda006133e897a24dee619a746","last_reissued_at":"2026-05-18T03:04:58.959407Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:58.959407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.7294","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":"2026-05-18T03:04:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2ezQU+MFR2tEVXYVdTqjZmNYWg3qJFEmLhaqrD7G3piUe1sj3plDF5anVv/c/FztXiD/xGaQKQ0QJDiI+6v8Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:01:34.301038Z"},"content_sha256":"bddb549d1f519a081342601a22a6cb2a170b08af2f98dc4581b6c4751261feae","schema_version":"1.0","event_id":"sha256:bddb549d1f519a081342601a22a6cb2a170b08af2f98dc4581b6c4751261feae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:5XN6J3BHPN2IN3OFY2FUR64J7M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Irreducible constituents of minimal degree in supercharacters of the finite unitriangular groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Qiong Guo, Richard Dipper","submitted_at":"2013-11-28T12:06:24Z","abstract_excerpt":"Let $q$ be a prime power and $U$ the group of lower unitriangular matrices of order $n$ for some natural number $n$. We give a lower bound for the degrees of irreducible constituents of Andr\\'{e}-Yan supercharacters and classify the supercharacters having constituents whose degree assume this lower bound. Moreover we show that the number of distinct irreducible characters of $U$ meeting this condition is a polynomial in $(q-1)$ with nonnegative integral coefficients and exhibit monomial sources for those."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7294","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":"2026-05-18T03:04:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X6P21ojbLE7ZerTRFqeaSDdHFcNjrcLGMB0yrPLySQNajVNoO3CvKjd8Hy4gYvlWMzFKqDj+vP+5Ma//qtmjDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:01:34.301405Z"},"content_sha256":"be8d2a0caab84b411778b0794b0082f222605c6f782a5389645b79c241ce88b6","schema_version":"1.0","event_id":"sha256:be8d2a0caab84b411778b0794b0082f222605c6f782a5389645b79c241ce88b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5XN6J3BHPN2IN3OFY2FUR64J7M/bundle.json","state_url":"https://pith.science/pith/5XN6J3BHPN2IN3OFY2FUR64J7M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5XN6J3BHPN2IN3OFY2FUR64J7M/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":"2026-06-23T03:01:34Z","links":{"resolver":"https://pith.science/pith/5XN6J3BHPN2IN3OFY2FUR64J7M","bundle":"https://pith.science/pith/5XN6J3BHPN2IN3OFY2FUR64J7M/bundle.json","state":"https://pith.science/pith/5XN6J3BHPN2IN3OFY2FUR64J7M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5XN6J3BHPN2IN3OFY2FUR64J7M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5XN6J3BHPN2IN3OFY2FUR64J7M","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":"393306479c495ef987e7a4dcd8988ef37892ec921240730fa1611cf7ed4c5aba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-11-28T12:06:24Z","title_canon_sha256":"5b3002b2fe9315d0dcadf9bc5ef21675aa3aa1c0186b9e323f7caaf012c023fe"},"schema_version":"1.0","source":{"id":"1311.7294","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.7294","created_at":"2026-05-18T03:04:58Z"},{"alias_kind":"arxiv_version","alias_value":"1311.7294v2","created_at":"2026-05-18T03:04:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7294","created_at":"2026-05-18T03:04:58Z"},{"alias_kind":"pith_short_12","alias_value":"5XN6J3BHPN2I","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5XN6J3BHPN2IN3OF","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5XN6J3BH","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:be8d2a0caab84b411778b0794b0082f222605c6f782a5389645b79c241ce88b6","target":"graph","created_at":"2026-05-18T03:04:58Z","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":"Let $q$ be a prime power and $U$ the group of lower unitriangular matrices of order $n$ for some natural number $n$. We give a lower bound for the degrees of irreducible constituents of Andr\\'{e}-Yan supercharacters and classify the supercharacters having constituents whose degree assume this lower bound. Moreover we show that the number of distinct irreducible characters of $U$ meeting this condition is a polynomial in $(q-1)$ with nonnegative integral coefficients and exhibit monomial sources for those.","authors_text":"Qiong Guo, Richard Dipper","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-11-28T12:06:24Z","title":"Irreducible constituents of minimal degree in supercharacters of the finite unitriangular groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7294","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:bddb549d1f519a081342601a22a6cb2a170b08af2f98dc4581b6c4751261feae","target":"record","created_at":"2026-05-18T03:04:58Z","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":"393306479c495ef987e7a4dcd8988ef37892ec921240730fa1611cf7ed4c5aba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-11-28T12:06:24Z","title_canon_sha256":"5b3002b2fe9315d0dcadf9bc5ef21675aa3aa1c0186b9e323f7caaf012c023fe"},"schema_version":"1.0","source":{"id":"1311.7294","kind":"arxiv","version":2}},"canonical_sha256":"eddbe4ec277b7486edc5c68b48fb89fb36cb22fda006133e897a24dee619a746","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eddbe4ec277b7486edc5c68b48fb89fb36cb22fda006133e897a24dee619a746","first_computed_at":"2026-05-18T03:04:58.959407Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:58.959407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ASH9uxOr2D3M4LtX2ZdCYCk41ZI7uc4M1GTPRIzTGcvf3KbsfL9l2vESLaQhtyRZaY6c9Ygx00SnaIAmHPEgCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:58.959959Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.7294","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bddb549d1f519a081342601a22a6cb2a170b08af2f98dc4581b6c4751261feae","sha256:be8d2a0caab84b411778b0794b0082f222605c6f782a5389645b79c241ce88b6"],"state_sha256":"f87ff58730bf59e8460d71c76e4300945ed45abdfae12b965b02a7cd6dab4e32"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Y+CE/K5D7mpnvYfI7MvY2PrE7Jz+dcGJAPbmmjGFIMPKdSnBCl+1U0K9fnS2zMZvKo7ZqI0IkfGQz3PGGKlDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T03:01:34.303369Z","bundle_sha256":"545df7134b1943df59705b1bb77111cf98c4149e3dce942f9c6c4e8bcddbb8fc"}}