{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ER3MNTAU5YA7WYSUBDRZXF5RAV","short_pith_number":"pith:ER3MNTAU","canonical_record":{"source":{"id":"1609.02029","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-09-07T15:45:08Z","cross_cats_sorted":[],"title_canon_sha256":"8b815de3f640308d0dcb59a5233ae5e0fb019ba56d10d866790206d7c84df9d4","abstract_canon_sha256":"2c8d4feb07ca081ce069a686534285616bcd1ea66fd2e4e14c55513eb7fca98a"},"schema_version":"1.0"},"canonical_sha256":"2476c6cc14ee01fb625408e39b97b105479ff1f186432593ab9b1735cba39365","source":{"kind":"arxiv","id":"1609.02029","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.02029","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"arxiv_version","alias_value":"1609.02029v2","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.02029","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"pith_short_12","alias_value":"ER3MNTAU5YA7","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"ER3MNTAU5YA7WYSU","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"ER3MNTAU","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ER3MNTAU5YA7WYSUBDRZXF5RAV","target":"record","payload":{"canonical_record":{"source":{"id":"1609.02029","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-09-07T15:45:08Z","cross_cats_sorted":[],"title_canon_sha256":"8b815de3f640308d0dcb59a5233ae5e0fb019ba56d10d866790206d7c84df9d4","abstract_canon_sha256":"2c8d4feb07ca081ce069a686534285616bcd1ea66fd2e4e14c55513eb7fca98a"},"schema_version":"1.0"},"canonical_sha256":"2476c6cc14ee01fb625408e39b97b105479ff1f186432593ab9b1735cba39365","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:49.376769Z","signature_b64":"mkzv4JnAI6uW44gRf7W0SyvWV0Twt8y3lFCRNVJR7Otu5W8CwdFIuSjXQacf2i95GoD6sDssiJTX7XOgM1WbDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2476c6cc14ee01fb625408e39b97b105479ff1f186432593ab9b1735cba39365","last_reissued_at":"2026-05-18T01:04:49.376335Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:49.376335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.02029","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":"2026-05-18T01:04:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SLDXHar2l6BH8n2yy6vIhySxAXmGbDvfl2mfM4SG7dI00XY8aQjEtWARcmZbzzU1I9tOjqdAzYXIQVXI2wj4AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T03:43:43.885452Z"},"content_sha256":"57515ea3fbd020b0bcca25f2e6af59cd080bfcb7e96cca196c6ef1a0df0c0b0b","schema_version":"1.0","event_id":"sha256:57515ea3fbd020b0bcca25f2e6af59cd080bfcb7e96cca196c6ef1a0df0c0b0b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ER3MNTAU5YA7WYSUBDRZXF5RAV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"${\\rm B}_\\pi$-characters and quotients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Mark L. Lewis","submitted_at":"2016-09-07T15:45:08Z","abstract_excerpt":"Let $\\pi$ be a set of primes, and let $G$ be a finite $\\pi$-separable group. We consider the Isaacs ${\\rm B}_\\pi$-characters. We show that if $N$ is a normal subgroup of $G$, then ${\\rm B}_\\pi (G/N) = {\\rm Irr} (G/N) \\cap {\\rm B}_\\pi (G)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02029","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":"2026-05-18T01:04:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OId/rrsXPW6sfWw/LS4F9epkH+epb4tyBMR1CgI2YFN8/q63rtGHXwzdcaPDz19+m3/iFp9dks2mduYImooHCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T03:43:43.885792Z"},"content_sha256":"15b794416d94d945b6c08395a97b4a9878e16e7a5822c3fb1b2c408f9399a653","schema_version":"1.0","event_id":"sha256:15b794416d94d945b6c08395a97b4a9878e16e7a5822c3fb1b2c408f9399a653"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ER3MNTAU5YA7WYSUBDRZXF5RAV/bundle.json","state_url":"https://pith.science/pith/ER3MNTAU5YA7WYSUBDRZXF5RAV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ER3MNTAU5YA7WYSUBDRZXF5RAV/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":"2026-06-20T03:43:43Z","links":{"resolver":"https://pith.science/pith/ER3MNTAU5YA7WYSUBDRZXF5RAV","bundle":"https://pith.science/pith/ER3MNTAU5YA7WYSUBDRZXF5RAV/bundle.json","state":"https://pith.science/pith/ER3MNTAU5YA7WYSUBDRZXF5RAV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ER3MNTAU5YA7WYSUBDRZXF5RAV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ER3MNTAU5YA7WYSUBDRZXF5RAV","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":"2c8d4feb07ca081ce069a686534285616bcd1ea66fd2e4e14c55513eb7fca98a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-09-07T15:45:08Z","title_canon_sha256":"8b815de3f640308d0dcb59a5233ae5e0fb019ba56d10d866790206d7c84df9d4"},"schema_version":"1.0","source":{"id":"1609.02029","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.02029","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"arxiv_version","alias_value":"1609.02029v2","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.02029","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"pith_short_12","alias_value":"ER3MNTAU5YA7","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"ER3MNTAU5YA7WYSU","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"ER3MNTAU","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:15b794416d94d945b6c08395a97b4a9878e16e7a5822c3fb1b2c408f9399a653","target":"graph","created_at":"2026-05-18T01:04:49Z","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 $\\pi$ be a set of primes, and let $G$ be a finite $\\pi$-separable group. We consider the Isaacs ${\\rm B}_\\pi$-characters. We show that if $N$ is a normal subgroup of $G$, then ${\\rm B}_\\pi (G/N) = {\\rm Irr} (G/N) \\cap {\\rm B}_\\pi (G)$.","authors_text":"Mark L. Lewis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-09-07T15:45:08Z","title":"${\\rm B}_\\pi$-characters and quotients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02029","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":"sha256:57515ea3fbd020b0bcca25f2e6af59cd080bfcb7e96cca196c6ef1a0df0c0b0b","target":"record","created_at":"2026-05-18T01:04:49Z","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":"2c8d4feb07ca081ce069a686534285616bcd1ea66fd2e4e14c55513eb7fca98a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-09-07T15:45:08Z","title_canon_sha256":"8b815de3f640308d0dcb59a5233ae5e0fb019ba56d10d866790206d7c84df9d4"},"schema_version":"1.0","source":{"id":"1609.02029","kind":"arxiv","version":2}},"canonical_sha256":"2476c6cc14ee01fb625408e39b97b105479ff1f186432593ab9b1735cba39365","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2476c6cc14ee01fb625408e39b97b105479ff1f186432593ab9b1735cba39365","first_computed_at":"2026-05-18T01:04:49.376335Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:49.376335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mkzv4JnAI6uW44gRf7W0SyvWV0Twt8y3lFCRNVJR7Otu5W8CwdFIuSjXQacf2i95GoD6sDssiJTX7XOgM1WbDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:49.376769Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.02029","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57515ea3fbd020b0bcca25f2e6af59cd080bfcb7e96cca196c6ef1a0df0c0b0b","sha256:15b794416d94d945b6c08395a97b4a9878e16e7a5822c3fb1b2c408f9399a653"],"state_sha256":"e2331be46681514e328e160c4842edd018d005c800d8b0fb27710c43a8d44920"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y9gMDvC80Q2y2SdTHBij43x9BmqGSPqfk+OkxQsTwPIdHYEZ9ekLvFwyijw8gTIXhZA+5DBkNPGVrvP1fucABg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T03:43:43.887732Z","bundle_sha256":"1c981cb828f3dcc3e3a0d6c82b2ab4305caa70fce43fa70f86c9f98e2b0ce235"}}