{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:RDSOLHUBA37GGA7ZHKWQLV43EN","short_pith_number":"pith:RDSOLHUB","canonical_record":{"source":{"id":"1612.06913","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-12-20T23:03:02Z","cross_cats_sorted":[],"title_canon_sha256":"4effa0a9d9198922c9bd46fc34e7807bec00680b29e1f9c0cb35d3c29398e1b3","abstract_canon_sha256":"500d97bb2b32b060329360894e9db11ef3f5cb0800564b8e7922fe8d982b7b7f"},"schema_version":"1.0"},"canonical_sha256":"88e4e59e8106fe6303f93aad05d79b23594dab94a0dffe2de5310405734fb597","source":{"kind":"arxiv","id":"1612.06913","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06913","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06913v1","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06913","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"pith_short_12","alias_value":"RDSOLHUBA37G","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RDSOLHUBA37GGA7Z","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RDSOLHUB","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:RDSOLHUBA37GGA7ZHKWQLV43EN","target":"record","payload":{"canonical_record":{"source":{"id":"1612.06913","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-12-20T23:03:02Z","cross_cats_sorted":[],"title_canon_sha256":"4effa0a9d9198922c9bd46fc34e7807bec00680b29e1f9c0cb35d3c29398e1b3","abstract_canon_sha256":"500d97bb2b32b060329360894e9db11ef3f5cb0800564b8e7922fe8d982b7b7f"},"schema_version":"1.0"},"canonical_sha256":"88e4e59e8106fe6303f93aad05d79b23594dab94a0dffe2de5310405734fb597","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:15.070958Z","signature_b64":"0/gBwjxj6DCSw9qMD4w18xGQi4BFzOd7T4UwRik3anmob3aZ346HZUFEP6ch+x3YyQ8IHaW7etxp3ES66vy0Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88e4e59e8106fe6303f93aad05d79b23594dab94a0dffe2de5310405734fb597","last_reissued_at":"2026-05-18T00:54:15.070570Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:15.070570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.06913","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:54:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Acw7AnIrc+dpiWzTM55pjdJlMPRLtNRrftN/ZgEtQMWgqk3yICBN6vP/Os4MHQ4cZfIF95SM9ecIyH6RbFQBAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T02:59:05.828860Z"},"content_sha256":"fd89fa2f98ed7b4d83a8100012896caf5a18bea3c4a0351bf639ce3e688188be","schema_version":"1.0","event_id":"sha256:fd89fa2f98ed7b4d83a8100012896caf5a18bea3c4a0351bf639ce3e688188be"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:RDSOLHUBA37GGA7ZHKWQLV43EN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Supercharacter theories of dihedral groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jonathan Lamar","submitted_at":"2016-12-20T23:03:02Z","abstract_excerpt":"The set of supercharacter theories of a fixed group $G$ forms a natural lattice. An open question in the study of supercharacter theories is to classify this lattice, and to date, this has only been done for the cyclic groups $\\mathbb{Z}_n$. In this paper, we classify the supercharacter theory lattice of the dihedral groups $D_{2n}$ in terms of their cyclic subgroups of rotations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06913","kind":"arxiv","version":1},"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":"2026-05-18T00:54:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OnLJtERQmYz1SeTH24fyR1tO87xenRoPFUvI8tVZ8/7MD3dqvOD0Y/E9rZGkQCes9IFymvJ3rm91lX748fJPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T02:59:05.829201Z"},"content_sha256":"c88367da109f92902833da58e36412d79d32970736656f958a3974630d1a2a0b","schema_version":"1.0","event_id":"sha256:c88367da109f92902833da58e36412d79d32970736656f958a3974630d1a2a0b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RDSOLHUBA37GGA7ZHKWQLV43EN/bundle.json","state_url":"https://pith.science/pith/RDSOLHUBA37GGA7ZHKWQLV43EN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RDSOLHUBA37GGA7ZHKWQLV43EN/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":"2026-06-20T02:59:05Z","links":{"resolver":"https://pith.science/pith/RDSOLHUBA37GGA7ZHKWQLV43EN","bundle":"https://pith.science/pith/RDSOLHUBA37GGA7ZHKWQLV43EN/bundle.json","state":"https://pith.science/pith/RDSOLHUBA37GGA7ZHKWQLV43EN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RDSOLHUBA37GGA7ZHKWQLV43EN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RDSOLHUBA37GGA7ZHKWQLV43EN","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":"500d97bb2b32b060329360894e9db11ef3f5cb0800564b8e7922fe8d982b7b7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-12-20T23:03:02Z","title_canon_sha256":"4effa0a9d9198922c9bd46fc34e7807bec00680b29e1f9c0cb35d3c29398e1b3"},"schema_version":"1.0","source":{"id":"1612.06913","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06913","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06913v1","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06913","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"pith_short_12","alias_value":"RDSOLHUBA37G","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RDSOLHUBA37GGA7Z","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RDSOLHUB","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:c88367da109f92902833da58e36412d79d32970736656f958a3974630d1a2a0b","target":"graph","created_at":"2026-05-18T00:54:15Z","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":"The set of supercharacter theories of a fixed group $G$ forms a natural lattice. An open question in the study of supercharacter theories is to classify this lattice, and to date, this has only been done for the cyclic groups $\\mathbb{Z}_n$. In this paper, we classify the supercharacter theory lattice of the dihedral groups $D_{2n}$ in terms of their cyclic subgroups of rotations.","authors_text":"Jonathan Lamar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-12-20T23:03:02Z","title":"Supercharacter theories of dihedral groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06913","kind":"arxiv","version":1},"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:fd89fa2f98ed7b4d83a8100012896caf5a18bea3c4a0351bf639ce3e688188be","target":"record","created_at":"2026-05-18T00:54:15Z","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":"500d97bb2b32b060329360894e9db11ef3f5cb0800564b8e7922fe8d982b7b7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-12-20T23:03:02Z","title_canon_sha256":"4effa0a9d9198922c9bd46fc34e7807bec00680b29e1f9c0cb35d3c29398e1b3"},"schema_version":"1.0","source":{"id":"1612.06913","kind":"arxiv","version":1}},"canonical_sha256":"88e4e59e8106fe6303f93aad05d79b23594dab94a0dffe2de5310405734fb597","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88e4e59e8106fe6303f93aad05d79b23594dab94a0dffe2de5310405734fb597","first_computed_at":"2026-05-18T00:54:15.070570Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:15.070570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0/gBwjxj6DCSw9qMD4w18xGQi4BFzOd7T4UwRik3anmob3aZ346HZUFEP6ch+x3YyQ8IHaW7etxp3ES66vy0Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:15.070958Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.06913","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd89fa2f98ed7b4d83a8100012896caf5a18bea3c4a0351bf639ce3e688188be","sha256:c88367da109f92902833da58e36412d79d32970736656f958a3974630d1a2a0b"],"state_sha256":"bc229a42732e46cc007102d8d47ea84bfccbd307a4ab3ba1ac34cdcba8262256"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zbn/fJpoXZg5ulw0q48qGYrqd6KoSi9ajKye7RnLZKIt8kS9hFtZggjijrg6roeZvdRqilO1H9XrvhWEV5/iCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T02:59:05.831147Z","bundle_sha256":"657147654f030eab8e500d9c3f62039657afee4e2d6008b1891e205768db9908"}}