{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:NWMX5ZMUTC6SBNO4LHSGZBGUBT","short_pith_number":"pith:NWMX5ZMU","canonical_record":{"source":{"id":"0905.1190","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-05-08T16:24:33Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"e10424a2cdd3e645d4644c637af82a0c6436874505ee24b35382cad804882194","abstract_canon_sha256":"4b682e8a4ccad0c5f36b7836f3e02a05521647ac65942726df8a443260b460c1"},"schema_version":"1.0"},"canonical_sha256":"6d997ee59498bd20b5dc59e46c84d40cebea67584cec0cdb77b43bb73b6f3f52","source":{"kind":"arxiv","id":"0905.1190","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.1190","created_at":"2026-05-18T03:49:12Z"},{"alias_kind":"arxiv_version","alias_value":"0905.1190v2","created_at":"2026-05-18T03:49:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.1190","created_at":"2026-05-18T03:49:12Z"},{"alias_kind":"pith_short_12","alias_value":"NWMX5ZMUTC6S","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"NWMX5ZMUTC6SBNO4","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"NWMX5ZMU","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:NWMX5ZMUTC6SBNO4LHSGZBGUBT","target":"record","payload":{"canonical_record":{"source":{"id":"0905.1190","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-05-08T16:24:33Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"e10424a2cdd3e645d4644c637af82a0c6436874505ee24b35382cad804882194","abstract_canon_sha256":"4b682e8a4ccad0c5f36b7836f3e02a05521647ac65942726df8a443260b460c1"},"schema_version":"1.0"},"canonical_sha256":"6d997ee59498bd20b5dc59e46c84d40cebea67584cec0cdb77b43bb73b6f3f52","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:12.276676Z","signature_b64":"Q5Ls2KVJb47LH11UhskYU6sIO+ZLQY0AbyS3+KE2OXlVtixMoPOdTI5nlmiBrglfkAdFQYAOM2kAxjt7axCjDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d997ee59498bd20b5dc59e46c84d40cebea67584cec0cdb77b43bb73b6f3f52","last_reissued_at":"2026-05-18T03:49:12.276071Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:12.276071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0905.1190","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":"2026-05-18T03:49:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Ldwu0kUrmB2BEzf5A+U4fLY1ikAqRWgCUgDD4MYLAnZ+uWZz5pve4HWgb9xsjbJNuC6YPNfPJzYD3ZG3A90AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:11:07.535541Z"},"content_sha256":"a5ccaa23fdf7aca757692702edf9d913a9d5baf337cff8b389c9ec96f9287acd","schema_version":"1.0","event_id":"sha256:a5ccaa23fdf7aca757692702edf9d913a9d5baf337cff8b389c9ec96f9287acd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:NWMX5ZMUTC6SBNO4LHSGZBGUBT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"G-graphs and special representations for binary dihedral groups in GL(2,C)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"\\'Alvaro Nolla de Celis","submitted_at":"2009-05-08T16:24:33Z","abstract_excerpt":"We give the classification of all possible G-graphs for any small binary dihedral subgroup G in GL(2,C) and use this classification to give the combinatorial description of the special representations of G in terms of its maximal cyclic normal subgroup."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.1190","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":"2026-05-18T03:49:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uawsYwvrTqvpqFH8ge43SiFtr/Whpn3VLaVwAdS0+K81tPajDFSj0BUguGjPE3BEXnA1E+3KQ3OCeUjsFrGZDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:11:07.536304Z"},"content_sha256":"b08b1d0059ff6cca747295324f6b23767526a1d3b318d33752dd7d5fda4f0bec","schema_version":"1.0","event_id":"sha256:b08b1d0059ff6cca747295324f6b23767526a1d3b318d33752dd7d5fda4f0bec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NWMX5ZMUTC6SBNO4LHSGZBGUBT/bundle.json","state_url":"https://pith.science/pith/NWMX5ZMUTC6SBNO4LHSGZBGUBT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NWMX5ZMUTC6SBNO4LHSGZBGUBT/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":"2026-05-30T08:11:07Z","links":{"resolver":"https://pith.science/pith/NWMX5ZMUTC6SBNO4LHSGZBGUBT","bundle":"https://pith.science/pith/NWMX5ZMUTC6SBNO4LHSGZBGUBT/bundle.json","state":"https://pith.science/pith/NWMX5ZMUTC6SBNO4LHSGZBGUBT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NWMX5ZMUTC6SBNO4LHSGZBGUBT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:NWMX5ZMUTC6SBNO4LHSGZBGUBT","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":"4b682e8a4ccad0c5f36b7836f3e02a05521647ac65942726df8a443260b460c1","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-05-08T16:24:33Z","title_canon_sha256":"e10424a2cdd3e645d4644c637af82a0c6436874505ee24b35382cad804882194"},"schema_version":"1.0","source":{"id":"0905.1190","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.1190","created_at":"2026-05-18T03:49:12Z"},{"alias_kind":"arxiv_version","alias_value":"0905.1190v2","created_at":"2026-05-18T03:49:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.1190","created_at":"2026-05-18T03:49:12Z"},{"alias_kind":"pith_short_12","alias_value":"NWMX5ZMUTC6S","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"NWMX5ZMUTC6SBNO4","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"NWMX5ZMU","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:b08b1d0059ff6cca747295324f6b23767526a1d3b318d33752dd7d5fda4f0bec","target":"graph","created_at":"2026-05-18T03:49:12Z","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 give the classification of all possible G-graphs for any small binary dihedral subgroup G in GL(2,C) and use this classification to give the combinatorial description of the special representations of G in terms of its maximal cyclic normal subgroup.","authors_text":"\\'Alvaro Nolla de Celis","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-05-08T16:24:33Z","title":"G-graphs and special representations for binary dihedral groups in GL(2,C)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.1190","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:a5ccaa23fdf7aca757692702edf9d913a9d5baf337cff8b389c9ec96f9287acd","target":"record","created_at":"2026-05-18T03:49:12Z","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":"4b682e8a4ccad0c5f36b7836f3e02a05521647ac65942726df8a443260b460c1","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-05-08T16:24:33Z","title_canon_sha256":"e10424a2cdd3e645d4644c637af82a0c6436874505ee24b35382cad804882194"},"schema_version":"1.0","source":{"id":"0905.1190","kind":"arxiv","version":2}},"canonical_sha256":"6d997ee59498bd20b5dc59e46c84d40cebea67584cec0cdb77b43bb73b6f3f52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d997ee59498bd20b5dc59e46c84d40cebea67584cec0cdb77b43bb73b6f3f52","first_computed_at":"2026-05-18T03:49:12.276071Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:12.276071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q5Ls2KVJb47LH11UhskYU6sIO+ZLQY0AbyS3+KE2OXlVtixMoPOdTI5nlmiBrglfkAdFQYAOM2kAxjt7axCjDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:12.276676Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.1190","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5ccaa23fdf7aca757692702edf9d913a9d5baf337cff8b389c9ec96f9287acd","sha256:b08b1d0059ff6cca747295324f6b23767526a1d3b318d33752dd7d5fda4f0bec"],"state_sha256":"a8cba5642f6031dfb2d43ad32c6b5e3eb9a4fe103f906932b37abc39770cad11"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cXkHZmCJBmASkJWiGiM49vFn3mdiT7NoBQkTjifWVJcxnQjKOqz1kITZECXfo54s9xqNkj/dLIiKUU18/lUhDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:11:07.539950Z","bundle_sha256":"b9905a3d83a9ae132ab60b6a7500cc0a77897a5fe4086600aa467be08eac67bc"}}