{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:GFUTAFHQYWR4HRHTTJUIVYBA2D","short_pith_number":"pith:GFUTAFHQ","canonical_record":{"source":{"id":"1004.3550","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-04-20T20:05:48Z","cross_cats_sorted":["math.CO","math.RT"],"title_canon_sha256":"a26aea36a0d4ad444523450bf7cf6784103fcba02c6d45e628ca30da76a2dd9a","abstract_canon_sha256":"b8c9d6244c9f2e8ede17d8c5d24d07516889807c46d85370adbd6492657b4dc2"},"schema_version":"1.0"},"canonical_sha256":"31693014f0c5a3c3c4f39a688ae020d0d33b1670e6f9cbb55031b0a4444efc59","source":{"kind":"arxiv","id":"1004.3550","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.3550","created_at":"2026-05-18T04:24:06Z"},{"alias_kind":"arxiv_version","alias_value":"1004.3550v2","created_at":"2026-05-18T04:24:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.3550","created_at":"2026-05-18T04:24:06Z"},{"alias_kind":"pith_short_12","alias_value":"GFUTAFHQYWR4","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GFUTAFHQYWR4HRHT","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GFUTAFHQ","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:GFUTAFHQYWR4HRHTTJUIVYBA2D","target":"record","payload":{"canonical_record":{"source":{"id":"1004.3550","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-04-20T20:05:48Z","cross_cats_sorted":["math.CO","math.RT"],"title_canon_sha256":"a26aea36a0d4ad444523450bf7cf6784103fcba02c6d45e628ca30da76a2dd9a","abstract_canon_sha256":"b8c9d6244c9f2e8ede17d8c5d24d07516889807c46d85370adbd6492657b4dc2"},"schema_version":"1.0"},"canonical_sha256":"31693014f0c5a3c3c4f39a688ae020d0d33b1670e6f9cbb55031b0a4444efc59","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:06.305626Z","signature_b64":"gE/8k8PfvZJj9eb3roBeWGkXH42tI2sUWI3qJRkFKDlUNNVk156bV4Pwx6dZUxqchqvkLUPncxHn/EbzuPOqAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31693014f0c5a3c3c4f39a688ae020d0d33b1670e6f9cbb55031b0a4444efc59","last_reissued_at":"2026-05-18T04:24:06.305119Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:06.305119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.3550","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":"2026-05-18T04:24:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wl4n63GVqU6blYTOsiMmrrbdmZimXf7Dr/YQvAvAci9k4tauRx9k9TdYVgAlTlv22NxcJV0nzyRTmPe+SlnQAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T16:09:35.282138Z"},"content_sha256":"cbf9b8e4cb6d6c437a9b49581bd4b95550c5e446b0ac9c00866363dc86c3eb78","schema_version":"1.0","event_id":"sha256:cbf9b8e4cb6d6c437a9b49581bd4b95550c5e446b0ac9c00866363dc86c3eb78"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:GFUTAFHQYWR4HRHTTJUIVYBA2D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classical Kloosterman sums: representation theory, magic squares, and Ramanujan multigraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.RT"],"primary_cat":"math.NT","authors_text":"Gizem Karaali, Patrick S. Fleming, Stephan Ramon Garcia","submitted_at":"2010-04-20T20:05:48Z","abstract_excerpt":"We study the representation theory of a certain finite group for which Kloosterman sums appear as character values. This leads us to consider a concrete family of commuting hermitian matrices which have Kloosterman sums as eigenvalues. These matrices satisfy a number of \"magical\" combinatorial properties and they encode various arithmetic properties of Kloosterman sums. These matrices can also be regarded as adjacency matrices for multigraphs which display Ramanujan-like behavior."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3550","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":"2026-05-18T04:24:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"spv1ucDIsuh6NJxVJNCeUv6BuSF0S4hX1mZZi9ynxlNDbHyNOyZl2ZMP78q5HacxF5fElfFzhw90WW4MfPK+Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T16:09:35.282499Z"},"content_sha256":"5760a09e4dbbd4921e7d71fb859fddb45d02d7d17abb7ac4bc60d56fa8205358","schema_version":"1.0","event_id":"sha256:5760a09e4dbbd4921e7d71fb859fddb45d02d7d17abb7ac4bc60d56fa8205358"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GFUTAFHQYWR4HRHTTJUIVYBA2D/bundle.json","state_url":"https://pith.science/pith/GFUTAFHQYWR4HRHTTJUIVYBA2D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GFUTAFHQYWR4HRHTTJUIVYBA2D/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":"2026-06-24T16:09:35Z","links":{"resolver":"https://pith.science/pith/GFUTAFHQYWR4HRHTTJUIVYBA2D","bundle":"https://pith.science/pith/GFUTAFHQYWR4HRHTTJUIVYBA2D/bundle.json","state":"https://pith.science/pith/GFUTAFHQYWR4HRHTTJUIVYBA2D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GFUTAFHQYWR4HRHTTJUIVYBA2D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:GFUTAFHQYWR4HRHTTJUIVYBA2D","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":"b8c9d6244c9f2e8ede17d8c5d24d07516889807c46d85370adbd6492657b4dc2","cross_cats_sorted":["math.CO","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-04-20T20:05:48Z","title_canon_sha256":"a26aea36a0d4ad444523450bf7cf6784103fcba02c6d45e628ca30da76a2dd9a"},"schema_version":"1.0","source":{"id":"1004.3550","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.3550","created_at":"2026-05-18T04:24:06Z"},{"alias_kind":"arxiv_version","alias_value":"1004.3550v2","created_at":"2026-05-18T04:24:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.3550","created_at":"2026-05-18T04:24:06Z"},{"alias_kind":"pith_short_12","alias_value":"GFUTAFHQYWR4","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GFUTAFHQYWR4HRHT","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GFUTAFHQ","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:5760a09e4dbbd4921e7d71fb859fddb45d02d7d17abb7ac4bc60d56fa8205358","target":"graph","created_at":"2026-05-18T04:24:06Z","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 study the representation theory of a certain finite group for which Kloosterman sums appear as character values. This leads us to consider a concrete family of commuting hermitian matrices which have Kloosterman sums as eigenvalues. These matrices satisfy a number of \"magical\" combinatorial properties and they encode various arithmetic properties of Kloosterman sums. These matrices can also be regarded as adjacency matrices for multigraphs which display Ramanujan-like behavior.","authors_text":"Gizem Karaali, Patrick S. Fleming, Stephan Ramon Garcia","cross_cats":["math.CO","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-04-20T20:05:48Z","title":"Classical Kloosterman sums: representation theory, magic squares, and Ramanujan multigraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3550","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:cbf9b8e4cb6d6c437a9b49581bd4b95550c5e446b0ac9c00866363dc86c3eb78","target":"record","created_at":"2026-05-18T04:24:06Z","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":"b8c9d6244c9f2e8ede17d8c5d24d07516889807c46d85370adbd6492657b4dc2","cross_cats_sorted":["math.CO","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-04-20T20:05:48Z","title_canon_sha256":"a26aea36a0d4ad444523450bf7cf6784103fcba02c6d45e628ca30da76a2dd9a"},"schema_version":"1.0","source":{"id":"1004.3550","kind":"arxiv","version":2}},"canonical_sha256":"31693014f0c5a3c3c4f39a688ae020d0d33b1670e6f9cbb55031b0a4444efc59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31693014f0c5a3c3c4f39a688ae020d0d33b1670e6f9cbb55031b0a4444efc59","first_computed_at":"2026-05-18T04:24:06.305119Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:06.305119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gE/8k8PfvZJj9eb3roBeWGkXH42tI2sUWI3qJRkFKDlUNNVk156bV4Pwx6dZUxqchqvkLUPncxHn/EbzuPOqAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:06.305626Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.3550","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cbf9b8e4cb6d6c437a9b49581bd4b95550c5e446b0ac9c00866363dc86c3eb78","sha256:5760a09e4dbbd4921e7d71fb859fddb45d02d7d17abb7ac4bc60d56fa8205358"],"state_sha256":"6a6c0f9822737ea9abf53830ef11bc1dc58ed806523f1a288d790c048778a72d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UdHn35iBNYh/qU54ym8gTLbCdrXBQYWieDUWVXyTq5/28WmjeXJ9hZaYaVbY3+ByQHgRuxkpMcrBOJ10kaTQBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T16:09:35.284465Z","bundle_sha256":"c8fe14094d331f0e24a216b1bbabeb09f43573bc0c8b3d529085974612996d8b"}}