{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7VQUDUXBD3FHBY5UYK4RRPDX5K","short_pith_number":"pith:7VQUDUXB","canonical_record":{"source":{"id":"1109.3362","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-09-15T14:29:00Z","cross_cats_sorted":[],"title_canon_sha256":"63ae15b6b9b54abc932140a5e493f2f978782f8dc4d257a0cabf5dd93b72564a","abstract_canon_sha256":"3c3614cb55c4044cdde3db9bea4d283c2c3f8492e60f6f85be2b347d1924db46"},"schema_version":"1.0"},"canonical_sha256":"fd6141d2e11eca70e3b4c2b918bc77ea94d38137046d09f1474bd68599036c43","source":{"kind":"arxiv","id":"1109.3362","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.3362","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"arxiv_version","alias_value":"1109.3362v1","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.3362","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"pith_short_12","alias_value":"7VQUDUXBD3FH","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7VQUDUXBD3FHBY5U","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7VQUDUXB","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7VQUDUXBD3FHBY5UYK4RRPDX5K","target":"record","payload":{"canonical_record":{"source":{"id":"1109.3362","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-09-15T14:29:00Z","cross_cats_sorted":[],"title_canon_sha256":"63ae15b6b9b54abc932140a5e493f2f978782f8dc4d257a0cabf5dd93b72564a","abstract_canon_sha256":"3c3614cb55c4044cdde3db9bea4d283c2c3f8492e60f6f85be2b347d1924db46"},"schema_version":"1.0"},"canonical_sha256":"fd6141d2e11eca70e3b4c2b918bc77ea94d38137046d09f1474bd68599036c43","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:56.894215Z","signature_b64":"bAwiPZUkd1bivoqRddMK+/Dk84HJfFXjs8Wgjxq3gKSPLHQxe4n11hrTsDVe71mAar/65VRjF6BwTMbxvn5HBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd6141d2e11eca70e3b4c2b918bc77ea94d38137046d09f1474bd68599036c43","last_reissued_at":"2026-05-18T04:12:56.893546Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:56.893546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.3362","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":"2026-05-18T04:12:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QouQPvMnYK+8kPpSFLQ3eeP3NgfAaML1l8Ym/Yt4TWn5pyKxvp6yy9dpqIln5FOqYskrH31Y5B7l+2j+0jhOAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:52:36.754468Z"},"content_sha256":"0fc84862a50450972db367b8375a5fdc9ebc9655cfdcc12af2e96492c6d2d30e","schema_version":"1.0","event_id":"sha256:0fc84862a50450972db367b8375a5fdc9ebc9655cfdcc12af2e96492c6d2d30e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7VQUDUXBD3FHBY5UYK4RRPDX5K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Traces of Hecke operators in level 1 and Gaussian hypergeometric functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jenny G. Fuselier","submitted_at":"2011-09-15T14:29:00Z","abstract_excerpt":"We provide formulas for traces of p-th Hecke operators in level 1 in terms of values of finite field 2F1-hypergeometric functions, extending previous work of the author to all odd primes p, instead of only those p=1 (mod 12). We first give a general level 1 trace formula in terms of the trace of Frobenius on a family of elliptic curves, and then we draw on recent work of Lennon to produce level 1 trace formulas in terms of hypergeometric functions for all primes p >3."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3362","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":"2026-05-18T04:12:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k8SRCzkC/IJwgTHWJUAUm/9ztIEsOBqfnnsqQmUASVl9GNmkC6Jc2OvZpBEZsMDREcXa3BUhTcnJAgYiH/IaAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:52:36.755037Z"},"content_sha256":"76a0fbff56f99c0f14e624a7b010596bdede38cd2df466e50624fd36c2ae4ce2","schema_version":"1.0","event_id":"sha256:76a0fbff56f99c0f14e624a7b010596bdede38cd2df466e50624fd36c2ae4ce2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7VQUDUXBD3FHBY5UYK4RRPDX5K/bundle.json","state_url":"https://pith.science/pith/7VQUDUXBD3FHBY5UYK4RRPDX5K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7VQUDUXBD3FHBY5UYK4RRPDX5K/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":"2026-06-02T06:52:36Z","links":{"resolver":"https://pith.science/pith/7VQUDUXBD3FHBY5UYK4RRPDX5K","bundle":"https://pith.science/pith/7VQUDUXBD3FHBY5UYK4RRPDX5K/bundle.json","state":"https://pith.science/pith/7VQUDUXBD3FHBY5UYK4RRPDX5K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7VQUDUXBD3FHBY5UYK4RRPDX5K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7VQUDUXBD3FHBY5UYK4RRPDX5K","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":"3c3614cb55c4044cdde3db9bea4d283c2c3f8492e60f6f85be2b347d1924db46","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-09-15T14:29:00Z","title_canon_sha256":"63ae15b6b9b54abc932140a5e493f2f978782f8dc4d257a0cabf5dd93b72564a"},"schema_version":"1.0","source":{"id":"1109.3362","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.3362","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"arxiv_version","alias_value":"1109.3362v1","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.3362","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"pith_short_12","alias_value":"7VQUDUXBD3FH","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7VQUDUXBD3FHBY5U","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7VQUDUXB","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:76a0fbff56f99c0f14e624a7b010596bdede38cd2df466e50624fd36c2ae4ce2","target":"graph","created_at":"2026-05-18T04:12:56Z","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 provide formulas for traces of p-th Hecke operators in level 1 in terms of values of finite field 2F1-hypergeometric functions, extending previous work of the author to all odd primes p, instead of only those p=1 (mod 12). We first give a general level 1 trace formula in terms of the trace of Frobenius on a family of elliptic curves, and then we draw on recent work of Lennon to produce level 1 trace formulas in terms of hypergeometric functions for all primes p >3.","authors_text":"Jenny G. Fuselier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-09-15T14:29:00Z","title":"Traces of Hecke operators in level 1 and Gaussian hypergeometric functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3362","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":"sha256:0fc84862a50450972db367b8375a5fdc9ebc9655cfdcc12af2e96492c6d2d30e","target":"record","created_at":"2026-05-18T04:12:56Z","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":"3c3614cb55c4044cdde3db9bea4d283c2c3f8492e60f6f85be2b347d1924db46","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-09-15T14:29:00Z","title_canon_sha256":"63ae15b6b9b54abc932140a5e493f2f978782f8dc4d257a0cabf5dd93b72564a"},"schema_version":"1.0","source":{"id":"1109.3362","kind":"arxiv","version":1}},"canonical_sha256":"fd6141d2e11eca70e3b4c2b918bc77ea94d38137046d09f1474bd68599036c43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd6141d2e11eca70e3b4c2b918bc77ea94d38137046d09f1474bd68599036c43","first_computed_at":"2026-05-18T04:12:56.893546Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:56.893546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bAwiPZUkd1bivoqRddMK+/Dk84HJfFXjs8Wgjxq3gKSPLHQxe4n11hrTsDVe71mAar/65VRjF6BwTMbxvn5HBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:56.894215Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.3362","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fc84862a50450972db367b8375a5fdc9ebc9655cfdcc12af2e96492c6d2d30e","sha256:76a0fbff56f99c0f14e624a7b010596bdede38cd2df466e50624fd36c2ae4ce2"],"state_sha256":"2442a0ea2e6eb1c6824016c4459e086bb9134cb3ce1c2a4a006ed4a6cc10a6b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MdB7o2h8KCXhcUnVk2fE+9YWysXvcXLiTM3wwkBjlK04rdv1VGY18aV5kb51Y8PQ+mOjiWZ770ydit6UABerDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T06:52:36.758041Z","bundle_sha256":"2287041d6970cd2f18d7783caff968e38d9a48ba8d5cbd6056d9bdba7b981b6f"}}