{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:3PTIIRP6323RUCUB7HLLX74VRS","short_pith_number":"pith:3PTIIRP6","canonical_record":{"source":{"id":"2310.17047","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-10-25T22:54:05Z","cross_cats_sorted":[],"title_canon_sha256":"be96abab5079f8e1916e53a03dd0e41c16d62fb4964937e06cc7119a33a1bca2","abstract_canon_sha256":"499b1a8af0b7ae976c11cc8977f35162b38c082eaaebfeb4b1a50a4ee252d3c1"},"schema_version":"1.0"},"canonical_sha256":"dbe68445fedeb71a0a81f9d6bbff958cad56d5fa833ee436c72aee8549a255ab","source":{"kind":"arxiv","id":"2310.17047","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.17047","created_at":"2026-07-05T11:32:13Z"},{"alias_kind":"arxiv_version","alias_value":"2310.17047v3","created_at":"2026-07-05T11:32:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.17047","created_at":"2026-07-05T11:32:13Z"},{"alias_kind":"pith_short_12","alias_value":"3PTIIRP6323R","created_at":"2026-07-05T11:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"3PTIIRP6323RUCUB","created_at":"2026-07-05T11:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"3PTIIRP6","created_at":"2026-07-05T11:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:3PTIIRP6323RUCUB7HLLX74VRS","target":"record","payload":{"canonical_record":{"source":{"id":"2310.17047","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-10-25T22:54:05Z","cross_cats_sorted":[],"title_canon_sha256":"be96abab5079f8e1916e53a03dd0e41c16d62fb4964937e06cc7119a33a1bca2","abstract_canon_sha256":"499b1a8af0b7ae976c11cc8977f35162b38c082eaaebfeb4b1a50a4ee252d3c1"},"schema_version":"1.0"},"canonical_sha256":"dbe68445fedeb71a0a81f9d6bbff958cad56d5fa833ee436c72aee8549a255ab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:32:13.641763Z","signature_b64":"zBDnILz+bC0uLuRWxf14CcEu7/MpPxONeiKTNwNkRA0Tx95m3HR07DAGh8dhTb4Ae582AlSmhTZBicYB6aGgAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dbe68445fedeb71a0a81f9d6bbff958cad56d5fa833ee436c72aee8549a255ab","last_reissued_at":"2026-07-05T11:32:13.641276Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:32:13.641276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2310.17047","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:32:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qFTUkaYwtNIqBgpuS4Vd5UOxoKlEtl2geOkLwiuyorXrYvcsWFZT0QZSNCpXS+kAJU3/c26eXveBz6zW8+jHBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T20:39:18.709844Z"},"content_sha256":"0c1700a59d75d103b254129781d12b9e16afd0d3fbef8b4f723dafc7f28d0e22","schema_version":"1.0","event_id":"sha256:0c1700a59d75d103b254129781d12b9e16afd0d3fbef8b4f723dafc7f28d0e22"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:3PTIIRP6323RUCUB7HLLX74VRS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counting locally supercuspidal newforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrew Knightly","submitted_at":"2023-10-25T22:54:05Z","abstract_excerpt":"The trace formula is a versatile tool for computing sums of spectral data across families of automorphic forms. Using specialized test functions, one can treat small families with refined spectral properties. This has proven fruitful in analytic applications. We detail such methodology here, with the aim of counting newforms in certain small families. The result (Theorem 7.1) is a general formula for the number of holomorphic newforms of weight $k$ and level $N$ whose local representation type at each $p|N$ is a fixed supercuspidal representation $\\sigma_p$ of $\\operatorname{GL}_2(\\mathbf{Q}_p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.17047","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2310.17047/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:32:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6e2g6RCHEN6omhN6D33oepdM9C1YwHz9/eA7DT/Cz/+qigHO6W5+fm+WISJYJchMF+lV/rb1OaIA8/hak0bgBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T20:39:18.710340Z"},"content_sha256":"9a244483bb5a2218f078111c97b6f22ecd576195838a69595a445cec9cd41e32","schema_version":"1.0","event_id":"sha256:9a244483bb5a2218f078111c97b6f22ecd576195838a69595a445cec9cd41e32"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3PTIIRP6323RUCUB7HLLX74VRS/bundle.json","state_url":"https://pith.science/pith/3PTIIRP6323RUCUB7HLLX74VRS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3PTIIRP6323RUCUB7HLLX74VRS/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":"2026-08-09T20:39:18Z","links":{"resolver":"https://pith.science/pith/3PTIIRP6323RUCUB7HLLX74VRS","bundle":"https://pith.science/pith/3PTIIRP6323RUCUB7HLLX74VRS/bundle.json","state":"https://pith.science/pith/3PTIIRP6323RUCUB7HLLX74VRS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3PTIIRP6323RUCUB7HLLX74VRS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:3PTIIRP6323RUCUB7HLLX74VRS","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":"499b1a8af0b7ae976c11cc8977f35162b38c082eaaebfeb4b1a50a4ee252d3c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-10-25T22:54:05Z","title_canon_sha256":"be96abab5079f8e1916e53a03dd0e41c16d62fb4964937e06cc7119a33a1bca2"},"schema_version":"1.0","source":{"id":"2310.17047","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.17047","created_at":"2026-07-05T11:32:13Z"},{"alias_kind":"arxiv_version","alias_value":"2310.17047v3","created_at":"2026-07-05T11:32:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.17047","created_at":"2026-07-05T11:32:13Z"},{"alias_kind":"pith_short_12","alias_value":"3PTIIRP6323R","created_at":"2026-07-05T11:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"3PTIIRP6323RUCUB","created_at":"2026-07-05T11:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"3PTIIRP6","created_at":"2026-07-05T11:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:9a244483bb5a2218f078111c97b6f22ecd576195838a69595a445cec9cd41e32","target":"graph","created_at":"2026-07-05T11:32:13Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2310.17047/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The trace formula is a versatile tool for computing sums of spectral data across families of automorphic forms. Using specialized test functions, one can treat small families with refined spectral properties. This has proven fruitful in analytic applications. We detail such methodology here, with the aim of counting newforms in certain small families. The result (Theorem 7.1) is a general formula for the number of holomorphic newforms of weight $k$ and level $N$ whose local representation type at each $p|N$ is a fixed supercuspidal representation $\\sigma_p$ of $\\operatorname{GL}_2(\\mathbf{Q}_p","authors_text":"Andrew Knightly","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-10-25T22:54:05Z","title":"Counting locally supercuspidal newforms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.17047","kind":"arxiv","version":3},"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":"sha256:0c1700a59d75d103b254129781d12b9e16afd0d3fbef8b4f723dafc7f28d0e22","target":"record","created_at":"2026-07-05T11:32:13Z","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":"499b1a8af0b7ae976c11cc8977f35162b38c082eaaebfeb4b1a50a4ee252d3c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-10-25T22:54:05Z","title_canon_sha256":"be96abab5079f8e1916e53a03dd0e41c16d62fb4964937e06cc7119a33a1bca2"},"schema_version":"1.0","source":{"id":"2310.17047","kind":"arxiv","version":3}},"canonical_sha256":"dbe68445fedeb71a0a81f9d6bbff958cad56d5fa833ee436c72aee8549a255ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dbe68445fedeb71a0a81f9d6bbff958cad56d5fa833ee436c72aee8549a255ab","first_computed_at":"2026-07-05T11:32:13.641276Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:32:13.641276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zBDnILz+bC0uLuRWxf14CcEu7/MpPxONeiKTNwNkRA0Tx95m3HR07DAGh8dhTb4Ae582AlSmhTZBicYB6aGgAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:32:13.641763Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.17047","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c1700a59d75d103b254129781d12b9e16afd0d3fbef8b4f723dafc7f28d0e22","sha256:9a244483bb5a2218f078111c97b6f22ecd576195838a69595a445cec9cd41e32"],"state_sha256":"f351617911f147ecf660c60eef406f95f9d9ecf759b16d08c3c7a90ef145e03f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JS2RDSGxNzBltfOfV5t4Gs5DlqNqRrSh8GnpgCT4Sr7tRIwALJo7wWAjRQjpXqHNDR1WXga63AbcxxLBbJptDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T20:39:18.714250Z","bundle_sha256":"0b7834d75f38153c0ae2ba7f016bd2a9182ce2e1ac1ad3d7754ea842b2c30022"}}