{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:D33X4RBBAYRKAA5JODUJXUG47D","short_pith_number":"pith:D33X4RBB","canonical_record":{"source":{"id":"1310.3306","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-10-11T22:40:11Z","cross_cats_sorted":[],"title_canon_sha256":"7043f56a15008c1221b2924c6d2c3107894ea562e3962ad89c09219616c38a02","abstract_canon_sha256":"0853559b49e165a29b27d58c2c50ac82fcbf1a6fe387eb1827e4c4ebfc8512d4"},"schema_version":"1.0"},"canonical_sha256":"1ef77e44210622a003a970e89bd0dcf8d9643983612c96df245dacc7361db4b6","source":{"kind":"arxiv","id":"1310.3306","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.3306","created_at":"2026-05-18T00:53:11Z"},{"alias_kind":"arxiv_version","alias_value":"1310.3306v1","created_at":"2026-05-18T00:53:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3306","created_at":"2026-05-18T00:53:11Z"},{"alias_kind":"pith_short_12","alias_value":"D33X4RBBAYRK","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"D33X4RBBAYRKAA5J","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"D33X4RBB","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:D33X4RBBAYRKAA5JODUJXUG47D","target":"record","payload":{"canonical_record":{"source":{"id":"1310.3306","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-10-11T22:40:11Z","cross_cats_sorted":[],"title_canon_sha256":"7043f56a15008c1221b2924c6d2c3107894ea562e3962ad89c09219616c38a02","abstract_canon_sha256":"0853559b49e165a29b27d58c2c50ac82fcbf1a6fe387eb1827e4c4ebfc8512d4"},"schema_version":"1.0"},"canonical_sha256":"1ef77e44210622a003a970e89bd0dcf8d9643983612c96df245dacc7361db4b6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:11.135026Z","signature_b64":"3kCmeCrhbavk5LiWxv1UgjQvQ/exF57voqCX3DH6TZ6XDTUhuaT/0kk1rV6aeepIzO6HPkw85fJchyqJsdZdAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ef77e44210622a003a970e89bd0dcf8d9643983612c96df245dacc7361db4b6","last_reissued_at":"2026-05-18T00:53:11.134437Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:11.134437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.3306","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":"2026-05-18T00:53:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GNW5NgTxNh1WAzhH0ds3eLMVJeSn17/FB/gUFrl6w23Yll1zbiaoixGwNMvpIbFt1qSIZNmOWpcAbhZ8o3plDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:55:16.611251Z"},"content_sha256":"1854be564ed2ff5cffcf55d6cd5c5cd230e9ecc1b8b83a13dc2396b23b322374","schema_version":"1.0","event_id":"sha256:1854be564ed2ff5cffcf55d6cd5c5cd230e9ecc1b8b83a13dc2396b23b322374"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:D33X4RBBAYRKAA5JODUJXUG47D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability of character sums for positive-depth, supercuspidal representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Loren Spice, Stephen DeBacker","submitted_at":"2013-10-11T22:40:11Z","abstract_excerpt":"We re-write the character formul{\\ae} of Adler and the second-named author in a form amenable to explicit computations in $p$-adic harmonic analysis, and use them to prove the stability of character sums for a modification of Reeder's conjectural positive-depth, unramified, toral supercuspidal L-packets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3306","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":"2026-05-18T00:53:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BjdlbnQURnWexFJybxr67qCSWoki7obaqh852FZwyF+/uc01bjSvbsRIU+24uR23tMfaadmgLJQn4kHf7FCUBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:55:16.611831Z"},"content_sha256":"b59085a5bc0b3653decc97bed102d70253e0ecb6dd5d3cd7667dd039dc1fe24a","schema_version":"1.0","event_id":"sha256:b59085a5bc0b3653decc97bed102d70253e0ecb6dd5d3cd7667dd039dc1fe24a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D33X4RBBAYRKAA5JODUJXUG47D/bundle.json","state_url":"https://pith.science/pith/D33X4RBBAYRKAA5JODUJXUG47D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D33X4RBBAYRKAA5JODUJXUG47D/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":"2026-05-31T00:55:16Z","links":{"resolver":"https://pith.science/pith/D33X4RBBAYRKAA5JODUJXUG47D","bundle":"https://pith.science/pith/D33X4RBBAYRKAA5JODUJXUG47D/bundle.json","state":"https://pith.science/pith/D33X4RBBAYRKAA5JODUJXUG47D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D33X4RBBAYRKAA5JODUJXUG47D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:D33X4RBBAYRKAA5JODUJXUG47D","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":"0853559b49e165a29b27d58c2c50ac82fcbf1a6fe387eb1827e4c4ebfc8512d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-10-11T22:40:11Z","title_canon_sha256":"7043f56a15008c1221b2924c6d2c3107894ea562e3962ad89c09219616c38a02"},"schema_version":"1.0","source":{"id":"1310.3306","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.3306","created_at":"2026-05-18T00:53:11Z"},{"alias_kind":"arxiv_version","alias_value":"1310.3306v1","created_at":"2026-05-18T00:53:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3306","created_at":"2026-05-18T00:53:11Z"},{"alias_kind":"pith_short_12","alias_value":"D33X4RBBAYRK","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"D33X4RBBAYRKAA5J","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"D33X4RBB","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:b59085a5bc0b3653decc97bed102d70253e0ecb6dd5d3cd7667dd039dc1fe24a","target":"graph","created_at":"2026-05-18T00:53:11Z","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 re-write the character formul{\\ae} of Adler and the second-named author in a form amenable to explicit computations in $p$-adic harmonic analysis, and use them to prove the stability of character sums for a modification of Reeder's conjectural positive-depth, unramified, toral supercuspidal L-packets.","authors_text":"Loren Spice, Stephen DeBacker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-10-11T22:40:11Z","title":"Stability of character sums for positive-depth, supercuspidal representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3306","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":"sha256:1854be564ed2ff5cffcf55d6cd5c5cd230e9ecc1b8b83a13dc2396b23b322374","target":"record","created_at":"2026-05-18T00:53:11Z","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":"0853559b49e165a29b27d58c2c50ac82fcbf1a6fe387eb1827e4c4ebfc8512d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-10-11T22:40:11Z","title_canon_sha256":"7043f56a15008c1221b2924c6d2c3107894ea562e3962ad89c09219616c38a02"},"schema_version":"1.0","source":{"id":"1310.3306","kind":"arxiv","version":1}},"canonical_sha256":"1ef77e44210622a003a970e89bd0dcf8d9643983612c96df245dacc7361db4b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ef77e44210622a003a970e89bd0dcf8d9643983612c96df245dacc7361db4b6","first_computed_at":"2026-05-18T00:53:11.134437Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:11.134437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3kCmeCrhbavk5LiWxv1UgjQvQ/exF57voqCX3DH6TZ6XDTUhuaT/0kk1rV6aeepIzO6HPkw85fJchyqJsdZdAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:11.135026Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.3306","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1854be564ed2ff5cffcf55d6cd5c5cd230e9ecc1b8b83a13dc2396b23b322374","sha256:b59085a5bc0b3653decc97bed102d70253e0ecb6dd5d3cd7667dd039dc1fe24a"],"state_sha256":"3e4a150efcc8a2a32d2372c9d5b32cf59103b5663f363fcfca2fccc86154fff7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/EEajw9rz5Snt4F0a6pFVCrKaIESLR8vWPjQctREtU4aGqIE+VNYkrMoroFy0PWDjdnVyict88JpXEQe6NIjBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T00:55:16.614880Z","bundle_sha256":"00a1c4dc5c520ad56c0e26a631c214b1fb0b08bd21e9c710e667d59ee7ee6ac6"}}