{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:P6RA6IYHDQJSJ453U2OUCLVPU6","short_pith_number":"pith:P6RA6IYH","canonical_record":{"source":{"id":"2004.12490","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-04-26T22:12:02Z","cross_cats_sorted":[],"title_canon_sha256":"ce9a29ae8c5c8ce34e5e271eecffb2bca953f2b620f05b81afc839d56525331f","abstract_canon_sha256":"ab4c1e19b77576574a9964255fe9f6ac992866755374bab1f09f52d78ae58cc4"},"schema_version":"1.0"},"canonical_sha256":"7fa20f23071c1324f3bba69d412eafa784cab92bf6d4d73a1f7c9e1dbde54c97","source":{"kind":"arxiv","id":"2004.12490","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.12490","created_at":"2026-07-05T01:07:13Z"},{"alias_kind":"arxiv_version","alias_value":"2004.12490v2","created_at":"2026-07-05T01:07:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.12490","created_at":"2026-07-05T01:07:13Z"},{"alias_kind":"pith_short_12","alias_value":"P6RA6IYHDQJS","created_at":"2026-07-05T01:07:13Z"},{"alias_kind":"pith_short_16","alias_value":"P6RA6IYHDQJSJ453","created_at":"2026-07-05T01:07:13Z"},{"alias_kind":"pith_short_8","alias_value":"P6RA6IYH","created_at":"2026-07-05T01:07:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:P6RA6IYHDQJSJ453U2OUCLVPU6","target":"record","payload":{"canonical_record":{"source":{"id":"2004.12490","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-04-26T22:12:02Z","cross_cats_sorted":[],"title_canon_sha256":"ce9a29ae8c5c8ce34e5e271eecffb2bca953f2b620f05b81afc839d56525331f","abstract_canon_sha256":"ab4c1e19b77576574a9964255fe9f6ac992866755374bab1f09f52d78ae58cc4"},"schema_version":"1.0"},"canonical_sha256":"7fa20f23071c1324f3bba69d412eafa784cab92bf6d4d73a1f7c9e1dbde54c97","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:07:13.652647Z","signature_b64":"XS3NzQUFfH02xlMfQxd2ttW1DJHsZSZeckpeOeEZ462D0iDx7blFfDp5dX78OexKOMkEgZ/iTrpEy2BTfNBzCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fa20f23071c1324f3bba69d412eafa784cab92bf6d4d73a1f7c9e1dbde54c97","last_reissued_at":"2026-07-05T01:07:13.652230Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:07:13.652230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2004.12490","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":"2026-07-05T01:07:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J9oWBQvLiyNepwLBOVQyDYcnEx63C5xIyB/OE8yM6Lj6Uu/VANx62UWwrNxwLGMvgO9q5EPU6YGbrjwNZMj7BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T07:56:04.171455Z"},"content_sha256":"b386da2356049ce29d83408ab67f25c1bcb3c74c484f0e572e11a8cf3c4641f0","schema_version":"1.0","event_id":"sha256:b386da2356049ce29d83408ab67f25c1bcb3c74c484f0e572e11a8cf3c4641f0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:P6RA6IYHDQJSJ453U2OUCLVPU6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Slopes in eigenvarieties for definite unitary groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Lynnelle Ye","submitted_at":"2020-04-26T22:12:02Z","abstract_excerpt":"We generalize bounds of Liu-Wan-Xiao for slopes in eigencurves for definite unitary groups of rank $2$ to slopes in eigenvarieties for definite unitary groups of any rank. We show that for a definite unitary group of rank $n$, the Newton polygon of the characteristic power series of the $U_p$ Hecke operator has exact growth rate $x^{1+\\frac2{n(n-1)}}$, times a constant proportional to the distance of the weight from the boundary of weight space. The proof goes through the classification of forms associated to principal series representations. We also give a consequence for the geometry of thes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.12490","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2004.12490/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":"2026-07-05T01:07:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ui9S3FJBkwHfBa7qRlh4rg3eWE6+6TqPGzN7lIRpa/4+jDrYO/Olrs+a+epXCmzdfDJpCU7Vlt8LmDE8idMnCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T07:56:04.171868Z"},"content_sha256":"98305d2798c85d81328fa31914b1f77d09e6b5d784c7fe46110463f5c0bd4e4a","schema_version":"1.0","event_id":"sha256:98305d2798c85d81328fa31914b1f77d09e6b5d784c7fe46110463f5c0bd4e4a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P6RA6IYHDQJSJ453U2OUCLVPU6/bundle.json","state_url":"https://pith.science/pith/P6RA6IYHDQJSJ453U2OUCLVPU6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P6RA6IYHDQJSJ453U2OUCLVPU6/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":"2026-08-13T07:56:04Z","links":{"resolver":"https://pith.science/pith/P6RA6IYHDQJSJ453U2OUCLVPU6","bundle":"https://pith.science/pith/P6RA6IYHDQJSJ453U2OUCLVPU6/bundle.json","state":"https://pith.science/pith/P6RA6IYHDQJSJ453U2OUCLVPU6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P6RA6IYHDQJSJ453U2OUCLVPU6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:P6RA6IYHDQJSJ453U2OUCLVPU6","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":"ab4c1e19b77576574a9964255fe9f6ac992866755374bab1f09f52d78ae58cc4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-04-26T22:12:02Z","title_canon_sha256":"ce9a29ae8c5c8ce34e5e271eecffb2bca953f2b620f05b81afc839d56525331f"},"schema_version":"1.0","source":{"id":"2004.12490","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.12490","created_at":"2026-07-05T01:07:13Z"},{"alias_kind":"arxiv_version","alias_value":"2004.12490v2","created_at":"2026-07-05T01:07:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.12490","created_at":"2026-07-05T01:07:13Z"},{"alias_kind":"pith_short_12","alias_value":"P6RA6IYHDQJS","created_at":"2026-07-05T01:07:13Z"},{"alias_kind":"pith_short_16","alias_value":"P6RA6IYHDQJSJ453","created_at":"2026-07-05T01:07:13Z"},{"alias_kind":"pith_short_8","alias_value":"P6RA6IYH","created_at":"2026-07-05T01:07:13Z"}],"graph_snapshots":[{"event_id":"sha256:98305d2798c85d81328fa31914b1f77d09e6b5d784c7fe46110463f5c0bd4e4a","target":"graph","created_at":"2026-07-05T01:07:13Z","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/2004.12490/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We generalize bounds of Liu-Wan-Xiao for slopes in eigencurves for definite unitary groups of rank $2$ to slopes in eigenvarieties for definite unitary groups of any rank. We show that for a definite unitary group of rank $n$, the Newton polygon of the characteristic power series of the $U_p$ Hecke operator has exact growth rate $x^{1+\\frac2{n(n-1)}}$, times a constant proportional to the distance of the weight from the boundary of weight space. The proof goes through the classification of forms associated to principal series representations. We also give a consequence for the geometry of thes","authors_text":"Lynnelle Ye","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-04-26T22:12:02Z","title":"Slopes in eigenvarieties for definite unitary groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.12490","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:b386da2356049ce29d83408ab67f25c1bcb3c74c484f0e572e11a8cf3c4641f0","target":"record","created_at":"2026-07-05T01:07:13Z","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":"ab4c1e19b77576574a9964255fe9f6ac992866755374bab1f09f52d78ae58cc4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-04-26T22:12:02Z","title_canon_sha256":"ce9a29ae8c5c8ce34e5e271eecffb2bca953f2b620f05b81afc839d56525331f"},"schema_version":"1.0","source":{"id":"2004.12490","kind":"arxiv","version":2}},"canonical_sha256":"7fa20f23071c1324f3bba69d412eafa784cab92bf6d4d73a1f7c9e1dbde54c97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fa20f23071c1324f3bba69d412eafa784cab92bf6d4d73a1f7c9e1dbde54c97","first_computed_at":"2026-07-05T01:07:13.652230Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:07:13.652230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XS3NzQUFfH02xlMfQxd2ttW1DJHsZSZeckpeOeEZ462D0iDx7blFfDp5dX78OexKOMkEgZ/iTrpEy2BTfNBzCw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:07:13.652647Z","signed_message":"canonical_sha256_bytes"},"source_id":"2004.12490","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b386da2356049ce29d83408ab67f25c1bcb3c74c484f0e572e11a8cf3c4641f0","sha256:98305d2798c85d81328fa31914b1f77d09e6b5d784c7fe46110463f5c0bd4e4a"],"state_sha256":"36b3ac35bc06346ff097062a89f59bd33def7de3ec728ad136624ba559ee52a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rCwEZH6YyomnrJz9NzC5ayfqc8UDsLGdD/owdetGVbDSn3s18OhwXpCk+bAzkYYaTrYniDXNPqgZowyhbjq8BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T07:56:04.174990Z","bundle_sha256":"3d252fcb2299651ad572162fb567444d7210318c116054edc0a9f0a7d4001157"}}