{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:ABRS2S2TRMSBRM4SKEERNJOIHN","short_pith_number":"pith:ABRS2S2T","canonical_record":{"source":{"id":"2507.23102","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-07-30T21:07:24Z","cross_cats_sorted":[],"title_canon_sha256":"01bf1e1d42fdbb147011ada2c374a36bf0cd49d5b629526ff636528bcdc3d79e","abstract_canon_sha256":"d044428fa1348473fb0afc381e7357805ffd69b4c1117e9c0154d9669ece4720"},"schema_version":"1.0"},"canonical_sha256":"00632d4b538b2418b392510916a5c83b459386bfac25ab1a87b5d7edc88e4b00","source":{"kind":"arxiv","id":"2507.23102","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.23102","created_at":"2026-05-20T00:00:22Z"},{"alias_kind":"arxiv_version","alias_value":"2507.23102v2","created_at":"2026-05-20T00:00:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.23102","created_at":"2026-05-20T00:00:22Z"},{"alias_kind":"pith_short_12","alias_value":"ABRS2S2TRMSB","created_at":"2026-05-20T00:00:22Z"},{"alias_kind":"pith_short_16","alias_value":"ABRS2S2TRMSBRM4S","created_at":"2026-05-20T00:00:22Z"},{"alias_kind":"pith_short_8","alias_value":"ABRS2S2T","created_at":"2026-05-20T00:00:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:ABRS2S2TRMSBRM4SKEERNJOIHN","target":"record","payload":{"canonical_record":{"source":{"id":"2507.23102","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-07-30T21:07:24Z","cross_cats_sorted":[],"title_canon_sha256":"01bf1e1d42fdbb147011ada2c374a36bf0cd49d5b629526ff636528bcdc3d79e","abstract_canon_sha256":"d044428fa1348473fb0afc381e7357805ffd69b4c1117e9c0154d9669ece4720"},"schema_version":"1.0"},"canonical_sha256":"00632d4b538b2418b392510916a5c83b459386bfac25ab1a87b5d7edc88e4b00","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:00:22.461152Z","signature_b64":"1x245YO/Tx/QpxZwrK56hKKmsSlaCB4M+/025s206wE8tzhib2zLMkk1GCYEFqx90tB8EGmDmPTCpLJTPo+lCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00632d4b538b2418b392510916a5c83b459386bfac25ab1a87b5d7edc88e4b00","last_reissued_at":"2026-05-20T00:00:22.460527Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:00:22.460527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.23102","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":"2026-05-20T00:00:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZlWW3Ccd1uNi8auER8z9GXQYyq2lM4S33ribSctu6flBODSvtg5egDsyFf92EN1BbSs4uoW5gI1HW/H/ZsxqBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:48:17.932502Z"},"content_sha256":"b6d5381335a1db0ca346cf367b9d7ec41249ce7659002317515959ea802cc046","schema_version":"1.0","event_id":"sha256:b6d5381335a1db0ca346cf367b9d7ec41249ce7659002317515959ea802cc046"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:ABRS2S2TRMSBRM4SKEERNJOIHN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonzero $\\mathfrak{n}$-cohomology of Totally Degenerate Limit of Discrete Series representations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jin Kunwoo Lee","submitted_at":"2025-07-30T21:07:24Z","abstract_excerpt":"We show that a totally degenerate limit of discrete series representation admits a choice of n-cohomology group that is nonvanishing at a canonically defined degree. We then show that these groups satisfy Serre duality. This produces two n-cohomology groups, each for a totally degenerate limit of discrete series of U(n+1) and U(n), which are nonvanishing at the same degree. This suggests Gan-Gross-Prasad type branching laws for the TDLDS of unitary groups of any rank. We conclude by constructing an intertwining map of TDLDS for SU(2,1) and SU(1,1). This map will vanish on the minimal K type bu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.23102","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/2507.23102/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":"2026-05-20T00:00:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mWQg0jJwdvpBKJn3S1YX8K1xwSqO3axPBJ1JY1eYexN0XTvDWPeESY6eaBWx5NFymyTax/YaUiR/uWtA8KA4Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:48:17.933301Z"},"content_sha256":"457e10b42bf4013f40202871ffbf9647aaff74805760e2611c18e4230d9af11a","schema_version":"1.0","event_id":"sha256:457e10b42bf4013f40202871ffbf9647aaff74805760e2611c18e4230d9af11a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ABRS2S2TRMSBRM4SKEERNJOIHN/bundle.json","state_url":"https://pith.science/pith/ABRS2S2TRMSBRM4SKEERNJOIHN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ABRS2S2TRMSBRM4SKEERNJOIHN/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":"2026-06-11T22:48:17Z","links":{"resolver":"https://pith.science/pith/ABRS2S2TRMSBRM4SKEERNJOIHN","bundle":"https://pith.science/pith/ABRS2S2TRMSBRM4SKEERNJOIHN/bundle.json","state":"https://pith.science/pith/ABRS2S2TRMSBRM4SKEERNJOIHN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ABRS2S2TRMSBRM4SKEERNJOIHN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ABRS2S2TRMSBRM4SKEERNJOIHN","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":"d044428fa1348473fb0afc381e7357805ffd69b4c1117e9c0154d9669ece4720","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-07-30T21:07:24Z","title_canon_sha256":"01bf1e1d42fdbb147011ada2c374a36bf0cd49d5b629526ff636528bcdc3d79e"},"schema_version":"1.0","source":{"id":"2507.23102","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.23102","created_at":"2026-05-20T00:00:22Z"},{"alias_kind":"arxiv_version","alias_value":"2507.23102v2","created_at":"2026-05-20T00:00:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.23102","created_at":"2026-05-20T00:00:22Z"},{"alias_kind":"pith_short_12","alias_value":"ABRS2S2TRMSB","created_at":"2026-05-20T00:00:22Z"},{"alias_kind":"pith_short_16","alias_value":"ABRS2S2TRMSBRM4S","created_at":"2026-05-20T00:00:22Z"},{"alias_kind":"pith_short_8","alias_value":"ABRS2S2T","created_at":"2026-05-20T00:00:22Z"}],"graph_snapshots":[{"event_id":"sha256:457e10b42bf4013f40202871ffbf9647aaff74805760e2611c18e4230d9af11a","target":"graph","created_at":"2026-05-20T00:00:22Z","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/2507.23102/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that a totally degenerate limit of discrete series representation admits a choice of n-cohomology group that is nonvanishing at a canonically defined degree. We then show that these groups satisfy Serre duality. This produces two n-cohomology groups, each for a totally degenerate limit of discrete series of U(n+1) and U(n), which are nonvanishing at the same degree. This suggests Gan-Gross-Prasad type branching laws for the TDLDS of unitary groups of any rank. We conclude by constructing an intertwining map of TDLDS for SU(2,1) and SU(1,1). This map will vanish on the minimal K type bu","authors_text":"Jin Kunwoo Lee","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-07-30T21:07:24Z","title":"Nonzero $\\mathfrak{n}$-cohomology of Totally Degenerate Limit of Discrete Series representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.23102","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:b6d5381335a1db0ca346cf367b9d7ec41249ce7659002317515959ea802cc046","target":"record","created_at":"2026-05-20T00:00:22Z","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":"d044428fa1348473fb0afc381e7357805ffd69b4c1117e9c0154d9669ece4720","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-07-30T21:07:24Z","title_canon_sha256":"01bf1e1d42fdbb147011ada2c374a36bf0cd49d5b629526ff636528bcdc3d79e"},"schema_version":"1.0","source":{"id":"2507.23102","kind":"arxiv","version":2}},"canonical_sha256":"00632d4b538b2418b392510916a5c83b459386bfac25ab1a87b5d7edc88e4b00","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00632d4b538b2418b392510916a5c83b459386bfac25ab1a87b5d7edc88e4b00","first_computed_at":"2026-05-20T00:00:22.460527Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:00:22.460527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1x245YO/Tx/QpxZwrK56hKKmsSlaCB4M+/025s206wE8tzhib2zLMkk1GCYEFqx90tB8EGmDmPTCpLJTPo+lCw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:00:22.461152Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.23102","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6d5381335a1db0ca346cf367b9d7ec41249ce7659002317515959ea802cc046","sha256:457e10b42bf4013f40202871ffbf9647aaff74805760e2611c18e4230d9af11a"],"state_sha256":"0173446ef683604d04b24ab10b5b74886522d9080e92a87207b83e1365dbd06a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eQU/0fBP9Z/6zZf+5YzCdyjwiRtinAADB7UMImUzKYNu34A82q6FZfDXNNoKY/E/+v3sYmhUOYW9x7ruppnRDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T22:48:17.938080Z","bundle_sha256":"56ce58f3f21b7c5e5a9ba322247559306817b173fbcabd31665f72baab90e3ea"}}