{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:TRCSQMZQAOHNROVWC4YXUTGZW5","short_pith_number":"pith:TRCSQMZQ","canonical_record":{"source":{"id":"1002.3006","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-02-16T05:50:32Z","cross_cats_sorted":[],"title_canon_sha256":"5645e4006cb3e2ae09f11d7528287a5644eab3f7094d3f69325a6cf2dd20843f","abstract_canon_sha256":"79dda6ba9de1d00d454505e27534a45600cbd685a9223f890f292346d9a9decc"},"schema_version":"1.0"},"canonical_sha256":"9c45283330038ed8bab617317a4cd9b77bda209284bbd7523403428591869902","source":{"kind":"arxiv","id":"1002.3006","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.3006","created_at":"2026-05-18T04:19:33Z"},{"alias_kind":"arxiv_version","alias_value":"1002.3006v3","created_at":"2026-05-18T04:19:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.3006","created_at":"2026-05-18T04:19:33Z"},{"alias_kind":"pith_short_12","alias_value":"TRCSQMZQAOHN","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"TRCSQMZQAOHNROVW","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"TRCSQMZQ","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:TRCSQMZQAOHNROVWC4YXUTGZW5","target":"record","payload":{"canonical_record":{"source":{"id":"1002.3006","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-02-16T05:50:32Z","cross_cats_sorted":[],"title_canon_sha256":"5645e4006cb3e2ae09f11d7528287a5644eab3f7094d3f69325a6cf2dd20843f","abstract_canon_sha256":"79dda6ba9de1d00d454505e27534a45600cbd685a9223f890f292346d9a9decc"},"schema_version":"1.0"},"canonical_sha256":"9c45283330038ed8bab617317a4cd9b77bda209284bbd7523403428591869902","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:33.562147Z","signature_b64":"fy+IH7eBbxPnGG7PU8GhFwlKs+WXNzUi8e6ZbBZUZwLp+GmmgUiJ1kY8YFGERgkCIOY2fuNqEJT47MigxIMqDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c45283330038ed8bab617317a4cd9b77bda209284bbd7523403428591869902","last_reissued_at":"2026-05-18T04:19:33.561753Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:33.561753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.3006","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":"2026-05-18T04:19:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qseriv/0JQVjsdC0SnZIQRL7dx2U+sGIsVl9AdR3j1K2gMwpsUcQilU1LCoGcv5eOmJdU6I74Jt1i4lDtyEFDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:50:36.767976Z"},"content_sha256":"9d76cb91168313932e75c78fb393085cbc6e794ef04d463d8d779132e166ace2","schema_version":"1.0","event_id":"sha256:9d76cb91168313932e75c78fb393085cbc6e794ef04d463d8d779132e166ace2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:TRCSQMZQAOHNROVWC4YXUTGZW5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric analysis on small unitary representations of GL(N,R)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Bent {\\O}rsted, Michael Pevzner, Toshiyuki Kobayashi","submitted_at":"2010-02-16T05:50:32Z","abstract_excerpt":"The most degenerate unitary principal series representations {\\pi}_{i{\\lambda},{\\delta}} (with {\\lambda} \\in R, \\delta \\in Z/2Z) of G = GL(N,R) attain the minimum of the Gelfand-Kirillov dimension among all irreducible unitary representations of G. This article gives an explicit formula of the irreducible decomposition of the restriction {\\pi}_{i{\\lambda},{\\delta}}|_H (branching law) with respect to all symmetric pairs (G,H). For N=2n with n \\geq 2, the restriction {\\pi}_{i{\\lambda},{\\delta}}|_H remains irreducible for H=Sp(n,R) if {\\lambda}\\neq0 and splits into two irreducible representations"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.3006","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":""},"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":"2026-05-18T04:19:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dKErKd69tsSwzAWUKZ6UmPzaV4JeIjl3/vnJNuEx4fMUuiHGI908Lbv7LZ9sV4QqgfT7mDw/TFnqBUG5U1eVBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:50:36.768632Z"},"content_sha256":"e15fc6d349e1504de8e7e82b78b3e0f4df4c93fb8c8b5238a5aa07ce5aa9f4bb","schema_version":"1.0","event_id":"sha256:e15fc6d349e1504de8e7e82b78b3e0f4df4c93fb8c8b5238a5aa07ce5aa9f4bb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TRCSQMZQAOHNROVWC4YXUTGZW5/bundle.json","state_url":"https://pith.science/pith/TRCSQMZQAOHNROVWC4YXUTGZW5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TRCSQMZQAOHNROVWC4YXUTGZW5/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":"2026-05-26T15:50:36Z","links":{"resolver":"https://pith.science/pith/TRCSQMZQAOHNROVWC4YXUTGZW5","bundle":"https://pith.science/pith/TRCSQMZQAOHNROVWC4YXUTGZW5/bundle.json","state":"https://pith.science/pith/TRCSQMZQAOHNROVWC4YXUTGZW5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TRCSQMZQAOHNROVWC4YXUTGZW5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:TRCSQMZQAOHNROVWC4YXUTGZW5","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":"79dda6ba9de1d00d454505e27534a45600cbd685a9223f890f292346d9a9decc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-02-16T05:50:32Z","title_canon_sha256":"5645e4006cb3e2ae09f11d7528287a5644eab3f7094d3f69325a6cf2dd20843f"},"schema_version":"1.0","source":{"id":"1002.3006","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.3006","created_at":"2026-05-18T04:19:33Z"},{"alias_kind":"arxiv_version","alias_value":"1002.3006v3","created_at":"2026-05-18T04:19:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.3006","created_at":"2026-05-18T04:19:33Z"},{"alias_kind":"pith_short_12","alias_value":"TRCSQMZQAOHN","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"TRCSQMZQAOHNROVW","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"TRCSQMZQ","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:e15fc6d349e1504de8e7e82b78b3e0f4df4c93fb8c8b5238a5aa07ce5aa9f4bb","target":"graph","created_at":"2026-05-18T04:19:33Z","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":"The most degenerate unitary principal series representations {\\pi}_{i{\\lambda},{\\delta}} (with {\\lambda} \\in R, \\delta \\in Z/2Z) of G = GL(N,R) attain the minimum of the Gelfand-Kirillov dimension among all irreducible unitary representations of G. This article gives an explicit formula of the irreducible decomposition of the restriction {\\pi}_{i{\\lambda},{\\delta}}|_H (branching law) with respect to all symmetric pairs (G,H). For N=2n with n \\geq 2, the restriction {\\pi}_{i{\\lambda},{\\delta}}|_H remains irreducible for H=Sp(n,R) if {\\lambda}\\neq0 and splits into two irreducible representations","authors_text":"Bent {\\O}rsted, Michael Pevzner, Toshiyuki Kobayashi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-02-16T05:50:32Z","title":"Geometric analysis on small unitary representations of GL(N,R)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.3006","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":"sha256:9d76cb91168313932e75c78fb393085cbc6e794ef04d463d8d779132e166ace2","target":"record","created_at":"2026-05-18T04:19:33Z","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":"79dda6ba9de1d00d454505e27534a45600cbd685a9223f890f292346d9a9decc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-02-16T05:50:32Z","title_canon_sha256":"5645e4006cb3e2ae09f11d7528287a5644eab3f7094d3f69325a6cf2dd20843f"},"schema_version":"1.0","source":{"id":"1002.3006","kind":"arxiv","version":3}},"canonical_sha256":"9c45283330038ed8bab617317a4cd9b77bda209284bbd7523403428591869902","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c45283330038ed8bab617317a4cd9b77bda209284bbd7523403428591869902","first_computed_at":"2026-05-18T04:19:33.561753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:33.561753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fy+IH7eBbxPnGG7PU8GhFwlKs+WXNzUi8e6ZbBZUZwLp+GmmgUiJ1kY8YFGERgkCIOY2fuNqEJT47MigxIMqDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:33.562147Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.3006","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d76cb91168313932e75c78fb393085cbc6e794ef04d463d8d779132e166ace2","sha256:e15fc6d349e1504de8e7e82b78b3e0f4df4c93fb8c8b5238a5aa07ce5aa9f4bb"],"state_sha256":"b4bcd2f47a42881917e0bee4c207c02cbf67f35b673c4f6dd79e227bc34ef4bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IGHxCJX1MJ+7FLrKvCStPJ7gUMfgK6jNd38r6qSNHNbK067glLKYfK3D0oiK3rPP4LwkMhcXAmwJln2gRhVtCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T15:50:36.781151Z","bundle_sha256":"0948eb68feb8d6c2122775be6022d366298decf070dc3221ec60c3ada1f04d96"}}