{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:AMTJTYNTP5NDMCFDPB6KI3HDCK","short_pith_number":"pith:AMTJTYNT","canonical_record":{"source":{"id":"1309.0930","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-09-04T07:04:58Z","cross_cats_sorted":[],"title_canon_sha256":"f88bcef2edd271a6ad9097511ef47c90a8cb4aed5c962fbed4fc0b435ae96f5c","abstract_canon_sha256":"e2b5574d368ffe080978a1064a7e8e51ad416cd5ca9eca16bfa98ad93b7d431d"},"schema_version":"1.0"},"canonical_sha256":"032699e1b37f5a3608a3787ca46ce3128a6c920a94ac05853939ede83b1716f4","source":{"kind":"arxiv","id":"1309.0930","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0930","created_at":"2026-05-18T00:29:49Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0930v2","created_at":"2026-05-18T00:29:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0930","created_at":"2026-05-18T00:29:49Z"},{"alias_kind":"pith_short_12","alias_value":"AMTJTYNTP5ND","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AMTJTYNTP5NDMCFD","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AMTJTYNT","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:AMTJTYNTP5NDMCFDPB6KI3HDCK","target":"record","payload":{"canonical_record":{"source":{"id":"1309.0930","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-09-04T07:04:58Z","cross_cats_sorted":[],"title_canon_sha256":"f88bcef2edd271a6ad9097511ef47c90a8cb4aed5c962fbed4fc0b435ae96f5c","abstract_canon_sha256":"e2b5574d368ffe080978a1064a7e8e51ad416cd5ca9eca16bfa98ad93b7d431d"},"schema_version":"1.0"},"canonical_sha256":"032699e1b37f5a3608a3787ca46ce3128a6c920a94ac05853939ede83b1716f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:49.527332Z","signature_b64":"xpi2ng7IIk7UWYh8erAol3c4yDi5ViLGa3EheTE8XhaPSLi+ZldBn04ySDlCMdN/vU1X63bBhyUHolD8EOvnCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"032699e1b37f5a3608a3787ca46ce3128a6c920a94ac05853939ede83b1716f4","last_reissued_at":"2026-05-18T00:29:49.526802Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:49.526802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.0930","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":"2026-05-18T00:29:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2E/+ZD0lXTgKU73oWaU8qqXjFvhjaYUYTB7Qtok8WVz6FRk4TK3lAZfDLSKmCaThzXTlfNtNwdrn0V2wxHElDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T14:11:40.278195Z"},"content_sha256":"03b15514663b5a56f1d19b8cc384a9d241a10a546e7adfea60546667211e53ae","schema_version":"1.0","event_id":"sha256:03b15514663b5a56f1d19b8cc384a9d241a10a546e7adfea60546667211e53ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:AMTJTYNTP5NDMCFDPB6KI3HDCK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multiplicity bounds and the subrepresentation theorem for real spherical spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Bernhard Kr\\\"otz, Henrik Schlichtkrull","submitted_at":"2013-09-04T07:04:58Z","abstract_excerpt":"Let G be a real semi-simple Lie group and H a closed subgroup which admits an open orbit on the flag manifold of a minimal parabolic subgroup. Let V be a Harish-Chandra module. A sharp finite bound is given for the dimension of the space of H-fixed distribution vectors for V and a related subrepresentation theorem is derived. Extended final version. To appear in Trans. Amer. Math. Soc."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0930","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":""},"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":"2026-05-18T00:29:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lzddhcp2+pkSLplIJCtZLPMnG30JDzzME4jdXa8+t22aGrBdrSjgAQjOzimFjeNo8t45k2ZC1KmtntXR+LxOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T14:11:40.278853Z"},"content_sha256":"ee7d67e10a812f94fb72fd7b2fb7d26238c976f9182a3029f1af6013b6058fb7","schema_version":"1.0","event_id":"sha256:ee7d67e10a812f94fb72fd7b2fb7d26238c976f9182a3029f1af6013b6058fb7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AMTJTYNTP5NDMCFDPB6KI3HDCK/bundle.json","state_url":"https://pith.science/pith/AMTJTYNTP5NDMCFDPB6KI3HDCK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AMTJTYNTP5NDMCFDPB6KI3HDCK/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":"2026-05-26T14:11:40Z","links":{"resolver":"https://pith.science/pith/AMTJTYNTP5NDMCFDPB6KI3HDCK","bundle":"https://pith.science/pith/AMTJTYNTP5NDMCFDPB6KI3HDCK/bundle.json","state":"https://pith.science/pith/AMTJTYNTP5NDMCFDPB6KI3HDCK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AMTJTYNTP5NDMCFDPB6KI3HDCK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:AMTJTYNTP5NDMCFDPB6KI3HDCK","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":"e2b5574d368ffe080978a1064a7e8e51ad416cd5ca9eca16bfa98ad93b7d431d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-09-04T07:04:58Z","title_canon_sha256":"f88bcef2edd271a6ad9097511ef47c90a8cb4aed5c962fbed4fc0b435ae96f5c"},"schema_version":"1.0","source":{"id":"1309.0930","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0930","created_at":"2026-05-18T00:29:49Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0930v2","created_at":"2026-05-18T00:29:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0930","created_at":"2026-05-18T00:29:49Z"},{"alias_kind":"pith_short_12","alias_value":"AMTJTYNTP5ND","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AMTJTYNTP5NDMCFD","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AMTJTYNT","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:ee7d67e10a812f94fb72fd7b2fb7d26238c976f9182a3029f1af6013b6058fb7","target":"graph","created_at":"2026-05-18T00:29:49Z","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":"Let G be a real semi-simple Lie group and H a closed subgroup which admits an open orbit on the flag manifold of a minimal parabolic subgroup. Let V be a Harish-Chandra module. A sharp finite bound is given for the dimension of the space of H-fixed distribution vectors for V and a related subrepresentation theorem is derived. Extended final version. To appear in Trans. Amer. Math. Soc.","authors_text":"Bernhard Kr\\\"otz, Henrik Schlichtkrull","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-09-04T07:04:58Z","title":"Multiplicity bounds and the subrepresentation theorem for real spherical spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0930","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":"sha256:03b15514663b5a56f1d19b8cc384a9d241a10a546e7adfea60546667211e53ae","target":"record","created_at":"2026-05-18T00:29:49Z","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":"e2b5574d368ffe080978a1064a7e8e51ad416cd5ca9eca16bfa98ad93b7d431d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-09-04T07:04:58Z","title_canon_sha256":"f88bcef2edd271a6ad9097511ef47c90a8cb4aed5c962fbed4fc0b435ae96f5c"},"schema_version":"1.0","source":{"id":"1309.0930","kind":"arxiv","version":2}},"canonical_sha256":"032699e1b37f5a3608a3787ca46ce3128a6c920a94ac05853939ede83b1716f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"032699e1b37f5a3608a3787ca46ce3128a6c920a94ac05853939ede83b1716f4","first_computed_at":"2026-05-18T00:29:49.526802Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:49.526802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xpi2ng7IIk7UWYh8erAol3c4yDi5ViLGa3EheTE8XhaPSLi+ZldBn04ySDlCMdN/vU1X63bBhyUHolD8EOvnCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:49.527332Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.0930","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03b15514663b5a56f1d19b8cc384a9d241a10a546e7adfea60546667211e53ae","sha256:ee7d67e10a812f94fb72fd7b2fb7d26238c976f9182a3029f1af6013b6058fb7"],"state_sha256":"3549dd3e104f9052c4d9fab0604373c4fcc92ecbf2fc81c4f8ef2e4469f55c4d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VPdLsW7TDwRf2syJD+R6Q8UUDSi7uaIErwoAyQRSUmFCQN5/+9mqpu6aYom9H4Ug7XHGjbOsxpjh+S61ImHrAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T14:11:40.282059Z","bundle_sha256":"e6bc98333ae0e39888e740b34e07ff6fe7564189511cfd8efd6f518786ca3c7e"}}