{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NP2CR5F6XJOC53KNUIBQFWO6GK","short_pith_number":"pith:NP2CR5F6","canonical_record":{"source":{"id":"1501.01479","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-01-07T13:02:47Z","cross_cats_sorted":[],"title_canon_sha256":"50e619cf45e0651fa6ab6616430b3d465516ca66cfec5a5468427a85e9ab4de3","abstract_canon_sha256":"fd358b296b73ce51604b282679696481f69b12bad9e6f00fd1b07a890c5d7b66"},"schema_version":"1.0"},"canonical_sha256":"6bf428f4beba5c2eed4da20302d9de32b56d7f05f6c693d5fd5bb3f3680290b6","source":{"kind":"arxiv","id":"1501.01479","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01479","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01479v2","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01479","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"pith_short_12","alias_value":"NP2CR5F6XJOC","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NP2CR5F6XJOC53KN","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NP2CR5F6","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NP2CR5F6XJOC53KNUIBQFWO6GK","target":"record","payload":{"canonical_record":{"source":{"id":"1501.01479","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-01-07T13:02:47Z","cross_cats_sorted":[],"title_canon_sha256":"50e619cf45e0651fa6ab6616430b3d465516ca66cfec5a5468427a85e9ab4de3","abstract_canon_sha256":"fd358b296b73ce51604b282679696481f69b12bad9e6f00fd1b07a890c5d7b66"},"schema_version":"1.0"},"canonical_sha256":"6bf428f4beba5c2eed4da20302d9de32b56d7f05f6c693d5fd5bb3f3680290b6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:33.492011Z","signature_b64":"3Pmj3+Tup5Yv6Q9qs2YdSxOBIkt5lYUM08nM8u3mVRMdpD9ukDdwHoRcsh+TH4rbldAiXNwAr7HbaRbi7rslCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6bf428f4beba5c2eed4da20302d9de32b56d7f05f6c693d5fd5bb3f3680290b6","last_reissued_at":"2026-05-18T01:16:33.491353Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:33.491353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.01479","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":"2026-05-18T01:16:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0d60NPi4ittXqyCFgQRaG/0rik9VyLuTvvSD6lxMKqWQMCLCY4/CfKfl0Zi4Wd3RpGk+G5Ndhuf89gT2fXVnBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T18:54:33.478745Z"},"content_sha256":"c9dcab182d20f230b82d367bf073732cf85a24be80dc64a19e09cf5604c3b830","schema_version":"1.0","event_id":"sha256:c9dcab182d20f230b82d367bf073732cf85a24be80dc64a19e09cf5604c3b830"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NP2CR5F6XJOC53KNUIBQFWO6GK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Holonomicity of relative characters and applications to multiplicity bounds for spherical pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Andrey Minchenko, Avraham Aizenbud, Dmitry Gourevitch","submitted_at":"2015-01-07T13:02:47Z","abstract_excerpt":"In this paper, we prove that any relative character (a.k.a. spherical character) of any admissible representation of a real reductive group with respect to any pair of spherical subgroups is a holonomic distribution on the group. This implies that the restriction of the relative character to an open dense subset is given by an analytic function. The proof is based on an argument from algebraic geometry and thus implies also analogous results in the p-adic case.\n  As an application, we give a short proof of some results from [KO13,KS16] on boundedness and finiteness of multiplicities of irreduc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01479","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":"2026-05-18T01:16:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WhYukenohJuJE+zeVg9l1V4ni8t69z+Ycv8OB9MFicw/kuvXYbTDm5voPk4ztHaEiHE5deSs22J2UeyuzMA/Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T18:54:33.479085Z"},"content_sha256":"5f4217808566d2447a01b94fa8e027ec81d983eac7e856e5564f72349b5a9faf","schema_version":"1.0","event_id":"sha256:5f4217808566d2447a01b94fa8e027ec81d983eac7e856e5564f72349b5a9faf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NP2CR5F6XJOC53KNUIBQFWO6GK/bundle.json","state_url":"https://pith.science/pith/NP2CR5F6XJOC53KNUIBQFWO6GK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NP2CR5F6XJOC53KNUIBQFWO6GK/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":"2026-06-30T18:54:33Z","links":{"resolver":"https://pith.science/pith/NP2CR5F6XJOC53KNUIBQFWO6GK","bundle":"https://pith.science/pith/NP2CR5F6XJOC53KNUIBQFWO6GK/bundle.json","state":"https://pith.science/pith/NP2CR5F6XJOC53KNUIBQFWO6GK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NP2CR5F6XJOC53KNUIBQFWO6GK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NP2CR5F6XJOC53KNUIBQFWO6GK","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":"fd358b296b73ce51604b282679696481f69b12bad9e6f00fd1b07a890c5d7b66","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-01-07T13:02:47Z","title_canon_sha256":"50e619cf45e0651fa6ab6616430b3d465516ca66cfec5a5468427a85e9ab4de3"},"schema_version":"1.0","source":{"id":"1501.01479","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01479","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01479v2","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01479","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"pith_short_12","alias_value":"NP2CR5F6XJOC","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NP2CR5F6XJOC53KN","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NP2CR5F6","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:5f4217808566d2447a01b94fa8e027ec81d983eac7e856e5564f72349b5a9faf","target":"graph","created_at":"2026-05-18T01:16:33Z","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":"In this paper, we prove that any relative character (a.k.a. spherical character) of any admissible representation of a real reductive group with respect to any pair of spherical subgroups is a holonomic distribution on the group. This implies that the restriction of the relative character to an open dense subset is given by an analytic function. The proof is based on an argument from algebraic geometry and thus implies also analogous results in the p-adic case.\n  As an application, we give a short proof of some results from [KO13,KS16] on boundedness and finiteness of multiplicities of irreduc","authors_text":"Andrey Minchenko, Avraham Aizenbud, Dmitry Gourevitch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-01-07T13:02:47Z","title":"Holonomicity of relative characters and applications to multiplicity bounds for spherical pairs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01479","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:c9dcab182d20f230b82d367bf073732cf85a24be80dc64a19e09cf5604c3b830","target":"record","created_at":"2026-05-18T01:16:33Z","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":"fd358b296b73ce51604b282679696481f69b12bad9e6f00fd1b07a890c5d7b66","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-01-07T13:02:47Z","title_canon_sha256":"50e619cf45e0651fa6ab6616430b3d465516ca66cfec5a5468427a85e9ab4de3"},"schema_version":"1.0","source":{"id":"1501.01479","kind":"arxiv","version":2}},"canonical_sha256":"6bf428f4beba5c2eed4da20302d9de32b56d7f05f6c693d5fd5bb3f3680290b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6bf428f4beba5c2eed4da20302d9de32b56d7f05f6c693d5fd5bb3f3680290b6","first_computed_at":"2026-05-18T01:16:33.491353Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:33.491353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3Pmj3+Tup5Yv6Q9qs2YdSxOBIkt5lYUM08nM8u3mVRMdpD9ukDdwHoRcsh+TH4rbldAiXNwAr7HbaRbi7rslCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:33.492011Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.01479","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9dcab182d20f230b82d367bf073732cf85a24be80dc64a19e09cf5604c3b830","sha256:5f4217808566d2447a01b94fa8e027ec81d983eac7e856e5564f72349b5a9faf"],"state_sha256":"cdfba69dedc5b2c7036058a32523702d3f529a59f87983c6598d53d39101002a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZS3mwSfnJlrPjKnfSm/V2Tjy0zB78M6AEWbhJ7BSMh/X+cZJUapUD0uo/deu3j1do0fvoSaEDH0xPnjdiHwMAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T18:54:33.480996Z","bundle_sha256":"3bd0c87e05dbf83d499062f5a1a0a5a457368165aa6e0aac5a2460578a4cfc11"}}