{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:BEOXTYLEVVDMDG3LS4MSR6FZRG","short_pith_number":"pith:BEOXTYLE","canonical_record":{"source":{"id":"1608.03442","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-11T12:51:26Z","cross_cats_sorted":[],"title_canon_sha256":"c306a98823ac78d712d9a2bc8441f91e8d5bdd9c326f818e9d3bc7dbfc9e767e","abstract_canon_sha256":"6ba0c50aadbefc9ab8470abddcab03df58169b6398995786bd10d21c28a88af3"},"schema_version":"1.0"},"canonical_sha256":"091d79e164ad46c19b6b971928f8b989833004a7a8168a6317c1b1c6d820a66c","source":{"kind":"arxiv","id":"1608.03442","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03442","created_at":"2026-05-18T00:27:30Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03442v3","created_at":"2026-05-18T00:27:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03442","created_at":"2026-05-18T00:27:30Z"},{"alias_kind":"pith_short_12","alias_value":"BEOXTYLEVVDM","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BEOXTYLEVVDMDG3L","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BEOXTYLE","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:BEOXTYLEVVDMDG3LS4MSR6FZRG","target":"record","payload":{"canonical_record":{"source":{"id":"1608.03442","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-11T12:51:26Z","cross_cats_sorted":[],"title_canon_sha256":"c306a98823ac78d712d9a2bc8441f91e8d5bdd9c326f818e9d3bc7dbfc9e767e","abstract_canon_sha256":"6ba0c50aadbefc9ab8470abddcab03df58169b6398995786bd10d21c28a88af3"},"schema_version":"1.0"},"canonical_sha256":"091d79e164ad46c19b6b971928f8b989833004a7a8168a6317c1b1c6d820a66c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:30.663280Z","signature_b64":"MNNjna/qBUG1fGC83otopuCU+Q6AZH3eWUo5bgjDDYg3bsaJ4lEFRByizX1kMSJiSNmkAr6jSGdUorD3DtirDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"091d79e164ad46c19b6b971928f8b989833004a7a8168a6317c1b1c6d820a66c","last_reissued_at":"2026-05-18T00:27:30.662486Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:30.662486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.03442","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":"2026-05-18T00:27:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2db6ZKXhNgWy/wAO+u0m0HdtiuDn+0FbbLFl9EEhu2SgaRKl+Mbc68UDMCM0c14eWQrq4HxcGW4WgJrnA8q2Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:29:50.123266Z"},"content_sha256":"067710c8bb555ca2f18a665c024cee318138da1380fb1a44b8f87e4030312382","schema_version":"1.0","event_id":"sha256:067710c8bb555ca2f18a665c024cee318138da1380fb1a44b8f87e4030312382"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:BEOXTYLEVVDMDG3LS4MSR6FZRG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytic continuation of equivariant distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Dmitry Gourevitch, Eitan Sayag, Siddhartha Sahi","submitted_at":"2016-08-11T12:51:26Z","abstract_excerpt":"We establish a method for constructing equivariant distributions on smooth real algebraic varieties from equivariant distributions on Zariski open subsets. This is based on Bernstein's theory of analytic continuation of holonomic distributions. We use this to construct $H$-equivariant functionals on principal series representations of $G$, where $G$ is a real reductive group and $H$ is an algebraic subgroup. We also deduce the existence of generalized Whittaker models for degenerate principal series representations. As a special case, this gives short proofs of existence of Whittaker models on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03442","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":"2026-05-18T00:27:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5xjA8tLUrD042jLfwWqCOt3upKRztUJ5LSSqR370/m7OOzPXxUtGbqGcuuC43W2cryHB9aYdxOn8gHv+Wjh1DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:29:50.123666Z"},"content_sha256":"6017f4f5167363dd07440579c6b627a30f6f2deb6a091fc70ea212bacceda9a8","schema_version":"1.0","event_id":"sha256:6017f4f5167363dd07440579c6b627a30f6f2deb6a091fc70ea212bacceda9a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BEOXTYLEVVDMDG3LS4MSR6FZRG/bundle.json","state_url":"https://pith.science/pith/BEOXTYLEVVDMDG3LS4MSR6FZRG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BEOXTYLEVVDMDG3LS4MSR6FZRG/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":"2026-06-04T15:29:50Z","links":{"resolver":"https://pith.science/pith/BEOXTYLEVVDMDG3LS4MSR6FZRG","bundle":"https://pith.science/pith/BEOXTYLEVVDMDG3LS4MSR6FZRG/bundle.json","state":"https://pith.science/pith/BEOXTYLEVVDMDG3LS4MSR6FZRG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BEOXTYLEVVDMDG3LS4MSR6FZRG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BEOXTYLEVVDMDG3LS4MSR6FZRG","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":"6ba0c50aadbefc9ab8470abddcab03df58169b6398995786bd10d21c28a88af3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-11T12:51:26Z","title_canon_sha256":"c306a98823ac78d712d9a2bc8441f91e8d5bdd9c326f818e9d3bc7dbfc9e767e"},"schema_version":"1.0","source":{"id":"1608.03442","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03442","created_at":"2026-05-18T00:27:30Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03442v3","created_at":"2026-05-18T00:27:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03442","created_at":"2026-05-18T00:27:30Z"},{"alias_kind":"pith_short_12","alias_value":"BEOXTYLEVVDM","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BEOXTYLEVVDMDG3L","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BEOXTYLE","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:6017f4f5167363dd07440579c6b627a30f6f2deb6a091fc70ea212bacceda9a8","target":"graph","created_at":"2026-05-18T00:27:30Z","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":"We establish a method for constructing equivariant distributions on smooth real algebraic varieties from equivariant distributions on Zariski open subsets. This is based on Bernstein's theory of analytic continuation of holonomic distributions. We use this to construct $H$-equivariant functionals on principal series representations of $G$, where $G$ is a real reductive group and $H$ is an algebraic subgroup. We also deduce the existence of generalized Whittaker models for degenerate principal series representations. As a special case, this gives short proofs of existence of Whittaker models on","authors_text":"Dmitry Gourevitch, Eitan Sayag, Siddhartha Sahi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-11T12:51:26Z","title":"Analytic continuation of equivariant distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03442","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":"sha256:067710c8bb555ca2f18a665c024cee318138da1380fb1a44b8f87e4030312382","target":"record","created_at":"2026-05-18T00:27:30Z","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":"6ba0c50aadbefc9ab8470abddcab03df58169b6398995786bd10d21c28a88af3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-11T12:51:26Z","title_canon_sha256":"c306a98823ac78d712d9a2bc8441f91e8d5bdd9c326f818e9d3bc7dbfc9e767e"},"schema_version":"1.0","source":{"id":"1608.03442","kind":"arxiv","version":3}},"canonical_sha256":"091d79e164ad46c19b6b971928f8b989833004a7a8168a6317c1b1c6d820a66c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"091d79e164ad46c19b6b971928f8b989833004a7a8168a6317c1b1c6d820a66c","first_computed_at":"2026-05-18T00:27:30.662486Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:30.662486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MNNjna/qBUG1fGC83otopuCU+Q6AZH3eWUo5bgjDDYg3bsaJ4lEFRByizX1kMSJiSNmkAr6jSGdUorD3DtirDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:30.663280Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.03442","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:067710c8bb555ca2f18a665c024cee318138da1380fb1a44b8f87e4030312382","sha256:6017f4f5167363dd07440579c6b627a30f6f2deb6a091fc70ea212bacceda9a8"],"state_sha256":"1654c57c0af6bcac2b973c14c4c1d4f964dc5963ec47ae60f53b59114f02c787"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bMZGxvGh9M020wkNAWAtIA83iwFv9wirGk9udCw70OmnW/8Wa8jq5PRziHOmDPO0J8nXvSh8JlWHTQU1QjLiAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T15:29:50.125657Z","bundle_sha256":"a90eedd172612ba7525ca21fac80b428a8fe1abb1406ab544a7205fbdee15c7b"}}