{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:HTLNACXCI74VUH5ZWU7HWEZDQ7","short_pith_number":"pith:HTLNACXC","canonical_record":{"source":{"id":"1603.07874","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-03-25T10:51:08Z","cross_cats_sorted":[],"title_canon_sha256":"c9f3cff996e1502dfa8a97dd10a2494b1538fd933401fd49b735e4a198416052","abstract_canon_sha256":"477ac02d6d864534c6a21aadd208be91e673b3d54ace9deb99771558ebedb81c"},"schema_version":"1.0"},"canonical_sha256":"3cd6d00ae247f95a1fb9b53e7b132387ffbc1b661a77383b208b41788e00cc49","source":{"kind":"arxiv","id":"1603.07874","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07874","created_at":"2026-05-18T01:18:16Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07874v1","created_at":"2026-05-18T01:18:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07874","created_at":"2026-05-18T01:18:16Z"},{"alias_kind":"pith_short_12","alias_value":"HTLNACXCI74V","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"HTLNACXCI74VUH5Z","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"HTLNACXC","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:HTLNACXCI74VUH5ZWU7HWEZDQ7","target":"record","payload":{"canonical_record":{"source":{"id":"1603.07874","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-03-25T10:51:08Z","cross_cats_sorted":[],"title_canon_sha256":"c9f3cff996e1502dfa8a97dd10a2494b1538fd933401fd49b735e4a198416052","abstract_canon_sha256":"477ac02d6d864534c6a21aadd208be91e673b3d54ace9deb99771558ebedb81c"},"schema_version":"1.0"},"canonical_sha256":"3cd6d00ae247f95a1fb9b53e7b132387ffbc1b661a77383b208b41788e00cc49","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:16.025331Z","signature_b64":"KkmQsMNECY5InsEYhvyV5ic9OKjOxPsw2tUqumNJAG2XVG48EW9U5cEwXyLgcR4kKnscOpHl6XTyVirMBYHfDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3cd6d00ae247f95a1fb9b53e7b132387ffbc1b661a77383b208b41788e00cc49","last_reissued_at":"2026-05-18T01:18:16.024744Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:16.024744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.07874","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:18:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pDpAtfw4HBRMdqIC+DVOfMPPgXaB2EDHZjM7ic1pYt7RnqIGbzejnE304f8Ptb1s5PfJWp87pLmZzUPYU0GKAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:40:31.653585Z"},"content_sha256":"0bb8bdec2283191d20042838754d532c364855c91ff5aa0f4e3fa3fa4d957710","schema_version":"1.0","event_id":"sha256:0bb8bdec2283191d20042838754d532c364855c91ff5aa0f4e3fa3fa4d957710"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:HTLNACXCI74VUH5ZWU7HWEZDQ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Shalika germs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"David Kazhdan","submitted_at":"2016-03-25T10:51:08Z","abstract_excerpt":"Let $G$ be a reductive group over a local field $F$ satisfying the assumptions of \\cite{Deb1}, $G_{reg}\\subset G$ the subset of regular elements. Let $T\\subset G$ be a maximal torus. We write $T_{reg}=T\\cap G_{reg}$. Let $dg ,dt$ be Haar measures on $G$ and $T$. They define an invariant measure $dg/dt$ on $G/T$. Let $\\mathcal{H}$ be the space of complex valued locally constant functions on $G$ with compact support. For any $f\\in \\mathcal{H} ,t\\in T_{reg}$ we define $I_t(f)=\\int_{G/T}f(\\bar gt\\bar g^{-1})dg/dt$. Let $P$ be the set of conjugacy classes of unipotent elements in $G$. For any $\\Ome"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07874","kind":"arxiv","version":1},"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":"2026-05-18T01:18:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MDYv+i+yVbGPgZtIgNeCcx6IDMg29jLRRVQlCQ/Eh2Ss5rAlbKCOPRcECl/dogzdVdkKsVKICiww9hjU4NHCAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:40:31.654235Z"},"content_sha256":"f0da2ceb757b8807247ed5e05b777b63803116e781795b304bda58afdae9f1da","schema_version":"1.0","event_id":"sha256:f0da2ceb757b8807247ed5e05b777b63803116e781795b304bda58afdae9f1da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HTLNACXCI74VUH5ZWU7HWEZDQ7/bundle.json","state_url":"https://pith.science/pith/HTLNACXCI74VUH5ZWU7HWEZDQ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HTLNACXCI74VUH5ZWU7HWEZDQ7/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":"2026-05-25T23:40:31Z","links":{"resolver":"https://pith.science/pith/HTLNACXCI74VUH5ZWU7HWEZDQ7","bundle":"https://pith.science/pith/HTLNACXCI74VUH5ZWU7HWEZDQ7/bundle.json","state":"https://pith.science/pith/HTLNACXCI74VUH5ZWU7HWEZDQ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HTLNACXCI74VUH5ZWU7HWEZDQ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HTLNACXCI74VUH5ZWU7HWEZDQ7","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":"477ac02d6d864534c6a21aadd208be91e673b3d54ace9deb99771558ebedb81c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-03-25T10:51:08Z","title_canon_sha256":"c9f3cff996e1502dfa8a97dd10a2494b1538fd933401fd49b735e4a198416052"},"schema_version":"1.0","source":{"id":"1603.07874","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07874","created_at":"2026-05-18T01:18:16Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07874v1","created_at":"2026-05-18T01:18:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07874","created_at":"2026-05-18T01:18:16Z"},{"alias_kind":"pith_short_12","alias_value":"HTLNACXCI74V","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"HTLNACXCI74VUH5Z","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"HTLNACXC","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:f0da2ceb757b8807247ed5e05b777b63803116e781795b304bda58afdae9f1da","target":"graph","created_at":"2026-05-18T01:18:16Z","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 reductive group over a local field $F$ satisfying the assumptions of \\cite{Deb1}, $G_{reg}\\subset G$ the subset of regular elements. Let $T\\subset G$ be a maximal torus. We write $T_{reg}=T\\cap G_{reg}$. Let $dg ,dt$ be Haar measures on $G$ and $T$. They define an invariant measure $dg/dt$ on $G/T$. Let $\\mathcal{H}$ be the space of complex valued locally constant functions on $G$ with compact support. For any $f\\in \\mathcal{H} ,t\\in T_{reg}$ we define $I_t(f)=\\int_{G/T}f(\\bar gt\\bar g^{-1})dg/dt$. Let $P$ be the set of conjugacy classes of unipotent elements in $G$. For any $\\Ome","authors_text":"David Kazhdan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-03-25T10:51:08Z","title":"On Shalika germs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07874","kind":"arxiv","version":1},"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":"sha256:0bb8bdec2283191d20042838754d532c364855c91ff5aa0f4e3fa3fa4d957710","target":"record","created_at":"2026-05-18T01:18:16Z","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":"477ac02d6d864534c6a21aadd208be91e673b3d54ace9deb99771558ebedb81c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-03-25T10:51:08Z","title_canon_sha256":"c9f3cff996e1502dfa8a97dd10a2494b1538fd933401fd49b735e4a198416052"},"schema_version":"1.0","source":{"id":"1603.07874","kind":"arxiv","version":1}},"canonical_sha256":"3cd6d00ae247f95a1fb9b53e7b132387ffbc1b661a77383b208b41788e00cc49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3cd6d00ae247f95a1fb9b53e7b132387ffbc1b661a77383b208b41788e00cc49","first_computed_at":"2026-05-18T01:18:16.024744Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:16.024744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KkmQsMNECY5InsEYhvyV5ic9OKjOxPsw2tUqumNJAG2XVG48EW9U5cEwXyLgcR4kKnscOpHl6XTyVirMBYHfDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:16.025331Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.07874","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bb8bdec2283191d20042838754d532c364855c91ff5aa0f4e3fa3fa4d957710","sha256:f0da2ceb757b8807247ed5e05b777b63803116e781795b304bda58afdae9f1da"],"state_sha256":"bff7a3512a34a6fc107dbf1777bd794cddb9f622d9338acaa294392a6a060b22"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"inc4W45EEovSgUtloSnEAGUgg0MkkeFoAu6Kq7lkGjz9eP/5++LEXUerMs/JYySi+l+iSjlBIKyeCfFijXkIAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T23:40:31.657573Z","bundle_sha256":"3ef051d8baa0fbf2a050d74d0751ecaf87cf86e2d682186ea120a43bfd422682"}}