{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:I6WNVPSEHAQKUOXCK4JRDRHOZC","short_pith_number":"pith:I6WNVPSE","canonical_record":{"source":{"id":"1211.6149","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-11-26T22:28:40Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"3347c1cb6b306ea5e946ba22a4365086e21842bd00063f018b17ef852f1e18e1","abstract_canon_sha256":"d3fa83b052b3fc41abb5446529b0fd13651976c58c40cb9e142387c060c8935e"},"schema_version":"1.0"},"canonical_sha256":"47acdabe443820aa3ae2571311c4eec8b3af7234c657193178e97a5a95b3e69e","source":{"kind":"arxiv","id":"1211.6149","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.6149","created_at":"2026-05-18T03:39:52Z"},{"alias_kind":"arxiv_version","alias_value":"1211.6149v1","created_at":"2026-05-18T03:39:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.6149","created_at":"2026-05-18T03:39:52Z"},{"alias_kind":"pith_short_12","alias_value":"I6WNVPSEHAQK","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"I6WNVPSEHAQKUOXC","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"I6WNVPSE","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:I6WNVPSEHAQKUOXCK4JRDRHOZC","target":"record","payload":{"canonical_record":{"source":{"id":"1211.6149","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-11-26T22:28:40Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"3347c1cb6b306ea5e946ba22a4365086e21842bd00063f018b17ef852f1e18e1","abstract_canon_sha256":"d3fa83b052b3fc41abb5446529b0fd13651976c58c40cb9e142387c060c8935e"},"schema_version":"1.0"},"canonical_sha256":"47acdabe443820aa3ae2571311c4eec8b3af7234c657193178e97a5a95b3e69e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:52.470394Z","signature_b64":"n3mWUVwwadbQt2J4gxX3Q+jnCW+RLJZCP+3IWIe5K7DYkLYrK5OdbBxN2ox8exFJ3K/u0Fc4WJI22y5I/xdaCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47acdabe443820aa3ae2571311c4eec8b3af7234c657193178e97a5a95b3e69e","last_reissued_at":"2026-05-18T03:39:52.469676Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:52.469676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.6149","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":"2026-05-18T03:39:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zkYCL+mCmkmUMQ3/Y9GM1TtcmKt9LTItBskvmZtirT5IY5PR6gH+hEUvnfVD9Koqt879IEo/+TXMa97toILDCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T05:30:07.947919Z"},"content_sha256":"98bfd8bf3958a5986d84675cab08e22c2ed35bf467bdf0d2512044d18e95ebc4","schema_version":"1.0","event_id":"sha256:98bfd8bf3958a5986d84675cab08e22c2ed35bf467bdf0d2512044d18e95ebc4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:I6WNVPSEHAQKUOXCK4JRDRHOZC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On concentration of convolutions of double cosets at infinite-dimensional limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Yury A. Neretin","submitted_at":"2012-11-26T22:28:40Z","abstract_excerpt":"For infinite-dimensional groups $G\\supset K$ the double cosets $K\\setminus G/K$ quite often admit a structure of a semigroup; these semigroups act in $K$-fixed vectors of unitary representations of $G$. We show that such semigroups can be obtained as limits of double cosets hypergroups (or Iwahori--Hecke type algebras) on finite-dimensional (or finite) groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6149","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":"2026-05-18T03:39:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9RD0z/6R3AxP/u67TBmo6J267g7AuAOL0uKBfLnM6R1JO3KstkeUOR07qqP3FLpizGqqdBJpaoYIUimCtIUzDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T05:30:07.948512Z"},"content_sha256":"a3cb6b8ab1eba1af615c878d9d30e52bbeaa2ae0f27d7fa36ba176f0b1cff362","schema_version":"1.0","event_id":"sha256:a3cb6b8ab1eba1af615c878d9d30e52bbeaa2ae0f27d7fa36ba176f0b1cff362"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I6WNVPSEHAQKUOXCK4JRDRHOZC/bundle.json","state_url":"https://pith.science/pith/I6WNVPSEHAQKUOXCK4JRDRHOZC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I6WNVPSEHAQKUOXCK4JRDRHOZC/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":"2026-06-11T05:30:07Z","links":{"resolver":"https://pith.science/pith/I6WNVPSEHAQKUOXCK4JRDRHOZC","bundle":"https://pith.science/pith/I6WNVPSEHAQKUOXCK4JRDRHOZC/bundle.json","state":"https://pith.science/pith/I6WNVPSEHAQKUOXCK4JRDRHOZC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I6WNVPSEHAQKUOXCK4JRDRHOZC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:I6WNVPSEHAQKUOXCK4JRDRHOZC","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":"d3fa83b052b3fc41abb5446529b0fd13651976c58c40cb9e142387c060c8935e","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-11-26T22:28:40Z","title_canon_sha256":"3347c1cb6b306ea5e946ba22a4365086e21842bd00063f018b17ef852f1e18e1"},"schema_version":"1.0","source":{"id":"1211.6149","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.6149","created_at":"2026-05-18T03:39:52Z"},{"alias_kind":"arxiv_version","alias_value":"1211.6149v1","created_at":"2026-05-18T03:39:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.6149","created_at":"2026-05-18T03:39:52Z"},{"alias_kind":"pith_short_12","alias_value":"I6WNVPSEHAQK","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"I6WNVPSEHAQKUOXC","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"I6WNVPSE","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:a3cb6b8ab1eba1af615c878d9d30e52bbeaa2ae0f27d7fa36ba176f0b1cff362","target":"graph","created_at":"2026-05-18T03:39:52Z","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":"For infinite-dimensional groups $G\\supset K$ the double cosets $K\\setminus G/K$ quite often admit a structure of a semigroup; these semigroups act in $K$-fixed vectors of unitary representations of $G$. We show that such semigroups can be obtained as limits of double cosets hypergroups (or Iwahori--Hecke type algebras) on finite-dimensional (or finite) groups.","authors_text":"Yury A. Neretin","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-11-26T22:28:40Z","title":"On concentration of convolutions of double cosets at infinite-dimensional limit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6149","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":"sha256:98bfd8bf3958a5986d84675cab08e22c2ed35bf467bdf0d2512044d18e95ebc4","target":"record","created_at":"2026-05-18T03:39:52Z","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":"d3fa83b052b3fc41abb5446529b0fd13651976c58c40cb9e142387c060c8935e","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-11-26T22:28:40Z","title_canon_sha256":"3347c1cb6b306ea5e946ba22a4365086e21842bd00063f018b17ef852f1e18e1"},"schema_version":"1.0","source":{"id":"1211.6149","kind":"arxiv","version":1}},"canonical_sha256":"47acdabe443820aa3ae2571311c4eec8b3af7234c657193178e97a5a95b3e69e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47acdabe443820aa3ae2571311c4eec8b3af7234c657193178e97a5a95b3e69e","first_computed_at":"2026-05-18T03:39:52.469676Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:52.469676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n3mWUVwwadbQt2J4gxX3Q+jnCW+RLJZCP+3IWIe5K7DYkLYrK5OdbBxN2ox8exFJ3K/u0Fc4WJI22y5I/xdaCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:52.470394Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.6149","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98bfd8bf3958a5986d84675cab08e22c2ed35bf467bdf0d2512044d18e95ebc4","sha256:a3cb6b8ab1eba1af615c878d9d30e52bbeaa2ae0f27d7fa36ba176f0b1cff362"],"state_sha256":"984983821001f2dd08df1feb13320a99b5b546a1b02b31f941c87aedfe42c536"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8921yLvtx8XC2Vw8/YtX6614lrfnEBRWxo5cC03vMYxTTmCnHI96phWxQINrLHu1Bit+t/GRvWngeR0hoIv+Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T05:30:07.954933Z","bundle_sha256":"71eabda39e44f32d8ffe78ec022203202eb3d7e022e1f4bdf462e5db87524689"}}