{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:CGEGQJR35CGSYHUCQDJQIZ3UJ3","short_pith_number":"pith:CGEGQJR3","canonical_record":{"source":{"id":"1106.1161","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-06-06T19:36:09Z","cross_cats_sorted":["math.CO","math.GR"],"title_canon_sha256":"5bc0d4f4dda9229678ec361e241439dea0bba18cd166835941e11fa1c6ad73d7","abstract_canon_sha256":"778b876adff9dcaab720c88fe0472b15ff36f9072665ffcc9c5d92e2480c36a8"},"schema_version":"1.0"},"canonical_sha256":"118868263be88d2c1e8280d30467744efd5bc0bf467217c95c2bc92f7b0bf9bb","source":{"kind":"arxiv","id":"1106.1161","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1161","created_at":"2026-05-18T00:25:29Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1161v1","created_at":"2026-05-18T00:25:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1161","created_at":"2026-05-18T00:25:29Z"},{"alias_kind":"pith_short_12","alias_value":"CGEGQJR35CGS","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CGEGQJR35CGSYHUC","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CGEGQJR3","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:CGEGQJR35CGSYHUCQDJQIZ3UJ3","target":"record","payload":{"canonical_record":{"source":{"id":"1106.1161","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-06-06T19:36:09Z","cross_cats_sorted":["math.CO","math.GR"],"title_canon_sha256":"5bc0d4f4dda9229678ec361e241439dea0bba18cd166835941e11fa1c6ad73d7","abstract_canon_sha256":"778b876adff9dcaab720c88fe0472b15ff36f9072665ffcc9c5d92e2480c36a8"},"schema_version":"1.0"},"canonical_sha256":"118868263be88d2c1e8280d30467744efd5bc0bf467217c95c2bc92f7b0bf9bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:29.734476Z","signature_b64":"ZLytK1N66w7wMM32utgkRtMb92jNkPRE8YC1i6JLwO24deUHRI76ye75r/LNeTP4SyGecVWDT1AVSH/PfympDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"118868263be88d2c1e8280d30467744efd5bc0bf467217c95c2bc92f7b0bf9bb","last_reissued_at":"2026-05-18T00:25:29.733822Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:29.733822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.1161","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":"2026-05-18T00:25:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3BHkMRqjis4by/a6cqTmuZEsLGL8JL6nhCL1T+eHUc2Ww35sQvmsdUFx1bRkZT0G7qHwQpar7NBtcLJHLG9hBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:44:35.952678Z"},"content_sha256":"9d4c6843534be5fa3b81622bfc751f7028a30b94005a1f70c69a025645a2a5d0","schema_version":"1.0","event_id":"sha256:9d4c6843534be5fa3b81622bfc751f7028a30b94005a1f70c69a025645a2a5d0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:CGEGQJR35CGSYHUCQDJQIZ3UJ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Infinite symmetric group and combinatorial descriptions of semigroups of double cosets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GR"],"primary_cat":"math.RT","authors_text":"Yury A. Neretin","submitted_at":"2011-06-06T19:36:09Z","abstract_excerpt":"We show that double cosets of the infinite symmetric group with respect to some special subgroups admit natural structures of semigroups. We interpret elements of such semigroups in combinatorial terms (chips, colored graphs, two-dimensional surfaces with polygonal tiling) and describe explicitly the multiplications."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1161","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":"2026-05-18T00:25:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nUq+XWGmr9q9+jjr4WzNAv4cbhHaleiIjTuLwa8eSKTmGX9x+twTxvgl3E6J3dymZS1jCzpWl/3P0ca/nrmwBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:44:35.953400Z"},"content_sha256":"c4b1b7e3b35b57e20775cf777eb100c4aea61a2d38c411aa9a711712f1299237","schema_version":"1.0","event_id":"sha256:c4b1b7e3b35b57e20775cf777eb100c4aea61a2d38c411aa9a711712f1299237"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CGEGQJR35CGSYHUCQDJQIZ3UJ3/bundle.json","state_url":"https://pith.science/pith/CGEGQJR35CGSYHUCQDJQIZ3UJ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CGEGQJR35CGSYHUCQDJQIZ3UJ3/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":"2026-06-11T00:44:35Z","links":{"resolver":"https://pith.science/pith/CGEGQJR35CGSYHUCQDJQIZ3UJ3","bundle":"https://pith.science/pith/CGEGQJR35CGSYHUCQDJQIZ3UJ3/bundle.json","state":"https://pith.science/pith/CGEGQJR35CGSYHUCQDJQIZ3UJ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CGEGQJR35CGSYHUCQDJQIZ3UJ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CGEGQJR35CGSYHUCQDJQIZ3UJ3","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":"778b876adff9dcaab720c88fe0472b15ff36f9072665ffcc9c5d92e2480c36a8","cross_cats_sorted":["math.CO","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-06-06T19:36:09Z","title_canon_sha256":"5bc0d4f4dda9229678ec361e241439dea0bba18cd166835941e11fa1c6ad73d7"},"schema_version":"1.0","source":{"id":"1106.1161","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1161","created_at":"2026-05-18T00:25:29Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1161v1","created_at":"2026-05-18T00:25:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1161","created_at":"2026-05-18T00:25:29Z"},{"alias_kind":"pith_short_12","alias_value":"CGEGQJR35CGS","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CGEGQJR35CGSYHUC","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CGEGQJR3","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:c4b1b7e3b35b57e20775cf777eb100c4aea61a2d38c411aa9a711712f1299237","target":"graph","created_at":"2026-05-18T00:25:29Z","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 show that double cosets of the infinite symmetric group with respect to some special subgroups admit natural structures of semigroups. We interpret elements of such semigroups in combinatorial terms (chips, colored graphs, two-dimensional surfaces with polygonal tiling) and describe explicitly the multiplications.","authors_text":"Yury A. Neretin","cross_cats":["math.CO","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-06-06T19:36:09Z","title":"Infinite symmetric group and combinatorial descriptions of semigroups of double cosets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1161","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":"sha256:9d4c6843534be5fa3b81622bfc751f7028a30b94005a1f70c69a025645a2a5d0","target":"record","created_at":"2026-05-18T00:25:29Z","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":"778b876adff9dcaab720c88fe0472b15ff36f9072665ffcc9c5d92e2480c36a8","cross_cats_sorted":["math.CO","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-06-06T19:36:09Z","title_canon_sha256":"5bc0d4f4dda9229678ec361e241439dea0bba18cd166835941e11fa1c6ad73d7"},"schema_version":"1.0","source":{"id":"1106.1161","kind":"arxiv","version":1}},"canonical_sha256":"118868263be88d2c1e8280d30467744efd5bc0bf467217c95c2bc92f7b0bf9bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"118868263be88d2c1e8280d30467744efd5bc0bf467217c95c2bc92f7b0bf9bb","first_computed_at":"2026-05-18T00:25:29.733822Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:29.733822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZLytK1N66w7wMM32utgkRtMb92jNkPRE8YC1i6JLwO24deUHRI76ye75r/LNeTP4SyGecVWDT1AVSH/PfympDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:29.734476Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.1161","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d4c6843534be5fa3b81622bfc751f7028a30b94005a1f70c69a025645a2a5d0","sha256:c4b1b7e3b35b57e20775cf777eb100c4aea61a2d38c411aa9a711712f1299237"],"state_sha256":"225c1ca2459900b09f6a7fb335244c0d59dc35775f90fab990c1f1068e1f3825"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jegye/bGjSCGFSS0z7j4DcLO9HpDfdy9vSiBeIh1yJ3ELw3re/j7S4Tf9X/pxjPxQOFpoDevmZpobc75MD8HCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T00:44:35.957764Z","bundle_sha256":"9c27080be20c4f812b4de812ba4434003e84778602e1210d37baeb83371e30a2"}}