{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:4Q4HPPA4VDSYDQVGMZ3LC2C4BH","short_pith_number":"pith:4Q4HPPA4","canonical_record":{"source":{"id":"1501.04062","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-01-16T17:39:13Z","cross_cats_sorted":["math.AT","math.GR","math.GT"],"title_canon_sha256":"c82fabcf9f749e897b7bc35f6353e7dcf2b2cebf685cbb0352be5959667739c6","abstract_canon_sha256":"a7b47b1f8a29854f170e6e88775daf3c95044d5cc2b4442270be54a8fcb48050"},"schema_version":"1.0"},"canonical_sha256":"e43877bc1ca8e581c2a66676b1685c09c8f3f7fd0df66953c6633d33f28c3e48","source":{"kind":"arxiv","id":"1501.04062","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04062","created_at":"2026-05-17T23:58:23Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04062v1","created_at":"2026-05-17T23:58:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04062","created_at":"2026-05-17T23:58:23Z"},{"alias_kind":"pith_short_12","alias_value":"4Q4HPPA4VDSY","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4Q4HPPA4VDSYDQVG","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4Q4HPPA4","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:4Q4HPPA4VDSYDQVGMZ3LC2C4BH","target":"record","payload":{"canonical_record":{"source":{"id":"1501.04062","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-01-16T17:39:13Z","cross_cats_sorted":["math.AT","math.GR","math.GT"],"title_canon_sha256":"c82fabcf9f749e897b7bc35f6353e7dcf2b2cebf685cbb0352be5959667739c6","abstract_canon_sha256":"a7b47b1f8a29854f170e6e88775daf3c95044d5cc2b4442270be54a8fcb48050"},"schema_version":"1.0"},"canonical_sha256":"e43877bc1ca8e581c2a66676b1685c09c8f3f7fd0df66953c6633d33f28c3e48","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:23.465411Z","signature_b64":"nunPOqfVVfFgFhjlLERgNqPyPU5ovmmZPK/FUyjceL6aJblEcL4Rr4wjiGwvNZsQ5uvA/rPWxISfbAerw2x+DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e43877bc1ca8e581c2a66676b1685c09c8f3f7fd0df66953c6633d33f28c3e48","last_reissued_at":"2026-05-17T23:58:23.464725Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:23.464725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.04062","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":"2026-05-17T23:58:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ll0GtLADJgLdgL7u0jdCsnpXqBPF/WL8wUEEqaL6lDMH6Ye15tY8RLiFlueCJMuZgcOJlVFBJ0g9A8eCaJj2CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:55:27.071211Z"},"content_sha256":"fd2c6dcad1c0ee25932d791dca4d97d4dd3e6c5a57fa9364fba9e58b7f12b976","schema_version":"1.0","event_id":"sha256:fd2c6dcad1c0ee25932d791dca4d97d4dd3e6c5a57fa9364fba9e58b7f12b976"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:4Q4HPPA4VDSYDQVGMZ3LC2C4BH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Infinite symmetric group and bordisms of pseudomanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.GR","math.GT"],"primary_cat":"math.RT","authors_text":"Alexander A. Gaifullin, Yury A. Neretin","submitted_at":"2015-01-16T17:39:13Z","abstract_excerpt":"We consider a category whose morphisms are bordisms of $n$-dimensional pseudomanifolds equipped with a certain additional structure (coloring). On the other hand, we consider the product $G$ of $(n+1)$ copies of infinite symmetric group. We show that unitary representations of $G$ produce functors from the category of $(n-1)$-dimensional bordisms to the category of Hilbert spaces and bounded linear operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04062","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":"2026-05-17T23:58:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TpFKSAxd7vrF0Z1iB/lsMMC7rSy6NRHk51kLvhP3kgSj5L41iesfi1M9eaRlmM6SIzu+n/JnO3k4AaHvnJOrCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:55:27.071598Z"},"content_sha256":"5478f6170a721aeaa23cfb955fc41bf66c4b018cf404a5a7129a6cab488787fb","schema_version":"1.0","event_id":"sha256:5478f6170a721aeaa23cfb955fc41bf66c4b018cf404a5a7129a6cab488787fb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4Q4HPPA4VDSYDQVGMZ3LC2C4BH/bundle.json","state_url":"https://pith.science/pith/4Q4HPPA4VDSYDQVGMZ3LC2C4BH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4Q4HPPA4VDSYDQVGMZ3LC2C4BH/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":"2026-06-10T21:55:27Z","links":{"resolver":"https://pith.science/pith/4Q4HPPA4VDSYDQVGMZ3LC2C4BH","bundle":"https://pith.science/pith/4Q4HPPA4VDSYDQVGMZ3LC2C4BH/bundle.json","state":"https://pith.science/pith/4Q4HPPA4VDSYDQVGMZ3LC2C4BH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4Q4HPPA4VDSYDQVGMZ3LC2C4BH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4Q4HPPA4VDSYDQVGMZ3LC2C4BH","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":"a7b47b1f8a29854f170e6e88775daf3c95044d5cc2b4442270be54a8fcb48050","cross_cats_sorted":["math.AT","math.GR","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-01-16T17:39:13Z","title_canon_sha256":"c82fabcf9f749e897b7bc35f6353e7dcf2b2cebf685cbb0352be5959667739c6"},"schema_version":"1.0","source":{"id":"1501.04062","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04062","created_at":"2026-05-17T23:58:23Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04062v1","created_at":"2026-05-17T23:58:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04062","created_at":"2026-05-17T23:58:23Z"},{"alias_kind":"pith_short_12","alias_value":"4Q4HPPA4VDSY","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4Q4HPPA4VDSYDQVG","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4Q4HPPA4","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:5478f6170a721aeaa23cfb955fc41bf66c4b018cf404a5a7129a6cab488787fb","target":"graph","created_at":"2026-05-17T23:58:23Z","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 consider a category whose morphisms are bordisms of $n$-dimensional pseudomanifolds equipped with a certain additional structure (coloring). On the other hand, we consider the product $G$ of $(n+1)$ copies of infinite symmetric group. We show that unitary representations of $G$ produce functors from the category of $(n-1)$-dimensional bordisms to the category of Hilbert spaces and bounded linear operators.","authors_text":"Alexander A. Gaifullin, Yury A. Neretin","cross_cats":["math.AT","math.GR","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-01-16T17:39:13Z","title":"Infinite symmetric group and bordisms of pseudomanifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04062","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:fd2c6dcad1c0ee25932d791dca4d97d4dd3e6c5a57fa9364fba9e58b7f12b976","target":"record","created_at":"2026-05-17T23:58:23Z","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":"a7b47b1f8a29854f170e6e88775daf3c95044d5cc2b4442270be54a8fcb48050","cross_cats_sorted":["math.AT","math.GR","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-01-16T17:39:13Z","title_canon_sha256":"c82fabcf9f749e897b7bc35f6353e7dcf2b2cebf685cbb0352be5959667739c6"},"schema_version":"1.0","source":{"id":"1501.04062","kind":"arxiv","version":1}},"canonical_sha256":"e43877bc1ca8e581c2a66676b1685c09c8f3f7fd0df66953c6633d33f28c3e48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e43877bc1ca8e581c2a66676b1685c09c8f3f7fd0df66953c6633d33f28c3e48","first_computed_at":"2026-05-17T23:58:23.464725Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:23.464725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nunPOqfVVfFgFhjlLERgNqPyPU5ovmmZPK/FUyjceL6aJblEcL4Rr4wjiGwvNZsQ5uvA/rPWxISfbAerw2x+DQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:23.465411Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.04062","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd2c6dcad1c0ee25932d791dca4d97d4dd3e6c5a57fa9364fba9e58b7f12b976","sha256:5478f6170a721aeaa23cfb955fc41bf66c4b018cf404a5a7129a6cab488787fb"],"state_sha256":"7aa6ae9fa1338dd2d1a7da0b5bc764b4c2c02b047eb11792a43f78b9286d4da4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xAA7c3TOFL7Lk+4cflNI6gLiY5FCU33q+O88KYZyDYt8WYQ/unxezTlZ0XFqe5cpzwlNcRdAXRuyTlp1g6ZgAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T21:55:27.073533Z","bundle_sha256":"02304057acc727c09d805aa3139d375c156f509805cfd4c70b5bf4e47b5d4378"}}