{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MEWN2FNT4N4GW3SKOIYQDUSQHX","short_pith_number":"pith:MEWN2FNT","canonical_record":{"source":{"id":"1509.06424","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-09-21T23:07:04Z","cross_cats_sorted":[],"title_canon_sha256":"65eddc5fe8c5a77cca3d1cbfc849a249df6e07bc9675843cce75cb85abe37946","abstract_canon_sha256":"34963315ec19928cbb008f796394e1b1775fbb4519a9f75886d71e9252441533"},"schema_version":"1.0"},"canonical_sha256":"612cdd15b3e3786b6e4a723101d2503dcd05b1c443956df81a5184b0d0a3a683","source":{"kind":"arxiv","id":"1509.06424","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06424","created_at":"2026-05-18T01:32:20Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06424v1","created_at":"2026-05-18T01:32:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06424","created_at":"2026-05-18T01:32:20Z"},{"alias_kind":"pith_short_12","alias_value":"MEWN2FNT4N4G","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MEWN2FNT4N4GW3SK","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MEWN2FNT","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MEWN2FNT4N4GW3SKOIYQDUSQHX","target":"record","payload":{"canonical_record":{"source":{"id":"1509.06424","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-09-21T23:07:04Z","cross_cats_sorted":[],"title_canon_sha256":"65eddc5fe8c5a77cca3d1cbfc849a249df6e07bc9675843cce75cb85abe37946","abstract_canon_sha256":"34963315ec19928cbb008f796394e1b1775fbb4519a9f75886d71e9252441533"},"schema_version":"1.0"},"canonical_sha256":"612cdd15b3e3786b6e4a723101d2503dcd05b1c443956df81a5184b0d0a3a683","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:20.347444Z","signature_b64":"zhNoTTtwPKTSYe+03QRR27dawA3Z9l7ov5+z/oOLkNYJzyhcHrjUUHaeG741geamycOsTqPhAU1Nz0Hnjdl5Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"612cdd15b3e3786b6e4a723101d2503dcd05b1c443956df81a5184b0d0a3a683","last_reissued_at":"2026-05-18T01:32:20.346661Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:20.346661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.06424","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":"2026-05-18T01:32:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kncCwE11GfNjWFI6j6C5brIWHyeBDeC/3zuEnAtlScTiEmzwapB1C1KLlZ5G36YiWh6K8+hqHS7J7AHws8vVAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T01:51:48.533189Z"},"content_sha256":"92e235df99e99e919597a574b3a3d1f0664c447710dd43e1a3d31981a56bd27b","schema_version":"1.0","event_id":"sha256:92e235df99e99e919597a574b3a3d1f0664c447710dd43e1a3d31981a56bd27b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MEWN2FNT4N4GW3SKOIYQDUSQHX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Twisted Simplicial Groups and Twisted Homology of Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"J. Wu, J. Y. Li, V. V. Vershinin","submitted_at":"2015-09-21T23:07:04Z","abstract_excerpt":"Let $A$ be either a simplicial complex $K$ or a small category $\\mathcal C$ with $V(A)$ as its set of vertices or objects. We define a twisted structure on $A$ with coefficients in a simplicial group $G$ as a function $$ \\delta\\colon V(A)\\longrightarrow \\operatorname{End}(G), \\quad v\\mapsto \\delta_v $$ such that $\\delta_v\\circ \\delta_w=\\delta_w\\circ \\delta_v$ if there exists an edge in $A$ joining $v$ with $w$ or an arrow either from $v$ to $w$ or from $w$ to $v$. We give a canonical construction of twisted simplicial group as well as twisted homology for $A$ with a given twisted structure. Al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06424","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":"2026-05-18T01:32:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+683tdgk8T3rhxoW0MrhsI00A231nzRwMkG5kIw6psg5A8REHfO+yPVayFsp790DwMmdc4yX4Do264dIqrcfAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T01:51:48.533562Z"},"content_sha256":"561976fb838ec1bea435feb46fb8f68be2b4ee380bb609372dee7b9b560a960e","schema_version":"1.0","event_id":"sha256:561976fb838ec1bea435feb46fb8f68be2b4ee380bb609372dee7b9b560a960e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MEWN2FNT4N4GW3SKOIYQDUSQHX/bundle.json","state_url":"https://pith.science/pith/MEWN2FNT4N4GW3SKOIYQDUSQHX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MEWN2FNT4N4GW3SKOIYQDUSQHX/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":"2026-06-22T01:51:48Z","links":{"resolver":"https://pith.science/pith/MEWN2FNT4N4GW3SKOIYQDUSQHX","bundle":"https://pith.science/pith/MEWN2FNT4N4GW3SKOIYQDUSQHX/bundle.json","state":"https://pith.science/pith/MEWN2FNT4N4GW3SKOIYQDUSQHX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MEWN2FNT4N4GW3SKOIYQDUSQHX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MEWN2FNT4N4GW3SKOIYQDUSQHX","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":"34963315ec19928cbb008f796394e1b1775fbb4519a9f75886d71e9252441533","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-09-21T23:07:04Z","title_canon_sha256":"65eddc5fe8c5a77cca3d1cbfc849a249df6e07bc9675843cce75cb85abe37946"},"schema_version":"1.0","source":{"id":"1509.06424","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06424","created_at":"2026-05-18T01:32:20Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06424v1","created_at":"2026-05-18T01:32:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06424","created_at":"2026-05-18T01:32:20Z"},{"alias_kind":"pith_short_12","alias_value":"MEWN2FNT4N4G","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MEWN2FNT4N4GW3SK","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MEWN2FNT","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:561976fb838ec1bea435feb46fb8f68be2b4ee380bb609372dee7b9b560a960e","target":"graph","created_at":"2026-05-18T01:32:20Z","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 $A$ be either a simplicial complex $K$ or a small category $\\mathcal C$ with $V(A)$ as its set of vertices or objects. We define a twisted structure on $A$ with coefficients in a simplicial group $G$ as a function $$ \\delta\\colon V(A)\\longrightarrow \\operatorname{End}(G), \\quad v\\mapsto \\delta_v $$ such that $\\delta_v\\circ \\delta_w=\\delta_w\\circ \\delta_v$ if there exists an edge in $A$ joining $v$ with $w$ or an arrow either from $v$ to $w$ or from $w$ to $v$. We give a canonical construction of twisted simplicial group as well as twisted homology for $A$ with a given twisted structure. Al","authors_text":"J. Wu, J. Y. Li, V. V. Vershinin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-09-21T23:07:04Z","title":"Twisted Simplicial Groups and Twisted Homology of Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06424","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":"sha256:92e235df99e99e919597a574b3a3d1f0664c447710dd43e1a3d31981a56bd27b","target":"record","created_at":"2026-05-18T01:32:20Z","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":"34963315ec19928cbb008f796394e1b1775fbb4519a9f75886d71e9252441533","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-09-21T23:07:04Z","title_canon_sha256":"65eddc5fe8c5a77cca3d1cbfc849a249df6e07bc9675843cce75cb85abe37946"},"schema_version":"1.0","source":{"id":"1509.06424","kind":"arxiv","version":1}},"canonical_sha256":"612cdd15b3e3786b6e4a723101d2503dcd05b1c443956df81a5184b0d0a3a683","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"612cdd15b3e3786b6e4a723101d2503dcd05b1c443956df81a5184b0d0a3a683","first_computed_at":"2026-05-18T01:32:20.346661Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:20.346661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zhNoTTtwPKTSYe+03QRR27dawA3Z9l7ov5+z/oOLkNYJzyhcHrjUUHaeG741geamycOsTqPhAU1Nz0Hnjdl5Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:20.347444Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.06424","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92e235df99e99e919597a574b3a3d1f0664c447710dd43e1a3d31981a56bd27b","sha256:561976fb838ec1bea435feb46fb8f68be2b4ee380bb609372dee7b9b560a960e"],"state_sha256":"44f004e1e638af44f0331b09a0ac48770026e89a493059e5548dd6f51cd14b0f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZGMzqInW/rtCBk4Ordcs5URNGsx6lBdHogyljsox4JL1aiz6NmKO367glhXnD1q6IQkqh+zPm/BLE90ECQSsBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T01:51:48.535590Z","bundle_sha256":"7523dc894074c886c93dc49205256ee84071d71b0e03700b96b967e1b603d381"}}