{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5K6YUNOJDO5K3U5EC44LEU56YS","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":"7f682e0546fbd395b4f26daf90991aa0e9b8293f621d555ed37af515b2260562","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-03-11T11:55:47Z","title_canon_sha256":"88de2b06e18f77c3aceb4b219c26c6db1402f66b107230fae23185de5e8db953"},"schema_version":"1.0","source":{"id":"1703.03960","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.03960","created_at":"2026-05-17T23:54:11Z"},{"alias_kind":"arxiv_version","alias_value":"1703.03960v1","created_at":"2026-05-17T23:54:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.03960","created_at":"2026-05-17T23:54:11Z"},{"alias_kind":"pith_short_12","alias_value":"5K6YUNOJDO5K","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5K6YUNOJDO5K3U5E","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5K6YUNOJ","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:9047d0026ca0abd98f9d09d04bbc4f31f7a467322baee5cba44baf4b01cf3cad","target":"graph","created_at":"2026-05-17T23:54:11Z","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 use combinatorial group theory methods to extend the definition of a classical James-Hopf invariant to a simplicial group setting. This allow us to realize certain coalgebra idempotents at sSet -level and obtain a functorial decomposition of the spectral sequence, associated with the lower p-central series filtration on the free simplicial group.","authors_text":"Fedor Pavutnitskiy, Jie Wu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-03-11T11:55:47Z","title":"Simplicial James-Hopf map and decompositions of the unstable Adams spectral sequence for suspensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03960","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":"sha256:3076bd1dadbdc004346ca088b51b6f7cb49c4961ba206370eaaa8f753d114051","target":"record","created_at":"2026-05-17T23:54:11Z","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":"7f682e0546fbd395b4f26daf90991aa0e9b8293f621d555ed37af515b2260562","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-03-11T11:55:47Z","title_canon_sha256":"88de2b06e18f77c3aceb4b219c26c6db1402f66b107230fae23185de5e8db953"},"schema_version":"1.0","source":{"id":"1703.03960","kind":"arxiv","version":1}},"canonical_sha256":"eabd8a35c91bbaadd3a41738b253bec4afaf56b0a0eed1eeeccc0c6451421e7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eabd8a35c91bbaadd3a41738b253bec4afaf56b0a0eed1eeeccc0c6451421e7d","first_computed_at":"2026-05-17T23:54:11.866910Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:11.866910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"59tXspz2t69r5Bfs99tnPCKAwdnsDlW0ieZCuz2M8Am03T+6OGWrEKTL4FCeJzh/+ki2SJKdKci9dWJA+BfqCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:11.867556Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.03960","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3076bd1dadbdc004346ca088b51b6f7cb49c4961ba206370eaaa8f753d114051","sha256:9047d0026ca0abd98f9d09d04bbc4f31f7a467322baee5cba44baf4b01cf3cad"],"state_sha256":"63019be23b7186b3b8b9a9e3da2504b2d0fc3fc372cc59e20ec19f48ea059ba5"}