{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:USJ7R2HB6A6I4RXW2JI2QPR5MK","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":"3ad9ed6a2208ca00a389f825b3605dcb2f70d0c4a819dc4af60c0ca32c0a9baf","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.GR","submitted_at":"2025-07-13T14:04:15Z","title_canon_sha256":"f0b444ab122e9a7291ab12b35cb85b471d952161155aae55ecad14e5df7d9ea0"},"schema_version":"1.0","source":{"id":"2507.09636","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.09636","created_at":"2026-07-05T11:36:37Z"},{"alias_kind":"arxiv_version","alias_value":"2507.09636v1","created_at":"2026-07-05T11:36:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.09636","created_at":"2026-07-05T11:36:37Z"},{"alias_kind":"pith_short_12","alias_value":"USJ7R2HB6A6I","created_at":"2026-07-05T11:36:37Z"},{"alias_kind":"pith_short_16","alias_value":"USJ7R2HB6A6I4RXW","created_at":"2026-07-05T11:36:37Z"},{"alias_kind":"pith_short_8","alias_value":"USJ7R2HB","created_at":"2026-07-05T11:36:37Z"}],"graph_snapshots":[{"event_id":"sha256:cf93eb2360db760823e74a4788a3a7d797dfb2ad90b83d5bb31cc57b8410a246","target":"graph","created_at":"2026-07-05T11:36:37Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2507.09636/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a new elementary proof of the theorem that a natural map from Milnor's construction $F[S^1]$ to the simplicial group $\\mathrm{AP}$ of pure braids is injective. Our approach is group-theoretic and does not rely on Lie algebras.","authors_text":"Vasily Ionin","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.GR","submitted_at":"2025-07-13T14:04:15Z","title":"On injectivity of Cohen-Wu homomorphism"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.09636","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":"sha256:38948d8b10e8eaa2736f9bd4e13481dd7b7706c0797044d9eb0a640c6102a54e","target":"record","created_at":"2026-07-05T11:36:37Z","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":"3ad9ed6a2208ca00a389f825b3605dcb2f70d0c4a819dc4af60c0ca32c0a9baf","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.GR","submitted_at":"2025-07-13T14:04:15Z","title_canon_sha256":"f0b444ab122e9a7291ab12b35cb85b471d952161155aae55ecad14e5df7d9ea0"},"schema_version":"1.0","source":{"id":"2507.09636","kind":"arxiv","version":1}},"canonical_sha256":"a493f8e8e1f03c8e46f6d251a83e3d62bc99a5b7c68eb51b92a1321853eed86d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a493f8e8e1f03c8e46f6d251a83e3d62bc99a5b7c68eb51b92a1321853eed86d","first_computed_at":"2026-07-05T11:36:37.184514Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:36:37.184514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tesUg6xByILUQN2JDyF5phqovTIAmFSc5OW5b213FiKdXQvqoMo/Y2TIJfxWU2uneaKTckvToqqRxJAdgGewCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:36:37.184997Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.09636","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38948d8b10e8eaa2736f9bd4e13481dd7b7706c0797044d9eb0a640c6102a54e","sha256:cf93eb2360db760823e74a4788a3a7d797dfb2ad90b83d5bb31cc57b8410a246"],"state_sha256":"65975aeee9f5f9430fecd68ea7403b69e33f516bf87e438e2da46a512ed0768b"}