{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7YSZ447VLK75LFOKAEJRAQPPQH","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":"4ce4796344eb108985a46f1369dcbfc3623ceff7f7bdde7d4ffd5c9925d50ac4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-05-21T17:11:59Z","title_canon_sha256":"f1c66c48454831fd01a064155de8c949878ae8b89b3b000a149a8cd36e02d152"},"schema_version":"1.0","source":{"id":"1305.4887","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.4887","created_at":"2026-05-18T01:19:14Z"},{"alias_kind":"arxiv_version","alias_value":"1305.4887v3","created_at":"2026-05-18T01:19:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.4887","created_at":"2026-05-18T01:19:14Z"},{"alias_kind":"pith_short_12","alias_value":"7YSZ447VLK75","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"7YSZ447VLK75LFOK","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"7YSZ447V","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:b172d1a01d723c02d27b5a75c757fd843700f1d0422ce09a8f8370939aa7395f","target":"graph","created_at":"2026-05-18T01:19:14Z","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":"It is shown that a finitely generated pro-p group G which is a virtually free pro-p product splits either as a free pro-p product with amalgamation or as a pro-p HNN-extension over a finite p-group. More precisely, G is the pro-p fundamental group of a finite graph of finitely generated pro-p groups with finite edge groups. This generalizes previous results of W. Herfort and the second author (cf. [2]).","authors_text":"Pavel Zalesskii, Thomas Weigel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-05-21T17:11:59Z","title":"Virtually free pro-p products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4887","kind":"arxiv","version":3},"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:cfa8ea967ffd2fa053644e03c1bdcc57866bbeec2986778728d744fe14608b79","target":"record","created_at":"2026-05-18T01:19:14Z","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":"4ce4796344eb108985a46f1369dcbfc3623ceff7f7bdde7d4ffd5c9925d50ac4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-05-21T17:11:59Z","title_canon_sha256":"f1c66c48454831fd01a064155de8c949878ae8b89b3b000a149a8cd36e02d152"},"schema_version":"1.0","source":{"id":"1305.4887","kind":"arxiv","version":3}},"canonical_sha256":"fe259e73f55abfd595ca01131041ef81f56a39c5897184c80ef5bb4a74e78a34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe259e73f55abfd595ca01131041ef81f56a39c5897184c80ef5bb4a74e78a34","first_computed_at":"2026-05-18T01:19:14.562032Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:14.562032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DyXgogaFqZrAHPJq2pq12Aa2yxSd6U6Er2nIVXAGECJAssgh1PNTO9xazn6Q43QVcgWv8waZBXqYBIcvK6YiAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:14.562638Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.4887","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfa8ea967ffd2fa053644e03c1bdcc57866bbeec2986778728d744fe14608b79","sha256:b172d1a01d723c02d27b5a75c757fd843700f1d0422ce09a8f8370939aa7395f"],"state_sha256":"91b75d461cb549ebe80d6ec894a7bdca5d94b47593fbe81c2db4f9de8bbd793c"}