{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:33HHCEWDXAQISAFTL44Z2H2PDS","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":"bb243a9b50f283959cda14d6e13d59bb2d80c9ded2c2d922bfd81102013bc5d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-08-23T13:52:58Z","title_canon_sha256":"de17cdef226cb4f49736692e8c605395d73c5dee549f1cd02badebd196d63c7e"},"schema_version":"1.0","source":{"id":"1908.08826","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.08826","created_at":"2026-07-04T23:59:24Z"},{"alias_kind":"arxiv_version","alias_value":"1908.08826v1","created_at":"2026-07-04T23:59:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08826","created_at":"2026-07-04T23:59:24Z"},{"alias_kind":"pith_short_12","alias_value":"33HHCEWDXAQI","created_at":"2026-07-04T23:59:24Z"},{"alias_kind":"pith_short_16","alias_value":"33HHCEWDXAQISAFT","created_at":"2026-07-04T23:59:24Z"},{"alias_kind":"pith_short_8","alias_value":"33HHCEWD","created_at":"2026-07-04T23:59:24Z"}],"graph_snapshots":[{"event_id":"sha256:2816794a08ca3b8f1140417c113a3cecb6cad92f1939a73642cb4943503f92a7","target":"graph","created_at":"2026-07-04T23:59:24Z","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/1908.08826/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that if $H$ is an almost normal subgroup of $G$ such that both $H$ and $G$ are of type $VFP$ and vcd($G$) = vcd($H$) + 1, then $G$ is the fundamental group of a graph of groups in which all vertex and edge groups are commensurable to $H$. We also investigate almost normal subgroups of one-relator groups and duality groups.","authors_text":"Alexander Margolis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-08-23T13:52:58Z","title":"Groups of cohomological codimension one"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08826","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":"sha256:710a0dd89efae8b8d45a15e91cb6ea9150b2d43be4cfb7b2f883a4e3e8e13b4f","target":"record","created_at":"2026-07-04T23:59:24Z","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":"bb243a9b50f283959cda14d6e13d59bb2d80c9ded2c2d922bfd81102013bc5d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-08-23T13:52:58Z","title_canon_sha256":"de17cdef226cb4f49736692e8c605395d73c5dee549f1cd02badebd196d63c7e"},"schema_version":"1.0","source":{"id":"1908.08826","kind":"arxiv","version":1}},"canonical_sha256":"dece7112c3b8208900b35f399d1f4f1ca8e5d4d86e62beac8d4bdc6a7037986e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dece7112c3b8208900b35f399d1f4f1ca8e5d4d86e62beac8d4bdc6a7037986e","first_computed_at":"2026-07-04T23:59:24.358251Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:59:24.358251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1JnN+klT0pQByaG2ZbsTK7+OENfIU7+as0gEB4JR5PwnbuMrTn6ZZ/vCtOD5bu3LvfPKZDZ9PXawq3qC/u48AA==","signature_status":"signed_v1","signed_at":"2026-07-04T23:59:24.358860Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.08826","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:710a0dd89efae8b8d45a15e91cb6ea9150b2d43be4cfb7b2f883a4e3e8e13b4f","sha256:2816794a08ca3b8f1140417c113a3cecb6cad92f1939a73642cb4943503f92a7"],"state_sha256":"b47c73f6a1c17f763cfaf7affdf3978e20caa2ea2accdc0c0fee67f082be658f"}