{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ILTHQZAOKDS7X4QFADVGPTRIYW","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":"6f6e61cccdc8108421bec4ad00279f5c314827fcdce8e840a756f7af23b1888c","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-04-03T22:24:22Z","title_canon_sha256":"68343041f7cf8d38b6cde4b080fa5467afb2091b5addabcfb94d31aba07a3874"},"schema_version":"1.0","source":{"id":"1904.02258","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.02258","created_at":"2026-05-17T23:49:24Z"},{"alias_kind":"arxiv_version","alias_value":"1904.02258v1","created_at":"2026-05-17T23:49:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02258","created_at":"2026-05-17T23:49:24Z"},{"alias_kind":"pith_short_12","alias_value":"ILTHQZAOKDS7","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"ILTHQZAOKDS7X4QF","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"ILTHQZAO","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:1aed424c69defb029f07d3ac62ff754d2c14c21877c8fa78d29b44ee4c3dda02","target":"graph","created_at":"2026-05-17T23:49:24Z","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"},"paper":{"abstract_excerpt":"We confirm the Hanna Neumann conjecture for topologically finitely generated closed subgroups $U$ and $W$ of a nonsolvable Demushkin group $G$. Namely, we show that \\begin{equation*} \\sum_{g \\in U \\backslash G/W} \\bar d(U \\cap gWg^{-1}) \\leq \\bar d(U) \\bar d(W) \\end{equation*} where $\\bar d(K) = \\max\\{d(K) - 1, 0\\}$ and $d(K)$ is the least cardinality of a topological generating set for the group $K$.","authors_text":"Andrei Jaikin-Zapirain, Mark Shusterman","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-04-03T22:24:22Z","title":"The Hanna Neumann conjecture for Demushkin Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02258","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":"sha256:6e8a5a9062c3014a9761f4742eaf65455325c08cf2fa30ce2ddf970b93b5edcb","target":"record","created_at":"2026-05-17T23:49:24Z","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":"6f6e61cccdc8108421bec4ad00279f5c314827fcdce8e840a756f7af23b1888c","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-04-03T22:24:22Z","title_canon_sha256":"68343041f7cf8d38b6cde4b080fa5467afb2091b5addabcfb94d31aba07a3874"},"schema_version":"1.0","source":{"id":"1904.02258","kind":"arxiv","version":1}},"canonical_sha256":"42e678640e50e5fbf20500ea67ce28c5a83e205078eab6e1463b051e42c210e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42e678640e50e5fbf20500ea67ce28c5a83e205078eab6e1463b051e42c210e1","first_computed_at":"2026-05-17T23:49:24.075096Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:24.075096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2XbUnQGezkZVt5XCDwfoEO0OACq2sxmzQ62oLXMXrOrk78J7GqweNEXp5cDSchcQbb8b1vpJBEdJuTpSa2k6CA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:24.075533Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.02258","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e8a5a9062c3014a9761f4742eaf65455325c08cf2fa30ce2ddf970b93b5edcb","sha256:1aed424c69defb029f07d3ac62ff754d2c14c21877c8fa78d29b44ee4c3dda02"],"state_sha256":"efdecd254074716c277c3917ba51d86e8a549b7b07c39eb8180a3404137b95ac"}