{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:X52SQKO5DXPWOHSHSFLERI4EKD","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":"817cf3a4e6e7b36906dd276c23e97175709f088371ba249e8ab68bfbc087d883","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-02-15T18:58:12Z","title_canon_sha256":"b15c682471a91f00199db14eac9812bb33631584e169a763d65654ebd4ec64c1"},"schema_version":"1.0","source":{"id":"1802.05705","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.05705","created_at":"2026-05-18T00:16:07Z"},{"alias_kind":"arxiv_version","alias_value":"1802.05705v3","created_at":"2026-05-18T00:16:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.05705","created_at":"2026-05-18T00:16:07Z"},{"alias_kind":"pith_short_12","alias_value":"X52SQKO5DXPW","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"X52SQKO5DXPWOHSH","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"X52SQKO5","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:f2535526e8380bac95bec405e7e9231862209908ba064edf4ead53ffde1252dd","target":"graph","created_at":"2026-05-18T00:16:07Z","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 prove that given a finite rank free group $\\mathbb{F}$ of rank $\\geq 3$ and two exponentially growing outer automorphisms $\\psi$ and $\\phi$ with dual lamination pairs $\\Lambda^\\pm_\\psi$ and $\\Lambda^\\pm_\\phi$ associated to them, and given a free factor system $\\mathcal{F}$ with co-edge number $\\geq 2$, $\\phi, \\psi $ each preserving $\\mathcal{F}$, so that the pair $(\\phi, \\Lambda^\\pm_\\phi), (\\psi, \\Lambda^\\pm_\\psi)$ is independent relative to $\\mathcal{F}$, then there $\\exists$ $M\\geq 1$, such that for any integer $m,n \\geq M$, the group $\\langle \\phi^m, \\psi^n \\rangle$ is a free group of ra","authors_text":"Pritam Ghosh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-02-15T18:58:12Z","title":"Relatively irreducible free subroups in Out($\\mathbb{F}$)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.05705","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:fcccfde3cf09c93cff11397b202dd840d4815d4ac3ca363ec013f7a0010916a6","target":"record","created_at":"2026-05-18T00:16:07Z","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":"817cf3a4e6e7b36906dd276c23e97175709f088371ba249e8ab68bfbc087d883","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-02-15T18:58:12Z","title_canon_sha256":"b15c682471a91f00199db14eac9812bb33631584e169a763d65654ebd4ec64c1"},"schema_version":"1.0","source":{"id":"1802.05705","kind":"arxiv","version":3}},"canonical_sha256":"bf752829dd1ddf671e47915648a38450ec42f89e0884d9b9a821b46808778f3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf752829dd1ddf671e47915648a38450ec42f89e0884d9b9a821b46808778f3d","first_computed_at":"2026-05-18T00:16:07.857981Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:07.857981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a6+tToZYTl8KmvdNnbzVJfg+diOaEhxnnyWXC6RuvKklHtfNazojs1Taxgc20HhfAQDutrRS+ZeDj8IhFCMjCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:07.858644Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.05705","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fcccfde3cf09c93cff11397b202dd840d4815d4ac3ca363ec013f7a0010916a6","sha256:f2535526e8380bac95bec405e7e9231862209908ba064edf4ead53ffde1252dd"],"state_sha256":"8e0d815f78729b72bd942a094eb1d43ec9cf12b534943bb2e523f8406b3f6f37"}