{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:P6NDIIBTF2AOF7GZTOAMVNJCJJ","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":"7190e868c622fc04fcd7f0f2bc394e8b41cb52a16b4e5333f7b04a61304740bb","cross_cats_sorted":["math.DS","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-05-07T19:18:58Z","title_canon_sha256":"05bd1e729f033d0610be8e7bb63df8294d06d37270d8a2860db3970e6f3f5fb8"},"schema_version":"1.0","source":{"id":"1305.1613","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1613","created_at":"2026-05-18T01:35:37Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1613v3","created_at":"2026-05-18T01:35:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1613","created_at":"2026-05-18T01:35:37Z"},{"alias_kind":"pith_short_12","alias_value":"P6NDIIBTF2AO","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"P6NDIIBTF2AOF7GZ","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"P6NDIIBT","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:169332695ff19ebd83f70b7f7a4df7a9d0acefcc8280ac81c4b052008e1b9440","target":"graph","created_at":"2026-05-18T01:35:37Z","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"},"paper":{"abstract_excerpt":"Given a free group $F_n$, a fully irreducible automorphism $f \\in \\aut$, and a generic element $x \\in F_n$, the elements $f^k(x)$ converge in the appropriate sense to an object called an attracting lamination of $f$. When the action of $f$ on $\\frac{F_n}{[F_n, F_n]}$ has finite order, we introduce a homological version of this convergence, in which the attracting object is a convex polytope with rational vertices, together with a measure supported at a point with algebraic coordinates.","authors_text":"Asaf Hadari","cross_cats":["math.DS","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-05-07T19:18:58Z","title":"Homological shadows of attracting laminations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1613","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":"sha256:30745cb47c8720804366ea4707000a307b55b18968a6637d8ed8b1af2ab3eb9c","target":"record","created_at":"2026-05-18T01:35:37Z","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":"7190e868c622fc04fcd7f0f2bc394e8b41cb52a16b4e5333f7b04a61304740bb","cross_cats_sorted":["math.DS","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-05-07T19:18:58Z","title_canon_sha256":"05bd1e729f033d0610be8e7bb63df8294d06d37270d8a2860db3970e6f3f5fb8"},"schema_version":"1.0","source":{"id":"1305.1613","kind":"arxiv","version":3}},"canonical_sha256":"7f9a3420332e80e2fcd99b80cab5224a6b2a1adddbe2e4bee737e02ad7904833","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f9a3420332e80e2fcd99b80cab5224a6b2a1adddbe2e4bee737e02ad7904833","first_computed_at":"2026-05-18T01:35:37.213632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:37.213632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tU9sZdFTq1ENovneOh4LYDVfHtTXymYP8RHtxZ6JQ+/zFD+8uQiSF0irBwxtHyUDKT4BHMbSPsyFTuPg3cXdAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:37.214228Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.1613","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30745cb47c8720804366ea4707000a307b55b18968a6637d8ed8b1af2ab3eb9c","sha256:169332695ff19ebd83f70b7f7a4df7a9d0acefcc8280ac81c4b052008e1b9440"],"state_sha256":"d248288dfac2b9152093f62c63982822161bfbc7fedb37d52681d45e749ed863"}