{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:4B7MHPJS626YZTNK42EE2IM7EI","short_pith_number":"pith:4B7MHPJS","schema_version":"1.0","canonical_sha256":"e07ec3bd32f6bd8ccdaae6884d219f223c373bf047cd6de131a99273611ecc4a","source":{"kind":"arxiv","id":"2605.14159","version":1},"attestation_state":"computed","paper":{"title":"Boundary dynamics, triple transitivity, and mixed identities in weakly hyperbolic groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A dynamical lim-free criterion for hyperbolic group actions is equivalent to being mixed identity free.","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ekaterina Rybak","submitted_at":"2026-05-13T22:24:20Z","abstract_excerpt":"We study the interplay between the algebraic and dynamical properties of groups that admit a general type action on a $\\delta$-hyperbolic space such that the induced action on the limit set of the Gromov boundary is faithful. We divide the class of such groups into two subclasses based on a dynamical criterion, which we call lim-free. We prove that satisfying the criterion is equivalent to a purely algebraic property of being mixed identity free, generalizing results from \\cite{FMMS} and \\cite{BM}. For the subclass of not lim-free groups, we give the rigidity result for all $3$-transitive fait"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":true,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.14159","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-05-13T22:24:20Z","cross_cats_sorted":[],"title_canon_sha256":"c0b667674541d24b55b158e87ae93638b688644883b9da8af122243f4fca65ca","abstract_canon_sha256":"2b9fab2128cb992dc4f6a53ec262eb8a70f94fa7741586c2a183396e9ff15121"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:11.503998Z","signature_b64":"AGk7n/ygPgvz8wbjIMc3tfSGb77G+jdGWIwdp1aIxZ/S3NetEOvwDFKirnUgyqNXua06g31kL6j5WgEUnYWVCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e07ec3bd32f6bd8ccdaae6884d219f223c373bf047cd6de131a99273611ecc4a","last_reissued_at":"2026-05-17T23:39:11.503475Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:11.503475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Boundary dynamics, triple transitivity, and mixed identities in weakly hyperbolic groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A dynamical lim-free criterion for hyperbolic group actions is equivalent to being mixed identity free.","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ekaterina Rybak","submitted_at":"2026-05-13T22:24:20Z","abstract_excerpt":"We study the interplay between the algebraic and dynamical properties of groups that admit a general type action on a $\\delta$-hyperbolic space such that the induced action on the limit set of the Gromov boundary is faithful. We divide the class of such groups into two subclasses based on a dynamical criterion, which we call lim-free. We prove that satisfying the criterion is equivalent to a purely algebraic property of being mixed identity free, generalizing results from \\cite{FMMS} and \\cite{BM}. For the subclass of not lim-free groups, we give the rigidity result for all $3$-transitive fait"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"satisfying the criterion is equivalent to a purely algebraic property of being mixed identity free, generalizing results from FMMS and BM. For the subclass of not lim-free groups, we give the rigidity result for all 3-transitive faithful actions and bound the transitivity degree by 3.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The groups admit a general type action on a δ-hyperbolic space such that the induced action on the limit set of the Gromov boundary is faithful.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Lim-free dynamical criterion for faithful boundary actions on hyperbolic spaces is equivalent to the algebraic property of being mixed identity free, with transitivity degree bounded by 3 for non-lim-free groups.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A dynamical lim-free criterion for hyperbolic group actions is equivalent to being mixed identity free.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"154f8da298fada344e344e72101ed29a68c5d2932e3005e319d901e851882bdb"},"source":{"id":"2605.14159","kind":"arxiv","version":1},"verdict":{"id":"9b9c5641-05c1-4ebe-b9b8-b32bd090e921","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T01:57:48.963197Z","strongest_claim":"satisfying the criterion is equivalent to a purely algebraic property of being mixed identity free, generalizing results from FMMS and BM. For the subclass of not lim-free groups, we give the rigidity result for all 3-transitive faithful actions and bound the transitivity degree by 3.","one_line_summary":"Lim-free dynamical criterion for faithful boundary actions on hyperbolic spaces is equivalent to the algebraic property of being mixed identity free, with transitivity degree bounded by 3 for non-lim-free groups.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The groups admit a general type action on a δ-hyperbolic space such that the induced action on the limit set of the Gromov boundary is faithful.","pith_extraction_headline":"A dynamical lim-free criterion for hyperbolic group actions is equivalent to being mixed identity free."},"references":{"count":27,"sample":[{"doi":"","year":2023,"title":"[AMS] R. Aoun, P. Mathieu and C ¸ . Sert, Random walks on hyperbolic spaces: second order expansion of the rate function at the drift, J. ´Ec. polytech. Math.10(2023), 549–573. [AS] R. Aoun and C ¸ . ","work_id":"e67b02c8-9b40-4d52-ab26-4d6bab6d8551","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1993,"title":"Bass, Covering theory for graphs of groups,J","work_id":"8644bf0e-995d-4a6b-afdc-c88d78504370","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"[BEH] C. Bleak, L. Elliott, J. T. Hyde, Sufficient conditions for a group of homeomorphisms of the Cantor set to be two-generated,J. Inst. Math. Jussieu23(2024), no. 6, 2825 –","work_id":"5383a2ed-8ada-4dbd-8519-89685ed210cb","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"[BFFHZ] J. Belk, F. Fournier-Facio, J. Hyde, M. C. B. Zaremsky, Boone-Higman embed- dings ofAut(F n) and mapping class groups of punctured surfaces, arXiv:2503.21882v2. [BFGS] S.Balasubramanya, F. Fou","work_id":"b2fb7b5b-b9c1-4262-b6fc-a0e79e6793e1","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"[BM] A. Le Boudec, N. Matte Bon, Triple transitivity and non-free actions in dimension one,J. Lond. Math. Soc.105(2022), 2, 884 –","work_id":"03435cbb-5f0c-4cbd-b08e-3887fda71818","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":27,"snapshot_sha256":"6da15f186653e1d7caf536e3c95b7ba4dd724370c9fd58793a8763e4eedf6ee2","internal_anchors":1},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2605.14159","created_at":"2026-05-17T23:39:11.503571+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.14159v1","created_at":"2026-05-17T23:39:11.503571+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.14159","created_at":"2026-05-17T23:39:11.503571+00:00"},{"alias_kind":"pith_short_12","alias_value":"4B7MHPJS626Y","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"4B7MHPJS626YZTNK","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"4B7MHPJS","created_at":"2026-05-18T12:33:37.589309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4B7MHPJS626YZTNK42EE2IM7EI","json":"https://pith.science/pith/4B7MHPJS626YZTNK42EE2IM7EI.json","graph_json":"https://pith.science/api/pith-number/4B7MHPJS626YZTNK42EE2IM7EI/graph.json","events_json":"https://pith.science/api/pith-number/4B7MHPJS626YZTNK42EE2IM7EI/events.json","paper":"https://pith.science/paper/4B7MHPJS"},"agent_actions":{"view_html":"https://pith.science/pith/4B7MHPJS626YZTNK42EE2IM7EI","download_json":"https://pith.science/pith/4B7MHPJS626YZTNK42EE2IM7EI.json","view_paper":"https://pith.science/paper/4B7MHPJS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.14159&json=true","fetch_graph":"https://pith.science/api/pith-number/4B7MHPJS626YZTNK42EE2IM7EI/graph.json","fetch_events":"https://pith.science/api/pith-number/4B7MHPJS626YZTNK42EE2IM7EI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4B7MHPJS626YZTNK42EE2IM7EI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4B7MHPJS626YZTNK42EE2IM7EI/action/storage_attestation","attest_author":"https://pith.science/pith/4B7MHPJS626YZTNK42EE2IM7EI/action/author_attestation","sign_citation":"https://pith.science/pith/4B7MHPJS626YZTNK42EE2IM7EI/action/citation_signature","submit_replication":"https://pith.science/pith/4B7MHPJS626YZTNK42EE2IM7EI/action/replication_record"}},"created_at":"2026-05-17T23:39:11.503571+00:00","updated_at":"2026-05-17T23:39:11.503571+00:00"}