{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:QE2QOAITDLL7X4J66NWTIT52GN","short_pith_number":"pith:QE2QOAIT","schema_version":"1.0","canonical_sha256":"81350701131ad7fbf13ef36d344fba337783eb002ab0e0bbd4e570f554ac5507","source":{"kind":"arxiv","id":"2503.00185","version":1},"attestation_state":"computed","paper":{"title":"On the fixed-point proportion of self-similar groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Jorge Fari\\~na-Asategui, Santiago Radi","submitted_at":"2025-02-28T21:03:42Z","abstract_excerpt":"We prove that super strongly fractal groups acting on regular rooted trees have null fixed-point proportion. In particular, we show that the fixed-point proportion of an infinite family of iterated monodromy groups of exceptional complex polynomials have the same property. The proof uses the approach of Rafe Jones in [15] based on martingales and a recent result of the first author on the dynamics of self-similar groups [6]."},"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":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2503.00185","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2025-02-28T21:03:42Z","cross_cats_sorted":[],"title_canon_sha256":"bb3596b3aa4dbbf5b9f3187d8045092a29b95044428fe612f50da3c0735f4984","abstract_canon_sha256":"9677e472a4533418cd1074037e6af92bbf894a2b2d69a603f563754c3344df22"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:22:18.769009Z","signature_b64":"O9vZlOqYsQzbFJ6Y3gwi5bqHdMZ0Gsw/7xfWiSiSZaSnb9gKT9G4wPPEqiokJHSef+wx53sotYkk5y1X4vVDAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81350701131ad7fbf13ef36d344fba337783eb002ab0e0bbd4e570f554ac5507","last_reissued_at":"2026-07-05T10:22:18.768480Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:22:18.768480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the fixed-point proportion of self-similar groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Jorge Fari\\~na-Asategui, Santiago Radi","submitted_at":"2025-02-28T21:03:42Z","abstract_excerpt":"We prove that super strongly fractal groups acting on regular rooted trees have null fixed-point proportion. In particular, we show that the fixed-point proportion of an infinite family of iterated monodromy groups of exceptional complex polynomials have the same property. The proof uses the approach of Rafe Jones in [15] based on martingales and a recent result of the first author on the dynamics of self-similar groups [6]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.00185","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.00185/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"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":"2503.00185","created_at":"2026-07-05T10:22:18.768544+00:00"},{"alias_kind":"arxiv_version","alias_value":"2503.00185v1","created_at":"2026-07-05T10:22:18.768544+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.00185","created_at":"2026-07-05T10:22:18.768544+00:00"},{"alias_kind":"pith_short_12","alias_value":"QE2QOAITDLL7","created_at":"2026-07-05T10:22:18.768544+00:00"},{"alias_kind":"pith_short_16","alias_value":"QE2QOAITDLL7X4J6","created_at":"2026-07-05T10:22:18.768544+00:00"},{"alias_kind":"pith_short_8","alias_value":"QE2QOAIT","created_at":"2026-07-05T10:22:18.768544+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.03927","citing_title":"Groups of finite type: classification and structural properties","ref_index":17,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QE2QOAITDLL7X4J66NWTIT52GN","json":"https://pith.science/pith/QE2QOAITDLL7X4J66NWTIT52GN.json","graph_json":"https://pith.science/api/pith-number/QE2QOAITDLL7X4J66NWTIT52GN/graph.json","events_json":"https://pith.science/api/pith-number/QE2QOAITDLL7X4J66NWTIT52GN/events.json","paper":"https://pith.science/paper/QE2QOAIT"},"agent_actions":{"view_html":"https://pith.science/pith/QE2QOAITDLL7X4J66NWTIT52GN","download_json":"https://pith.science/pith/QE2QOAITDLL7X4J66NWTIT52GN.json","view_paper":"https://pith.science/paper/QE2QOAIT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2503.00185&json=true","fetch_graph":"https://pith.science/api/pith-number/QE2QOAITDLL7X4J66NWTIT52GN/graph.json","fetch_events":"https://pith.science/api/pith-number/QE2QOAITDLL7X4J66NWTIT52GN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QE2QOAITDLL7X4J66NWTIT52GN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QE2QOAITDLL7X4J66NWTIT52GN/action/storage_attestation","attest_author":"https://pith.science/pith/QE2QOAITDLL7X4J66NWTIT52GN/action/author_attestation","sign_citation":"https://pith.science/pith/QE2QOAITDLL7X4J66NWTIT52GN/action/citation_signature","submit_replication":"https://pith.science/pith/QE2QOAITDLL7X4J66NWTIT52GN/action/replication_record"}},"created_at":"2026-07-05T10:22:18.768544+00:00","updated_at":"2026-07-05T10:22:18.768544+00:00"}