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We analyze the measure of the set of {\\theta} for which ||W_n({\\theta})|| \\geq {\\lambda}?^(n*{\\delta}), (0 < {\\delta} < 1). This can be regarded as a model problem for the so-called Bochi-Fayad conjecture."},"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":"1106.2903","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-06-15T08:24:47Z","cross_cats_sorted":[],"title_canon_sha256":"7e731acd0fb1fc89091f0262463170f7aabf161bdb8a58f997f1b56897a0c79b","abstract_canon_sha256":"77511d8636f91f0027038a622033266b59dc841b162ddc476d4fb34b21962aec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:55.381171Z","signature_b64":"00FpZfrpptI4d2wePPIxkasRKVpaRI7rAMbFe0wex38FtjExDqsBrcrGEDRaZyMXZVAOJUBRRb5mnTV78qedCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"738a7f8f68b34269a4d9bdd28196870802e21ce54e227ef07f9c72d039676785","last_reissued_at":"2026-05-18T04:19:55.380477Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:55.380477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Size of the Resonant Set for the Products of 2x2 Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Benjamin Seeger, Deborah Unger, Jeffrey Allen","submitted_at":"2011-06-15T08:24:47Z","abstract_excerpt":"For {\\theta} \\in [0, 2{\\pi}), consider the rotation matrix R? and h = ({\\lambda}, 0; 0, 0), {\\lambda} > 1. Let W_n({\\theta}) denote the product of m R?'s and n h's with the condition m \\leq [\\epsilon\\astn], (0 < \\epsilon < 1). We analyze the measure of the set of {\\theta} for which ||W_n({\\theta})|| \\geq {\\lambda}?^(n*{\\delta}), (0 < {\\delta} < 1). This can be regarded as a model problem for the so-called Bochi-Fayad conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2903","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":""},"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":"1106.2903","created_at":"2026-05-18T04:19:55.380591+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.2903v1","created_at":"2026-05-18T04:19:55.380591+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.2903","created_at":"2026-05-18T04:19:55.380591+00:00"},{"alias_kind":"pith_short_12","alias_value":"OOFH7D3IWNBG","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"OOFH7D3IWNBGTJGZ","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"OOFH7D3I","created_at":"2026-05-18T12:26:37.096874+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/OOFH7D3IWNBGTJGZXXJIDFUHBA","json":"https://pith.science/pith/OOFH7D3IWNBGTJGZXXJIDFUHBA.json","graph_json":"https://pith.science/api/pith-number/OOFH7D3IWNBGTJGZXXJIDFUHBA/graph.json","events_json":"https://pith.science/api/pith-number/OOFH7D3IWNBGTJGZXXJIDFUHBA/events.json","paper":"https://pith.science/paper/OOFH7D3I"},"agent_actions":{"view_html":"https://pith.science/pith/OOFH7D3IWNBGTJGZXXJIDFUHBA","download_json":"https://pith.science/pith/OOFH7D3IWNBGTJGZXXJIDFUHBA.json","view_paper":"https://pith.science/paper/OOFH7D3I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.2903&json=true","fetch_graph":"https://pith.science/api/pith-number/OOFH7D3IWNBGTJGZXXJIDFUHBA/graph.json","fetch_events":"https://pith.science/api/pith-number/OOFH7D3IWNBGTJGZXXJIDFUHBA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OOFH7D3IWNBGTJGZXXJIDFUHBA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OOFH7D3IWNBGTJGZXXJIDFUHBA/action/storage_attestation","attest_author":"https://pith.science/pith/OOFH7D3IWNBGTJGZXXJIDFUHBA/action/author_attestation","sign_citation":"https://pith.science/pith/OOFH7D3IWNBGTJGZXXJIDFUHBA/action/citation_signature","submit_replication":"https://pith.science/pith/OOFH7D3IWNBGTJGZXXJIDFUHBA/action/replication_record"}},"created_at":"2026-05-18T04:19:55.380591+00:00","updated_at":"2026-05-18T04:19:55.380591+00:00"}