{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:DZ2WKXBHK5ASJC57JSRJHP5SSY","short_pith_number":"pith:DZ2WKXBH","canonical_record":{"source":{"id":"1710.05261","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-10-15T02:04:50Z","cross_cats_sorted":[],"title_canon_sha256":"cb000fc5389a04c0370b05b97f5d2650b23e3d56215069d60ea0b80af16ef019","abstract_canon_sha256":"52090564d757c6274983890732f0af00c856baa6a3adccaf21060582ab048abe"},"schema_version":"1.0"},"canonical_sha256":"1e75655c275741248bbf4ca293bfb296216b90b8a8803d6b0422782eac99e16f","source":{"kind":"arxiv","id":"1710.05261","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.05261","created_at":"2026-05-18T00:32:53Z"},{"alias_kind":"arxiv_version","alias_value":"1710.05261v1","created_at":"2026-05-18T00:32:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05261","created_at":"2026-05-18T00:32:53Z"},{"alias_kind":"pith_short_12","alias_value":"DZ2WKXBHK5AS","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DZ2WKXBHK5ASJC57","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DZ2WKXBH","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:DZ2WKXBHK5ASJC57JSRJHP5SSY","target":"record","payload":{"canonical_record":{"source":{"id":"1710.05261","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-10-15T02:04:50Z","cross_cats_sorted":[],"title_canon_sha256":"cb000fc5389a04c0370b05b97f5d2650b23e3d56215069d60ea0b80af16ef019","abstract_canon_sha256":"52090564d757c6274983890732f0af00c856baa6a3adccaf21060582ab048abe"},"schema_version":"1.0"},"canonical_sha256":"1e75655c275741248bbf4ca293bfb296216b90b8a8803d6b0422782eac99e16f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:53.813758Z","signature_b64":"e48KPu6q2D6iKQq6QtCONH3F6+OHe6W0Djbt9mA9NnZ8aFY41hu8t+Tq00hwygrM3HqeDDtWIZYN6I16AaT0Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e75655c275741248bbf4ca293bfb296216b90b8a8803d6b0422782eac99e16f","last_reissued_at":"2026-05-18T00:32:53.813052Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:53.813052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.05261","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fcl++9ZCLDwOMyb/5+TT1+oHjd+sF+boSQNL9WclJdu9w01yfWQMiUamgMT3eHvTdZyewHOZKJwM4ucuXRoCBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:28:05.702514Z"},"content_sha256":"8d073291e49fa46984e3ef6e197a74b3df733b1e1acf7be572ec0ff678389df8","schema_version":"1.0","event_id":"sha256:8d073291e49fa46984e3ef6e197a74b3df733b1e1acf7be572ec0ff678389df8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:DZ2WKXBHK5ASJC57JSRJHP5SSY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nearly Maximal Hausdorff Dimension in Finitely Constrained Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Andrew Penland","submitted_at":"2017-10-15T02:04:50Z","abstract_excerpt":"This work continues the study of the properties of finitely constrained groups of binary tree automorphisms in terms of their Hausdorff dimension. We prove that there are exactly $2^{2d-3}$ finitely constrained groups of binary tree automorphisms with pattern size $d$ and having Hausdorff dimension $1 - \\frac{2}{2^{d-1}}$. As part of this proof, we describe the finite patterns that can define such groups, which leads to the fact that all finitely constrained groups of nearly maximal Hausdorff dimension have additive portraits. Additionally, we give an upper bound, in terms of the pattern size "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05261","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uOKKnGpZvOPs44+qUCGwCHG4/hjJcy+MwEyVSsaUut5+EzwyPy/Paj0Ksz3/2WypoqMMLfWRqoU4TZIZ+xYGAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:28:05.702865Z"},"content_sha256":"e74fcdba2aa6ddf92c924320a996a4b3c3fadae3ad5d3030b3d13522704c58cc","schema_version":"1.0","event_id":"sha256:e74fcdba2aa6ddf92c924320a996a4b3c3fadae3ad5d3030b3d13522704c58cc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DZ2WKXBHK5ASJC57JSRJHP5SSY/bundle.json","state_url":"https://pith.science/pith/DZ2WKXBHK5ASJC57JSRJHP5SSY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DZ2WKXBHK5ASJC57JSRJHP5SSY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-21T22:28:05Z","links":{"resolver":"https://pith.science/pith/DZ2WKXBHK5ASJC57JSRJHP5SSY","bundle":"https://pith.science/pith/DZ2WKXBHK5ASJC57JSRJHP5SSY/bundle.json","state":"https://pith.science/pith/DZ2WKXBHK5ASJC57JSRJHP5SSY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DZ2WKXBHK5ASJC57JSRJHP5SSY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DZ2WKXBHK5ASJC57JSRJHP5SSY","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":"52090564d757c6274983890732f0af00c856baa6a3adccaf21060582ab048abe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-10-15T02:04:50Z","title_canon_sha256":"cb000fc5389a04c0370b05b97f5d2650b23e3d56215069d60ea0b80af16ef019"},"schema_version":"1.0","source":{"id":"1710.05261","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.05261","created_at":"2026-05-18T00:32:53Z"},{"alias_kind":"arxiv_version","alias_value":"1710.05261v1","created_at":"2026-05-18T00:32:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05261","created_at":"2026-05-18T00:32:53Z"},{"alias_kind":"pith_short_12","alias_value":"DZ2WKXBHK5AS","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DZ2WKXBHK5ASJC57","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DZ2WKXBH","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:e74fcdba2aa6ddf92c924320a996a4b3c3fadae3ad5d3030b3d13522704c58cc","target":"graph","created_at":"2026-05-18T00:32:53Z","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":"This work continues the study of the properties of finitely constrained groups of binary tree automorphisms in terms of their Hausdorff dimension. We prove that there are exactly $2^{2d-3}$ finitely constrained groups of binary tree automorphisms with pattern size $d$ and having Hausdorff dimension $1 - \\frac{2}{2^{d-1}}$. As part of this proof, we describe the finite patterns that can define such groups, which leads to the fact that all finitely constrained groups of nearly maximal Hausdorff dimension have additive portraits. Additionally, we give an upper bound, in terms of the pattern size ","authors_text":"Andrew Penland","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-10-15T02:04:50Z","title":"Nearly Maximal Hausdorff Dimension in Finitely Constrained Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05261","kind":"arxiv","version":1},"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":"sha256:8d073291e49fa46984e3ef6e197a74b3df733b1e1acf7be572ec0ff678389df8","target":"record","created_at":"2026-05-18T00:32:53Z","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":"52090564d757c6274983890732f0af00c856baa6a3adccaf21060582ab048abe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-10-15T02:04:50Z","title_canon_sha256":"cb000fc5389a04c0370b05b97f5d2650b23e3d56215069d60ea0b80af16ef019"},"schema_version":"1.0","source":{"id":"1710.05261","kind":"arxiv","version":1}},"canonical_sha256":"1e75655c275741248bbf4ca293bfb296216b90b8a8803d6b0422782eac99e16f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e75655c275741248bbf4ca293bfb296216b90b8a8803d6b0422782eac99e16f","first_computed_at":"2026-05-18T00:32:53.813052Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:53.813052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e48KPu6q2D6iKQq6QtCONH3F6+OHe6W0Djbt9mA9NnZ8aFY41hu8t+Tq00hwygrM3HqeDDtWIZYN6I16AaT0Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:53.813758Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.05261","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d073291e49fa46984e3ef6e197a74b3df733b1e1acf7be572ec0ff678389df8","sha256:e74fcdba2aa6ddf92c924320a996a4b3c3fadae3ad5d3030b3d13522704c58cc"],"state_sha256":"fec09c9ea5fc9490c949455608d187aeb0679e2f18888a64762e2861d3d40393"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DsrxC2IDuUKWgzOQrCJF/0JpcI0+pCEgdzJsvSKYKaLUmsNhPSf8VD90vfPcB/tsjMRWhlseWDH+ZIzwyG48DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T22:28:05.704919Z","bundle_sha256":"902fadca0681d25e7fa278d53ba1a4354fd16fa9028cecbf793bed1b46496c50"}}