{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:BFL47LEOAJ4UY6PBV6V5XEIQW6","short_pith_number":"pith:BFL47LEO","canonical_record":{"source":{"id":"0912.0061","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-12-01T03:14:04Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"c8df075f982f390274409df07fc027d38d48b9335ae0f4d8e78f73056a13690b","abstract_canon_sha256":"33b20bfbae0e7b129975852df94475ec72454da3dbd5a615f518dd2ae207bc0f"},"schema_version":"1.0"},"canonical_sha256":"0957cfac8e02794c79e1afabdb9110b7bad7e224dd3260a12bbb59117556afd8","source":{"kind":"arxiv","id":"0912.0061","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.0061","created_at":"2026-05-18T04:34:37Z"},{"alias_kind":"arxiv_version","alias_value":"0912.0061v4","created_at":"2026-05-18T04:34:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0061","created_at":"2026-05-18T04:34:37Z"},{"alias_kind":"pith_short_12","alias_value":"BFL47LEOAJ4U","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"BFL47LEOAJ4UY6PB","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"BFL47LEO","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:BFL47LEOAJ4UY6PBV6V5XEIQW6","target":"record","payload":{"canonical_record":{"source":{"id":"0912.0061","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-12-01T03:14:04Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"c8df075f982f390274409df07fc027d38d48b9335ae0f4d8e78f73056a13690b","abstract_canon_sha256":"33b20bfbae0e7b129975852df94475ec72454da3dbd5a615f518dd2ae207bc0f"},"schema_version":"1.0"},"canonical_sha256":"0957cfac8e02794c79e1afabdb9110b7bad7e224dd3260a12bbb59117556afd8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:37.258097Z","signature_b64":"kbf7GZmvDyhMtNWh3bp6iC5DtMfs8ObhXJhwEf1ZS2CheEYMYLEsviBi0SeXfppmtOT8iY1o7XB3DTyS0cE9BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0957cfac8e02794c79e1afabdb9110b7bad7e224dd3260a12bbb59117556afd8","last_reissued_at":"2026-05-18T04:34:37.257567Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:37.257567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0912.0061","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:34:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TEvCHl1cIJuUxJXzL9YKOCdjoC9MF9ES1w1mNYf7UfVwaRmeNToECQx8qa+gghGTomGD/ZhX1fkxh4/x2kvbDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:46:18.429996Z"},"content_sha256":"e77f92ff5b1a5efd8674cf6e7b4632792d4337a1019f702cb168079688842673","schema_version":"1.0","event_id":"sha256:e77f92ff5b1a5efd8674cf6e7b4632792d4337a1019f702cb168079688842673"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:BFL47LEOAJ4UY6PBV6V5XEIQW6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On boundaries of Coxeter groups and topological fractal structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Tetsuya Hosaka","submitted_at":"2009-12-01T03:14:04Z","abstract_excerpt":"In this paper, based on research on rank-one isometries by W.Ballmann and M.Brin and recent research on rank-one isometries of Coxeter groups by P.Caprace and K.Fujiwara, we study a topological fractal structure of boundaries of Coxeter groups. We also show that the limit-point set is dense in a boundary of a Coxeter group and introduce some remarks on boundaries of CAT(0) groups with rank-one isometries."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0061","kind":"arxiv","version":4},"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":"2026-05-18T04:34:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WjfN0Q3OcvmN5d22h5Xv0rrThHPh1+ple7HMKDkGceqGlOSVlMbaz3FrXK8gHqQfo5agg7M661hwwrMLEkxfCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:46:18.430339Z"},"content_sha256":"ab7dfe49baba576ef8c39ec00d79faa682c8b0284680b71a2cc36c0b9aa1957e","schema_version":"1.0","event_id":"sha256:ab7dfe49baba576ef8c39ec00d79faa682c8b0284680b71a2cc36c0b9aa1957e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BFL47LEOAJ4UY6PBV6V5XEIQW6/bundle.json","state_url":"https://pith.science/pith/BFL47LEOAJ4UY6PBV6V5XEIQW6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BFL47LEOAJ4UY6PBV6V5XEIQW6/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":"2026-06-25T19:46:18Z","links":{"resolver":"https://pith.science/pith/BFL47LEOAJ4UY6PBV6V5XEIQW6","bundle":"https://pith.science/pith/BFL47LEOAJ4UY6PBV6V5XEIQW6/bundle.json","state":"https://pith.science/pith/BFL47LEOAJ4UY6PBV6V5XEIQW6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BFL47LEOAJ4UY6PBV6V5XEIQW6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:BFL47LEOAJ4UY6PBV6V5XEIQW6","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":"33b20bfbae0e7b129975852df94475ec72454da3dbd5a615f518dd2ae207bc0f","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-12-01T03:14:04Z","title_canon_sha256":"c8df075f982f390274409df07fc027d38d48b9335ae0f4d8e78f73056a13690b"},"schema_version":"1.0","source":{"id":"0912.0061","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.0061","created_at":"2026-05-18T04:34:37Z"},{"alias_kind":"arxiv_version","alias_value":"0912.0061v4","created_at":"2026-05-18T04:34:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0061","created_at":"2026-05-18T04:34:37Z"},{"alias_kind":"pith_short_12","alias_value":"BFL47LEOAJ4U","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"BFL47LEOAJ4UY6PB","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"BFL47LEO","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:ab7dfe49baba576ef8c39ec00d79faa682c8b0284680b71a2cc36c0b9aa1957e","target":"graph","created_at":"2026-05-18T04:34:37Z","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":"In this paper, based on research on rank-one isometries by W.Ballmann and M.Brin and recent research on rank-one isometries of Coxeter groups by P.Caprace and K.Fujiwara, we study a topological fractal structure of boundaries of Coxeter groups. We also show that the limit-point set is dense in a boundary of a Coxeter group and introduce some remarks on boundaries of CAT(0) groups with rank-one isometries.","authors_text":"Tetsuya Hosaka","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-12-01T03:14:04Z","title":"On boundaries of Coxeter groups and topological fractal structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0061","kind":"arxiv","version":4},"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:e77f92ff5b1a5efd8674cf6e7b4632792d4337a1019f702cb168079688842673","target":"record","created_at":"2026-05-18T04:34:37Z","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":"33b20bfbae0e7b129975852df94475ec72454da3dbd5a615f518dd2ae207bc0f","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-12-01T03:14:04Z","title_canon_sha256":"c8df075f982f390274409df07fc027d38d48b9335ae0f4d8e78f73056a13690b"},"schema_version":"1.0","source":{"id":"0912.0061","kind":"arxiv","version":4}},"canonical_sha256":"0957cfac8e02794c79e1afabdb9110b7bad7e224dd3260a12bbb59117556afd8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0957cfac8e02794c79e1afabdb9110b7bad7e224dd3260a12bbb59117556afd8","first_computed_at":"2026-05-18T04:34:37.257567Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:37.257567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kbf7GZmvDyhMtNWh3bp6iC5DtMfs8ObhXJhwEf1ZS2CheEYMYLEsviBi0SeXfppmtOT8iY1o7XB3DTyS0cE9BA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:37.258097Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.0061","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e77f92ff5b1a5efd8674cf6e7b4632792d4337a1019f702cb168079688842673","sha256:ab7dfe49baba576ef8c39ec00d79faa682c8b0284680b71a2cc36c0b9aa1957e"],"state_sha256":"d28c9a562d65723dbb05f5b6109bfb10268e325b69f0146ce9cd723e0af7bbc7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jAdi6VqwtR7Ep5bgwH5RgIjm0UfV8xXTIOiA42Ug54oj5jYjl3RYLPrsretJMfQE44MEuobpIfu3V3rnDvUVBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T19:46:18.432231Z","bundle_sha256":"ec03211618469f6e0032fbdbe27e81f4d14e27a61281cfc49ebd80da785caaf7"}}