{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:SV4U46ILP7JQRXPLM7IKFEA4CM","short_pith_number":"pith:SV4U46IL","canonical_record":{"source":{"id":"1101.1784","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-01-10T11:50:55Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"9de66457295b27299926fa94d81c52ffaf7d371d311d0de2b8711b469bd67f00","abstract_canon_sha256":"642cac051d45f287705646dc898ff1909bb122573730ebd98c83db7201be46b3"},"schema_version":"1.0"},"canonical_sha256":"95794e790b7fd308ddeb67d0a2901c13013a72cb15567856e187bc9f23754cf7","source":{"kind":"arxiv","id":"1101.1784","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.1784","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"1101.1784v2","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1784","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"SV4U46ILP7JQ","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SV4U46ILP7JQRXPL","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SV4U46IL","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:SV4U46ILP7JQRXPLM7IKFEA4CM","target":"record","payload":{"canonical_record":{"source":{"id":"1101.1784","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-01-10T11:50:55Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"9de66457295b27299926fa94d81c52ffaf7d371d311d0de2b8711b469bd67f00","abstract_canon_sha256":"642cac051d45f287705646dc898ff1909bb122573730ebd98c83db7201be46b3"},"schema_version":"1.0"},"canonical_sha256":"95794e790b7fd308ddeb67d0a2901c13013a72cb15567856e187bc9f23754cf7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:36.766288Z","signature_b64":"ieSFgkK3/I1sNsnSnO3dpmQpuPlOgz8TD6WgZKRdq/lqfj7AIH0zdxqmljfydPScnv6juSoy7APwMB5SaS81BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95794e790b7fd308ddeb67d0a2901c13013a72cb15567856e187bc9f23754cf7","last_reissued_at":"2026-05-17T23:53:36.765439Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:36.765439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.1784","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FH28jEgP7XTsG/9qcjy2gipV9KTMEt3hry54pqccKS+NHLshfNK4rZpoTL4Wu2r+HE6IcKRcUTaPQ61dlApyDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:14:24.680869Z"},"content_sha256":"0a02f707b96e56b8d68daa698c74f624f8aba4e27c3bebf214ce55cd3ebefc6b","schema_version":"1.0","event_id":"sha256:0a02f707b96e56b8d68daa698c74f624f8aba4e27c3bebf214ce55cd3ebefc6b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:SV4U46ILP7JQRXPLM7IKFEA4CM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Connectedness of fractals associated with Arnoux-Rauzy substitutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Anne Siegel, Timo Jolivet, Val\\'erie Berth\\'e","submitted_at":"2011-01-10T11:50:55Z","abstract_excerpt":"Rauzy fractals are compact sets with fractal boundary that can be associated with any unimodular Pisot irreducible substitution. These fractals can be defined as the Hausdorff limit of a sequence of compact sets, where each set is a renormalized projection of a finite union of faces of unit cubes. We exploit this combinatorial definition to prove the connectedness of the Rauzy fractal associated with any finite product of three-letter Arnoux-Rauzy substitutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1784","kind":"arxiv","version":2},"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":"2026-05-17T23:53:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P/AlSpPTUakRcMxYRpmt9w0ondVz+Yg3Q5/kn4F9EkH/Qj/tsFfkrR3N2OrKXpd+kcgz8jWVuVs1W8VOEshnCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:14:24.681221Z"},"content_sha256":"a8eae33e0936d3dea3b9f748ce5bc7fafb65b1b656c26b7907cb867c480f54df","schema_version":"1.0","event_id":"sha256:a8eae33e0936d3dea3b9f748ce5bc7fafb65b1b656c26b7907cb867c480f54df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SV4U46ILP7JQRXPLM7IKFEA4CM/bundle.json","state_url":"https://pith.science/pith/SV4U46ILP7JQRXPLM7IKFEA4CM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SV4U46ILP7JQRXPLM7IKFEA4CM/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":"2026-06-23T07:14:24Z","links":{"resolver":"https://pith.science/pith/SV4U46ILP7JQRXPLM7IKFEA4CM","bundle":"https://pith.science/pith/SV4U46ILP7JQRXPLM7IKFEA4CM/bundle.json","state":"https://pith.science/pith/SV4U46ILP7JQRXPLM7IKFEA4CM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SV4U46ILP7JQRXPLM7IKFEA4CM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SV4U46ILP7JQRXPLM7IKFEA4CM","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":"642cac051d45f287705646dc898ff1909bb122573730ebd98c83db7201be46b3","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-01-10T11:50:55Z","title_canon_sha256":"9de66457295b27299926fa94d81c52ffaf7d371d311d0de2b8711b469bd67f00"},"schema_version":"1.0","source":{"id":"1101.1784","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.1784","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"1101.1784v2","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1784","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"SV4U46ILP7JQ","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SV4U46ILP7JQRXPL","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SV4U46IL","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:a8eae33e0936d3dea3b9f748ce5bc7fafb65b1b656c26b7907cb867c480f54df","target":"graph","created_at":"2026-05-17T23:53:36Z","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":"Rauzy fractals are compact sets with fractal boundary that can be associated with any unimodular Pisot irreducible substitution. These fractals can be defined as the Hausdorff limit of a sequence of compact sets, where each set is a renormalized projection of a finite union of faces of unit cubes. We exploit this combinatorial definition to prove the connectedness of the Rauzy fractal associated with any finite product of three-letter Arnoux-Rauzy substitutions.","authors_text":"Anne Siegel, Timo Jolivet, Val\\'erie Berth\\'e","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-01-10T11:50:55Z","title":"Connectedness of fractals associated with Arnoux-Rauzy substitutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1784","kind":"arxiv","version":2},"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":"sha256:0a02f707b96e56b8d68daa698c74f624f8aba4e27c3bebf214ce55cd3ebefc6b","target":"record","created_at":"2026-05-17T23:53:36Z","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":"642cac051d45f287705646dc898ff1909bb122573730ebd98c83db7201be46b3","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-01-10T11:50:55Z","title_canon_sha256":"9de66457295b27299926fa94d81c52ffaf7d371d311d0de2b8711b469bd67f00"},"schema_version":"1.0","source":{"id":"1101.1784","kind":"arxiv","version":2}},"canonical_sha256":"95794e790b7fd308ddeb67d0a2901c13013a72cb15567856e187bc9f23754cf7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95794e790b7fd308ddeb67d0a2901c13013a72cb15567856e187bc9f23754cf7","first_computed_at":"2026-05-17T23:53:36.765439Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:36.765439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ieSFgkK3/I1sNsnSnO3dpmQpuPlOgz8TD6WgZKRdq/lqfj7AIH0zdxqmljfydPScnv6juSoy7APwMB5SaS81BQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:36.766288Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.1784","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a02f707b96e56b8d68daa698c74f624f8aba4e27c3bebf214ce55cd3ebefc6b","sha256:a8eae33e0936d3dea3b9f748ce5bc7fafb65b1b656c26b7907cb867c480f54df"],"state_sha256":"54dfc3088fb5ff285be54cc00292397845fd8f18b1d29a7e5bc4976f7a3d7310"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O0Du0UYTVwiQJlzce9+byLLSSKub85rMMl6w3PGgD6qyt8CHnHaFoExKKhemk17zak0XuCy1S7kr5fxA4RL1DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T07:14:24.683297Z","bundle_sha256":"3f2a990c918f37ffc20cf66343c7236820b670a268bb26101919d7b063b72ead"}}