{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:GWGBSGIKQRXKU2SZXTJOR5E3NZ","short_pith_number":"pith:GWGBSGIK","canonical_record":{"source":{"id":"1803.06201","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-03-16T12:59:39Z","cross_cats_sorted":[],"title_canon_sha256":"1a3a214fb213cd23a3b0315375864c8e601378d58dc6b496c94b00d0744d256b","abstract_canon_sha256":"812b8fd89d075b131c581e44486df3954e92c07532f3aac5f80231cfec9c011b"},"schema_version":"1.0"},"canonical_sha256":"358c19190a846eaa6a59bcd2e8f49b6e55087f946a32144c4986d7555cb7f3bf","source":{"kind":"arxiv","id":"1803.06201","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.06201","created_at":"2026-05-17T23:56:29Z"},{"alias_kind":"arxiv_version","alias_value":"1803.06201v2","created_at":"2026-05-17T23:56:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.06201","created_at":"2026-05-17T23:56:29Z"},{"alias_kind":"pith_short_12","alias_value":"GWGBSGIKQRXK","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GWGBSGIKQRXKU2SZ","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GWGBSGIK","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:GWGBSGIKQRXKU2SZXTJOR5E3NZ","target":"record","payload":{"canonical_record":{"source":{"id":"1803.06201","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-03-16T12:59:39Z","cross_cats_sorted":[],"title_canon_sha256":"1a3a214fb213cd23a3b0315375864c8e601378d58dc6b496c94b00d0744d256b","abstract_canon_sha256":"812b8fd89d075b131c581e44486df3954e92c07532f3aac5f80231cfec9c011b"},"schema_version":"1.0"},"canonical_sha256":"358c19190a846eaa6a59bcd2e8f49b6e55087f946a32144c4986d7555cb7f3bf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:29.934044Z","signature_b64":"UKzYlQ/fRqgSEpzi9WKVVb3ceBFBhdwERIhh6PdJITy2zDf8rc4+awTLzrEPEJqARqU8VMWvA4LUhacS8sKQCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"358c19190a846eaa6a59bcd2e8f49b6e55087f946a32144c4986d7555cb7f3bf","last_reissued_at":"2026-05-17T23:56:29.933682Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:29.933682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.06201","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":"2026-05-17T23:56:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cZ/qiqGgbEcUFa0McmE9yEc8pM2fosf2Va+gWWhJvs7oEqSMa16hK9meb1+sgnE2dTWJPHDLphJNfNBXqcj1CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:18:44.085179Z"},"content_sha256":"ea663fcef36de95e2b97d96edbd38331c9be56b065934c01217f6f7eb6a347dd","schema_version":"1.0","event_id":"sha256:ea663fcef36de95e2b97d96edbd38331c9be56b065934c01217f6f7eb6a347dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:GWGBSGIKQRXKU2SZXTJOR5E3NZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mobius disjointness conjecture for local dendrite maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"el Houcein el Abdalaoui, Ghassen Askri, Habib Marzougui","submitted_at":"2018-03-16T12:59:39Z","abstract_excerpt":"We prove that the M\\\"obius disjointness conjecture holds for graph maps and for all monotone local dendrite maps. We further show that this also hold for continuous map on certain class of dendrites. Moreover, we see that there is a transitive dendrite map with zero entropy for which M\\\"obius disjointness holds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06201","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":"2026-05-17T23:56:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IgtFL0B7x61NY6HJeja//sa+t775FP5JhhJq4aeVYH4FTzD3qw0n/navE/c2ioO1vBYSiXR9gZ0yafkfPbUdCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:18:44.085567Z"},"content_sha256":"cc3ca059b9dd8267b183513f3a15a7c2b51ee68e198bd5c2bacf63a3280b812d","schema_version":"1.0","event_id":"sha256:cc3ca059b9dd8267b183513f3a15a7c2b51ee68e198bd5c2bacf63a3280b812d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GWGBSGIKQRXKU2SZXTJOR5E3NZ/bundle.json","state_url":"https://pith.science/pith/GWGBSGIKQRXKU2SZXTJOR5E3NZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GWGBSGIKQRXKU2SZXTJOR5E3NZ/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":"2026-06-01T19:18:44Z","links":{"resolver":"https://pith.science/pith/GWGBSGIKQRXKU2SZXTJOR5E3NZ","bundle":"https://pith.science/pith/GWGBSGIKQRXKU2SZXTJOR5E3NZ/bundle.json","state":"https://pith.science/pith/GWGBSGIKQRXKU2SZXTJOR5E3NZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GWGBSGIKQRXKU2SZXTJOR5E3NZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GWGBSGIKQRXKU2SZXTJOR5E3NZ","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":"812b8fd89d075b131c581e44486df3954e92c07532f3aac5f80231cfec9c011b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-03-16T12:59:39Z","title_canon_sha256":"1a3a214fb213cd23a3b0315375864c8e601378d58dc6b496c94b00d0744d256b"},"schema_version":"1.0","source":{"id":"1803.06201","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.06201","created_at":"2026-05-17T23:56:29Z"},{"alias_kind":"arxiv_version","alias_value":"1803.06201v2","created_at":"2026-05-17T23:56:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.06201","created_at":"2026-05-17T23:56:29Z"},{"alias_kind":"pith_short_12","alias_value":"GWGBSGIKQRXK","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GWGBSGIKQRXKU2SZ","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GWGBSGIK","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:cc3ca059b9dd8267b183513f3a15a7c2b51ee68e198bd5c2bacf63a3280b812d","target":"graph","created_at":"2026-05-17T23:56:29Z","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":"We prove that the M\\\"obius disjointness conjecture holds for graph maps and for all monotone local dendrite maps. We further show that this also hold for continuous map on certain class of dendrites. Moreover, we see that there is a transitive dendrite map with zero entropy for which M\\\"obius disjointness holds.","authors_text":"el Houcein el Abdalaoui, Ghassen Askri, Habib Marzougui","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-03-16T12:59:39Z","title":"Mobius disjointness conjecture for local dendrite maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06201","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:ea663fcef36de95e2b97d96edbd38331c9be56b065934c01217f6f7eb6a347dd","target":"record","created_at":"2026-05-17T23:56:29Z","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":"812b8fd89d075b131c581e44486df3954e92c07532f3aac5f80231cfec9c011b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-03-16T12:59:39Z","title_canon_sha256":"1a3a214fb213cd23a3b0315375864c8e601378d58dc6b496c94b00d0744d256b"},"schema_version":"1.0","source":{"id":"1803.06201","kind":"arxiv","version":2}},"canonical_sha256":"358c19190a846eaa6a59bcd2e8f49b6e55087f946a32144c4986d7555cb7f3bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"358c19190a846eaa6a59bcd2e8f49b6e55087f946a32144c4986d7555cb7f3bf","first_computed_at":"2026-05-17T23:56:29.933682Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:29.933682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UKzYlQ/fRqgSEpzi9WKVVb3ceBFBhdwERIhh6PdJITy2zDf8rc4+awTLzrEPEJqARqU8VMWvA4LUhacS8sKQCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:29.934044Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.06201","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea663fcef36de95e2b97d96edbd38331c9be56b065934c01217f6f7eb6a347dd","sha256:cc3ca059b9dd8267b183513f3a15a7c2b51ee68e198bd5c2bacf63a3280b812d"],"state_sha256":"e25c210a27d70214d676be6cf58caa46447774a53e3f313bc14cdfa56b294e79"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SJcser5uQLED0WsFba4GxbMGNu4vRpbZ9t9qgfYj6ZIRWo/PLt6IUhIMrs4rVJt7npn2rcLoFnZrfU8bNVRIDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T19:18:44.088085Z","bundle_sha256":"f2804ea1083d1950630f4d60d96918f1417469acd1e2f0af3b9652bc545a8b5a"}}