{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:LOBOBFWJUL7EELABN4LV33X32K","short_pith_number":"pith:LOBOBFWJ","canonical_record":{"source":{"id":"1411.4522","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-11-17T15:59:31Z","cross_cats_sorted":[],"title_canon_sha256":"e5989e98126ad82a369dc74e493555ee3579bb240ff6049974f170a7c7dcdc8d","abstract_canon_sha256":"460352cb7a1d0adcb04d17538e860bf672cfe24b02b86996b8b482369052126c"},"schema_version":"1.0"},"canonical_sha256":"5b82e096c9a2fe422c016f175deefbd2ad4af582270e59d39144ccb8a5cc478d","source":{"kind":"arxiv","id":"1411.4522","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4522","created_at":"2026-05-18T01:55:52Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4522v2","created_at":"2026-05-18T01:55:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4522","created_at":"2026-05-18T01:55:52Z"},{"alias_kind":"pith_short_12","alias_value":"LOBOBFWJUL7E","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LOBOBFWJUL7EELAB","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LOBOBFWJ","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:LOBOBFWJUL7EELABN4LV33X32K","target":"record","payload":{"canonical_record":{"source":{"id":"1411.4522","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-11-17T15:59:31Z","cross_cats_sorted":[],"title_canon_sha256":"e5989e98126ad82a369dc74e493555ee3579bb240ff6049974f170a7c7dcdc8d","abstract_canon_sha256":"460352cb7a1d0adcb04d17538e860bf672cfe24b02b86996b8b482369052126c"},"schema_version":"1.0"},"canonical_sha256":"5b82e096c9a2fe422c016f175deefbd2ad4af582270e59d39144ccb8a5cc478d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:52.963451Z","signature_b64":"TUx88bgmyLdPiIEJ08Hk8bHvUvYpT9TUKx+xR9zBYSxCpv6Zvdjfi6eACds1ibe/SPIqARcO15ARmyZZS+sNBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b82e096c9a2fe422c016f175deefbd2ad4af582270e59d39144ccb8a5cc478d","last_reissued_at":"2026-05-18T01:55:52.963003Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:52.963003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.4522","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":"2026-05-18T01:55:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nWnX1pgqv7vManx9MpdT+OcgPsOaLAwqqa5c6k9j8qO9opskwhBlEvjmIskeegMGopnjf0NQ4Rko42pOEgkTDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T17:33:56.461156Z"},"content_sha256":"f0ce8effacd47f69acef71c4b82a08717d97871903096622df8c474fc5af1894","schema_version":"1.0","event_id":"sha256:f0ce8effacd47f69acef71c4b82a08717d97871903096622df8c474fc5af1894"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:LOBOBFWJUL7EELABN4LV33X32K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equidistribution and measure rigidity under $\\times p,\\times q$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Huichi Huang","submitted_at":"2014-11-17T15:59:31Z","abstract_excerpt":"We show that equidistribution of irrational orbits on the unit circle implies Furstenberg's conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4522","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":"2026-05-18T01:55:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"llD+emABCkWlhuNQ9WrQ2MbAkMSHg55mEb9ivnYpOM3L/JyalDYPcI8ivlVwxDu/2oA+MxV4OhxdfWq5yjb5Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T17:33:56.461504Z"},"content_sha256":"248ed0cdeaa4988876b378f225cc1cc68e87a8737489a0ff7bfbcb69670a9270","schema_version":"1.0","event_id":"sha256:248ed0cdeaa4988876b378f225cc1cc68e87a8737489a0ff7bfbcb69670a9270"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LOBOBFWJUL7EELABN4LV33X32K/bundle.json","state_url":"https://pith.science/pith/LOBOBFWJUL7EELABN4LV33X32K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LOBOBFWJUL7EELABN4LV33X32K/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":"2026-06-24T17:33:56Z","links":{"resolver":"https://pith.science/pith/LOBOBFWJUL7EELABN4LV33X32K","bundle":"https://pith.science/pith/LOBOBFWJUL7EELABN4LV33X32K/bundle.json","state":"https://pith.science/pith/LOBOBFWJUL7EELABN4LV33X32K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LOBOBFWJUL7EELABN4LV33X32K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LOBOBFWJUL7EELABN4LV33X32K","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":"460352cb7a1d0adcb04d17538e860bf672cfe24b02b86996b8b482369052126c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-11-17T15:59:31Z","title_canon_sha256":"e5989e98126ad82a369dc74e493555ee3579bb240ff6049974f170a7c7dcdc8d"},"schema_version":"1.0","source":{"id":"1411.4522","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4522","created_at":"2026-05-18T01:55:52Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4522v2","created_at":"2026-05-18T01:55:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4522","created_at":"2026-05-18T01:55:52Z"},{"alias_kind":"pith_short_12","alias_value":"LOBOBFWJUL7E","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LOBOBFWJUL7EELAB","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LOBOBFWJ","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:248ed0cdeaa4988876b378f225cc1cc68e87a8737489a0ff7bfbcb69670a9270","target":"graph","created_at":"2026-05-18T01:55:52Z","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 show that equidistribution of irrational orbits on the unit circle implies Furstenberg's conjecture.","authors_text":"Huichi Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-11-17T15:59:31Z","title":"Equidistribution and measure rigidity under $\\times p,\\times q$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4522","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:f0ce8effacd47f69acef71c4b82a08717d97871903096622df8c474fc5af1894","target":"record","created_at":"2026-05-18T01:55:52Z","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":"460352cb7a1d0adcb04d17538e860bf672cfe24b02b86996b8b482369052126c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-11-17T15:59:31Z","title_canon_sha256":"e5989e98126ad82a369dc74e493555ee3579bb240ff6049974f170a7c7dcdc8d"},"schema_version":"1.0","source":{"id":"1411.4522","kind":"arxiv","version":2}},"canonical_sha256":"5b82e096c9a2fe422c016f175deefbd2ad4af582270e59d39144ccb8a5cc478d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b82e096c9a2fe422c016f175deefbd2ad4af582270e59d39144ccb8a5cc478d","first_computed_at":"2026-05-18T01:55:52.963003Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:52.963003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TUx88bgmyLdPiIEJ08Hk8bHvUvYpT9TUKx+xR9zBYSxCpv6Zvdjfi6eACds1ibe/SPIqARcO15ARmyZZS+sNBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:52.963451Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.4522","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0ce8effacd47f69acef71c4b82a08717d97871903096622df8c474fc5af1894","sha256:248ed0cdeaa4988876b378f225cc1cc68e87a8737489a0ff7bfbcb69670a9270"],"state_sha256":"73bf1af1aef4b647ead2d72faa2157eb8f0ddf2d01f7bfdba569273a65761a0b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ROPqO5DBE58n3+Zk8e2v1oaUDjiJLSQsDiOXYqqG9AJ1gxnmE3Sm3szi2jXmWZ65o6wQqscGDsZJLEuJkC0xCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T17:33:56.463472Z","bundle_sha256":"33b752d4b33d6f3b120f9a4aee2acfef135c8f952f83011167ceb42277128c69"}}