{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:MHFDXOKKRWQWFXLGURDCJDT26A","short_pith_number":"pith:MHFDXOKK","canonical_record":{"source":{"id":"1405.6312","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-05-24T15:24:29Z","cross_cats_sorted":[],"title_canon_sha256":"ac2646880242bd4bf49b8cd399b84aaf0d66ca6ae8cf12a1dd427bcdbdfe06a6","abstract_canon_sha256":"74d2e3a64e733ac393eaa3bddfca0031ae1c123eaf2ebca54312c27435f8f9ac"},"schema_version":"1.0"},"canonical_sha256":"61ca3bb94a8da162dd66a446248e7af034f8f79b3df646358a3279611d2a3bae","source":{"kind":"arxiv","id":"1405.6312","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6312","created_at":"2026-05-18T02:50:22Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6312v3","created_at":"2026-05-18T02:50:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6312","created_at":"2026-05-18T02:50:22Z"},{"alias_kind":"pith_short_12","alias_value":"MHFDXOKKRWQW","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MHFDXOKKRWQWFXLG","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MHFDXOKK","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:MHFDXOKKRWQWFXLGURDCJDT26A","target":"record","payload":{"canonical_record":{"source":{"id":"1405.6312","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-05-24T15:24:29Z","cross_cats_sorted":[],"title_canon_sha256":"ac2646880242bd4bf49b8cd399b84aaf0d66ca6ae8cf12a1dd427bcdbdfe06a6","abstract_canon_sha256":"74d2e3a64e733ac393eaa3bddfca0031ae1c123eaf2ebca54312c27435f8f9ac"},"schema_version":"1.0"},"canonical_sha256":"61ca3bb94a8da162dd66a446248e7af034f8f79b3df646358a3279611d2a3bae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:22.491570Z","signature_b64":"t6HyQFB3z24R/Z9OuvvxckQylo0ryArrckdmCVO0VVyPxj5MtSi3BCsXKHzFWbwJ41n8cUHJhVjiRkC9uiGKDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61ca3bb94a8da162dd66a446248e7af034f8f79b3df646358a3279611d2a3bae","last_reissued_at":"2026-05-18T02:50:22.490899Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:22.490899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.6312","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:50:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hmeNAyHkRKtDThrc9WJ01/jDyykmAZVmSDyqDnx4cJhFBgbe1WIw5C6KJ/g2zVAjFxUx8ukKDEX5dLQ6wF6MBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:09:36.209821Z"},"content_sha256":"ca0425b872d0e3cba26698b4327b229c2a7f8682211a744885fe335a0cacffef","schema_version":"1.0","event_id":"sha256:ca0425b872d0e3cba26698b4327b229c2a7f8682211a744885fe335a0cacffef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:MHFDXOKKRWQWFXLGURDCJDT26A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On zeros of Martin-L\\\"of random Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Kelty Allen, Laurent Bienvenu, Theodore Slaman","submitted_at":"2014-05-24T15:24:29Z","abstract_excerpt":"We investigate the sample path properties of Martin-L\\\"of random Brownian motion. We show (1) that many classical results which are known to hold almost surely hold for every Martin-L\\\"of random Brownian path, (2) that the effective dimension of zeroes of a Martin-L\\\"of random Brownian path must be at least 1/2, and conversely that every real with effective dimension greater than 1/2 must be a zero of some Martin-L\\\"of random Brownian path, and (3) we will demonstrate a new proof that the solution to the Dirichlet problem in the plane is computable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6312","kind":"arxiv","version":3},"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":"2026-05-18T02:50:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c9N3EhXJ3FVP4v2Qg9tNeSgdzCz1dy+Q9muY/II6ETnNbN5K8SvRsCwbDhAN2B90fpu+Wf/XdzCA5CDE8bDUCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:09:36.210510Z"},"content_sha256":"bc90d0a77f73b658b0d2cd769e86eab671fe60910d6339c1aca9be9c70f64120","schema_version":"1.0","event_id":"sha256:bc90d0a77f73b658b0d2cd769e86eab671fe60910d6339c1aca9be9c70f64120"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MHFDXOKKRWQWFXLGURDCJDT26A/bundle.json","state_url":"https://pith.science/pith/MHFDXOKKRWQWFXLGURDCJDT26A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MHFDXOKKRWQWFXLGURDCJDT26A/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":"2026-05-26T00:09:36Z","links":{"resolver":"https://pith.science/pith/MHFDXOKKRWQWFXLGURDCJDT26A","bundle":"https://pith.science/pith/MHFDXOKKRWQWFXLGURDCJDT26A/bundle.json","state":"https://pith.science/pith/MHFDXOKKRWQWFXLGURDCJDT26A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MHFDXOKKRWQWFXLGURDCJDT26A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MHFDXOKKRWQWFXLGURDCJDT26A","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":"74d2e3a64e733ac393eaa3bddfca0031ae1c123eaf2ebca54312c27435f8f9ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-05-24T15:24:29Z","title_canon_sha256":"ac2646880242bd4bf49b8cd399b84aaf0d66ca6ae8cf12a1dd427bcdbdfe06a6"},"schema_version":"1.0","source":{"id":"1405.6312","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6312","created_at":"2026-05-18T02:50:22Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6312v3","created_at":"2026-05-18T02:50:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6312","created_at":"2026-05-18T02:50:22Z"},{"alias_kind":"pith_short_12","alias_value":"MHFDXOKKRWQW","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MHFDXOKKRWQWFXLG","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MHFDXOKK","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:bc90d0a77f73b658b0d2cd769e86eab671fe60910d6339c1aca9be9c70f64120","target":"graph","created_at":"2026-05-18T02:50:22Z","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 investigate the sample path properties of Martin-L\\\"of random Brownian motion. We show (1) that many classical results which are known to hold almost surely hold for every Martin-L\\\"of random Brownian path, (2) that the effective dimension of zeroes of a Martin-L\\\"of random Brownian path must be at least 1/2, and conversely that every real with effective dimension greater than 1/2 must be a zero of some Martin-L\\\"of random Brownian path, and (3) we will demonstrate a new proof that the solution to the Dirichlet problem in the plane is computable.","authors_text":"Kelty Allen, Laurent Bienvenu, Theodore Slaman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-05-24T15:24:29Z","title":"On zeros of Martin-L\\\"of random Brownian motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6312","kind":"arxiv","version":3},"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:ca0425b872d0e3cba26698b4327b229c2a7f8682211a744885fe335a0cacffef","target":"record","created_at":"2026-05-18T02:50:22Z","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":"74d2e3a64e733ac393eaa3bddfca0031ae1c123eaf2ebca54312c27435f8f9ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-05-24T15:24:29Z","title_canon_sha256":"ac2646880242bd4bf49b8cd399b84aaf0d66ca6ae8cf12a1dd427bcdbdfe06a6"},"schema_version":"1.0","source":{"id":"1405.6312","kind":"arxiv","version":3}},"canonical_sha256":"61ca3bb94a8da162dd66a446248e7af034f8f79b3df646358a3279611d2a3bae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61ca3bb94a8da162dd66a446248e7af034f8f79b3df646358a3279611d2a3bae","first_computed_at":"2026-05-18T02:50:22.490899Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:22.490899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t6HyQFB3z24R/Z9OuvvxckQylo0ryArrckdmCVO0VVyPxj5MtSi3BCsXKHzFWbwJ41n8cUHJhVjiRkC9uiGKDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:22.491570Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.6312","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca0425b872d0e3cba26698b4327b229c2a7f8682211a744885fe335a0cacffef","sha256:bc90d0a77f73b658b0d2cd769e86eab671fe60910d6339c1aca9be9c70f64120"],"state_sha256":"6db093690da79baa36d61dd1c9a2902eed4e9e94658c490d96fd6162c86f0c7a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4iR1QWEfzyC2nPa5ouv3sEw/5UCIdAlYKB8GtSGMEGXf6wAnPopZshJJHNShn8WXpLEZ1lUNh/enGBD6lD3hAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T00:09:36.214390Z","bundle_sha256":"f02a7c85e60c962f1617c510b12769979afcb7c127b0fb4b773502911fef363c"}}