{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:R74MSXOY76U4EUH6BO6SWHDGUO","short_pith_number":"pith:R74MSXOY","canonical_record":{"source":{"id":"1410.5775","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-10-21T18:28:31Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"bf05bbbd0266e49d78912f19062d7e834348df9b7242fa25257b08a053709ca2","abstract_canon_sha256":"449d07bb0295a3d44e6b1445f3aa4aa02424f3ba5d79c69d590ade39d17247af"},"schema_version":"1.0"},"canonical_sha256":"8ff8c95dd8ffa9c250fe0bbd2b1c66a3aa007712a7cb3e2734e358ac73d119f2","source":{"kind":"arxiv","id":"1410.5775","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5775","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5775v1","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5775","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"pith_short_12","alias_value":"R74MSXOY76U4","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"R74MSXOY76U4EUH6","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"R74MSXOY","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:R74MSXOY76U4EUH6BO6SWHDGUO","target":"record","payload":{"canonical_record":{"source":{"id":"1410.5775","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-10-21T18:28:31Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"bf05bbbd0266e49d78912f19062d7e834348df9b7242fa25257b08a053709ca2","abstract_canon_sha256":"449d07bb0295a3d44e6b1445f3aa4aa02424f3ba5d79c69d590ade39d17247af"},"schema_version":"1.0"},"canonical_sha256":"8ff8c95dd8ffa9c250fe0bbd2b1c66a3aa007712a7cb3e2734e358ac73d119f2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:39.154267Z","signature_b64":"1xJKeLlyvuUlp2W27q+BFs9ciI4hYc7rz3gjWapLr/lazi8k1UxleMfFCzRZ7POkEGWE3u0q8R6Uo+O+uAL0Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ff8c95dd8ffa9c250fe0bbd2b1c66a3aa007712a7cb3e2734e358ac73d119f2","last_reissued_at":"2026-05-18T02:39:39.153742Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:39.153742Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.5775","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:39:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6BK8+IdMkBfEsNDIGyGpiLTSD0RmlNPEDNFSf8uTB8IiEM3x9WmuyVltwRwjy6VNSP+mUAQBHajYevEnl3n4Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:24:16.670552Z"},"content_sha256":"2849c40277dce872918514690bf42ec347549ef9cd20c1bca05b1624490f2eb0","schema_version":"1.0","event_id":"sha256:2849c40277dce872918514690bf42ec347549ef9cd20c1bca05b1624490f2eb0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:R74MSXOY76U4EUH6BO6SWHDGUO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic billiards for sampling from the boundary of a convex set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.PR","authors_text":"A. B. Dieker, Santosh Vempala","submitted_at":"2014-10-21T18:28:31Z","abstract_excerpt":"Stochastic billiards can be used for approximate sampling from the boundary of a bounded convex set through the Markov Chain Monte Carlo (MCMC) paradigm. This paper studies how many steps of the underlying Markov chain are required to get samples (approximately) from the uniform distribution on the boundary of the set, for sets with an upper bound on the curvature of the boundary. Our main theorem implies a polynomial-time algorithm for sampling from the boundary of such sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5775","kind":"arxiv","version":1},"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":"2026-05-18T02:39:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E+BJRLcaBTV8x8QMjsZYAQvHenL/jMhRv6qqvIRmBnKn5/YDvz99OYy4EaQgZJkqP/Lbzl9Vg2/YoyauOxkCDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:24:16.671202Z"},"content_sha256":"ff6f7c2af40d4e48ad0d2e0323fb603d5a9dbab76c61f5df4a2441c8d357de8c","schema_version":"1.0","event_id":"sha256:ff6f7c2af40d4e48ad0d2e0323fb603d5a9dbab76c61f5df4a2441c8d357de8c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R74MSXOY76U4EUH6BO6SWHDGUO/bundle.json","state_url":"https://pith.science/pith/R74MSXOY76U4EUH6BO6SWHDGUO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R74MSXOY76U4EUH6BO6SWHDGUO/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":"2026-06-01T13:24:16Z","links":{"resolver":"https://pith.science/pith/R74MSXOY76U4EUH6BO6SWHDGUO","bundle":"https://pith.science/pith/R74MSXOY76U4EUH6BO6SWHDGUO/bundle.json","state":"https://pith.science/pith/R74MSXOY76U4EUH6BO6SWHDGUO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R74MSXOY76U4EUH6BO6SWHDGUO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:R74MSXOY76U4EUH6BO6SWHDGUO","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":"449d07bb0295a3d44e6b1445f3aa4aa02424f3ba5d79c69d590ade39d17247af","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-10-21T18:28:31Z","title_canon_sha256":"bf05bbbd0266e49d78912f19062d7e834348df9b7242fa25257b08a053709ca2"},"schema_version":"1.0","source":{"id":"1410.5775","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5775","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5775v1","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5775","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"pith_short_12","alias_value":"R74MSXOY76U4","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"R74MSXOY76U4EUH6","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"R74MSXOY","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:ff6f7c2af40d4e48ad0d2e0323fb603d5a9dbab76c61f5df4a2441c8d357de8c","target":"graph","created_at":"2026-05-18T02:39:39Z","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":"Stochastic billiards can be used for approximate sampling from the boundary of a bounded convex set through the Markov Chain Monte Carlo (MCMC) paradigm. This paper studies how many steps of the underlying Markov chain are required to get samples (approximately) from the uniform distribution on the boundary of the set, for sets with an upper bound on the curvature of the boundary. Our main theorem implies a polynomial-time algorithm for sampling from the boundary of such sets.","authors_text":"A. B. Dieker, Santosh Vempala","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-10-21T18:28:31Z","title":"Stochastic billiards for sampling from the boundary of a convex set"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5775","kind":"arxiv","version":1},"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":"sha256:2849c40277dce872918514690bf42ec347549ef9cd20c1bca05b1624490f2eb0","target":"record","created_at":"2026-05-18T02:39:39Z","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":"449d07bb0295a3d44e6b1445f3aa4aa02424f3ba5d79c69d590ade39d17247af","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-10-21T18:28:31Z","title_canon_sha256":"bf05bbbd0266e49d78912f19062d7e834348df9b7242fa25257b08a053709ca2"},"schema_version":"1.0","source":{"id":"1410.5775","kind":"arxiv","version":1}},"canonical_sha256":"8ff8c95dd8ffa9c250fe0bbd2b1c66a3aa007712a7cb3e2734e358ac73d119f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ff8c95dd8ffa9c250fe0bbd2b1c66a3aa007712a7cb3e2734e358ac73d119f2","first_computed_at":"2026-05-18T02:39:39.153742Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:39.153742Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1xJKeLlyvuUlp2W27q+BFs9ciI4hYc7rz3gjWapLr/lazi8k1UxleMfFCzRZ7POkEGWE3u0q8R6Uo+O+uAL0Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:39.154267Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.5775","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2849c40277dce872918514690bf42ec347549ef9cd20c1bca05b1624490f2eb0","sha256:ff6f7c2af40d4e48ad0d2e0323fb603d5a9dbab76c61f5df4a2441c8d357de8c"],"state_sha256":"a4f66eb6ece550e9619034bc5f95da12c276630e74fb827b07a01fd3e60ee899"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+ZtwcBrSfbQfEHOJ0qQh4+qFKQTKIN6+cunX32gYwlHoLS8cFntivzWT6A+H+Cxjk4x226YZ1aB5E8UnlsUeAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T13:24:16.674290Z","bundle_sha256":"896311d382966b3e6f255225676a5ffec51b36b3796bebb806ac5fb9bba5e001"}}