{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JXQBDZFTU34QEM7CTQCEYCVKK6","short_pith_number":"pith:JXQBDZFT","canonical_record":{"source":{"id":"1511.03633","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-11T19:59:51Z","cross_cats_sorted":[],"title_canon_sha256":"221bb6dac4982cd57d0b7cb1abb7b0d69a3c6fec9560948b3856fd4b5e4b70d8","abstract_canon_sha256":"ecb5d36d647ce4f80fea24415466b29f6e30a955985509e1c89b5ecfae0be26c"},"schema_version":"1.0"},"canonical_sha256":"4de011e4b3a6f90233e29c044c0aaa5792cd2d88b61fafe4af082b131b5d518f","source":{"kind":"arxiv","id":"1511.03633","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.03633","created_at":"2026-05-18T01:27:08Z"},{"alias_kind":"arxiv_version","alias_value":"1511.03633v1","created_at":"2026-05-18T01:27:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03633","created_at":"2026-05-18T01:27:08Z"},{"alias_kind":"pith_short_12","alias_value":"JXQBDZFTU34Q","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JXQBDZFTU34QEM7C","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JXQBDZFT","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JXQBDZFTU34QEM7CTQCEYCVKK6","target":"record","payload":{"canonical_record":{"source":{"id":"1511.03633","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-11T19:59:51Z","cross_cats_sorted":[],"title_canon_sha256":"221bb6dac4982cd57d0b7cb1abb7b0d69a3c6fec9560948b3856fd4b5e4b70d8","abstract_canon_sha256":"ecb5d36d647ce4f80fea24415466b29f6e30a955985509e1c89b5ecfae0be26c"},"schema_version":"1.0"},"canonical_sha256":"4de011e4b3a6f90233e29c044c0aaa5792cd2d88b61fafe4af082b131b5d518f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:08.555723Z","signature_b64":"UjHM91oqVBF0yE67ICElmHIo5gdPgMAemyax7cKS9DISHRAGeapkvkRMrZY8lZO/ndSeqzjEsB5FjYhV7RulDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4de011e4b3a6f90233e29c044c0aaa5792cd2d88b61fafe4af082b131b5d518f","last_reissued_at":"2026-05-18T01:27:08.555115Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:08.555115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.03633","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":"2026-05-18T01:27:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PEjBocZnMTKmUCpt9/bvw8NiFjc0v5K3xY8vQEqA5s6kV8lFt7RcMhfYJPYBq/CSqLgBLOpdmWs7bi0kBNToBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:15:28.182815Z"},"content_sha256":"cd0fc7cbf8236cc7ab52bd013d503d7c9b88f4b6b0f6e697026d34095abf2c3f","schema_version":"1.0","event_id":"sha256:cd0fc7cbf8236cc7ab52bd013d503d7c9b88f4b6b0f6e697026d34095abf2c3f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JXQBDZFTU34QEM7CTQCEYCVKK6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Expected Regularized Total Variation of Brownian Motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Dunlap","submitted_at":"2015-11-11T19:59:51Z","abstract_excerpt":"We introduce a notion of regularized total variation on an interval for continuous functions with unbounded variation. The definition of regularized total variation is obtained from that of total variation by subtracting a penalty for the size of the partition used to estimate the variation. We present an explicit construction of a partition achieving the regularized total variation, and use this construction to estimate the expected regularized total variation of Brownian motion on an interval."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03633","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":"2026-05-18T01:27:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eTIGK0v7so/LDukyjie/O92B3ecwlQJeK1XR45VmBm89QDpHnS4acwyzs2UJgR9D5Hegn0tACJIH/a6QYo9gDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:15:28.183151Z"},"content_sha256":"9f22b26b865a9275b41948db8059c47e77c5ea86564c8f4ba42bb90eb66af00d","schema_version":"1.0","event_id":"sha256:9f22b26b865a9275b41948db8059c47e77c5ea86564c8f4ba42bb90eb66af00d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JXQBDZFTU34QEM7CTQCEYCVKK6/bundle.json","state_url":"https://pith.science/pith/JXQBDZFTU34QEM7CTQCEYCVKK6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JXQBDZFTU34QEM7CTQCEYCVKK6/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":"2026-06-03T08:15:28Z","links":{"resolver":"https://pith.science/pith/JXQBDZFTU34QEM7CTQCEYCVKK6","bundle":"https://pith.science/pith/JXQBDZFTU34QEM7CTQCEYCVKK6/bundle.json","state":"https://pith.science/pith/JXQBDZFTU34QEM7CTQCEYCVKK6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JXQBDZFTU34QEM7CTQCEYCVKK6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JXQBDZFTU34QEM7CTQCEYCVKK6","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":"ecb5d36d647ce4f80fea24415466b29f6e30a955985509e1c89b5ecfae0be26c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-11T19:59:51Z","title_canon_sha256":"221bb6dac4982cd57d0b7cb1abb7b0d69a3c6fec9560948b3856fd4b5e4b70d8"},"schema_version":"1.0","source":{"id":"1511.03633","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.03633","created_at":"2026-05-18T01:27:08Z"},{"alias_kind":"arxiv_version","alias_value":"1511.03633v1","created_at":"2026-05-18T01:27:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03633","created_at":"2026-05-18T01:27:08Z"},{"alias_kind":"pith_short_12","alias_value":"JXQBDZFTU34Q","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JXQBDZFTU34QEM7C","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JXQBDZFT","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:9f22b26b865a9275b41948db8059c47e77c5ea86564c8f4ba42bb90eb66af00d","target":"graph","created_at":"2026-05-18T01:27:08Z","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 introduce a notion of regularized total variation on an interval for continuous functions with unbounded variation. The definition of regularized total variation is obtained from that of total variation by subtracting a penalty for the size of the partition used to estimate the variation. We present an explicit construction of a partition achieving the regularized total variation, and use this construction to estimate the expected regularized total variation of Brownian motion on an interval.","authors_text":"Alexander Dunlap","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-11T19:59:51Z","title":"Expected Regularized Total Variation of Brownian Motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03633","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:cd0fc7cbf8236cc7ab52bd013d503d7c9b88f4b6b0f6e697026d34095abf2c3f","target":"record","created_at":"2026-05-18T01:27:08Z","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":"ecb5d36d647ce4f80fea24415466b29f6e30a955985509e1c89b5ecfae0be26c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-11T19:59:51Z","title_canon_sha256":"221bb6dac4982cd57d0b7cb1abb7b0d69a3c6fec9560948b3856fd4b5e4b70d8"},"schema_version":"1.0","source":{"id":"1511.03633","kind":"arxiv","version":1}},"canonical_sha256":"4de011e4b3a6f90233e29c044c0aaa5792cd2d88b61fafe4af082b131b5d518f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4de011e4b3a6f90233e29c044c0aaa5792cd2d88b61fafe4af082b131b5d518f","first_computed_at":"2026-05-18T01:27:08.555115Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:08.555115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UjHM91oqVBF0yE67ICElmHIo5gdPgMAemyax7cKS9DISHRAGeapkvkRMrZY8lZO/ndSeqzjEsB5FjYhV7RulDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:08.555723Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.03633","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd0fc7cbf8236cc7ab52bd013d503d7c9b88f4b6b0f6e697026d34095abf2c3f","sha256:9f22b26b865a9275b41948db8059c47e77c5ea86564c8f4ba42bb90eb66af00d"],"state_sha256":"be565dd41404c1865b223057f3c708dda2be58a605b8f251908e3ba38fc900ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CsGkgSjRyeBmCUvinH+lNFBskjBow5ZOfjwK6Pq0jqVVLj5Gw0Pe0l25UzVa71AxhmWHc9DuccFcKFFI+qcCAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T08:15:28.185102Z","bundle_sha256":"45f9c28aca7133dc29628862a7d57da88d37dceafd66b0b03dc265b0615ef72a"}}