{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:MU3YJ32UPSTZ4YNOHWUSUVD5J2","short_pith_number":"pith:MU3YJ32U","canonical_record":{"source":{"id":"1706.06850","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-21T12:09:56Z","cross_cats_sorted":[],"title_canon_sha256":"4ebe9d563efe9b3c022e8b4e93bcaca07de0db41b99e7779c2fdf1781e6283b5","abstract_canon_sha256":"b6543d56df66754a1728d1c3a2bbf436b0ea8811b7b33ae27be7be27a43477dc"},"schema_version":"1.0"},"canonical_sha256":"653784ef547ca79e61ae3da92a547d4e95c26ce3d1398ca84a00c32344bb8dd0","source":{"kind":"arxiv","id":"1706.06850","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.06850","created_at":"2026-05-18T00:24:37Z"},{"alias_kind":"arxiv_version","alias_value":"1706.06850v2","created_at":"2026-05-18T00:24:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06850","created_at":"2026-05-18T00:24:37Z"},{"alias_kind":"pith_short_12","alias_value":"MU3YJ32UPSTZ","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MU3YJ32UPSTZ4YNO","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MU3YJ32U","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:MU3YJ32UPSTZ4YNOHWUSUVD5J2","target":"record","payload":{"canonical_record":{"source":{"id":"1706.06850","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-21T12:09:56Z","cross_cats_sorted":[],"title_canon_sha256":"4ebe9d563efe9b3c022e8b4e93bcaca07de0db41b99e7779c2fdf1781e6283b5","abstract_canon_sha256":"b6543d56df66754a1728d1c3a2bbf436b0ea8811b7b33ae27be7be27a43477dc"},"schema_version":"1.0"},"canonical_sha256":"653784ef547ca79e61ae3da92a547d4e95c26ce3d1398ca84a00c32344bb8dd0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:37.639280Z","signature_b64":"CV1eFcKkDxg8ne3Oj1IR4h22NUPGROgFDqqS8bswUcbGmiJwL2A7HCXGc3NdZ3kJ0r97LdFQcolgm9jo0pg/CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"653784ef547ca79e61ae3da92a547d4e95c26ce3d1398ca84a00c32344bb8dd0","last_reissued_at":"2026-05-18T00:24:37.638682Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:37.638682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.06850","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":"2026-05-18T00:24:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n9nOXpTMdrmD7cWqXpZU/ori3JvaRQeNAPVwK8GyYGNxAQhC6Hwm93fNKR4a+q6KmL/2W4ALZ/jj5vZxO9xdAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:19:15.591379Z"},"content_sha256":"d8c2e63ead38148fb1d6d4e7b0e22fa6beda0c6537508f7430c27bc3ef2c5af6","schema_version":"1.0","event_id":"sha256:d8c2e63ead38148fb1d6d4e7b0e22fa6beda0c6537508f7430c27bc3ef2c5af6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:MU3YJ32UPSTZ4YNOHWUSUVD5J2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractal-Dimensional Properties of Subordinators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Adam Barker","submitted_at":"2017-06-21T12:09:56Z","abstract_excerpt":"This work looks at the box-counting dimension of sets related to subordinators (non-decreasing L\\'evy processes). It was recently shown in [Savov, 2014] that almost surely $\\lim_{\\delta\\to0}U(\\delta)N(t,\\delta) = t$, where $N(t,\\delta)$ is the minimal number of boxes of size at most $\\delta$ needed to cover a subordinator's range up to time $t$, and $U(\\delta)$ is the subordinator's renewal function. Our main result is a central limit theorem (CLT) for $N(t,\\delta)$, complementing and refining work in [Savov, 2014].\n  Box-counting dimension is defined in terms of $N(t,\\delta)$, but for subordi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06850","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":"2026-05-18T00:24:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4G0zIAOaii8iGYhjMU1SUYEKRErclV3RrHylauCb796fs+qlzkll5nv3LS9I8x5/gQ3QN2J0+3zk2v0XOeTBAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:19:15.591724Z"},"content_sha256":"b49eaa5f978e870faf5167c93d91c3504b2fbcb22c35447bbe1b147a1dd45fbe","schema_version":"1.0","event_id":"sha256:b49eaa5f978e870faf5167c93d91c3504b2fbcb22c35447bbe1b147a1dd45fbe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MU3YJ32UPSTZ4YNOHWUSUVD5J2/bundle.json","state_url":"https://pith.science/pith/MU3YJ32UPSTZ4YNOHWUSUVD5J2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MU3YJ32UPSTZ4YNOHWUSUVD5J2/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":"2026-06-03T17:19:15Z","links":{"resolver":"https://pith.science/pith/MU3YJ32UPSTZ4YNOHWUSUVD5J2","bundle":"https://pith.science/pith/MU3YJ32UPSTZ4YNOHWUSUVD5J2/bundle.json","state":"https://pith.science/pith/MU3YJ32UPSTZ4YNOHWUSUVD5J2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MU3YJ32UPSTZ4YNOHWUSUVD5J2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MU3YJ32UPSTZ4YNOHWUSUVD5J2","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":"b6543d56df66754a1728d1c3a2bbf436b0ea8811b7b33ae27be7be27a43477dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-21T12:09:56Z","title_canon_sha256":"4ebe9d563efe9b3c022e8b4e93bcaca07de0db41b99e7779c2fdf1781e6283b5"},"schema_version":"1.0","source":{"id":"1706.06850","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.06850","created_at":"2026-05-18T00:24:37Z"},{"alias_kind":"arxiv_version","alias_value":"1706.06850v2","created_at":"2026-05-18T00:24:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06850","created_at":"2026-05-18T00:24:37Z"},{"alias_kind":"pith_short_12","alias_value":"MU3YJ32UPSTZ","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MU3YJ32UPSTZ4YNO","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MU3YJ32U","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:b49eaa5f978e870faf5167c93d91c3504b2fbcb22c35447bbe1b147a1dd45fbe","target":"graph","created_at":"2026-05-18T00:24:37Z","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":"This work looks at the box-counting dimension of sets related to subordinators (non-decreasing L\\'evy processes). It was recently shown in [Savov, 2014] that almost surely $\\lim_{\\delta\\to0}U(\\delta)N(t,\\delta) = t$, where $N(t,\\delta)$ is the minimal number of boxes of size at most $\\delta$ needed to cover a subordinator's range up to time $t$, and $U(\\delta)$ is the subordinator's renewal function. Our main result is a central limit theorem (CLT) for $N(t,\\delta)$, complementing and refining work in [Savov, 2014].\n  Box-counting dimension is defined in terms of $N(t,\\delta)$, but for subordi","authors_text":"Adam Barker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-21T12:09:56Z","title":"Fractal-Dimensional Properties of Subordinators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06850","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:d8c2e63ead38148fb1d6d4e7b0e22fa6beda0c6537508f7430c27bc3ef2c5af6","target":"record","created_at":"2026-05-18T00:24:37Z","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":"b6543d56df66754a1728d1c3a2bbf436b0ea8811b7b33ae27be7be27a43477dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-21T12:09:56Z","title_canon_sha256":"4ebe9d563efe9b3c022e8b4e93bcaca07de0db41b99e7779c2fdf1781e6283b5"},"schema_version":"1.0","source":{"id":"1706.06850","kind":"arxiv","version":2}},"canonical_sha256":"653784ef547ca79e61ae3da92a547d4e95c26ce3d1398ca84a00c32344bb8dd0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"653784ef547ca79e61ae3da92a547d4e95c26ce3d1398ca84a00c32344bb8dd0","first_computed_at":"2026-05-18T00:24:37.638682Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:37.638682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CV1eFcKkDxg8ne3Oj1IR4h22NUPGROgFDqqS8bswUcbGmiJwL2A7HCXGc3NdZ3kJ0r97LdFQcolgm9jo0pg/CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:37.639280Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.06850","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8c2e63ead38148fb1d6d4e7b0e22fa6beda0c6537508f7430c27bc3ef2c5af6","sha256:b49eaa5f978e870faf5167c93d91c3504b2fbcb22c35447bbe1b147a1dd45fbe"],"state_sha256":"336941af574fac67d240ef3c5c456ae8d8f4759324a339cda6c82b73446d9c51"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YorfngUZcPaVOQoLUZZ6Mzsd+AgOtirZ691I7TN+96dfcB1E+ChmEufsIMgyHDem30bK0VFLPKniRd+OLiInAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T17:19:15.593663Z","bundle_sha256":"2346be1c9ac23cdb6c5199e6954e404b017304bcf9f852c61c835409e8b826f3"}}