{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:INKTZZFH37N7OQCOYUHRCS77GO","short_pith_number":"pith:INKTZZFH","schema_version":"1.0","canonical_sha256":"43553ce4a7dfdbf7404ec50f114bff33a0c93a261db4ae33872c8923e9086ebb","source":{"kind":"arxiv","id":"1608.02016","version":3},"attestation_state":"computed","paper":{"title":"Transporting random measures on the line and embedding excursions into Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"G\\\"unter Last, Hermann Thorisson, Wenpin Tang","submitted_at":"2016-08-05T20:31:54Z","abstract_excerpt":"We consider two jointly stationary and ergodic random measures $\\xi$ and $\\eta$ on the real line $\\mathbb{R}$ with equal intensities. An allocation is an equivariant random mapping from $\\mathbb{R}$ to $\\mathbb{R}$. We give sufficient and partially necessary conditions for the existence of allocations transporting $\\xi$ to $\\eta$. An important ingredient of our approach is to introduce a transport kernel balancing $\\xi$ and $\\eta$, provided these random measures are mutually singular. In the second part of the paper, we apply this result to the path decomposition of a two-sided Brownian motion"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1608.02016","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-05T20:31:54Z","cross_cats_sorted":[],"title_canon_sha256":"8430f80e0515828847d2e8896da7c5c39c3803187009b5f76de7500451958afa","abstract_canon_sha256":"8afdde5efdb8c5789e7677f5ccdf689b40cc82142b7dc3fd3b3353c051077b9e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:45.956600Z","signature_b64":"j4SZDpgywl/OZttK8MZWAjsqQerH9W5RmuIxU6mgMDXQ9S6BaQ4OS1O2LzQApL2lQ+9rxiRlfYa7NiQw6j9nBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43553ce4a7dfdbf7404ec50f114bff33a0c93a261db4ae33872c8923e9086ebb","last_reissued_at":"2026-05-18T00:02:45.956164Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:45.956164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Transporting random measures on the line and embedding excursions into Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"G\\\"unter Last, Hermann Thorisson, Wenpin Tang","submitted_at":"2016-08-05T20:31:54Z","abstract_excerpt":"We consider two jointly stationary and ergodic random measures $\\xi$ and $\\eta$ on the real line $\\mathbb{R}$ with equal intensities. An allocation is an equivariant random mapping from $\\mathbb{R}$ to $\\mathbb{R}$. We give sufficient and partially necessary conditions for the existence of allocations transporting $\\xi$ to $\\eta$. An important ingredient of our approach is to introduce a transport kernel balancing $\\xi$ and $\\eta$, provided these random measures are mutually singular. In the second part of the paper, we apply this result to the path decomposition of a two-sided Brownian motion"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02016","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1608.02016","created_at":"2026-05-18T00:02:45.956223+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.02016v3","created_at":"2026-05-18T00:02:45.956223+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.02016","created_at":"2026-05-18T00:02:45.956223+00:00"},{"alias_kind":"pith_short_12","alias_value":"INKTZZFH37N7","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"INKTZZFH37N7OQCO","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"INKTZZFH","created_at":"2026-05-18T12:30:22.444734+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/INKTZZFH37N7OQCOYUHRCS77GO","json":"https://pith.science/pith/INKTZZFH37N7OQCOYUHRCS77GO.json","graph_json":"https://pith.science/api/pith-number/INKTZZFH37N7OQCOYUHRCS77GO/graph.json","events_json":"https://pith.science/api/pith-number/INKTZZFH37N7OQCOYUHRCS77GO/events.json","paper":"https://pith.science/paper/INKTZZFH"},"agent_actions":{"view_html":"https://pith.science/pith/INKTZZFH37N7OQCOYUHRCS77GO","download_json":"https://pith.science/pith/INKTZZFH37N7OQCOYUHRCS77GO.json","view_paper":"https://pith.science/paper/INKTZZFH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.02016&json=true","fetch_graph":"https://pith.science/api/pith-number/INKTZZFH37N7OQCOYUHRCS77GO/graph.json","fetch_events":"https://pith.science/api/pith-number/INKTZZFH37N7OQCOYUHRCS77GO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/INKTZZFH37N7OQCOYUHRCS77GO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/INKTZZFH37N7OQCOYUHRCS77GO/action/storage_attestation","attest_author":"https://pith.science/pith/INKTZZFH37N7OQCOYUHRCS77GO/action/author_attestation","sign_citation":"https://pith.science/pith/INKTZZFH37N7OQCOYUHRCS77GO/action/citation_signature","submit_replication":"https://pith.science/pith/INKTZZFH37N7OQCOYUHRCS77GO/action/replication_record"}},"created_at":"2026-05-18T00:02:45.956223+00:00","updated_at":"2026-05-18T00:02:45.956223+00:00"}