{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JGSZK6TX7KJECTDTMVYDF56DAT","short_pith_number":"pith:JGSZK6TX","canonical_record":{"source":{"id":"1504.02965","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-12T12:33:08Z","cross_cats_sorted":[],"title_canon_sha256":"9eacc223a504d8708a11c0c3aed129a737f04c9ea71047ef7195c0c4612641c4","abstract_canon_sha256":"c794dd312b783d5ba5b2e1e8eac250025ac73b9bed12c59009d47a520499497a"},"schema_version":"1.0"},"canonical_sha256":"49a5957a77fa92414c73657032f7c304e660a6542f866073f2884f5ddd25fe9c","source":{"kind":"arxiv","id":"1504.02965","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.02965","created_at":"2026-05-18T00:47:29Z"},{"alias_kind":"arxiv_version","alias_value":"1504.02965v2","created_at":"2026-05-18T00:47:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02965","created_at":"2026-05-18T00:47:29Z"},{"alias_kind":"pith_short_12","alias_value":"JGSZK6TX7KJE","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JGSZK6TX7KJECTDT","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JGSZK6TX","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JGSZK6TX7KJECTDTMVYDF56DAT","target":"record","payload":{"canonical_record":{"source":{"id":"1504.02965","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-12T12:33:08Z","cross_cats_sorted":[],"title_canon_sha256":"9eacc223a504d8708a11c0c3aed129a737f04c9ea71047ef7195c0c4612641c4","abstract_canon_sha256":"c794dd312b783d5ba5b2e1e8eac250025ac73b9bed12c59009d47a520499497a"},"schema_version":"1.0"},"canonical_sha256":"49a5957a77fa92414c73657032f7c304e660a6542f866073f2884f5ddd25fe9c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:29.643884Z","signature_b64":"qRav9hBFZivs4gM3TmsNn6U6R65tNPq0rQT6/O7DXAZ/F6KWA8vi6oR1WAsIZVkL5hT7dK76HOOstt5LvYQ8CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49a5957a77fa92414c73657032f7c304e660a6542f866073f2884f5ddd25fe9c","last_reissued_at":"2026-05-18T00:47:29.643169Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:29.643169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.02965","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":"2026-05-18T00:47:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VrdPq63XSc7CSdqYY3FwGulEECZ/Zs3wJowA6obfyE5Gqkh/k1d8zIYPKWDjUhq+vw9BhcOkml2k7Gfcu6l4Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T22:57:26.198515Z"},"content_sha256":"56e6bbfd40ee8562d1cf90b02c36b87692d0893519bec2515adf198c188b70ec","schema_version":"1.0","event_id":"sha256:56e6bbfd40ee8562d1cf90b02c36b87692d0893519bec2515adf198c188b70ec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JGSZK6TX7KJECTDTMVYDF56DAT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stable transports between stationary random measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ali Khezeli, Mir-Omid Haji-Mirsadeghi","submitted_at":"2015-04-12T12:33:08Z","abstract_excerpt":"We give an algorithm to construct a translation-invariant transport kernel between ergodic stationary random measures $\\Phi$ and $\\Psi$ on $\\mathbb R^d$, given that they have equal intensities. As a result, this yields a construction of a shift-coupling of an ergodic stationary random measure and its Palm version. This algorithm constructs the transport kernel in a deterministic manner given realizations $\\varphi$ and $\\psi$ of the measures. The (non-constructive) existence of such a transport kernel was proved in [8]. Our algorithm is a generalization of the work of [3], in which a constructi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02965","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":"2026-05-18T00:47:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"csuGkcXeVm+XZLVqUcYdVqHJakVrm/JORkwaGntjDt02vOVtQoR/2lt4ETosL22a24QgiviGICiXkfPk1OScAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T22:57:26.199077Z"},"content_sha256":"5a5d80955be09fc5fdb99623172f8ccb4407c699a41caed830a70a9211bcfdec","schema_version":"1.0","event_id":"sha256:5a5d80955be09fc5fdb99623172f8ccb4407c699a41caed830a70a9211bcfdec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JGSZK6TX7KJECTDTMVYDF56DAT/bundle.json","state_url":"https://pith.science/pith/JGSZK6TX7KJECTDTMVYDF56DAT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JGSZK6TX7KJECTDTMVYDF56DAT/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":"2026-07-01T22:57:26Z","links":{"resolver":"https://pith.science/pith/JGSZK6TX7KJECTDTMVYDF56DAT","bundle":"https://pith.science/pith/JGSZK6TX7KJECTDTMVYDF56DAT/bundle.json","state":"https://pith.science/pith/JGSZK6TX7KJECTDTMVYDF56DAT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JGSZK6TX7KJECTDTMVYDF56DAT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JGSZK6TX7KJECTDTMVYDF56DAT","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":"c794dd312b783d5ba5b2e1e8eac250025ac73b9bed12c59009d47a520499497a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-12T12:33:08Z","title_canon_sha256":"9eacc223a504d8708a11c0c3aed129a737f04c9ea71047ef7195c0c4612641c4"},"schema_version":"1.0","source":{"id":"1504.02965","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.02965","created_at":"2026-05-18T00:47:29Z"},{"alias_kind":"arxiv_version","alias_value":"1504.02965v2","created_at":"2026-05-18T00:47:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02965","created_at":"2026-05-18T00:47:29Z"},{"alias_kind":"pith_short_12","alias_value":"JGSZK6TX7KJE","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JGSZK6TX7KJECTDT","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JGSZK6TX","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:5a5d80955be09fc5fdb99623172f8ccb4407c699a41caed830a70a9211bcfdec","target":"graph","created_at":"2026-05-18T00:47:29Z","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 give an algorithm to construct a translation-invariant transport kernel between ergodic stationary random measures $\\Phi$ and $\\Psi$ on $\\mathbb R^d$, given that they have equal intensities. As a result, this yields a construction of a shift-coupling of an ergodic stationary random measure and its Palm version. This algorithm constructs the transport kernel in a deterministic manner given realizations $\\varphi$ and $\\psi$ of the measures. The (non-constructive) existence of such a transport kernel was proved in [8]. Our algorithm is a generalization of the work of [3], in which a constructi","authors_text":"Ali Khezeli, Mir-Omid Haji-Mirsadeghi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-12T12:33:08Z","title":"Stable transports between stationary random measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02965","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":"sha256:56e6bbfd40ee8562d1cf90b02c36b87692d0893519bec2515adf198c188b70ec","target":"record","created_at":"2026-05-18T00:47:29Z","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":"c794dd312b783d5ba5b2e1e8eac250025ac73b9bed12c59009d47a520499497a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-12T12:33:08Z","title_canon_sha256":"9eacc223a504d8708a11c0c3aed129a737f04c9ea71047ef7195c0c4612641c4"},"schema_version":"1.0","source":{"id":"1504.02965","kind":"arxiv","version":2}},"canonical_sha256":"49a5957a77fa92414c73657032f7c304e660a6542f866073f2884f5ddd25fe9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49a5957a77fa92414c73657032f7c304e660a6542f866073f2884f5ddd25fe9c","first_computed_at":"2026-05-18T00:47:29.643169Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:29.643169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qRav9hBFZivs4gM3TmsNn6U6R65tNPq0rQT6/O7DXAZ/F6KWA8vi6oR1WAsIZVkL5hT7dK76HOOstt5LvYQ8CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:29.643884Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.02965","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56e6bbfd40ee8562d1cf90b02c36b87692d0893519bec2515adf198c188b70ec","sha256:5a5d80955be09fc5fdb99623172f8ccb4407c699a41caed830a70a9211bcfdec"],"state_sha256":"6b81dde2bf20aa31b40a5244f07647a4e5bfd40f2de2dcc489cabb3f5e369456"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EL5d0uGk3WV1tSiWdNtdca4sisj4rvbX4D3bTWc6svetoIW4UV2J721UB5ZWiHcCpgzoFnD+icuLKNSkpASSCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T22:57:26.202685Z","bundle_sha256":"e30817b5c281a32aaf8b9fbef50165b813b712748799b778b2adccf33a267a89"}}