{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YM2C7M4WT6WY2Q4HP754Q4F4CV","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":"43a0eb454d80ee05983b3260fbba06ba51a46ea4947727b2bf8fab00db60c7c8","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-24T19:12:35Z","title_canon_sha256":"80cf9745c1951033e235c6b656fc9cb31441e90542b4e7279f38b38058028b3f"},"schema_version":"1.0","source":{"id":"1111.5837","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.5837","created_at":"2026-05-18T01:18:15Z"},{"alias_kind":"arxiv_version","alias_value":"1111.5837v4","created_at":"2026-05-18T01:18:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5837","created_at":"2026-05-18T01:18:15Z"},{"alias_kind":"pith_short_12","alias_value":"YM2C7M4WT6WY","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YM2C7M4WT6WY2Q4H","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YM2C7M4W","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:f02b4fa8eba38246e8d3c280407f0f68563c2b84fa77f77a2d525dbedadb92d3","target":"graph","created_at":"2026-05-18T01:18:15Z","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":"The space of metric measure spaces (complete separable metric spaces with a probability measure) is becoming more and more important as state space for stochastic processes. Of particular interest is the subspace of (continuum) metric measure trees. Greven, Pfaffelhuber and Winter introduced the Gromov-Prohorov metric d_{GPW} on the space of metric measure spaces and showed that it induces the Gromov-weak topology. They also conjectured that this topology coincides with the topology induced by Gromov's Box_1 metric. Here, we show that this is indeed true, and the metrics are even bi-Lipschitz ","authors_text":"Wolfgang L\\\"ohr","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-24T19:12:35Z","title":"Equivalence of Gromov-Prohorov- and Gromov's Box-Metric on the Space of Metric Measure Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5837","kind":"arxiv","version":4},"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:e84140e7339d66b2ab2d2785341e972d5e9911ec2c51a1ee8b6be9cacf185bbc","target":"record","created_at":"2026-05-18T01:18:15Z","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":"43a0eb454d80ee05983b3260fbba06ba51a46ea4947727b2bf8fab00db60c7c8","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-24T19:12:35Z","title_canon_sha256":"80cf9745c1951033e235c6b656fc9cb31441e90542b4e7279f38b38058028b3f"},"schema_version":"1.0","source":{"id":"1111.5837","kind":"arxiv","version":4}},"canonical_sha256":"c3342fb3969fad8d43877ffbc870bc15512404410d73e14d1aaeb7e33805c0de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3342fb3969fad8d43877ffbc870bc15512404410d73e14d1aaeb7e33805c0de","first_computed_at":"2026-05-18T01:18:15.432386Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:15.432386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BebKmjurlM7syg6bMNchb0qR02qLVGzowYqSiggzW1v3I5+EGVNP8ZdhtEfD+vjK2QKPq+RxKrvm0TVfs+dsBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:15.433001Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.5837","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e84140e7339d66b2ab2d2785341e972d5e9911ec2c51a1ee8b6be9cacf185bbc","sha256:f02b4fa8eba38246e8d3c280407f0f68563c2b84fa77f77a2d525dbedadb92d3"],"state_sha256":"1bfbaa22ad5370a65338c3930064badcdd3fabfc99e1d7b1130a84a9bb852db2"}