{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:SQK4LYWKNW2D73LSDWDX7YCDFY","short_pith_number":"pith:SQK4LYWK","canonical_record":{"source":{"id":"2404.19681","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2024-04-30T16:16:30Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"8a8efce2f8e1ab0ae7959e3b080941ef817f4ac8cc84646e451c313e5beae8f5","abstract_canon_sha256":"8956936ad2a851ac48ef44afd05b23b81655f5c97f1c019c4c66cf19a59f1dad"},"schema_version":"1.0"},"canonical_sha256":"9415c5e2ca6db43fed721d877fe0432e271ff67d85956aaf69a34eef45e25d9d","source":{"kind":"arxiv","id":"2404.19681","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.19681","created_at":"2026-07-05T12:05:08Z"},{"alias_kind":"arxiv_version","alias_value":"2404.19681v2","created_at":"2026-07-05T12:05:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.19681","created_at":"2026-07-05T12:05:08Z"},{"alias_kind":"pith_short_12","alias_value":"SQK4LYWKNW2D","created_at":"2026-07-05T12:05:08Z"},{"alias_kind":"pith_short_16","alias_value":"SQK4LYWKNW2D73LS","created_at":"2026-07-05T12:05:08Z"},{"alias_kind":"pith_short_8","alias_value":"SQK4LYWK","created_at":"2026-07-05T12:05:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:SQK4LYWKNW2D73LSDWDX7YCDFY","target":"record","payload":{"canonical_record":{"source":{"id":"2404.19681","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2024-04-30T16:16:30Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"8a8efce2f8e1ab0ae7959e3b080941ef817f4ac8cc84646e451c313e5beae8f5","abstract_canon_sha256":"8956936ad2a851ac48ef44afd05b23b81655f5c97f1c019c4c66cf19a59f1dad"},"schema_version":"1.0"},"canonical_sha256":"9415c5e2ca6db43fed721d877fe0432e271ff67d85956aaf69a34eef45e25d9d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:05:08.480649Z","signature_b64":"5nA64+RAtRSAy5gZD7kGDHUCkNSfB8rCfGHEbCdR1HxVrOP8trg1ywclVI6r31AvjoWZPntebOmfAumpVDdXAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9415c5e2ca6db43fed721d877fe0432e271ff67d85956aaf69a34eef45e25d9d","last_reissued_at":"2026-07-05T12:05:08.480090Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:05:08.480090Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.19681","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":"2026-07-05T12:05:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Bev1p91+DLzdwXcxrSisz3crPPVu+fGmd+2aY1ATmMcGrhIfJ5wdFYXDFCKl6xAmuIE+zadZbdFoneGnwNBBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T04:54:39.681965Z"},"content_sha256":"0ef2a3e554d17edce3d2fb04bd101a6280382bfa973c4df3a454d4a2b157a418","schema_version":"1.0","event_id":"sha256:0ef2a3e554d17edce3d2fb04bd101a6280382bfa973c4df3a454d4a2b157a418"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:SQK4LYWKNW2D73LSDWDX7YCDFY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Metrization of Gromov-Hausdorff-type topologies on boundedly-compact metric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.MG","authors_text":"Ryoichiro Noda","submitted_at":"2024-04-30T16:16:30Z","abstract_excerpt":"We present a new general framework for metrization of Gromov-Hausdorff-type topologies on non-compact metric spaces. We also give easy-to-check conditions for separability and completeness and hence the measure theoretic requirements are provided to study convergence of random spaces with additional random objects. In particular, our framework enables us to define a metric inducing a suitable Gromov-Hausdorff-type topology on the space of rooted boundedly-compact metric spaces with laws of stochastic processes and/or random fields, which was not clear how to do in previous frameworks. In addit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.19681","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.19681/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T12:05:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AuxOhZDNKlN/3ElaGRN64T20kNlhQ8G46lJH5bBxbHBIJBgWXD8G9dqPxioTPnuSwwE0Zw0OGUsWGSc4TXndBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T04:54:39.682475Z"},"content_sha256":"16437514aa03aedfa99c5f77b1e40d74d04a948334582de2122362367e22306c","schema_version":"1.0","event_id":"sha256:16437514aa03aedfa99c5f77b1e40d74d04a948334582de2122362367e22306c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SQK4LYWKNW2D73LSDWDX7YCDFY/bundle.json","state_url":"https://pith.science/pith/SQK4LYWKNW2D73LSDWDX7YCDFY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SQK4LYWKNW2D73LSDWDX7YCDFY/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":"2026-08-12T04:54:39Z","links":{"resolver":"https://pith.science/pith/SQK4LYWKNW2D73LSDWDX7YCDFY","bundle":"https://pith.science/pith/SQK4LYWKNW2D73LSDWDX7YCDFY/bundle.json","state":"https://pith.science/pith/SQK4LYWKNW2D73LSDWDX7YCDFY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SQK4LYWKNW2D73LSDWDX7YCDFY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:SQK4LYWKNW2D73LSDWDX7YCDFY","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":"8956936ad2a851ac48ef44afd05b23b81655f5c97f1c019c4c66cf19a59f1dad","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2024-04-30T16:16:30Z","title_canon_sha256":"8a8efce2f8e1ab0ae7959e3b080941ef817f4ac8cc84646e451c313e5beae8f5"},"schema_version":"1.0","source":{"id":"2404.19681","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.19681","created_at":"2026-07-05T12:05:08Z"},{"alias_kind":"arxiv_version","alias_value":"2404.19681v2","created_at":"2026-07-05T12:05:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.19681","created_at":"2026-07-05T12:05:08Z"},{"alias_kind":"pith_short_12","alias_value":"SQK4LYWKNW2D","created_at":"2026-07-05T12:05:08Z"},{"alias_kind":"pith_short_16","alias_value":"SQK4LYWKNW2D73LS","created_at":"2026-07-05T12:05:08Z"},{"alias_kind":"pith_short_8","alias_value":"SQK4LYWK","created_at":"2026-07-05T12:05:08Z"}],"graph_snapshots":[{"event_id":"sha256:16437514aa03aedfa99c5f77b1e40d74d04a948334582de2122362367e22306c","target":"graph","created_at":"2026-07-05T12:05:08Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.19681/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a new general framework for metrization of Gromov-Hausdorff-type topologies on non-compact metric spaces. We also give easy-to-check conditions for separability and completeness and hence the measure theoretic requirements are provided to study convergence of random spaces with additional random objects. In particular, our framework enables us to define a metric inducing a suitable Gromov-Hausdorff-type topology on the space of rooted boundedly-compact metric spaces with laws of stochastic processes and/or random fields, which was not clear how to do in previous frameworks. In addit","authors_text":"Ryoichiro Noda","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2024-04-30T16:16:30Z","title":"Metrization of Gromov-Hausdorff-type topologies on boundedly-compact metric spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.19681","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":"sha256:0ef2a3e554d17edce3d2fb04bd101a6280382bfa973c4df3a454d4a2b157a418","target":"record","created_at":"2026-07-05T12:05:08Z","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":"8956936ad2a851ac48ef44afd05b23b81655f5c97f1c019c4c66cf19a59f1dad","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2024-04-30T16:16:30Z","title_canon_sha256":"8a8efce2f8e1ab0ae7959e3b080941ef817f4ac8cc84646e451c313e5beae8f5"},"schema_version":"1.0","source":{"id":"2404.19681","kind":"arxiv","version":2}},"canonical_sha256":"9415c5e2ca6db43fed721d877fe0432e271ff67d85956aaf69a34eef45e25d9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9415c5e2ca6db43fed721d877fe0432e271ff67d85956aaf69a34eef45e25d9d","first_computed_at":"2026-07-05T12:05:08.480090Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:05:08.480090Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5nA64+RAtRSAy5gZD7kGDHUCkNSfB8rCfGHEbCdR1HxVrOP8trg1ywclVI6r31AvjoWZPntebOmfAumpVDdXAg==","signature_status":"signed_v1","signed_at":"2026-07-05T12:05:08.480649Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.19681","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ef2a3e554d17edce3d2fb04bd101a6280382bfa973c4df3a454d4a2b157a418","sha256:16437514aa03aedfa99c5f77b1e40d74d04a948334582de2122362367e22306c"],"state_sha256":"eb64cf992f48bfbd9caa5c9e0fd726f52afe2d75b47d420be83b44b5b1eb155d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8vRUXFTvJtzTZ7z7ip1Q3XVU0K1v1HvVIXOIbf+uxNsQVcbNKnFH8gqgG1xvxxtjk/x8bH7Mc5QTRnb/NadEDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T04:54:39.687130Z","bundle_sha256":"63e3858787c700bec32b1540ad69e2224e1c1cecb4c57b14bfaae123a7492ecf"}}