{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:VA4OEGIR3EPU36GO26QKP6P2SL","short_pith_number":"pith:VA4OEGIR","canonical_record":{"source":{"id":"2209.14384","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-09-28T19:19:44Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"540bd34d51bf939789321553e1b47652004ffe1451f001ab50b27db15a74ddb9","abstract_canon_sha256":"f1e15d1441a9aa934fee70ba51555afdd3a9ff6de00f690872b773ce4dec3336"},"schema_version":"1.0"},"canonical_sha256":"a838e21911d91f4df8ced7a0a7f9fa92cc5a5b2ddf85fd923fbbf73408cf1f7e","source":{"kind":"arxiv","id":"2209.14384","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.14384","created_at":"2026-07-05T08:24:52Z"},{"alias_kind":"arxiv_version","alias_value":"2209.14384v3","created_at":"2026-07-05T08:24:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.14384","created_at":"2026-07-05T08:24:52Z"},{"alias_kind":"pith_short_12","alias_value":"VA4OEGIR3EPU","created_at":"2026-07-05T08:24:52Z"},{"alias_kind":"pith_short_16","alias_value":"VA4OEGIR3EPU36GO","created_at":"2026-07-05T08:24:52Z"},{"alias_kind":"pith_short_8","alias_value":"VA4OEGIR","created_at":"2026-07-05T08:24:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:VA4OEGIR3EPU36GO26QKP6P2SL","target":"record","payload":{"canonical_record":{"source":{"id":"2209.14384","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-09-28T19:19:44Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"540bd34d51bf939789321553e1b47652004ffe1451f001ab50b27db15a74ddb9","abstract_canon_sha256":"f1e15d1441a9aa934fee70ba51555afdd3a9ff6de00f690872b773ce4dec3336"},"schema_version":"1.0"},"canonical_sha256":"a838e21911d91f4df8ced7a0a7f9fa92cc5a5b2ddf85fd923fbbf73408cf1f7e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:24:52.920139Z","signature_b64":"EynY5NDYlHcW4k60+X4Edb9ZoCKMXE5vARUsEFEBUYPSbaYksu5Sg1JQMtc16DSLdTxpwR0ApyqZFsf8WASLCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a838e21911d91f4df8ced7a0a7f9fa92cc5a5b2ddf85fd923fbbf73408cf1f7e","last_reissued_at":"2026-07-05T08:24:52.919750Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:24:52.919750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2209.14384","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:24:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D9EJt33S86JKTYoDtJHjpC6F+33nrZ2iLALEBhHMbJqx+XMN3jSInzvPKXQkUyWt8QZo+5guLS3siYn+tOWlAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T17:58:42.769502Z"},"content_sha256":"0a1d6c1a58befa1ae74ff4a45873b33a8c4c2983aa99928bf34d7cb8d93ed9a7","schema_version":"1.0","event_id":"sha256:0a1d6c1a58befa1ae74ff4a45873b33a8c4c2983aa99928bf34d7cb8d93ed9a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:VA4OEGIR3EPU36GO26QKP6P2SL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lorentzian metric spaces and their Gromov-Hausdorff convergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.DG","authors_text":"E. Minguzzi, S. Suhr","submitted_at":"2022-09-28T19:19:44Z","abstract_excerpt":"We present an abstract approach to Lorentzian Gromov-Hausdorff distance and convergence, and an alternative approach to Lorentzian length spaces that does not use auxiliary ``positive signature'' metrics or other unobserved fields. We begin by defining a notion of (abstract) bounded Lorentzian-metric space which is sufficiently general to comprise compact causally convex subsets of globally hyperbolic spacetimes and causets. We define the Gromov-Hausdorff distance and show that two bounded Lorentzian-metric spaces at zero GH distance are indeed both isometric and homeomorphic. Then we show how"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.14384","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.14384/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":"2026-07-05T08:24:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/2qFdiguZcCaiufnWgU/YxmLo9bvxP2jPmvSSDh3hWWSbY/pRjdOHMOK+flwBC6kM1l90q+gQv2Dm1AH7PleBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T17:58:42.770019Z"},"content_sha256":"61ac79b0a32e5efc566fcd77e2e5f9c7f640c9fa3b37f38f4a8df2720ccc689a","schema_version":"1.0","event_id":"sha256:61ac79b0a32e5efc566fcd77e2e5f9c7f640c9fa3b37f38f4a8df2720ccc689a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VA4OEGIR3EPU36GO26QKP6P2SL/bundle.json","state_url":"https://pith.science/pith/VA4OEGIR3EPU36GO26QKP6P2SL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VA4OEGIR3EPU36GO26QKP6P2SL/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":"2026-08-09T17:58:42Z","links":{"resolver":"https://pith.science/pith/VA4OEGIR3EPU36GO26QKP6P2SL","bundle":"https://pith.science/pith/VA4OEGIR3EPU36GO26QKP6P2SL/bundle.json","state":"https://pith.science/pith/VA4OEGIR3EPU36GO26QKP6P2SL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VA4OEGIR3EPU36GO26QKP6P2SL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:VA4OEGIR3EPU36GO26QKP6P2SL","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":"f1e15d1441a9aa934fee70ba51555afdd3a9ff6de00f690872b773ce4dec3336","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-09-28T19:19:44Z","title_canon_sha256":"540bd34d51bf939789321553e1b47652004ffe1451f001ab50b27db15a74ddb9"},"schema_version":"1.0","source":{"id":"2209.14384","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.14384","created_at":"2026-07-05T08:24:52Z"},{"alias_kind":"arxiv_version","alias_value":"2209.14384v3","created_at":"2026-07-05T08:24:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.14384","created_at":"2026-07-05T08:24:52Z"},{"alias_kind":"pith_short_12","alias_value":"VA4OEGIR3EPU","created_at":"2026-07-05T08:24:52Z"},{"alias_kind":"pith_short_16","alias_value":"VA4OEGIR3EPU36GO","created_at":"2026-07-05T08:24:52Z"},{"alias_kind":"pith_short_8","alias_value":"VA4OEGIR","created_at":"2026-07-05T08:24:52Z"}],"graph_snapshots":[{"event_id":"sha256:61ac79b0a32e5efc566fcd77e2e5f9c7f640c9fa3b37f38f4a8df2720ccc689a","target":"graph","created_at":"2026-07-05T08:24:52Z","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/2209.14384/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present an abstract approach to Lorentzian Gromov-Hausdorff distance and convergence, and an alternative approach to Lorentzian length spaces that does not use auxiliary ``positive signature'' metrics or other unobserved fields. We begin by defining a notion of (abstract) bounded Lorentzian-metric space which is sufficiently general to comprise compact causally convex subsets of globally hyperbolic spacetimes and causets. We define the Gromov-Hausdorff distance and show that two bounded Lorentzian-metric spaces at zero GH distance are indeed both isometric and homeomorphic. Then we show how","authors_text":"E. Minguzzi, S. Suhr","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-09-28T19:19:44Z","title":"Lorentzian metric spaces and their Gromov-Hausdorff convergence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.14384","kind":"arxiv","version":3},"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":"sha256:0a1d6c1a58befa1ae74ff4a45873b33a8c4c2983aa99928bf34d7cb8d93ed9a7","target":"record","created_at":"2026-07-05T08:24:52Z","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":"f1e15d1441a9aa934fee70ba51555afdd3a9ff6de00f690872b773ce4dec3336","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-09-28T19:19:44Z","title_canon_sha256":"540bd34d51bf939789321553e1b47652004ffe1451f001ab50b27db15a74ddb9"},"schema_version":"1.0","source":{"id":"2209.14384","kind":"arxiv","version":3}},"canonical_sha256":"a838e21911d91f4df8ced7a0a7f9fa92cc5a5b2ddf85fd923fbbf73408cf1f7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a838e21911d91f4df8ced7a0a7f9fa92cc5a5b2ddf85fd923fbbf73408cf1f7e","first_computed_at":"2026-07-05T08:24:52.919750Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:24:52.919750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EynY5NDYlHcW4k60+X4Edb9ZoCKMXE5vARUsEFEBUYPSbaYksu5Sg1JQMtc16DSLdTxpwR0ApyqZFsf8WASLCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:24:52.920139Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.14384","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a1d6c1a58befa1ae74ff4a45873b33a8c4c2983aa99928bf34d7cb8d93ed9a7","sha256:61ac79b0a32e5efc566fcd77e2e5f9c7f640c9fa3b37f38f4a8df2720ccc689a"],"state_sha256":"0bb765a3ba0c850670341344c43b6135721f9d8413b6ca65077b981de2a293d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e8k0OArklnCwRlhCosI6HqX4X6vrKrwI4YYhxKbCxX0/A8dV6SMgnTKHOt4kSym+ZYL/4XhH/vImhb13O9XyDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T17:58:42.774099Z","bundle_sha256":"5f75ae712e5734a1f60c9181e7c6478bf2f4cc9fd2b4c05f32c52f4b2ea6d047"}}