{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:6MIQO5G6DU4CWUVE2EBU2DHFLZ","short_pith_number":"pith:6MIQO5G6","canonical_record":{"source":{"id":"2506.04154","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2025-06-04T16:51:28Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"b1d1729c543a2ab9d04db9e381f81a52b6dc52d1d5581c1636c2c8ee61b72a6d","abstract_canon_sha256":"e5558658a980d3d28aeeab039cd00a8924ce90e5f3e031793ce99f3dac9c527c"},"schema_version":"1.0"},"canonical_sha256":"f3110774de1d382b52a4d1034d0ce55e78fb31f57ddc0e85635097ee5cc37f6f","source":{"kind":"arxiv","id":"2506.04154","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.04154","created_at":"2026-07-05T11:15:58Z"},{"alias_kind":"arxiv_version","alias_value":"2506.04154v1","created_at":"2026-07-05T11:15:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.04154","created_at":"2026-07-05T11:15:58Z"},{"alias_kind":"pith_short_12","alias_value":"6MIQO5G6DU4C","created_at":"2026-07-05T11:15:58Z"},{"alias_kind":"pith_short_16","alias_value":"6MIQO5G6DU4CWUVE","created_at":"2026-07-05T11:15:58Z"},{"alias_kind":"pith_short_8","alias_value":"6MIQO5G6","created_at":"2026-07-05T11:15:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:6MIQO5G6DU4CWUVE2EBU2DHFLZ","target":"record","payload":{"canonical_record":{"source":{"id":"2506.04154","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2025-06-04T16:51:28Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"b1d1729c543a2ab9d04db9e381f81a52b6dc52d1d5581c1636c2c8ee61b72a6d","abstract_canon_sha256":"e5558658a980d3d28aeeab039cd00a8924ce90e5f3e031793ce99f3dac9c527c"},"schema_version":"1.0"},"canonical_sha256":"f3110774de1d382b52a4d1034d0ce55e78fb31f57ddc0e85635097ee5cc37f6f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:15:58.111530Z","signature_b64":"+dYzPky3X9Zf6JZlui8QcJo8FFDQgbD3QUojJdaUOY2vExv0uRWYIyPJanzm6Su56fTt1uKva5HrI9sfGlFNAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3110774de1d382b52a4d1034d0ce55e78fb31f57ddc0e85635097ee5cc37f6f","last_reissued_at":"2026-07-05T11:15:58.111059Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:15:58.111059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.04154","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:15:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5FVURZ8Cs07+bVzi+4gnNAxv7DV+rkvmw32ZaSkIRiE+0mQmC0twKGJF5hs7WoL816jMpzF8p8YnKwfZfMLJAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T13:16:33.905004Z"},"content_sha256":"f43184cf4ae62a8e88f5a4367710eb0d460761aa75007e1faa0478c88200023e","schema_version":"1.0","event_id":"sha256:f43184cf4ae62a8e88f5a4367710eb0d460761aa75007e1faa0478c88200023e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:6MIQO5G6DU4CWUVE2EBU2DHFLZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Metric functionals and weak convergence","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.FA","authors_text":"Armando W. Guti\\'errez, Olavi Nevanlinna","submitted_at":"2025-06-04T16:51:28Z","abstract_excerpt":"We introduce a notion of weak convergence in arbitrary metric spaces. Metric functionals are key in our analysis: weak convergence of sequences in a given metric space is tested against all the metric functionals defined on said space. When restricted to bounded sequences in normed linear spaces, we prove that our notion of weak convergence agrees with the standard one."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04154","kind":"arxiv","version":1},"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/2506.04154/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":"2026-07-05T11:15:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xvaz/hRPG06u6gJfqaeqyMohWDaOXPdyxM/GCuleXpi4q5fFwbAr8HzH3u+H3MCk4KaNLqK8Zb+MrNXBqwttCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T13:16:33.905512Z"},"content_sha256":"7232600d7a9145be8ab7e2fa2d9ed843298ebe27b02116d07e089b680dd890b3","schema_version":"1.0","event_id":"sha256:7232600d7a9145be8ab7e2fa2d9ed843298ebe27b02116d07e089b680dd890b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6MIQO5G6DU4CWUVE2EBU2DHFLZ/bundle.json","state_url":"https://pith.science/pith/6MIQO5G6DU4CWUVE2EBU2DHFLZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6MIQO5G6DU4CWUVE2EBU2DHFLZ/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":"2026-08-08T13:16:33Z","links":{"resolver":"https://pith.science/pith/6MIQO5G6DU4CWUVE2EBU2DHFLZ","bundle":"https://pith.science/pith/6MIQO5G6DU4CWUVE2EBU2DHFLZ/bundle.json","state":"https://pith.science/pith/6MIQO5G6DU4CWUVE2EBU2DHFLZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6MIQO5G6DU4CWUVE2EBU2DHFLZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:6MIQO5G6DU4CWUVE2EBU2DHFLZ","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":"e5558658a980d3d28aeeab039cd00a8924ce90e5f3e031793ce99f3dac9c527c","cross_cats_sorted":["math.MG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2025-06-04T16:51:28Z","title_canon_sha256":"b1d1729c543a2ab9d04db9e381f81a52b6dc52d1d5581c1636c2c8ee61b72a6d"},"schema_version":"1.0","source":{"id":"2506.04154","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.04154","created_at":"2026-07-05T11:15:58Z"},{"alias_kind":"arxiv_version","alias_value":"2506.04154v1","created_at":"2026-07-05T11:15:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.04154","created_at":"2026-07-05T11:15:58Z"},{"alias_kind":"pith_short_12","alias_value":"6MIQO5G6DU4C","created_at":"2026-07-05T11:15:58Z"},{"alias_kind":"pith_short_16","alias_value":"6MIQO5G6DU4CWUVE","created_at":"2026-07-05T11:15:58Z"},{"alias_kind":"pith_short_8","alias_value":"6MIQO5G6","created_at":"2026-07-05T11:15:58Z"}],"graph_snapshots":[{"event_id":"sha256:7232600d7a9145be8ab7e2fa2d9ed843298ebe27b02116d07e089b680dd890b3","target":"graph","created_at":"2026-07-05T11:15:58Z","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/2506.04154/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a notion of weak convergence in arbitrary metric spaces. Metric functionals are key in our analysis: weak convergence of sequences in a given metric space is tested against all the metric functionals defined on said space. When restricted to bounded sequences in normed linear spaces, we prove that our notion of weak convergence agrees with the standard one.","authors_text":"Armando W. Guti\\'errez, Olavi Nevanlinna","cross_cats":["math.MG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2025-06-04T16:51:28Z","title":"Metric functionals and weak convergence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04154","kind":"arxiv","version":1},"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:f43184cf4ae62a8e88f5a4367710eb0d460761aa75007e1faa0478c88200023e","target":"record","created_at":"2026-07-05T11:15:58Z","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":"e5558658a980d3d28aeeab039cd00a8924ce90e5f3e031793ce99f3dac9c527c","cross_cats_sorted":["math.MG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2025-06-04T16:51:28Z","title_canon_sha256":"b1d1729c543a2ab9d04db9e381f81a52b6dc52d1d5581c1636c2c8ee61b72a6d"},"schema_version":"1.0","source":{"id":"2506.04154","kind":"arxiv","version":1}},"canonical_sha256":"f3110774de1d382b52a4d1034d0ce55e78fb31f57ddc0e85635097ee5cc37f6f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3110774de1d382b52a4d1034d0ce55e78fb31f57ddc0e85635097ee5cc37f6f","first_computed_at":"2026-07-05T11:15:58.111059Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:15:58.111059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+dYzPky3X9Zf6JZlui8QcJo8FFDQgbD3QUojJdaUOY2vExv0uRWYIyPJanzm6Su56fTt1uKva5HrI9sfGlFNAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:15:58.111530Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.04154","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f43184cf4ae62a8e88f5a4367710eb0d460761aa75007e1faa0478c88200023e","sha256:7232600d7a9145be8ab7e2fa2d9ed843298ebe27b02116d07e089b680dd890b3"],"state_sha256":"9f17f4eba34409fff3cf5b7221b2c86370acdaeb2ec69202830553901107874a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hIGZ9fZRHWNpXZzXBH6AKsBRnoKYqdTBYnGGsNtZvZCLHLgEt/RN3aZ+rB+SyNJWris2RCKe/M4E7HVtUlTZCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T13:16:33.911001Z","bundle_sha256":"fa172759aa9ebfaa2c48e632eafab5fa39b0c62cbcd7ab816203969cecaf4bde"}}