{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:USB36X5KIMIOVLALYVM7EJZJND","short_pith_number":"pith:USB36X5K","canonical_record":{"source":{"id":"math/0512340","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"2005-12-14T19:01:48Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"ddb2dbdfb3fd51faec090379265f0987d7a1e0af125a82964df9c2ca93b40b06","abstract_canon_sha256":"4ec87355ec94e352b09a764ff4feb2f26ddf82024db2885f91bd07a988fcea5f"},"schema_version":"1.0"},"canonical_sha256":"a483bf5faa4310eaac0bc559f2272968c254ea653757d51b18c22d4968dc4b97","source":{"kind":"arxiv","id":"math/0512340","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0512340","created_at":"2026-07-04T14:52:15Z"},{"alias_kind":"arxiv_version","alias_value":"math/0512340v1","created_at":"2026-07-04T14:52:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0512340","created_at":"2026-07-04T14:52:15Z"},{"alias_kind":"pith_short_12","alias_value":"USB36X5KIMIO","created_at":"2026-07-04T14:52:15Z"},{"alias_kind":"pith_short_16","alias_value":"USB36X5KIMIOVLAL","created_at":"2026-07-04T14:52:15Z"},{"alias_kind":"pith_short_8","alias_value":"USB36X5K","created_at":"2026-07-04T14:52:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:USB36X5KIMIOVLALYVM7EJZJND","target":"record","payload":{"canonical_record":{"source":{"id":"math/0512340","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"2005-12-14T19:01:48Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"ddb2dbdfb3fd51faec090379265f0987d7a1e0af125a82964df9c2ca93b40b06","abstract_canon_sha256":"4ec87355ec94e352b09a764ff4feb2f26ddf82024db2885f91bd07a988fcea5f"},"schema_version":"1.0"},"canonical_sha256":"a483bf5faa4310eaac0bc559f2272968c254ea653757d51b18c22d4968dc4b97","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:52:15.333189Z","signature_b64":"Ynz8R934VIevg+r087qLx0xBAvBa7HlKYW1I30F6R7568h8OYEyScVmEoGaejAc2OrsMHq038bh2+y4Z9qjKDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a483bf5faa4310eaac0bc559f2272968c254ea653757d51b18c22d4968dc4b97","last_reissued_at":"2026-07-04T14:52:15.332843Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:52:15.332843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0512340","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":"2026-07-04T14:52:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eZX8JF8mmmtTVR2kPu81lF5r0/LiLGJmTl4HMPGA7SzsnRDX3vuDAjrBp+zE2GE/fmnAsFT7ye6dagw4hj/gBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T19:05:20.077252Z"},"content_sha256":"fff174ae41f345089189b75125233afae4f5b2e02ed16969a141f51c6c08f5cf","schema_version":"1.0","event_id":"sha256:fff174ae41f345089189b75125233afae4f5b2e02ed16969a141f51c6c08f5cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:USB36X5KIMIOVLALYVM7EJZJND","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Absolutely continuous functions with values in metric spaces","license":"","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CA","authors_text":"Jakub Duda","submitted_at":"2005-12-14T19:01:48Z","abstract_excerpt":"We present a general theory of absolutely continuous paths with values in metric spaces using the notion of metric derivatives. Among other results, we prove analogues of the Banach-Zarecki and Vallee Poussin theorems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512340","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/math/0512340/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":"2026-07-04T14:52:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lj3+PYQyJsqqIyBYl4KtwhPj56URqqr5hlOoEbQBLmZEtJFOvGDnZBKVCOWyD8Q4+wme26KArYy1PsIWRkfcCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T19:05:20.077679Z"},"content_sha256":"72285c88f5ce81410f0898bd1e7105d84c95ebcd25bfc256ee2577b91b3fac73","schema_version":"1.0","event_id":"sha256:72285c88f5ce81410f0898bd1e7105d84c95ebcd25bfc256ee2577b91b3fac73"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/USB36X5KIMIOVLALYVM7EJZJND/bundle.json","state_url":"https://pith.science/pith/USB36X5KIMIOVLALYVM7EJZJND/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/USB36X5KIMIOVLALYVM7EJZJND/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":"2026-07-06T19:05:20Z","links":{"resolver":"https://pith.science/pith/USB36X5KIMIOVLALYVM7EJZJND","bundle":"https://pith.science/pith/USB36X5KIMIOVLALYVM7EJZJND/bundle.json","state":"https://pith.science/pith/USB36X5KIMIOVLALYVM7EJZJND/state.json","well_known_bundle":"https://pith.science/.well-known/pith/USB36X5KIMIOVLALYVM7EJZJND/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:USB36X5KIMIOVLALYVM7EJZJND","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":"4ec87355ec94e352b09a764ff4feb2f26ddf82024db2885f91bd07a988fcea5f","cross_cats_sorted":["math.MG"],"license":"","primary_cat":"math.CA","submitted_at":"2005-12-14T19:01:48Z","title_canon_sha256":"ddb2dbdfb3fd51faec090379265f0987d7a1e0af125a82964df9c2ca93b40b06"},"schema_version":"1.0","source":{"id":"math/0512340","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0512340","created_at":"2026-07-04T14:52:15Z"},{"alias_kind":"arxiv_version","alias_value":"math/0512340v1","created_at":"2026-07-04T14:52:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0512340","created_at":"2026-07-04T14:52:15Z"},{"alias_kind":"pith_short_12","alias_value":"USB36X5KIMIO","created_at":"2026-07-04T14:52:15Z"},{"alias_kind":"pith_short_16","alias_value":"USB36X5KIMIOVLAL","created_at":"2026-07-04T14:52:15Z"},{"alias_kind":"pith_short_8","alias_value":"USB36X5K","created_at":"2026-07-04T14:52:15Z"}],"graph_snapshots":[{"event_id":"sha256:72285c88f5ce81410f0898bd1e7105d84c95ebcd25bfc256ee2577b91b3fac73","target":"graph","created_at":"2026-07-04T14:52:15Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0512340/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a general theory of absolutely continuous paths with values in metric spaces using the notion of metric derivatives. Among other results, we prove analogues of the Banach-Zarecki and Vallee Poussin theorems.","authors_text":"Jakub Duda","cross_cats":["math.MG"],"headline":"","license":"","primary_cat":"math.CA","submitted_at":"2005-12-14T19:01:48Z","title":"Absolutely continuous functions with values in metric spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512340","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:fff174ae41f345089189b75125233afae4f5b2e02ed16969a141f51c6c08f5cf","target":"record","created_at":"2026-07-04T14:52:15Z","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":"4ec87355ec94e352b09a764ff4feb2f26ddf82024db2885f91bd07a988fcea5f","cross_cats_sorted":["math.MG"],"license":"","primary_cat":"math.CA","submitted_at":"2005-12-14T19:01:48Z","title_canon_sha256":"ddb2dbdfb3fd51faec090379265f0987d7a1e0af125a82964df9c2ca93b40b06"},"schema_version":"1.0","source":{"id":"math/0512340","kind":"arxiv","version":1}},"canonical_sha256":"a483bf5faa4310eaac0bc559f2272968c254ea653757d51b18c22d4968dc4b97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a483bf5faa4310eaac0bc559f2272968c254ea653757d51b18c22d4968dc4b97","first_computed_at":"2026-07-04T14:52:15.332843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:52:15.332843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ynz8R934VIevg+r087qLx0xBAvBa7HlKYW1I30F6R7568h8OYEyScVmEoGaejAc2OrsMHq038bh2+y4Z9qjKDA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:52:15.333189Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0512340","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fff174ae41f345089189b75125233afae4f5b2e02ed16969a141f51c6c08f5cf","sha256:72285c88f5ce81410f0898bd1e7105d84c95ebcd25bfc256ee2577b91b3fac73"],"state_sha256":"448a40fa26c23928214690d809fa1ea57ccc6d9eea9496afb52eeac615bbacf3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YZ8vegtQb1q+ZXyN/7Q48o90SPspgwg+m0Ay6DSzQ63e+AGqvmi8HTtesRvRD63B3aIVqI9HTM8jCdrK3LguBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T19:05:20.079702Z","bundle_sha256":"db6a0c9c4b6081d2b168b4ae73b1d992b5a5ea9fe0ed789fac4f363a5f3e4ce0"}}