{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:EAGW35AYK5U3HDAAA3HSROZWNT","short_pith_number":"pith:EAGW35AY","canonical_record":{"source":{"id":"1811.07233","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-17T22:13:52Z","cross_cats_sorted":[],"title_canon_sha256":"ce589892b1bc5030a4abea04019f7d5515859dd5e9535f33df6d090a04d7a2c2","abstract_canon_sha256":"eb29d14538a1b3d359a7cd0adc69588d751224619bd692e199a1defdeab9770d"},"schema_version":"1.0"},"canonical_sha256":"200d6df4185769b38c0006cf28bb366cf96659a44979987cc1412571df02d3bd","source":{"kind":"arxiv","id":"1811.07233","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.07233","created_at":"2026-05-18T00:00:28Z"},{"alias_kind":"arxiv_version","alias_value":"1811.07233v1","created_at":"2026-05-18T00:00:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.07233","created_at":"2026-05-18T00:00:28Z"},{"alias_kind":"pith_short_12","alias_value":"EAGW35AYK5U3","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EAGW35AYK5U3HDAA","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EAGW35AY","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:EAGW35AYK5U3HDAAA3HSROZWNT","target":"record","payload":{"canonical_record":{"source":{"id":"1811.07233","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-17T22:13:52Z","cross_cats_sorted":[],"title_canon_sha256":"ce589892b1bc5030a4abea04019f7d5515859dd5e9535f33df6d090a04d7a2c2","abstract_canon_sha256":"eb29d14538a1b3d359a7cd0adc69588d751224619bd692e199a1defdeab9770d"},"schema_version":"1.0"},"canonical_sha256":"200d6df4185769b38c0006cf28bb366cf96659a44979987cc1412571df02d3bd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:28.565654Z","signature_b64":"o2jnw1aM482qwxOgT4iw/CkUuUaW2ppslCNGGGBfwFQeyB72WmPOB1yTpLhr/D//d5WGOJuNK5hBd8Vxu7LGDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"200d6df4185769b38c0006cf28bb366cf96659a44979987cc1412571df02d3bd","last_reissued_at":"2026-05-18T00:00:28.565004Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:28.565004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.07233","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":"2026-05-18T00:00:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CuWVa3wItAmXlFYNcQ7u3hvMQyjtvkls5dR8TOHR9b1hMOcZcthx96RSUqVYuhozYvhssg9s3vj6GBRxZUy2Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T07:25:04.062677Z"},"content_sha256":"75a53ebcb21cdf7c084792fb8c49996fe29e8e0279babf034008737ca4cbe138","schema_version":"1.0","event_id":"sha256:75a53ebcb21cdf7c084792fb8c49996fe29e8e0279babf034008737ca4cbe138"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:EAGW35AYK5U3HDAAA3HSROZWNT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multivariate Bounded Variation Functions of Jordan-Wiener Type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. Brudnyi, Yu. Brudnyi","submitted_at":"2018-11-17T22:13:52Z","abstract_excerpt":"We introduce and study spaces of multivariate functions of bounded variation generalizing the classical Jordan and Wiener spaces. Multivariate generalizations of the Jordan space were given by several prominent researchers but each of them preserved only some special properties of the space used further in few selected applications. Unlike this the multivariate generalization of the Jordan space presented in this paper preserves all known and reveals some previously unknown properties of the space. These, in turn, are special cases of the basic properties of the introduced spaces proved in the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07233","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":""},"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":"2026-05-18T00:00:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7QFSYq8ZTOAc0IUqYtr30x3G9sE4moYh3OeLoDpRAKfysp3ID5AcxC2Ud8OQfhPEqH5sgzOvalmLq8yNJF32AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T07:25:04.063041Z"},"content_sha256":"4ae01d23e199cd2d6a8844f9d6ef9850e9fe3222edfc751cd487af2fd4dc5bd1","schema_version":"1.0","event_id":"sha256:4ae01d23e199cd2d6a8844f9d6ef9850e9fe3222edfc751cd487af2fd4dc5bd1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EAGW35AYK5U3HDAAA3HSROZWNT/bundle.json","state_url":"https://pith.science/pith/EAGW35AYK5U3HDAAA3HSROZWNT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EAGW35AYK5U3HDAAA3HSROZWNT/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":"2026-07-02T07:25:04Z","links":{"resolver":"https://pith.science/pith/EAGW35AYK5U3HDAAA3HSROZWNT","bundle":"https://pith.science/pith/EAGW35AYK5U3HDAAA3HSROZWNT/bundle.json","state":"https://pith.science/pith/EAGW35AYK5U3HDAAA3HSROZWNT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EAGW35AYK5U3HDAAA3HSROZWNT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EAGW35AYK5U3HDAAA3HSROZWNT","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":"eb29d14538a1b3d359a7cd0adc69588d751224619bd692e199a1defdeab9770d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-17T22:13:52Z","title_canon_sha256":"ce589892b1bc5030a4abea04019f7d5515859dd5e9535f33df6d090a04d7a2c2"},"schema_version":"1.0","source":{"id":"1811.07233","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.07233","created_at":"2026-05-18T00:00:28Z"},{"alias_kind":"arxiv_version","alias_value":"1811.07233v1","created_at":"2026-05-18T00:00:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.07233","created_at":"2026-05-18T00:00:28Z"},{"alias_kind":"pith_short_12","alias_value":"EAGW35AYK5U3","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EAGW35AYK5U3HDAA","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EAGW35AY","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:4ae01d23e199cd2d6a8844f9d6ef9850e9fe3222edfc751cd487af2fd4dc5bd1","target":"graph","created_at":"2026-05-18T00:00:28Z","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":"We introduce and study spaces of multivariate functions of bounded variation generalizing the classical Jordan and Wiener spaces. Multivariate generalizations of the Jordan space were given by several prominent researchers but each of them preserved only some special properties of the space used further in few selected applications. Unlike this the multivariate generalization of the Jordan space presented in this paper preserves all known and reveals some previously unknown properties of the space. These, in turn, are special cases of the basic properties of the introduced spaces proved in the","authors_text":"A. Brudnyi, Yu. Brudnyi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-17T22:13:52Z","title":"Multivariate Bounded Variation Functions of Jordan-Wiener Type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07233","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":"sha256:75a53ebcb21cdf7c084792fb8c49996fe29e8e0279babf034008737ca4cbe138","target":"record","created_at":"2026-05-18T00:00:28Z","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":"eb29d14538a1b3d359a7cd0adc69588d751224619bd692e199a1defdeab9770d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-17T22:13:52Z","title_canon_sha256":"ce589892b1bc5030a4abea04019f7d5515859dd5e9535f33df6d090a04d7a2c2"},"schema_version":"1.0","source":{"id":"1811.07233","kind":"arxiv","version":1}},"canonical_sha256":"200d6df4185769b38c0006cf28bb366cf96659a44979987cc1412571df02d3bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"200d6df4185769b38c0006cf28bb366cf96659a44979987cc1412571df02d3bd","first_computed_at":"2026-05-18T00:00:28.565004Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:28.565004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o2jnw1aM482qwxOgT4iw/CkUuUaW2ppslCNGGGBfwFQeyB72WmPOB1yTpLhr/D//d5WGOJuNK5hBd8Vxu7LGDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:28.565654Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.07233","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75a53ebcb21cdf7c084792fb8c49996fe29e8e0279babf034008737ca4cbe138","sha256:4ae01d23e199cd2d6a8844f9d6ef9850e9fe3222edfc751cd487af2fd4dc5bd1"],"state_sha256":"3d41c0dab9d3107e28f5ffb16add7deccafd9d0eb61269826b1458e2119e0792"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OxiB4lwiUWxsPjCtgLeNQh1rO5DI+yuW5u74bEFp1voh1XD32wPQg3uAxpw0Go3Udm/wA5TtK4V5ra80GU7GDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T07:25:04.065640Z","bundle_sha256":"1bf1a53c87df9d20b7e059c149b522b1fdb1e610ef2f9a4ce31988a79bdf2023"}}