{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NO4H7DFTE2CLY3RA7TVNFUKO5Q","short_pith_number":"pith:NO4H7DFT","canonical_record":{"source":{"id":"1806.07954","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-06-07T14:13:01Z","cross_cats_sorted":[],"title_canon_sha256":"b9c0f432ad607674ec92fb21b5d3a2ecb53c87bf0e137e2c9500451312803915","abstract_canon_sha256":"13655d9d6406e75af062198e90f0d27f8b506ecdd628283da06be6167199206d"},"schema_version":"1.0"},"canonical_sha256":"6bb87f8cb32684bc6e20fcead2d14eec1fcb8ceff0b614914a4a9ece140555c4","source":{"kind":"arxiv","id":"1806.07954","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.07954","created_at":"2026-05-18T00:12:42Z"},{"alias_kind":"arxiv_version","alias_value":"1806.07954v1","created_at":"2026-05-18T00:12:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07954","created_at":"2026-05-18T00:12:42Z"},{"alias_kind":"pith_short_12","alias_value":"NO4H7DFTE2CL","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NO4H7DFTE2CLY3RA","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NO4H7DFT","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NO4H7DFTE2CLY3RA7TVNFUKO5Q","target":"record","payload":{"canonical_record":{"source":{"id":"1806.07954","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-06-07T14:13:01Z","cross_cats_sorted":[],"title_canon_sha256":"b9c0f432ad607674ec92fb21b5d3a2ecb53c87bf0e137e2c9500451312803915","abstract_canon_sha256":"13655d9d6406e75af062198e90f0d27f8b506ecdd628283da06be6167199206d"},"schema_version":"1.0"},"canonical_sha256":"6bb87f8cb32684bc6e20fcead2d14eec1fcb8ceff0b614914a4a9ece140555c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:42.505702Z","signature_b64":"0fU7z7sMijVdM76N3ivZNVC637Ei1iuZbh4EUbWOIBTGNhC4AZ8NE83/3tk4vms8SCDd37ziJBF7xGNtHYf9Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6bb87f8cb32684bc6e20fcead2d14eec1fcb8ceff0b614914a4a9ece140555c4","last_reissued_at":"2026-05-18T00:12:42.505065Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:42.505065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.07954","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":"2026-05-18T00:12:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wJtja5ATGa0VuXbeHLYmGxMC9U00BUT9X9rlfu8qztN/ePFy12DcdhfLbs3NglkQ9HlIUxhp/FF4hBBfkw6fAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:18:57.139090Z"},"content_sha256":"e9688c5da3f000a4ebf5bc23ca797ba78418836ab6366f964df6fe806209217c","schema_version":"1.0","event_id":"sha256:e9688c5da3f000a4ebf5bc23ca797ba78418836ab6366f964df6fe806209217c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NO4H7DFTE2CLY3RA7TVNFUKO5Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the relationships between Stieltjes type integrals of Young, Dushnik and Kurzweil","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Milan Tvrd\\'y, Umi Mahnuna Hanung","submitted_at":"2018-06-07T14:13:01Z","abstract_excerpt":"Integral equations of the form $$ x(t)=x(t_0)+\\int_{t_0}^t d[A]\\,x=f(t)-f(t_0)$$ are natural generalizations of systems of linear differential equations. Their main goal is that they admit solutions which need not be absolutely continuous. Up to now such equations have been considered by several authors starting with J. Kurzweil and T.H. Hildebrandt. These authors worked with several different concepts of the Stieltjes type integral like Young's (Hildebrandt), Kurzweil's (Kurzweil, Schwabik and Tvrd\\'{y}), Dushnik's (H\\\"{o}nig) or Lebesgue's (Ashordia, Meng and Zhang). Thus an interesting ques"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07954","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":"2026-05-18T00:12:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kwI68FzMpx9E18zmNb2ibCdRD5qeZedUYMi7B3cyRWht2gGDJkG5ll/BvGzJSZTh7Dt7AtCrU/adz9qB7vieBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:18:57.139433Z"},"content_sha256":"3185ed43bc5f207d8de1991e377a331b57a4899eb1374aa0adb86e7ee6cd11ad","schema_version":"1.0","event_id":"sha256:3185ed43bc5f207d8de1991e377a331b57a4899eb1374aa0adb86e7ee6cd11ad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NO4H7DFTE2CLY3RA7TVNFUKO5Q/bundle.json","state_url":"https://pith.science/pith/NO4H7DFTE2CLY3RA7TVNFUKO5Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NO4H7DFTE2CLY3RA7TVNFUKO5Q/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":"2026-06-01T16:18:57Z","links":{"resolver":"https://pith.science/pith/NO4H7DFTE2CLY3RA7TVNFUKO5Q","bundle":"https://pith.science/pith/NO4H7DFTE2CLY3RA7TVNFUKO5Q/bundle.json","state":"https://pith.science/pith/NO4H7DFTE2CLY3RA7TVNFUKO5Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NO4H7DFTE2CLY3RA7TVNFUKO5Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NO4H7DFTE2CLY3RA7TVNFUKO5Q","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":"13655d9d6406e75af062198e90f0d27f8b506ecdd628283da06be6167199206d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-06-07T14:13:01Z","title_canon_sha256":"b9c0f432ad607674ec92fb21b5d3a2ecb53c87bf0e137e2c9500451312803915"},"schema_version":"1.0","source":{"id":"1806.07954","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.07954","created_at":"2026-05-18T00:12:42Z"},{"alias_kind":"arxiv_version","alias_value":"1806.07954v1","created_at":"2026-05-18T00:12:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07954","created_at":"2026-05-18T00:12:42Z"},{"alias_kind":"pith_short_12","alias_value":"NO4H7DFTE2CL","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NO4H7DFTE2CLY3RA","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NO4H7DFT","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:3185ed43bc5f207d8de1991e377a331b57a4899eb1374aa0adb86e7ee6cd11ad","target":"graph","created_at":"2026-05-18T00:12:42Z","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":"Integral equations of the form $$ x(t)=x(t_0)+\\int_{t_0}^t d[A]\\,x=f(t)-f(t_0)$$ are natural generalizations of systems of linear differential equations. Their main goal is that they admit solutions which need not be absolutely continuous. Up to now such equations have been considered by several authors starting with J. Kurzweil and T.H. Hildebrandt. These authors worked with several different concepts of the Stieltjes type integral like Young's (Hildebrandt), Kurzweil's (Kurzweil, Schwabik and Tvrd\\'{y}), Dushnik's (H\\\"{o}nig) or Lebesgue's (Ashordia, Meng and Zhang). Thus an interesting ques","authors_text":"Milan Tvrd\\'y, Umi Mahnuna Hanung","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-06-07T14:13:01Z","title":"On the relationships between Stieltjes type integrals of Young, Dushnik and Kurzweil"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07954","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:e9688c5da3f000a4ebf5bc23ca797ba78418836ab6366f964df6fe806209217c","target":"record","created_at":"2026-05-18T00:12:42Z","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":"13655d9d6406e75af062198e90f0d27f8b506ecdd628283da06be6167199206d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-06-07T14:13:01Z","title_canon_sha256":"b9c0f432ad607674ec92fb21b5d3a2ecb53c87bf0e137e2c9500451312803915"},"schema_version":"1.0","source":{"id":"1806.07954","kind":"arxiv","version":1}},"canonical_sha256":"6bb87f8cb32684bc6e20fcead2d14eec1fcb8ceff0b614914a4a9ece140555c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6bb87f8cb32684bc6e20fcead2d14eec1fcb8ceff0b614914a4a9ece140555c4","first_computed_at":"2026-05-18T00:12:42.505065Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:42.505065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0fU7z7sMijVdM76N3ivZNVC637Ei1iuZbh4EUbWOIBTGNhC4AZ8NE83/3tk4vms8SCDd37ziJBF7xGNtHYf9Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:42.505702Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.07954","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9688c5da3f000a4ebf5bc23ca797ba78418836ab6366f964df6fe806209217c","sha256:3185ed43bc5f207d8de1991e377a331b57a4899eb1374aa0adb86e7ee6cd11ad"],"state_sha256":"249fd59b6a8cfe4e2ab12fabe4b0c3f33a9ad30a265f4a57e057a6ecff99bd59"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d+u7jwQWg3ORIPMIKBMlbJAiBDuhq6sQWytl+9xLDkJGTauw7TunUFmEW99jbP87C7FEG5Syxkjq9o+VJ3z0Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T16:18:57.141211Z","bundle_sha256":"5d3902db0e1aa54d1848f956581fce3db72f89743ac23ba6765e0d18e2b10932"}}