{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:H6AY5N3XXLKQ2JNM2IFBNWNHK3","short_pith_number":"pith:H6AY5N3X","canonical_record":{"source":{"id":"1104.1422","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-04-07T22:19:43Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"05f56ce583df8be509ab40ddfc70e2d0c8f9e169c4c4805afd5aae3ecdba4103","abstract_canon_sha256":"202bd665484bb0b941cb62b561619ae80b2226b0c45a0eaa9befe6cbdc2303c1"},"schema_version":"1.0"},"canonical_sha256":"3f818eb777bad50d25acd20a16d9a756f681b95c2eda9ba448a4ce9418b1767e","source":{"kind":"arxiv","id":"1104.1422","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1422","created_at":"2026-05-18T03:39:43Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1422v4","created_at":"2026-05-18T03:39:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1422","created_at":"2026-05-18T03:39:43Z"},{"alias_kind":"pith_short_12","alias_value":"H6AY5N3XXLKQ","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"H6AY5N3XXLKQ2JNM","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"H6AY5N3X","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:H6AY5N3XXLKQ2JNM2IFBNWNHK3","target":"record","payload":{"canonical_record":{"source":{"id":"1104.1422","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-04-07T22:19:43Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"05f56ce583df8be509ab40ddfc70e2d0c8f9e169c4c4805afd5aae3ecdba4103","abstract_canon_sha256":"202bd665484bb0b941cb62b561619ae80b2226b0c45a0eaa9befe6cbdc2303c1"},"schema_version":"1.0"},"canonical_sha256":"3f818eb777bad50d25acd20a16d9a756f681b95c2eda9ba448a4ce9418b1767e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:43.836833Z","signature_b64":"xkwZPkxfTU5oa0iAKjs7CQ3HPsdn/MK9Q8Ikmey2icX/pwXd/OYL9WlDHKOJ3RNQfHyGdFHaJXE0rjEXIKV5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f818eb777bad50d25acd20a16d9a756f681b95c2eda9ba448a4ce9418b1767e","last_reissued_at":"2026-05-18T03:39:43.836400Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:43.836400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.1422","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:39:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kt+gZVxTc+Wl9j9mjx5NsBOzlxAgRITue34ih3QtQWoyDb77NNAGJTh2ZI6r9S2sVEC7KJJsKs/Rdlyt8oC3Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T08:19:18.460700Z"},"content_sha256":"ef95cc41b7ee01881f2fe03ac19a01da02ee051df8e71b330773dd2c0836b828","schema_version":"1.0","event_id":"sha256:ef95cc41b7ee01881f2fe03ac19a01da02ee051df8e71b330773dd2c0836b828"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:H6AY5N3XXLKQ2JNM2IFBNWNHK3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the substitution rule for Lebesgue-Stieltjes integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Gerald Teschl, Neil Falkner","submitted_at":"2011-04-07T22:19:43Z","abstract_excerpt":"We show how two change-of-variables formulae for Lebesgue-Stieltjes integrals generalize when all continuity hypotheses on the integrators are dropped. We find that a sort of \"mass splitting phenomenon\" arises."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1422","kind":"arxiv","version":4},"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":"2026-05-18T03:39:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iEcAi/KMWkjU7hoZU8+OdP8dTJzUrMGzjVvPolFckahyWZtVA5/u40tIQMPE7CHycDXmK6GWqvUkT8n9YuMkBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T08:19:18.461042Z"},"content_sha256":"4eaf5b4b20839851fa889719d29bbb4d5a8038ceaca254b77c1135c146864e5e","schema_version":"1.0","event_id":"sha256:4eaf5b4b20839851fa889719d29bbb4d5a8038ceaca254b77c1135c146864e5e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H6AY5N3XXLKQ2JNM2IFBNWNHK3/bundle.json","state_url":"https://pith.science/pith/H6AY5N3XXLKQ2JNM2IFBNWNHK3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H6AY5N3XXLKQ2JNM2IFBNWNHK3/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":"2026-06-12T08:19:18Z","links":{"resolver":"https://pith.science/pith/H6AY5N3XXLKQ2JNM2IFBNWNHK3","bundle":"https://pith.science/pith/H6AY5N3XXLKQ2JNM2IFBNWNHK3/bundle.json","state":"https://pith.science/pith/H6AY5N3XXLKQ2JNM2IFBNWNHK3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H6AY5N3XXLKQ2JNM2IFBNWNHK3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:H6AY5N3XXLKQ2JNM2IFBNWNHK3","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":"202bd665484bb0b941cb62b561619ae80b2226b0c45a0eaa9befe6cbdc2303c1","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-04-07T22:19:43Z","title_canon_sha256":"05f56ce583df8be509ab40ddfc70e2d0c8f9e169c4c4805afd5aae3ecdba4103"},"schema_version":"1.0","source":{"id":"1104.1422","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1422","created_at":"2026-05-18T03:39:43Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1422v4","created_at":"2026-05-18T03:39:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1422","created_at":"2026-05-18T03:39:43Z"},{"alias_kind":"pith_short_12","alias_value":"H6AY5N3XXLKQ","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"H6AY5N3XXLKQ2JNM","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"H6AY5N3X","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:4eaf5b4b20839851fa889719d29bbb4d5a8038ceaca254b77c1135c146864e5e","target":"graph","created_at":"2026-05-18T03:39:43Z","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 show how two change-of-variables formulae for Lebesgue-Stieltjes integrals generalize when all continuity hypotheses on the integrators are dropped. We find that a sort of \"mass splitting phenomenon\" arises.","authors_text":"Gerald Teschl, Neil Falkner","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-04-07T22:19:43Z","title":"On the substitution rule for Lebesgue-Stieltjes integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1422","kind":"arxiv","version":4},"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:ef95cc41b7ee01881f2fe03ac19a01da02ee051df8e71b330773dd2c0836b828","target":"record","created_at":"2026-05-18T03:39:43Z","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":"202bd665484bb0b941cb62b561619ae80b2226b0c45a0eaa9befe6cbdc2303c1","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-04-07T22:19:43Z","title_canon_sha256":"05f56ce583df8be509ab40ddfc70e2d0c8f9e169c4c4805afd5aae3ecdba4103"},"schema_version":"1.0","source":{"id":"1104.1422","kind":"arxiv","version":4}},"canonical_sha256":"3f818eb777bad50d25acd20a16d9a756f681b95c2eda9ba448a4ce9418b1767e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f818eb777bad50d25acd20a16d9a756f681b95c2eda9ba448a4ce9418b1767e","first_computed_at":"2026-05-18T03:39:43.836400Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:43.836400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xkwZPkxfTU5oa0iAKjs7CQ3HPsdn/MK9Q8Ikmey2icX/pwXd/OYL9WlDHKOJ3RNQfHyGdFHaJXE0rjEXIKV5AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:43.836833Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.1422","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef95cc41b7ee01881f2fe03ac19a01da02ee051df8e71b330773dd2c0836b828","sha256:4eaf5b4b20839851fa889719d29bbb4d5a8038ceaca254b77c1135c146864e5e"],"state_sha256":"ee4b24ce580413e7af6821c55cf2de80302ef6112526e1083c837d57abb47300"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o0zdWC7aLb0OOhx492Yt1DjkwHOLlU04gUhksZ75o8igVFHNgliYI6Gx7PlVRNMGHyySjLIH4VpHx3VNBi0kBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T08:19:18.463008Z","bundle_sha256":"0d77e23d8bed21d5592178dbdda3baf29372741e65606202da5b3554ca4d73fd"}}