{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:SBZMX3INACXLHRO2JJYT3HQRQH","short_pith_number":"pith:SBZMX3IN","canonical_record":{"source":{"id":"1106.4673","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-06-23T10:20:33Z","cross_cats_sorted":[],"title_canon_sha256":"f9eb7340efef007282a8c8b89167537ff897ee9e67de6372ff196db470878ab0","abstract_canon_sha256":"c6642bb0fac306329f6d521c59fcf37e44b454c90b47f7e1b7783ab099e342f3"},"schema_version":"1.0"},"canonical_sha256":"9072cbed0d00aeb3c5da4a713d9e1181cff4e2fedbb5ca8f55cf374a01d8a3db","source":{"kind":"arxiv","id":"1106.4673","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.4673","created_at":"2026-05-18T04:19:31Z"},{"alias_kind":"arxiv_version","alias_value":"1106.4673v1","created_at":"2026-05-18T04:19:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.4673","created_at":"2026-05-18T04:19:31Z"},{"alias_kind":"pith_short_12","alias_value":"SBZMX3INACXL","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SBZMX3INACXLHRO2","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SBZMX3IN","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:SBZMX3INACXLHRO2JJYT3HQRQH","target":"record","payload":{"canonical_record":{"source":{"id":"1106.4673","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-06-23T10:20:33Z","cross_cats_sorted":[],"title_canon_sha256":"f9eb7340efef007282a8c8b89167537ff897ee9e67de6372ff196db470878ab0","abstract_canon_sha256":"c6642bb0fac306329f6d521c59fcf37e44b454c90b47f7e1b7783ab099e342f3"},"schema_version":"1.0"},"canonical_sha256":"9072cbed0d00aeb3c5da4a713d9e1181cff4e2fedbb5ca8f55cf374a01d8a3db","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:31.708473Z","signature_b64":"Nz2uhGmXVnI/zgW4viyZJFHre0yFaYRTBW1ArinK/3zLdbenhwwcPy2yA/MemHmVxg2zTIs1R7jIfSDIgBZKAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9072cbed0d00aeb3c5da4a713d9e1181cff4e2fedbb5ca8f55cf374a01d8a3db","last_reissued_at":"2026-05-18T04:19:31.707893Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:31.707893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.4673","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":"2026-05-18T04:19:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/sZI58VqpM41ArzhzVyxPuT7Zx9/XrpqmoDaI3ZrO7qpMFXDscogrI1C3/63mC5GzfSIdrWAt8VpPIOSpS8uDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:59:21.382283Z"},"content_sha256":"be3ecc4a076bf6f5181bd372f79818704af29c172d08d7ed8852583f8bd13939","schema_version":"1.0","event_id":"sha256:be3ecc4a076bf6f5181bd372f79818704af29c172d08d7ed8852583f8bd13939"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:SBZMX3INACXLHRO2JJYT3HQRQH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Koksma-Hlawka inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"G. Gigante, G. Travaglini, L. Brandolini, L. Colzani","submitted_at":"2011-06-23T10:20:33Z","abstract_excerpt":"The classical Koksma Hlawka inequality does not apply to functions with simple discontinuities. Here we state a Koksma Hlawka type inequality which applies to piecewise smooth functions $f\\chi_{\\Omega}$, with $f$ smooth and $\\Omega $ a Borel subset of $[0,1]^{d}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4673","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":"2026-05-18T04:19:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CjZLHqyjOoFScFL020FVlJRgqPme0T0x16DY72N4unEyl35V7pLjjY6UEQYTDPuq5puH1gYEqXCdkMO5N6cFBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:59:21.382654Z"},"content_sha256":"6d0c94e53018a6081da1cbb4295de39af857da641cd511245bd073fd8805230e","schema_version":"1.0","event_id":"sha256:6d0c94e53018a6081da1cbb4295de39af857da641cd511245bd073fd8805230e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SBZMX3INACXLHRO2JJYT3HQRQH/bundle.json","state_url":"https://pith.science/pith/SBZMX3INACXLHRO2JJYT3HQRQH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SBZMX3INACXLHRO2JJYT3HQRQH/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":"2026-06-02T17:59:21Z","links":{"resolver":"https://pith.science/pith/SBZMX3INACXLHRO2JJYT3HQRQH","bundle":"https://pith.science/pith/SBZMX3INACXLHRO2JJYT3HQRQH/bundle.json","state":"https://pith.science/pith/SBZMX3INACXLHRO2JJYT3HQRQH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SBZMX3INACXLHRO2JJYT3HQRQH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SBZMX3INACXLHRO2JJYT3HQRQH","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":"c6642bb0fac306329f6d521c59fcf37e44b454c90b47f7e1b7783ab099e342f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-06-23T10:20:33Z","title_canon_sha256":"f9eb7340efef007282a8c8b89167537ff897ee9e67de6372ff196db470878ab0"},"schema_version":"1.0","source":{"id":"1106.4673","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.4673","created_at":"2026-05-18T04:19:31Z"},{"alias_kind":"arxiv_version","alias_value":"1106.4673v1","created_at":"2026-05-18T04:19:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.4673","created_at":"2026-05-18T04:19:31Z"},{"alias_kind":"pith_short_12","alias_value":"SBZMX3INACXL","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SBZMX3INACXLHRO2","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SBZMX3IN","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:6d0c94e53018a6081da1cbb4295de39af857da641cd511245bd073fd8805230e","target":"graph","created_at":"2026-05-18T04:19:31Z","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":"The classical Koksma Hlawka inequality does not apply to functions with simple discontinuities. Here we state a Koksma Hlawka type inequality which applies to piecewise smooth functions $f\\chi_{\\Omega}$, with $f$ smooth and $\\Omega $ a Borel subset of $[0,1]^{d}$.","authors_text":"G. Gigante, G. Travaglini, L. Brandolini, L. Colzani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-06-23T10:20:33Z","title":"On Koksma-Hlawka inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4673","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:be3ecc4a076bf6f5181bd372f79818704af29c172d08d7ed8852583f8bd13939","target":"record","created_at":"2026-05-18T04:19:31Z","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":"c6642bb0fac306329f6d521c59fcf37e44b454c90b47f7e1b7783ab099e342f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-06-23T10:20:33Z","title_canon_sha256":"f9eb7340efef007282a8c8b89167537ff897ee9e67de6372ff196db470878ab0"},"schema_version":"1.0","source":{"id":"1106.4673","kind":"arxiv","version":1}},"canonical_sha256":"9072cbed0d00aeb3c5da4a713d9e1181cff4e2fedbb5ca8f55cf374a01d8a3db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9072cbed0d00aeb3c5da4a713d9e1181cff4e2fedbb5ca8f55cf374a01d8a3db","first_computed_at":"2026-05-18T04:19:31.707893Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:31.707893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nz2uhGmXVnI/zgW4viyZJFHre0yFaYRTBW1ArinK/3zLdbenhwwcPy2yA/MemHmVxg2zTIs1R7jIfSDIgBZKAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:31.708473Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.4673","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be3ecc4a076bf6f5181bd372f79818704af29c172d08d7ed8852583f8bd13939","sha256:6d0c94e53018a6081da1cbb4295de39af857da641cd511245bd073fd8805230e"],"state_sha256":"ab3ff9225049397c45375fd7a266299ea5ab993f572c2b35e6b311ef2000ea8b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2imXJwpXYguUP+In6TE96qpkhtG4f0lJq/gVC0VmiWkfh+SH3ocFOBpimr/+8ftH+Kd8OvXmygA6QIUKL8gGAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T17:59:21.385339Z","bundle_sha256":"81b508b4a847435085bb70a81578f50533a61cd1e734a134f873189e82d8b10d"}}