{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:JEUFAS7V3R54B774SSCRGO32ME","short_pith_number":"pith:JEUFAS7V","canonical_record":{"source":{"id":"2505.22896","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-05-28T22:00:11Z","cross_cats_sorted":[],"title_canon_sha256":"2225efeb5433397ba9992111ba769e27cb1eaf5b2b8715e4908c0e1b5c6ac55c","abstract_canon_sha256":"3b806550a4b87f4e365e6dcd1f4e675a1ef3da690f03a5942b7b907150fe7753"},"schema_version":"1.0"},"canonical_sha256":"4928504bf5dc7bc0fffc9485133b7a6128e76d5f443a04a05de404735a673a8c","source":{"kind":"arxiv","id":"2505.22896","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.22896","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"arxiv_version","alias_value":"2505.22896v1","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.22896","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"pith_short_12","alias_value":"JEUFAS7V3R54","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"pith_short_16","alias_value":"JEUFAS7V3R54B774","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"pith_short_8","alias_value":"JEUFAS7V","created_at":"2026-07-05T11:11:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:JEUFAS7V3R54B774SSCRGO32ME","target":"record","payload":{"canonical_record":{"source":{"id":"2505.22896","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-05-28T22:00:11Z","cross_cats_sorted":[],"title_canon_sha256":"2225efeb5433397ba9992111ba769e27cb1eaf5b2b8715e4908c0e1b5c6ac55c","abstract_canon_sha256":"3b806550a4b87f4e365e6dcd1f4e675a1ef3da690f03a5942b7b907150fe7753"},"schema_version":"1.0"},"canonical_sha256":"4928504bf5dc7bc0fffc9485133b7a6128e76d5f443a04a05de404735a673a8c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:11:51.580922Z","signature_b64":"wlNYKwR6UXqULYS2Zd8j/MLKfsQWareOxFoZBbytQ5OwT3i+nvNuIWxdH7VPWjsjqB47nU83ZK7mqvAI+7WQDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4928504bf5dc7bc0fffc9485133b7a6128e76d5f443a04a05de404735a673a8c","last_reissued_at":"2026-07-05T11:11:51.580421Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:11:51.580421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.22896","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":"2026-07-05T11:11:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"piXvpoMikDjnUQbpCPacPtmZv28aYJG0H/x9Vr5jR1IvTqUJNo8whA+N7pewiVnDrvrMCAno7BbWrIdAw6bgDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T13:11:51.245578Z"},"content_sha256":"bebb6909dea2a3c9d6bd0f2647fe8552fb52a03f23f6bcb3421b8e0210401d6e","schema_version":"1.0","event_id":"sha256:bebb6909dea2a3c9d6bd0f2647fe8552fb52a03f23f6bcb3421b8e0210401d6e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:JEUFAS7V3R54B774SSCRGO32ME","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exploring Integration by Differentiation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"C. Vignat, R. D. George","submitted_at":"2025-05-28T22:00:11Z","abstract_excerpt":"This work validates and extends the method of integration by differentiation, initially introduced by A. Kempf et al., and demonstrates its compatibility with classical rules of integration. It provides applications to classical integrals, including one by Ramanujan, and extends the method to the multivariate setting. Volumes of simplexes are computed by acting with indicator functions on elementary kernels, and a rotationally invariant formulation is derived. Finally, the method is extended to Jackson's q-integral."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.22896","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/2505.22896/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":"2026-07-05T11:11:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gC9TmX2lyfMcwkv4chgN9yxNiGr9y8d3YpSGXi6fGOQXNQ5ooRb8XfkJIoA5/S5Wu+NkdeDIA1u9iDStTCN6AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T13:11:51.246096Z"},"content_sha256":"92415b1be07e944f68512f717fce4f37ed9b3957a8072f618941da20672fbc96","schema_version":"1.0","event_id":"sha256:92415b1be07e944f68512f717fce4f37ed9b3957a8072f618941da20672fbc96"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JEUFAS7V3R54B774SSCRGO32ME/bundle.json","state_url":"https://pith.science/pith/JEUFAS7V3R54B774SSCRGO32ME/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JEUFAS7V3R54B774SSCRGO32ME/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":"2026-08-04T13:11:51Z","links":{"resolver":"https://pith.science/pith/JEUFAS7V3R54B774SSCRGO32ME","bundle":"https://pith.science/pith/JEUFAS7V3R54B774SSCRGO32ME/bundle.json","state":"https://pith.science/pith/JEUFAS7V3R54B774SSCRGO32ME/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JEUFAS7V3R54B774SSCRGO32ME/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:JEUFAS7V3R54B774SSCRGO32ME","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":"3b806550a4b87f4e365e6dcd1f4e675a1ef3da690f03a5942b7b907150fe7753","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-05-28T22:00:11Z","title_canon_sha256":"2225efeb5433397ba9992111ba769e27cb1eaf5b2b8715e4908c0e1b5c6ac55c"},"schema_version":"1.0","source":{"id":"2505.22896","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.22896","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"arxiv_version","alias_value":"2505.22896v1","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.22896","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"pith_short_12","alias_value":"JEUFAS7V3R54","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"pith_short_16","alias_value":"JEUFAS7V3R54B774","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"pith_short_8","alias_value":"JEUFAS7V","created_at":"2026-07-05T11:11:51Z"}],"graph_snapshots":[{"event_id":"sha256:92415b1be07e944f68512f717fce4f37ed9b3957a8072f618941da20672fbc96","target":"graph","created_at":"2026-07-05T11:11:51Z","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/2505.22896/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This work validates and extends the method of integration by differentiation, initially introduced by A. Kempf et al., and demonstrates its compatibility with classical rules of integration. It provides applications to classical integrals, including one by Ramanujan, and extends the method to the multivariate setting. Volumes of simplexes are computed by acting with indicator functions on elementary kernels, and a rotationally invariant formulation is derived. Finally, the method is extended to Jackson's q-integral.","authors_text":"C. Vignat, R. D. George","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-05-28T22:00:11Z","title":"Exploring Integration by Differentiation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.22896","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:bebb6909dea2a3c9d6bd0f2647fe8552fb52a03f23f6bcb3421b8e0210401d6e","target":"record","created_at":"2026-07-05T11:11:51Z","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":"3b806550a4b87f4e365e6dcd1f4e675a1ef3da690f03a5942b7b907150fe7753","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-05-28T22:00:11Z","title_canon_sha256":"2225efeb5433397ba9992111ba769e27cb1eaf5b2b8715e4908c0e1b5c6ac55c"},"schema_version":"1.0","source":{"id":"2505.22896","kind":"arxiv","version":1}},"canonical_sha256":"4928504bf5dc7bc0fffc9485133b7a6128e76d5f443a04a05de404735a673a8c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4928504bf5dc7bc0fffc9485133b7a6128e76d5f443a04a05de404735a673a8c","first_computed_at":"2026-07-05T11:11:51.580421Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:11:51.580421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wlNYKwR6UXqULYS2Zd8j/MLKfsQWareOxFoZBbytQ5OwT3i+nvNuIWxdH7VPWjsjqB47nU83ZK7mqvAI+7WQDg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:11:51.580922Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.22896","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bebb6909dea2a3c9d6bd0f2647fe8552fb52a03f23f6bcb3421b8e0210401d6e","sha256:92415b1be07e944f68512f717fce4f37ed9b3957a8072f618941da20672fbc96"],"state_sha256":"6dac5eefbde5f311991bd1acda437ce61ee88df3a8ffeaf14e2c40be82c98676"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ayS3pKAjeSNB7Uc2sqTBwSzDj69uUdXxEQs0tB4ApEK9SDgCDsogyWlBPuitc4VX76jWvb3IPqngg5pOSY29BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T13:11:51.251192Z","bundle_sha256":"3c62067a56f55d0f4e7cecadc24e5ab347645e7cfbbd7ac70278b60abc5df5f0"}}