{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:H47PQHSA5QKHPLUO6NU67N3NOP","short_pith_number":"pith:H47PQHSA","canonical_record":{"source":{"id":"1610.09702","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-10-30T19:52:47Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"d310e32de41da9d1f070a3a13eb3837176ecf956303ccd55048229b4ea04a1e2","abstract_canon_sha256":"1ed14cac912063e3ec38d542242b1e9e4e1fe40537d502365befe073ad267ac0"},"schema_version":"1.0"},"canonical_sha256":"3f3ef81e40ec1477ae8ef369efb76d73d843a0e49503cdfa8f3f9d39f5423aa3","source":{"kind":"arxiv","id":"1610.09702","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09702","created_at":"2026-05-18T00:43:18Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09702v2","created_at":"2026-05-18T00:43:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09702","created_at":"2026-05-18T00:43:18Z"},{"alias_kind":"pith_short_12","alias_value":"H47PQHSA5QKH","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"H47PQHSA5QKHPLUO","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"H47PQHSA","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:H47PQHSA5QKHPLUO6NU67N3NOP","target":"record","payload":{"canonical_record":{"source":{"id":"1610.09702","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-10-30T19:52:47Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"d310e32de41da9d1f070a3a13eb3837176ecf956303ccd55048229b4ea04a1e2","abstract_canon_sha256":"1ed14cac912063e3ec38d542242b1e9e4e1fe40537d502365befe073ad267ac0"},"schema_version":"1.0"},"canonical_sha256":"3f3ef81e40ec1477ae8ef369efb76d73d843a0e49503cdfa8f3f9d39f5423aa3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:18.301420Z","signature_b64":"liEh8WSc/bnPveAotPtJnDkbes+hQOBQb7w8EiBxL5URZ17tAotWbyNKIxvZ16quEAZMurryr082xq60wj1LCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f3ef81e40ec1477ae8ef369efb76d73d843a0e49503cdfa8f3f9d39f5423aa3","last_reissued_at":"2026-05-18T00:43:18.300623Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:18.300623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.09702","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:43:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TWWCorSDlzUkYJ3x/+4GYJwJinrAqIgo2e4gRucDdWvXrgRg35DZBpJiN2OYxK0zVRBN1BphXI/pUKMvTY57Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T13:18:48.514940Z"},"content_sha256":"eee98e0458120e4a3a34b894cfaaf43b7d9e0b79da756f1d972372e60a8eeb39","schema_version":"1.0","event_id":"sha256:eee98e0458120e4a3a34b894cfaaf43b7d9e0b79da756f1d972372e60a8eeb39"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:H47PQHSA5QKHPLUO6NU67N3NOP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Integration by differentiation: new proofs, methods and examples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Achim Kempf, Ding Jia, Eugene Tang","submitted_at":"2016-10-30T19:52:47Z","abstract_excerpt":"Recently, new methods were introduced which allow one to solve ordinary integrals by performing only derivatives. These studies were originally motivated by the difficulties of the quantum field theoretic path integral, and correspondingly, the results were derived by heuristic methods. Here, we give rigorous proofs for the methods to hold on fully specified function spaces. We then illustrate the efficacy of the new methods by applying them to the study of the surprising behavior of so-called Borwein integrals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09702","kind":"arxiv","version":2},"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":"2026-05-18T00:43:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t9WJ15C56QHkcKu0NpPFZ1obp5y3AbWD2s/hGLUqVPEeIJH1PLhoNTBgu2sNnnAFMmEEjlhmKvRIdtDagmsDCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T13:18:48.515274Z"},"content_sha256":"3f196994d55b9e024c36ad8b4f4e14e8f3d3482eb78a4b982c6ff3c5d02d3aa2","schema_version":"1.0","event_id":"sha256:3f196994d55b9e024c36ad8b4f4e14e8f3d3482eb78a4b982c6ff3c5d02d3aa2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H47PQHSA5QKHPLUO6NU67N3NOP/bundle.json","state_url":"https://pith.science/pith/H47PQHSA5QKHPLUO6NU67N3NOP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H47PQHSA5QKHPLUO6NU67N3NOP/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":"2026-06-27T13:18:48Z","links":{"resolver":"https://pith.science/pith/H47PQHSA5QKHPLUO6NU67N3NOP","bundle":"https://pith.science/pith/H47PQHSA5QKHPLUO6NU67N3NOP/bundle.json","state":"https://pith.science/pith/H47PQHSA5QKHPLUO6NU67N3NOP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H47PQHSA5QKHPLUO6NU67N3NOP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:H47PQHSA5QKHPLUO6NU67N3NOP","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":"1ed14cac912063e3ec38d542242b1e9e4e1fe40537d502365befe073ad267ac0","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-10-30T19:52:47Z","title_canon_sha256":"d310e32de41da9d1f070a3a13eb3837176ecf956303ccd55048229b4ea04a1e2"},"schema_version":"1.0","source":{"id":"1610.09702","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09702","created_at":"2026-05-18T00:43:18Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09702v2","created_at":"2026-05-18T00:43:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09702","created_at":"2026-05-18T00:43:18Z"},{"alias_kind":"pith_short_12","alias_value":"H47PQHSA5QKH","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"H47PQHSA5QKHPLUO","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"H47PQHSA","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:3f196994d55b9e024c36ad8b4f4e14e8f3d3482eb78a4b982c6ff3c5d02d3aa2","target":"graph","created_at":"2026-05-18T00:43:18Z","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":"Recently, new methods were introduced which allow one to solve ordinary integrals by performing only derivatives. These studies were originally motivated by the difficulties of the quantum field theoretic path integral, and correspondingly, the results were derived by heuristic methods. Here, we give rigorous proofs for the methods to hold on fully specified function spaces. We then illustrate the efficacy of the new methods by applying them to the study of the surprising behavior of so-called Borwein integrals.","authors_text":"Achim Kempf, Ding Jia, Eugene Tang","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-10-30T19:52:47Z","title":"Integration by differentiation: new proofs, methods and examples"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09702","kind":"arxiv","version":2},"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:eee98e0458120e4a3a34b894cfaaf43b7d9e0b79da756f1d972372e60a8eeb39","target":"record","created_at":"2026-05-18T00:43:18Z","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":"1ed14cac912063e3ec38d542242b1e9e4e1fe40537d502365befe073ad267ac0","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-10-30T19:52:47Z","title_canon_sha256":"d310e32de41da9d1f070a3a13eb3837176ecf956303ccd55048229b4ea04a1e2"},"schema_version":"1.0","source":{"id":"1610.09702","kind":"arxiv","version":2}},"canonical_sha256":"3f3ef81e40ec1477ae8ef369efb76d73d843a0e49503cdfa8f3f9d39f5423aa3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f3ef81e40ec1477ae8ef369efb76d73d843a0e49503cdfa8f3f9d39f5423aa3","first_computed_at":"2026-05-18T00:43:18.300623Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:18.300623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"liEh8WSc/bnPveAotPtJnDkbes+hQOBQb7w8EiBxL5URZ17tAotWbyNKIxvZ16quEAZMurryr082xq60wj1LCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:18.301420Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.09702","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eee98e0458120e4a3a34b894cfaaf43b7d9e0b79da756f1d972372e60a8eeb39","sha256:3f196994d55b9e024c36ad8b4f4e14e8f3d3482eb78a4b982c6ff3c5d02d3aa2"],"state_sha256":"4f73678a65f7b57e94fbebed38acbf40c45b8affd924ad4fc6c2052a5c607aaa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aRKlUsvX+vKTe/LtbWn4e/4XuzbLGvdfujMy1+HBiRhOzE4/+Mae4vLy8Q1XBQew8b6d++d6VhK9DVxgvRBgCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T13:18:48.517107Z","bundle_sha256":"af88d2e3d9e7b10b7bc9e2fcb5994bbe45afe24a8ff310a76acb9ab4b581c72a"}}