{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:QY7X3O5TAYXYACC7ZD6IUYCDNW","short_pith_number":"pith:QY7X3O5T","canonical_record":{"source":{"id":"2209.02302","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-09-06T08:55:21Z","cross_cats_sorted":["cs.NA","hep-lat","physics.comp-ph"],"title_canon_sha256":"b60324e0776a0ec735115c5712d63ff35b38fd626479d2c3eef2afcb6b1e7cad","abstract_canon_sha256":"e458edb621d83c0ffb3b4b7111c77e09b471af0978e48f1582a481863db23ce7"},"schema_version":"1.0"},"canonical_sha256":"863f7dbbb3062f80085fc8fc8a60436db123a3d7fe6e927f0c8e761beac842f1","source":{"kind":"arxiv","id":"2209.02302","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.02302","created_at":"2026-05-18T02:44:39Z"},{"alias_kind":"arxiv_version","alias_value":"2209.02302v3","created_at":"2026-05-18T02:44:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.02302","created_at":"2026-05-18T02:44:39Z"},{"alias_kind":"pith_short_12","alias_value":"QY7X3O5TAYXY","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"QY7X3O5TAYXYACC7","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"QY7X3O5T","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:QY7X3O5TAYXYACC7ZD6IUYCDNW","target":"record","payload":{"canonical_record":{"source":{"id":"2209.02302","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-09-06T08:55:21Z","cross_cats_sorted":["cs.NA","hep-lat","physics.comp-ph"],"title_canon_sha256":"b60324e0776a0ec735115c5712d63ff35b38fd626479d2c3eef2afcb6b1e7cad","abstract_canon_sha256":"e458edb621d83c0ffb3b4b7111c77e09b471af0978e48f1582a481863db23ce7"},"schema_version":"1.0"},"canonical_sha256":"863f7dbbb3062f80085fc8fc8a60436db123a3d7fe6e927f0c8e761beac842f1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:39.900082Z","signature_b64":"YRyzcWmMBG1fZR5X4/K7lLLhll/agrYcFRdHDKhyYXRRRyRQapFWMJkqBqdry5WjryNhTV4+vTnkg7vzRatpDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"863f7dbbb3062f80085fc8fc8a60436db123a3d7fe6e927f0c8e761beac842f1","last_reissued_at":"2026-05-18T02:44:39.899563Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:39.899563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2209.02302","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:44:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7J5Ao7yEcxiGBx/nzCSEMa9vXUc9Ef0B5MUJJ/aPnibsyCoL7q4hV9IsYb2nz1sOtr1quOu/p3xf8hW5LIYQDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T07:04:38.046400Z"},"content_sha256":"5f08616b6d78a442b3787f3159a8534dafa23cc801d63a3887740de93d51b3e8","schema_version":"1.0","event_id":"sha256:5f08616b6d78a442b3787f3159a8534dafa23cc801d63a3887740de93d51b3e8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:QY7X3O5TAYXYACC7ZD6IUYCDNW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards non-linear quadrature formulae","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","hep-lat","physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Georg M. von Hippel","submitted_at":"2022-09-06T08:55:21Z","abstract_excerpt":"Prompted by an observation about the integral of exponential functions of the form $f(x)=\\lambda e^{\\alpha x}$, we investigate the possibility to exactly integrate families of functions generated from a given function by scaling or by affine transformations of the argument using nonlinear generalizations of quadrature formulae. The main result of this paper is that such formulae can be explicitly constructed for a wide class of functions, and have the same accuracy as Newton-Cotes formulae based on the same nodes, with the latter emerging as the linear case of our general formalism. We also de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.02302","kind":"arxiv","version":3},"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":"2026-05-18T02:44:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iGoePUoFMmJmElmttGoz0/tMt6qd8GaLFt3jASqyvYHKSB+LRnXEdJt+rRvDMGHs3obC5Bhgqg5MylDOY7vmDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T07:04:38.046740Z"},"content_sha256":"fbc15bedcc0bdf6f3d6bcc4dabab06e038bad703c407a2d82391da190c18c36f","schema_version":"1.0","event_id":"sha256:fbc15bedcc0bdf6f3d6bcc4dabab06e038bad703c407a2d82391da190c18c36f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QY7X3O5TAYXYACC7ZD6IUYCDNW/bundle.json","state_url":"https://pith.science/pith/QY7X3O5TAYXYACC7ZD6IUYCDNW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QY7X3O5TAYXYACC7ZD6IUYCDNW/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":"2026-06-27T07:04:38Z","links":{"resolver":"https://pith.science/pith/QY7X3O5TAYXYACC7ZD6IUYCDNW","bundle":"https://pith.science/pith/QY7X3O5TAYXYACC7ZD6IUYCDNW/bundle.json","state":"https://pith.science/pith/QY7X3O5TAYXYACC7ZD6IUYCDNW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QY7X3O5TAYXYACC7ZD6IUYCDNW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:QY7X3O5TAYXYACC7ZD6IUYCDNW","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":"e458edb621d83c0ffb3b4b7111c77e09b471af0978e48f1582a481863db23ce7","cross_cats_sorted":["cs.NA","hep-lat","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-09-06T08:55:21Z","title_canon_sha256":"b60324e0776a0ec735115c5712d63ff35b38fd626479d2c3eef2afcb6b1e7cad"},"schema_version":"1.0","source":{"id":"2209.02302","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.02302","created_at":"2026-05-18T02:44:39Z"},{"alias_kind":"arxiv_version","alias_value":"2209.02302v3","created_at":"2026-05-18T02:44:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.02302","created_at":"2026-05-18T02:44:39Z"},{"alias_kind":"pith_short_12","alias_value":"QY7X3O5TAYXY","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"QY7X3O5TAYXYACC7","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"QY7X3O5T","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:fbc15bedcc0bdf6f3d6bcc4dabab06e038bad703c407a2d82391da190c18c36f","target":"graph","created_at":"2026-05-18T02:44:39Z","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":"Prompted by an observation about the integral of exponential functions of the form $f(x)=\\lambda e^{\\alpha x}$, we investigate the possibility to exactly integrate families of functions generated from a given function by scaling or by affine transformations of the argument using nonlinear generalizations of quadrature formulae. The main result of this paper is that such formulae can be explicitly constructed for a wide class of functions, and have the same accuracy as Newton-Cotes formulae based on the same nodes, with the latter emerging as the linear case of our general formalism. We also de","authors_text":"Georg M. von Hippel","cross_cats":["cs.NA","hep-lat","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-09-06T08:55:21Z","title":"Towards non-linear quadrature formulae"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.02302","kind":"arxiv","version":3},"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":"sha256:5f08616b6d78a442b3787f3159a8534dafa23cc801d63a3887740de93d51b3e8","target":"record","created_at":"2026-05-18T02:44:39Z","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":"e458edb621d83c0ffb3b4b7111c77e09b471af0978e48f1582a481863db23ce7","cross_cats_sorted":["cs.NA","hep-lat","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-09-06T08:55:21Z","title_canon_sha256":"b60324e0776a0ec735115c5712d63ff35b38fd626479d2c3eef2afcb6b1e7cad"},"schema_version":"1.0","source":{"id":"2209.02302","kind":"arxiv","version":3}},"canonical_sha256":"863f7dbbb3062f80085fc8fc8a60436db123a3d7fe6e927f0c8e761beac842f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"863f7dbbb3062f80085fc8fc8a60436db123a3d7fe6e927f0c8e761beac842f1","first_computed_at":"2026-05-18T02:44:39.899563Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:39.899563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YRyzcWmMBG1fZR5X4/K7lLLhll/agrYcFRdHDKhyYXRRRyRQapFWMJkqBqdry5WjryNhTV4+vTnkg7vzRatpDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:39.900082Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.02302","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f08616b6d78a442b3787f3159a8534dafa23cc801d63a3887740de93d51b3e8","sha256:fbc15bedcc0bdf6f3d6bcc4dabab06e038bad703c407a2d82391da190c18c36f"],"state_sha256":"3df2bb889b73fb1d7c12eb442b4f683e2a073e0d7de6cc4772deb3d95944bac2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5qHu+E6OlkYI6TbxwTT6cGb/b1epgZ8Opd3dQTMzMxX6HAstBXuvvXax8vMfnf/iMMnrkPf+LiwGp9ajVM25Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T07:04:38.049488Z","bundle_sha256":"7b462b8d78f23e70eaad56beed0f46df2bb0c1fcb4b17915f458111c3beab098"}}