{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:HPZUJIAH6WYQGA2SKI7V4VS5I6","short_pith_number":"pith:HPZUJIAH","canonical_record":{"source":{"id":"2211.02834","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2022-11-05T07:34:44Z","cross_cats_sorted":[],"title_canon_sha256":"6e51435d77c8cec4db048fffd8ecc5cfd4dffc188866b477d2559483dcc4d0ed","abstract_canon_sha256":"a5cbe0bd421412e6e2cdcc5b3d6fdc5bbd3e74cc910166688959d02753964d2a"},"schema_version":"1.0"},"canonical_sha256":"3bf344a007f5b1030352523f5e565d47bd5bbeccb36e1e94efde52645da761be","source":{"kind":"arxiv","id":"2211.02834","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.02834","created_at":"2026-07-05T06:00:06Z"},{"alias_kind":"arxiv_version","alias_value":"2211.02834v2","created_at":"2026-07-05T06:00:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.02834","created_at":"2026-07-05T06:00:06Z"},{"alias_kind":"pith_short_12","alias_value":"HPZUJIAH6WYQ","created_at":"2026-07-05T06:00:06Z"},{"alias_kind":"pith_short_16","alias_value":"HPZUJIAH6WYQGA2S","created_at":"2026-07-05T06:00:06Z"},{"alias_kind":"pith_short_8","alias_value":"HPZUJIAH","created_at":"2026-07-05T06:00:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:HPZUJIAH6WYQGA2SKI7V4VS5I6","target":"record","payload":{"canonical_record":{"source":{"id":"2211.02834","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2022-11-05T07:34:44Z","cross_cats_sorted":[],"title_canon_sha256":"6e51435d77c8cec4db048fffd8ecc5cfd4dffc188866b477d2559483dcc4d0ed","abstract_canon_sha256":"a5cbe0bd421412e6e2cdcc5b3d6fdc5bbd3e74cc910166688959d02753964d2a"},"schema_version":"1.0"},"canonical_sha256":"3bf344a007f5b1030352523f5e565d47bd5bbeccb36e1e94efde52645da761be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:00:06.148535Z","signature_b64":"FEcPyQSoBALBBx1ESN1KnKciIyN/CECuRbRl5aXHSFryPLBqWYrm1r0BdmKnXpNVklpWbs10cLeh3shnaaCeBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3bf344a007f5b1030352523f5e565d47bd5bbeccb36e1e94efde52645da761be","last_reissued_at":"2026-07-05T06:00:06.148102Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:00:06.148102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2211.02834","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":"2026-07-05T06:00:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tgT7x6aCzWjSKRNNH4XElvRNF41lh8zXnW6VqRAZvGODLnR6J1I7QfmXkZZGNRXpc8M2H0qJxro7zDp9T4TSBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T21:13:44.358924Z"},"content_sha256":"32344f583448e6bbf75e3d3219da216499fa915924a37d45cf5b888501f589ad","schema_version":"1.0","event_id":"sha256:32344f583448e6bbf75e3d3219da216499fa915924a37d45cf5b888501f589ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:HPZUJIAH6WYQGA2SKI7V4VS5I6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multi-variable Integration with a Neural Network","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Daniel Ma\\^itre, Roi Santos-Mateos","submitted_at":"2022-11-05T07:34:44Z","abstract_excerpt":"In this article we present a method for automatic integration of parametric integrals over the unit hypercube using a neural network. The method fits a neural network to the primitive of the integrand using a loss function designed to minimize the difference between multiple derivatives of the network and the function to be integrated. We apply this method to two example integrals resulting from the sector decomposition of a one-loop and two-loop scalar integrals. Our method can achieve per-mil and percent accuracy for these integrals over a range of invariant values. Once the neural network i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.02834","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.02834/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":"2026-07-05T06:00:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QsBO0I9lpRWQvVZ4GHRYvs0PklxnZnyeYtUe4mbilsWujAeu63pMTxdJEy5d8g2ucXmpAdcR/br4eHYQsz0WBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T21:13:44.359403Z"},"content_sha256":"6cc4c961928e27b81edf534028fe15cfcbbbe352d394cdb2d54e4f05704168ec","schema_version":"1.0","event_id":"sha256:6cc4c961928e27b81edf534028fe15cfcbbbe352d394cdb2d54e4f05704168ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HPZUJIAH6WYQGA2SKI7V4VS5I6/bundle.json","state_url":"https://pith.science/pith/HPZUJIAH6WYQGA2SKI7V4VS5I6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HPZUJIAH6WYQGA2SKI7V4VS5I6/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":"2026-08-16T21:13:44Z","links":{"resolver":"https://pith.science/pith/HPZUJIAH6WYQGA2SKI7V4VS5I6","bundle":"https://pith.science/pith/HPZUJIAH6WYQGA2SKI7V4VS5I6/bundle.json","state":"https://pith.science/pith/HPZUJIAH6WYQGA2SKI7V4VS5I6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HPZUJIAH6WYQGA2SKI7V4VS5I6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:HPZUJIAH6WYQGA2SKI7V4VS5I6","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":"a5cbe0bd421412e6e2cdcc5b3d6fdc5bbd3e74cc910166688959d02753964d2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2022-11-05T07:34:44Z","title_canon_sha256":"6e51435d77c8cec4db048fffd8ecc5cfd4dffc188866b477d2559483dcc4d0ed"},"schema_version":"1.0","source":{"id":"2211.02834","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.02834","created_at":"2026-07-05T06:00:06Z"},{"alias_kind":"arxiv_version","alias_value":"2211.02834v2","created_at":"2026-07-05T06:00:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.02834","created_at":"2026-07-05T06:00:06Z"},{"alias_kind":"pith_short_12","alias_value":"HPZUJIAH6WYQ","created_at":"2026-07-05T06:00:06Z"},{"alias_kind":"pith_short_16","alias_value":"HPZUJIAH6WYQGA2S","created_at":"2026-07-05T06:00:06Z"},{"alias_kind":"pith_short_8","alias_value":"HPZUJIAH","created_at":"2026-07-05T06:00:06Z"}],"graph_snapshots":[{"event_id":"sha256:6cc4c961928e27b81edf534028fe15cfcbbbe352d394cdb2d54e4f05704168ec","target":"graph","created_at":"2026-07-05T06:00:06Z","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/2211.02834/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article we present a method for automatic integration of parametric integrals over the unit hypercube using a neural network. The method fits a neural network to the primitive of the integrand using a loss function designed to minimize the difference between multiple derivatives of the network and the function to be integrated. We apply this method to two example integrals resulting from the sector decomposition of a one-loop and two-loop scalar integrals. Our method can achieve per-mil and percent accuracy for these integrals over a range of invariant values. Once the neural network i","authors_text":"Daniel Ma\\^itre, Roi Santos-Mateos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2022-11-05T07:34:44Z","title":"Multi-variable Integration with a Neural Network"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.02834","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":"sha256:32344f583448e6bbf75e3d3219da216499fa915924a37d45cf5b888501f589ad","target":"record","created_at":"2026-07-05T06:00:06Z","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":"a5cbe0bd421412e6e2cdcc5b3d6fdc5bbd3e74cc910166688959d02753964d2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2022-11-05T07:34:44Z","title_canon_sha256":"6e51435d77c8cec4db048fffd8ecc5cfd4dffc188866b477d2559483dcc4d0ed"},"schema_version":"1.0","source":{"id":"2211.02834","kind":"arxiv","version":2}},"canonical_sha256":"3bf344a007f5b1030352523f5e565d47bd5bbeccb36e1e94efde52645da761be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3bf344a007f5b1030352523f5e565d47bd5bbeccb36e1e94efde52645da761be","first_computed_at":"2026-07-05T06:00:06.148102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:00:06.148102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FEcPyQSoBALBBx1ESN1KnKciIyN/CECuRbRl5aXHSFryPLBqWYrm1r0BdmKnXpNVklpWbs10cLeh3shnaaCeBg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:00:06.148535Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.02834","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32344f583448e6bbf75e3d3219da216499fa915924a37d45cf5b888501f589ad","sha256:6cc4c961928e27b81edf534028fe15cfcbbbe352d394cdb2d54e4f05704168ec"],"state_sha256":"841061791c2cbbaa94c00af264500a581cb5a8abce7205902a6fe655aff145fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0tODDZPSltaPBIXqRDXawUKEsLdkDYRuK5kFG44cirq89d8KHV7mRdIqoV6CB2i2LqWFq39elHvQ+9WzoHp1Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T21:13:44.364490Z","bundle_sha256":"ea64699ce08aafa09c9da984fc454acabb531a17023bf07d9af13c852db7c496"}}