{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:WFTGUZCYZDKEZUFZAWEOO77TNS","short_pith_number":"pith:WFTGUZCY","canonical_record":{"source":{"id":"2312.03672","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"hep-ph","submitted_at":"2023-12-06T18:37:51Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"bfbd42a8bb2f30f3c8d3e5276bfd17f8a11bf02d490819eba4af731fb420e0dd","abstract_canon_sha256":"2c4eae51e682af9ed871da813ad75534d1f4d1f169e9746f7bf13e7b137f1e75"},"schema_version":"1.0"},"canonical_sha256":"b1666a6458c8d44cd0b90588e77ff36c80797ef5d01b2490db80033159e81e93","source":{"kind":"arxiv","id":"2312.03672","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.03672","created_at":"2026-07-05T09:08:22Z"},{"alias_kind":"arxiv_version","alias_value":"2312.03672v2","created_at":"2026-07-05T09:08:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.03672","created_at":"2026-07-05T09:08:22Z"},{"alias_kind":"pith_short_12","alias_value":"WFTGUZCYZDKE","created_at":"2026-07-05T09:08:22Z"},{"alias_kind":"pith_short_16","alias_value":"WFTGUZCYZDKEZUFZ","created_at":"2026-07-05T09:08:22Z"},{"alias_kind":"pith_short_8","alias_value":"WFTGUZCY","created_at":"2026-07-05T09:08:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:WFTGUZCYZDKEZUFZAWEOO77TNS","target":"record","payload":{"canonical_record":{"source":{"id":"2312.03672","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"hep-ph","submitted_at":"2023-12-06T18:37:51Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"bfbd42a8bb2f30f3c8d3e5276bfd17f8a11bf02d490819eba4af731fb420e0dd","abstract_canon_sha256":"2c4eae51e682af9ed871da813ad75534d1f4d1f169e9746f7bf13e7b137f1e75"},"schema_version":"1.0"},"canonical_sha256":"b1666a6458c8d44cd0b90588e77ff36c80797ef5d01b2490db80033159e81e93","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:08:22.024412Z","signature_b64":"bsUAwV4Q0pUbapVkm8p+3Ie4ATRTVlFdLkIpbp2yxNmVGDx04ppr9jHdgUz9Mir+9mYP5VB0crLhy0YFVcKDCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1666a6458c8d44cd0b90588e77ff36c80797ef5d01b2490db80033159e81e93","last_reissued_at":"2026-07-05T09:08:22.023820Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:08:22.023820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.03672","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":"2026-07-05T09:08:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LtS6AcsUQO3ca9VzAWP8xvpxqqN/NUNNWVM+pjrDKhdad5Ob/s15jp+NcuuslOicmZrO9xOiEIeXume8HrZoDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T07:08:38.255592Z"},"content_sha256":"7b78927fe2b7b3cb4fbe16ab7aeb0480cd65567032091d3279ae6eb2cf1e2aec","schema_version":"1.0","event_id":"sha256:7b78927fe2b7b3cb4fbe16ab7aeb0480cd65567032091d3279ae6eb2cf1e2aec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:WFTGUZCYZDKEZUFZAWEOO77TNS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"p-adic reconstruction of rational functions in multi-loop amplitudes","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"Herschel A. Chawdhry","submitted_at":"2023-12-06T18:37:51Z","abstract_excerpt":"Numerical reconstruction techniques are widely employed in the calculation of multi-loop scattering amplitudes. In recent years, it has been observed that the rational functions in multi-loop calculations greatly simplify under partial fractioning. In this article, we present a technique to reconstruct rational functions directly in partial-fractioned form, by evaluating the functions at special integer points chosen for their properties under a p-adic metric. As an application, we apply this technique to reconstruct the largest rational function in the integration-by-parts reduction of one of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.03672","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/2312.03672/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":"2026-07-05T09:08:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WiMVBvzq/GYmAcz8A9F/Y4vHz9LQsceWJtwjFWxqrTBAUdt+VoVLklHNVxsylo3JZXHxeTmfRYF3H6H7nDZYDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T07:08:38.256216Z"},"content_sha256":"fc37ee0d266db7c35334c93a62ed36542f5eca62785bb1584e8a0a6831d4849c","schema_version":"1.0","event_id":"sha256:fc37ee0d266db7c35334c93a62ed36542f5eca62785bb1584e8a0a6831d4849c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WFTGUZCYZDKEZUFZAWEOO77TNS/bundle.json","state_url":"https://pith.science/pith/WFTGUZCYZDKEZUFZAWEOO77TNS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WFTGUZCYZDKEZUFZAWEOO77TNS/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":"2026-08-20T07:08:38Z","links":{"resolver":"https://pith.science/pith/WFTGUZCYZDKEZUFZAWEOO77TNS","bundle":"https://pith.science/pith/WFTGUZCYZDKEZUFZAWEOO77TNS/bundle.json","state":"https://pith.science/pith/WFTGUZCYZDKEZUFZAWEOO77TNS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WFTGUZCYZDKEZUFZAWEOO77TNS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:WFTGUZCYZDKEZUFZAWEOO77TNS","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":"2c4eae51e682af9ed871da813ad75534d1f4d1f169e9746f7bf13e7b137f1e75","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"hep-ph","submitted_at":"2023-12-06T18:37:51Z","title_canon_sha256":"bfbd42a8bb2f30f3c8d3e5276bfd17f8a11bf02d490819eba4af731fb420e0dd"},"schema_version":"1.0","source":{"id":"2312.03672","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.03672","created_at":"2026-07-05T09:08:22Z"},{"alias_kind":"arxiv_version","alias_value":"2312.03672v2","created_at":"2026-07-05T09:08:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.03672","created_at":"2026-07-05T09:08:22Z"},{"alias_kind":"pith_short_12","alias_value":"WFTGUZCYZDKE","created_at":"2026-07-05T09:08:22Z"},{"alias_kind":"pith_short_16","alias_value":"WFTGUZCYZDKEZUFZ","created_at":"2026-07-05T09:08:22Z"},{"alias_kind":"pith_short_8","alias_value":"WFTGUZCY","created_at":"2026-07-05T09:08:22Z"}],"graph_snapshots":[{"event_id":"sha256:fc37ee0d266db7c35334c93a62ed36542f5eca62785bb1584e8a0a6831d4849c","target":"graph","created_at":"2026-07-05T09:08:22Z","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/2312.03672/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Numerical reconstruction techniques are widely employed in the calculation of multi-loop scattering amplitudes. In recent years, it has been observed that the rational functions in multi-loop calculations greatly simplify under partial fractioning. In this article, we present a technique to reconstruct rational functions directly in partial-fractioned form, by evaluating the functions at special integer points chosen for their properties under a p-adic metric. As an application, we apply this technique to reconstruct the largest rational function in the integration-by-parts reduction of one of","authors_text":"Herschel A. Chawdhry","cross_cats":["hep-th"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"hep-ph","submitted_at":"2023-12-06T18:37:51Z","title":"p-adic reconstruction of rational functions in multi-loop amplitudes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.03672","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":"sha256:7b78927fe2b7b3cb4fbe16ab7aeb0480cd65567032091d3279ae6eb2cf1e2aec","target":"record","created_at":"2026-07-05T09:08:22Z","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":"2c4eae51e682af9ed871da813ad75534d1f4d1f169e9746f7bf13e7b137f1e75","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"hep-ph","submitted_at":"2023-12-06T18:37:51Z","title_canon_sha256":"bfbd42a8bb2f30f3c8d3e5276bfd17f8a11bf02d490819eba4af731fb420e0dd"},"schema_version":"1.0","source":{"id":"2312.03672","kind":"arxiv","version":2}},"canonical_sha256":"b1666a6458c8d44cd0b90588e77ff36c80797ef5d01b2490db80033159e81e93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1666a6458c8d44cd0b90588e77ff36c80797ef5d01b2490db80033159e81e93","first_computed_at":"2026-07-05T09:08:22.023820Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:08:22.023820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bsUAwV4Q0pUbapVkm8p+3Ie4ATRTVlFdLkIpbp2yxNmVGDx04ppr9jHdgUz9Mir+9mYP5VB0crLhy0YFVcKDCw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:08:22.024412Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.03672","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b78927fe2b7b3cb4fbe16ab7aeb0480cd65567032091d3279ae6eb2cf1e2aec","sha256:fc37ee0d266db7c35334c93a62ed36542f5eca62785bb1584e8a0a6831d4849c"],"state_sha256":"da0856aa15a360b3e59d0b25185df6d4b4bf341033407b0047b9be0853c042f8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NJ/wJ8JzC+oN7LadznbR+ykHfAFxYzzT5+Op9RpRVi45f1q9Y2yeWbgmzw42ACR3C8N4O4C7la0nJvOjyRTmBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T07:08:38.260693Z","bundle_sha256":"efe80a6da58cdba6bf627e3e4f18bb5d0b163adab01c2ac51be15c494360f683"}}