{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4BGXUBKKA2RNP5IOJ4LWDPZG3A","short_pith_number":"pith:4BGXUBKK","canonical_record":{"source":{"id":"1712.07050","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-12-19T17:06:01Z","cross_cats_sorted":["hep-ph","math.AG","math.CV"],"title_canon_sha256":"e6dcd9dee515d296df40210a27eea02c735b1a6b62eac580e10506a29415c1e7","abstract_canon_sha256":"94b55eaf93ea64bd5d7748647d5974a784a0c0bdb9092d4c1fccbc0135b4d022"},"schema_version":"1.0"},"canonical_sha256":"e04d7a054a06a2d7f50e4f1761bf26d82d09f3d5f2980653d46afb98e1a8e676","source":{"kind":"arxiv","id":"1712.07050","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.07050","created_at":"2026-05-18T00:04:13Z"},{"alias_kind":"arxiv_version","alias_value":"1712.07050v1","created_at":"2026-05-18T00:04:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.07050","created_at":"2026-05-18T00:04:13Z"},{"alias_kind":"pith_short_12","alias_value":"4BGXUBKKA2RN","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4BGXUBKKA2RNP5IO","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4BGXUBKK","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4BGXUBKKA2RNP5IOJ4LWDPZG3A","target":"record","payload":{"canonical_record":{"source":{"id":"1712.07050","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-12-19T17:06:01Z","cross_cats_sorted":["hep-ph","math.AG","math.CV"],"title_canon_sha256":"e6dcd9dee515d296df40210a27eea02c735b1a6b62eac580e10506a29415c1e7","abstract_canon_sha256":"94b55eaf93ea64bd5d7748647d5974a784a0c0bdb9092d4c1fccbc0135b4d022"},"schema_version":"1.0"},"canonical_sha256":"e04d7a054a06a2d7f50e4f1761bf26d82d09f3d5f2980653d46afb98e1a8e676","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:13.411504Z","signature_b64":"WFZL41zd9Xx7SQsZii7Eov3QSCqHXVJ+V07lVLTGi57jsDrC7XNZrQJscbVB1vR7y5nd07gk9ZgpDLsF+MGzCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e04d7a054a06a2d7f50e4f1761bf26d82d09f3d5f2980653d46afb98e1a8e676","last_reissued_at":"2026-05-18T00:04:13.410705Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:13.410705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.07050","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":"2026-05-18T00:04:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CF4e+2DKdOKTrvw5DS+4Bhjzaf9CUbr9vBxl0M7BdHfmyOeGaeoxOV2Rtqec01Q4YtLSuvIB2J6Przj4P2AlDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:47:22.757868Z"},"content_sha256":"e98d9247584b6b97eef20dc8b546a3a5511f12953e44e7352130dad961f444da","schema_version":"1.0","event_id":"sha256:e98d9247584b6b97eef20dc8b546a3a5511f12953e44e7352130dad961f444da"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4BGXUBKKA2RNP5IOJ4LWDPZG3A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"MultivariateResidues - a Mathematica package for computing multivariate residues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","math.AG","math.CV"],"primary_cat":"hep-th","authors_text":"Kasper J. Larsen, Robbert Rietkerk","submitted_at":"2017-12-19T17:06:01Z","abstract_excerpt":"We present the Mathematica package MultivariateResidues, which allows for the efficient evaluation of multivariate residues based on methods from computational algebraic geometry. Multivariate residues appear in several contexts of scattering amplitude computations. Examples include applications to the extraction of master integral coefficients from maximal unitarity cuts, the construction of canonical bases of loop integrals and the construction of tree amplitudes from scattering equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.07050","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":""},"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":"2026-05-18T00:04:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nq6z4HLVplha420mdV2UiaNPEEf3GJd5rdmQGX6YGHeDq9Ntbm+ypERrObAy/IOqFUgYkX/I3Rsohl3uj075Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:47:22.758219Z"},"content_sha256":"45680af952261a9bf955a823127eb94be93388807e01b418289c89505bddf3b0","schema_version":"1.0","event_id":"sha256:45680af952261a9bf955a823127eb94be93388807e01b418289c89505bddf3b0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4BGXUBKKA2RNP5IOJ4LWDPZG3A/bundle.json","state_url":"https://pith.science/pith/4BGXUBKKA2RNP5IOJ4LWDPZG3A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4BGXUBKKA2RNP5IOJ4LWDPZG3A/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":"2026-06-01T13:47:22Z","links":{"resolver":"https://pith.science/pith/4BGXUBKKA2RNP5IOJ4LWDPZG3A","bundle":"https://pith.science/pith/4BGXUBKKA2RNP5IOJ4LWDPZG3A/bundle.json","state":"https://pith.science/pith/4BGXUBKKA2RNP5IOJ4LWDPZG3A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4BGXUBKKA2RNP5IOJ4LWDPZG3A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4BGXUBKKA2RNP5IOJ4LWDPZG3A","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":"94b55eaf93ea64bd5d7748647d5974a784a0c0bdb9092d4c1fccbc0135b4d022","cross_cats_sorted":["hep-ph","math.AG","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-12-19T17:06:01Z","title_canon_sha256":"e6dcd9dee515d296df40210a27eea02c735b1a6b62eac580e10506a29415c1e7"},"schema_version":"1.0","source":{"id":"1712.07050","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.07050","created_at":"2026-05-18T00:04:13Z"},{"alias_kind":"arxiv_version","alias_value":"1712.07050v1","created_at":"2026-05-18T00:04:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.07050","created_at":"2026-05-18T00:04:13Z"},{"alias_kind":"pith_short_12","alias_value":"4BGXUBKKA2RN","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4BGXUBKKA2RNP5IO","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4BGXUBKK","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:45680af952261a9bf955a823127eb94be93388807e01b418289c89505bddf3b0","target":"graph","created_at":"2026-05-18T00:04:13Z","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":"We present the Mathematica package MultivariateResidues, which allows for the efficient evaluation of multivariate residues based on methods from computational algebraic geometry. Multivariate residues appear in several contexts of scattering amplitude computations. Examples include applications to the extraction of master integral coefficients from maximal unitarity cuts, the construction of canonical bases of loop integrals and the construction of tree amplitudes from scattering equations.","authors_text":"Kasper J. Larsen, Robbert Rietkerk","cross_cats":["hep-ph","math.AG","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-12-19T17:06:01Z","title":"MultivariateResidues - a Mathematica package for computing multivariate residues"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.07050","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:e98d9247584b6b97eef20dc8b546a3a5511f12953e44e7352130dad961f444da","target":"record","created_at":"2026-05-18T00:04:13Z","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":"94b55eaf93ea64bd5d7748647d5974a784a0c0bdb9092d4c1fccbc0135b4d022","cross_cats_sorted":["hep-ph","math.AG","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-12-19T17:06:01Z","title_canon_sha256":"e6dcd9dee515d296df40210a27eea02c735b1a6b62eac580e10506a29415c1e7"},"schema_version":"1.0","source":{"id":"1712.07050","kind":"arxiv","version":1}},"canonical_sha256":"e04d7a054a06a2d7f50e4f1761bf26d82d09f3d5f2980653d46afb98e1a8e676","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e04d7a054a06a2d7f50e4f1761bf26d82d09f3d5f2980653d46afb98e1a8e676","first_computed_at":"2026-05-18T00:04:13.410705Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:13.410705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WFZL41zd9Xx7SQsZii7Eov3QSCqHXVJ+V07lVLTGi57jsDrC7XNZrQJscbVB1vR7y5nd07gk9ZgpDLsF+MGzCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:13.411504Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.07050","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e98d9247584b6b97eef20dc8b546a3a5511f12953e44e7352130dad961f444da","sha256:45680af952261a9bf955a823127eb94be93388807e01b418289c89505bddf3b0"],"state_sha256":"542ea13c9800ea595632781cdfe49e1eace450929556d2fb25f9a68521e23ee5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"krAAwDXiFrM8TMgJiyU5QfidMonfTkg49VFP9CIoJxwf9QQNVpFP2zZpn04AmPldPYpWtbUWDDY6HjTPO6zzDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T13:47:22.760380Z","bundle_sha256":"eb92a1912fb6c5fce35abe3c626d6add96e74032ad82ad52a7e22eab0179d05d"}}