{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:T27BIMKSFGRQY2DCTW4JA66ZTU","short_pith_number":"pith:T27BIMKS","canonical_record":{"source":{"id":"1904.00009","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2019-03-29T18:54:01Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"8a43f88549fd959d056b9ca0d63450bf35343ad17bc51b5cd6f2edddbeca4825","abstract_canon_sha256":"b77e982f0ca5d6f20aee344d37950800737de85d48c6a428fc3d05f3c67ddef9"},"schema_version":"1.0"},"canonical_sha256":"9ebe14315229a30c68629db8907bd99d2c8ec00460266f82b474569b32599644","source":{"kind":"arxiv","id":"1904.00009","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.00009","created_at":"2026-07-05T00:22:23Z"},{"alias_kind":"arxiv_version","alias_value":"1904.00009v2","created_at":"2026-07-05T00:22:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.00009","created_at":"2026-07-05T00:22:23Z"},{"alias_kind":"pith_short_12","alias_value":"T27BIMKSFGRQ","created_at":"2026-07-05T00:22:23Z"},{"alias_kind":"pith_short_16","alias_value":"T27BIMKSFGRQY2DC","created_at":"2026-07-05T00:22:23Z"},{"alias_kind":"pith_short_8","alias_value":"T27BIMKS","created_at":"2026-07-05T00:22:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:T27BIMKSFGRQY2DCTW4JA66ZTU","target":"record","payload":{"canonical_record":{"source":{"id":"1904.00009","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2019-03-29T18:54:01Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"8a43f88549fd959d056b9ca0d63450bf35343ad17bc51b5cd6f2edddbeca4825","abstract_canon_sha256":"b77e982f0ca5d6f20aee344d37950800737de85d48c6a428fc3d05f3c67ddef9"},"schema_version":"1.0"},"canonical_sha256":"9ebe14315229a30c68629db8907bd99d2c8ec00460266f82b474569b32599644","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:22:23.684065Z","signature_b64":"qT2yRn2mggRR8z16dhYnRoMiuWLXD4dOTH8HbcFH9UfBlHY7JeQCIL1PjlPAN4NNfbs5dm31a6q58qv4Ui24Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ebe14315229a30c68629db8907bd99d2c8ec00460266f82b474569b32599644","last_reissued_at":"2026-07-05T00:22:23.683578Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:22:23.683578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.00009","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":"2026-07-05T00:22:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"58m1tPmF0WU9EZPMe1i9XIGuU8IT8+ovvibli7jmniGsoQYL0k90D/OYgdHJgYf/8KkdKe8Sdnk5uw+I10+DAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T06:12:45.409846Z"},"content_sha256":"51adbe7307c6c7d81aa695a58383770669a89ace533dc7baefe4e6ce2602dfee","schema_version":"1.0","event_id":"sha256:51adbe7307c6c7d81aa695a58383770669a89ace533dc7baefe4e6ce2602dfee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:T27BIMKSFGRQY2DCTW4JA66ZTU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reconstructing Rational Functions with $\\texttt{FireFly}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"cs.SC","authors_text":"Fabian Lange, Jonas Klappert","submitted_at":"2019-03-29T18:54:01Z","abstract_excerpt":"We present the open-source $\\texttt{C++}$ library $\\texttt{FireFly}$ for the reconstruction of multivariate rational functions over finite fields. We discuss the involved algorithms and their implementation. As an application, we use $\\texttt{FireFly}$ in the context of integration-by-parts reductions and compare runtime and memory consumption to a fully algebraic approach with the program $\\texttt{Kira}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.00009","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/1904.00009/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":"2026-07-05T00:22:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qXBsOARZAign96xVh0TzNK0rFdTGON8eOGeB9D1bCCaVS1qURNsol6/gFYgnz6+oqpCRVzRCghgpbPwcUqz6Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T06:12:45.410338Z"},"content_sha256":"30aa997601b53644549a2be4ea7e13bb146f26c3aaad80fe5f767718f8738971","schema_version":"1.0","event_id":"sha256:30aa997601b53644549a2be4ea7e13bb146f26c3aaad80fe5f767718f8738971"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T27BIMKSFGRQY2DCTW4JA66ZTU/bundle.json","state_url":"https://pith.science/pith/T27BIMKSFGRQY2DCTW4JA66ZTU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T27BIMKSFGRQY2DCTW4JA66ZTU/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":"2026-08-04T06:12:45Z","links":{"resolver":"https://pith.science/pith/T27BIMKSFGRQY2DCTW4JA66ZTU","bundle":"https://pith.science/pith/T27BIMKSFGRQY2DCTW4JA66ZTU/bundle.json","state":"https://pith.science/pith/T27BIMKSFGRQY2DCTW4JA66ZTU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T27BIMKSFGRQY2DCTW4JA66ZTU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:T27BIMKSFGRQY2DCTW4JA66ZTU","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":"b77e982f0ca5d6f20aee344d37950800737de85d48c6a428fc3d05f3c67ddef9","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2019-03-29T18:54:01Z","title_canon_sha256":"8a43f88549fd959d056b9ca0d63450bf35343ad17bc51b5cd6f2edddbeca4825"},"schema_version":"1.0","source":{"id":"1904.00009","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.00009","created_at":"2026-07-05T00:22:23Z"},{"alias_kind":"arxiv_version","alias_value":"1904.00009v2","created_at":"2026-07-05T00:22:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.00009","created_at":"2026-07-05T00:22:23Z"},{"alias_kind":"pith_short_12","alias_value":"T27BIMKSFGRQ","created_at":"2026-07-05T00:22:23Z"},{"alias_kind":"pith_short_16","alias_value":"T27BIMKSFGRQY2DC","created_at":"2026-07-05T00:22:23Z"},{"alias_kind":"pith_short_8","alias_value":"T27BIMKS","created_at":"2026-07-05T00:22:23Z"}],"graph_snapshots":[{"event_id":"sha256:30aa997601b53644549a2be4ea7e13bb146f26c3aaad80fe5f767718f8738971","target":"graph","created_at":"2026-07-05T00:22:23Z","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/1904.00009/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present the open-source $\\texttt{C++}$ library $\\texttt{FireFly}$ for the reconstruction of multivariate rational functions over finite fields. We discuss the involved algorithms and their implementation. As an application, we use $\\texttt{FireFly}$ in the context of integration-by-parts reductions and compare runtime and memory consumption to a fully algebraic approach with the program $\\texttt{Kira}$.","authors_text":"Fabian Lange, Jonas Klappert","cross_cats":["hep-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2019-03-29T18:54:01Z","title":"Reconstructing Rational Functions with $\\texttt{FireFly}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.00009","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":"sha256:51adbe7307c6c7d81aa695a58383770669a89ace533dc7baefe4e6ce2602dfee","target":"record","created_at":"2026-07-05T00:22:23Z","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":"b77e982f0ca5d6f20aee344d37950800737de85d48c6a428fc3d05f3c67ddef9","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2019-03-29T18:54:01Z","title_canon_sha256":"8a43f88549fd959d056b9ca0d63450bf35343ad17bc51b5cd6f2edddbeca4825"},"schema_version":"1.0","source":{"id":"1904.00009","kind":"arxiv","version":2}},"canonical_sha256":"9ebe14315229a30c68629db8907bd99d2c8ec00460266f82b474569b32599644","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ebe14315229a30c68629db8907bd99d2c8ec00460266f82b474569b32599644","first_computed_at":"2026-07-05T00:22:23.683578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:22:23.683578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qT2yRn2mggRR8z16dhYnRoMiuWLXD4dOTH8HbcFH9UfBlHY7JeQCIL1PjlPAN4NNfbs5dm31a6q58qv4Ui24Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T00:22:23.684065Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.00009","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51adbe7307c6c7d81aa695a58383770669a89ace533dc7baefe4e6ce2602dfee","sha256:30aa997601b53644549a2be4ea7e13bb146f26c3aaad80fe5f767718f8738971"],"state_sha256":"cc6641994530c390491592dd9c12479aafe937c3c04f537bd43eef881e17d9c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rnJRTNwwXAqdNj/pVEvEV9RAGt5PFh8n98cpbSABmmSUtD5/tvTi487fmcrecoFp2AOpyteX+1Tf0PTUYxAoCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T06:12:45.415228Z","bundle_sha256":"923ad5d36556930a8cff33133a2af36765f0b0f620a832e181f05e3e7b641ba5"}}