{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:QCRNUGFGE7TN577FBEZMV3MB5H","short_pith_number":"pith:QCRNUGFG","schema_version":"1.0","canonical_sha256":"80a2da18a627e6deffe50932caed81e9cc4b0ba0ff2a8bc35867be3c96dfd5bb","source":{"kind":"arxiv","id":"0808.2543","version":1},"attestation_state":"computed","paper":{"title":"A Refined Difference Field Theory for Symbolic Summation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"cs.SC","authors_text":"Carsten Schneider","submitted_at":"2008-08-19T07:46:04Z","abstract_excerpt":"In this article we present a refined summation theory based on Karr's difference field approach. The resulting algorithms find sum representations with optimal nested depth. For instance, the algorithms have been applied successively to evaluate Feynman integrals from Perturbative Quantum Field Theory."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0808.2543","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2008-08-19T07:46:04Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"0c66f7a9697ce79798c40b3d8de4da1403304ef040a49f8e453628bc2b35033b","abstract_canon_sha256":"c0ad7f8b8c3736d311d5b25a7948a41fb60680cc7988cc0ed966b96121187883"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:13:58.761857Z","signature_b64":"9Ha/UAiRYuIELrJ5UTcFREw7elJ9uCNX5JZ7l+N/MGYxD8LSRhaMXVBaqVddk/U5LTMtAVMarUQovmtqxjeoBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80a2da18a627e6deffe50932caed81e9cc4b0ba0ff2a8bc35867be3c96dfd5bb","last_reissued_at":"2026-07-04T15:13:58.761510Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:13:58.761510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Refined Difference Field Theory for Symbolic Summation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"cs.SC","authors_text":"Carsten Schneider","submitted_at":"2008-08-19T07:46:04Z","abstract_excerpt":"In this article we present a refined summation theory based on Karr's difference field approach. The resulting algorithms find sum representations with optimal nested depth. For instance, the algorithms have been applied successively to evaluate Feynman integrals from Perturbative Quantum Field Theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.2543","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0808.2543/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0808.2543","created_at":"2026-07-04T15:13:58.761573+00:00"},{"alias_kind":"arxiv_version","alias_value":"0808.2543v1","created_at":"2026-07-04T15:13:58.761573+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.2543","created_at":"2026-07-04T15:13:58.761573+00:00"},{"alias_kind":"pith_short_12","alias_value":"QCRNUGFGE7TN","created_at":"2026-07-04T15:13:58.761573+00:00"},{"alias_kind":"pith_short_16","alias_value":"QCRNUGFGE7TN577F","created_at":"2026-07-04T15:13:58.761573+00:00"},{"alias_kind":"pith_short_8","alias_value":"QCRNUGFG","created_at":"2026-07-04T15:13:58.761573+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.03779","citing_title":"The Polarized Three-Loop Anomalous Dimensions from On-Shell Massive Operator Matrix Elements","ref_index":67,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QCRNUGFGE7TN577FBEZMV3MB5H","json":"https://pith.science/pith/QCRNUGFGE7TN577FBEZMV3MB5H.json","graph_json":"https://pith.science/api/pith-number/QCRNUGFGE7TN577FBEZMV3MB5H/graph.json","events_json":"https://pith.science/api/pith-number/QCRNUGFGE7TN577FBEZMV3MB5H/events.json","paper":"https://pith.science/paper/QCRNUGFG"},"agent_actions":{"view_html":"https://pith.science/pith/QCRNUGFGE7TN577FBEZMV3MB5H","download_json":"https://pith.science/pith/QCRNUGFGE7TN577FBEZMV3MB5H.json","view_paper":"https://pith.science/paper/QCRNUGFG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0808.2543&json=true","fetch_graph":"https://pith.science/api/pith-number/QCRNUGFGE7TN577FBEZMV3MB5H/graph.json","fetch_events":"https://pith.science/api/pith-number/QCRNUGFGE7TN577FBEZMV3MB5H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QCRNUGFGE7TN577FBEZMV3MB5H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QCRNUGFGE7TN577FBEZMV3MB5H/action/storage_attestation","attest_author":"https://pith.science/pith/QCRNUGFGE7TN577FBEZMV3MB5H/action/author_attestation","sign_citation":"https://pith.science/pith/QCRNUGFGE7TN577FBEZMV3MB5H/action/citation_signature","submit_replication":"https://pith.science/pith/QCRNUGFGE7TN577FBEZMV3MB5H/action/replication_record"}},"created_at":"2026-07-04T15:13:58.761573+00:00","updated_at":"2026-07-04T15:13:58.761573+00:00"}