{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:J5NX44BEDQFTPICLJLFF4KBNDE","short_pith_number":"pith:J5NX44BE","schema_version":"1.0","canonical_sha256":"4f5b7e70241c0b37a04b4aca5e282d190d693d3f8bdedd32def999800170fbe5","source":{"kind":"arxiv","id":"2605.20106","version":1},"attestation_state":"computed","paper":{"title":"Motivic Galois theory for one-loop Feynman integrals in momentum space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Ulysse Mounoud","submitted_at":"2026-05-19T16:57:33Z","abstract_excerpt":"We develop a motivic framework for Feynman integrals of one-loop graphs in momentum space. Its advantage compared to the already existing framework in Feynman representation is that it naturally includes graphs with cuts. To each such graph, we associate a motivic local system over the space of generic kinematics. Our construction is functorial with respect to the natural operations on graphs: edge contraction and cutting. We compute the weight-graded pieces of the motivic local systems. They are Tate twists of quadratic Artin motives associated with maximally cut quotient graphs. We also deri"},"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":"2605.20106","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-05-19T16:57:33Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"94f17acd466ee2940bdad49fd87e368d25206490649e254468811c3d894cf272","abstract_canon_sha256":"c099dd8d881eb1d7939368257db9c94774849996e43d61806b7e3b5e27cdd150"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T02:06:02.284224Z","signature_b64":"Jvuib7bLgFasGitpWgB2hjF0d5EoZnm3NS+5rS1obcBXAonEWMPn1h9BTBYol94g3u5UXxTSxuHEc7XulZHQBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f5b7e70241c0b37a04b4aca5e282d190d693d3f8bdedd32def999800170fbe5","last_reissued_at":"2026-05-20T02:06:02.283472Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T02:06:02.283472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Motivic Galois theory for one-loop Feynman integrals in momentum space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Ulysse Mounoud","submitted_at":"2026-05-19T16:57:33Z","abstract_excerpt":"We develop a motivic framework for Feynman integrals of one-loop graphs in momentum space. Its advantage compared to the already existing framework in Feynman representation is that it naturally includes graphs with cuts. To each such graph, we associate a motivic local system over the space of generic kinematics. Our construction is functorial with respect to the natural operations on graphs: edge contraction and cutting. We compute the weight-graded pieces of the motivic local systems. They are Tate twists of quadratic Artin motives associated with maximally cut quotient graphs. We also deri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20106","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/2605.20106/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":"2605.20106","created_at":"2026-05-20T02:06:02.283585+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.20106v1","created_at":"2026-05-20T02:06:02.283585+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20106","created_at":"2026-05-20T02:06:02.283585+00:00"},{"alias_kind":"pith_short_12","alias_value":"J5NX44BEDQFT","created_at":"2026-05-20T02:06:02.283585+00:00"},{"alias_kind":"pith_short_16","alias_value":"J5NX44BEDQFTPICL","created_at":"2026-05-20T02:06:02.283585+00:00"},{"alias_kind":"pith_short_8","alias_value":"J5NX44BE","created_at":"2026-05-20T02:06:02.283585+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/J5NX44BEDQFTPICLJLFF4KBNDE","json":"https://pith.science/pith/J5NX44BEDQFTPICLJLFF4KBNDE.json","graph_json":"https://pith.science/api/pith-number/J5NX44BEDQFTPICLJLFF4KBNDE/graph.json","events_json":"https://pith.science/api/pith-number/J5NX44BEDQFTPICLJLFF4KBNDE/events.json","paper":"https://pith.science/paper/J5NX44BE"},"agent_actions":{"view_html":"https://pith.science/pith/J5NX44BEDQFTPICLJLFF4KBNDE","download_json":"https://pith.science/pith/J5NX44BEDQFTPICLJLFF4KBNDE.json","view_paper":"https://pith.science/paper/J5NX44BE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.20106&json=true","fetch_graph":"https://pith.science/api/pith-number/J5NX44BEDQFTPICLJLFF4KBNDE/graph.json","fetch_events":"https://pith.science/api/pith-number/J5NX44BEDQFTPICLJLFF4KBNDE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J5NX44BEDQFTPICLJLFF4KBNDE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J5NX44BEDQFTPICLJLFF4KBNDE/action/storage_attestation","attest_author":"https://pith.science/pith/J5NX44BEDQFTPICLJLFF4KBNDE/action/author_attestation","sign_citation":"https://pith.science/pith/J5NX44BEDQFTPICLJLFF4KBNDE/action/citation_signature","submit_replication":"https://pith.science/pith/J5NX44BEDQFTPICLJLFF4KBNDE/action/replication_record"}},"created_at":"2026-05-20T02:06:02.283585+00:00","updated_at":"2026-05-20T02:06:02.283585+00:00"}