{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:ADN6NLRANK6RWS5Q4QTJ4FBLQ4","short_pith_number":"pith:ADN6NLRA","schema_version":"1.0","canonical_sha256":"00dbe6ae206abd1b4bb0e4269e142b871daa8124bbe956a6fb14dc09180eabf4","source":{"kind":"arxiv","id":"1912.06201","version":2},"attestation_state":"computed","paper":{"title":"The $l$-loop Banana Amplitude from GKZ Systems and relative Calabi-Yau Periods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Albrecht Klemm, Christoph Nega, Reza Safari","submitted_at":"2019-12-12T20:44:54Z","abstract_excerpt":"We use the GKZ description of periods and certain classes of relative periods on families of Barth-Nieto Calabi-Yau $(l-1)$-folds in order to solve the $l$-loop banana amplitudes with their general mass dependence. As examples we compute the mass dependencies of the banana amplitudes up to the three-loop case and check the results against the known results for special mass values."},"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":"1912.06201","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-12T20:44:54Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"e69e2ce4f8232351f59bbd65eb27080f3f6a27311a11dead948ba7ad8cacb3c2","abstract_canon_sha256":"b46e8351826e8c4501e33a53eaf6488f6a5568b66baaec60dc80a5584e74bcdb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:04:09.591591Z","signature_b64":"8rVWQ8zUV0erGbhGXVGnq8d6M6UpB4HxEkeQKtRLVKJaboo9MfqOJWTLUxQEIxYRrSn3gy4sWYgoRZZ7jxmtAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00dbe6ae206abd1b4bb0e4269e142b871daa8124bbe956a6fb14dc09180eabf4","last_reissued_at":"2026-07-05T01:04:09.591102Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:04:09.591102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The $l$-loop Banana Amplitude from GKZ Systems and relative Calabi-Yau Periods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Albrecht Klemm, Christoph Nega, Reza Safari","submitted_at":"2019-12-12T20:44:54Z","abstract_excerpt":"We use the GKZ description of periods and certain classes of relative periods on families of Barth-Nieto Calabi-Yau $(l-1)$-folds in order to solve the $l$-loop banana amplitudes with their general mass dependence. As examples we compute the mass dependencies of the banana amplitudes up to the three-loop case and check the results against the known results for special mass values."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.06201","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/1912.06201/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":"1912.06201","created_at":"2026-07-05T01:04:09.591158+00:00"},{"alias_kind":"arxiv_version","alias_value":"1912.06201v2","created_at":"2026-07-05T01:04:09.591158+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.06201","created_at":"2026-07-05T01:04:09.591158+00:00"},{"alias_kind":"pith_short_12","alias_value":"ADN6NLRANK6R","created_at":"2026-07-05T01:04:09.591158+00:00"},{"alias_kind":"pith_short_16","alias_value":"ADN6NLRANK6RWS5Q","created_at":"2026-07-05T01:04:09.591158+00:00"},{"alias_kind":"pith_short_8","alias_value":"ADN6NLRA","created_at":"2026-07-05T01:04:09.591158+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":6,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.09978","citing_title":"Resonance and Differential Reduction of Feynman Integrals","ref_index":34,"is_internal_anchor":false},{"citing_arxiv_id":"2606.02744","citing_title":"IterInt: Evaluating iterated integrals via differential equations","ref_index":104,"is_internal_anchor":false},{"citing_arxiv_id":"2508.02800","citing_title":"Towards Motivic Coactions at Genus One from Zeta Generators","ref_index":80,"is_internal_anchor":false},{"citing_arxiv_id":"2604.09129","citing_title":"Picard-Fuchs Equations of Twisted Differential forms associated to Feynman Integrals","ref_index":15,"is_internal_anchor":false},{"citing_arxiv_id":"2604.08332","citing_title":"Discrete symmetries of Feynman integrals","ref_index":81,"is_internal_anchor":false},{"citing_arxiv_id":"2605.07729","citing_title":"Genus drop involving non-hyperelliptic curves in Feynman integrals","ref_index":51,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ADN6NLRANK6RWS5Q4QTJ4FBLQ4","json":"https://pith.science/pith/ADN6NLRANK6RWS5Q4QTJ4FBLQ4.json","graph_json":"https://pith.science/api/pith-number/ADN6NLRANK6RWS5Q4QTJ4FBLQ4/graph.json","events_json":"https://pith.science/api/pith-number/ADN6NLRANK6RWS5Q4QTJ4FBLQ4/events.json","paper":"https://pith.science/paper/ADN6NLRA"},"agent_actions":{"view_html":"https://pith.science/pith/ADN6NLRANK6RWS5Q4QTJ4FBLQ4","download_json":"https://pith.science/pith/ADN6NLRANK6RWS5Q4QTJ4FBLQ4.json","view_paper":"https://pith.science/paper/ADN6NLRA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1912.06201&json=true","fetch_graph":"https://pith.science/api/pith-number/ADN6NLRANK6RWS5Q4QTJ4FBLQ4/graph.json","fetch_events":"https://pith.science/api/pith-number/ADN6NLRANK6RWS5Q4QTJ4FBLQ4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ADN6NLRANK6RWS5Q4QTJ4FBLQ4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ADN6NLRANK6RWS5Q4QTJ4FBLQ4/action/storage_attestation","attest_author":"https://pith.science/pith/ADN6NLRANK6RWS5Q4QTJ4FBLQ4/action/author_attestation","sign_citation":"https://pith.science/pith/ADN6NLRANK6RWS5Q4QTJ4FBLQ4/action/citation_signature","submit_replication":"https://pith.science/pith/ADN6NLRANK6RWS5Q4QTJ4FBLQ4/action/replication_record"}},"created_at":"2026-07-05T01:04:09.591158+00:00","updated_at":"2026-07-05T01:04:09.591158+00:00"}