{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TMNBF5657JYT57EZHTNNNSB3CT","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":"4d206de3d93ef7642b78ee54fc7edb44a2d3b9cae1516813341947f04ad8f9e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-10-17T17:59:59Z","title_canon_sha256":"f529182f7c2c392c9f5057d27e655f66410301623e5bd662f104eb7397ea6869"},"schema_version":"1.0","source":{"id":"1810.07689","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.07689","created_at":"2026-05-17T23:55:11Z"},{"alias_kind":"arxiv_version","alias_value":"1810.07689v2","created_at":"2026-05-17T23:55:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.07689","created_at":"2026-05-17T23:55:11Z"},{"alias_kind":"pith_short_12","alias_value":"TMNBF5657JYT","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TMNBF5657JYT57EZ","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TMNBF565","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:0b55fd6f12e49c939d7f98324b8c90139eff8ea0cf70d384c4c5bdf0649a163a","target":"graph","created_at":"2026-05-17T23:55:11Z","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 define the rigidity of a Feynman integral to be the smallest dimension over which it is non-polylogarithmic. We argue that massless Feynman integrals in four dimensions have a rigidity bounded by 2(L-1) at L loops, and we show that this bound may be saturated for integrals that we call marginal: those with (L+1)D/2 propagators in (even) D dimensions. We show that marginal Feynman integrals in D dimensions generically involve Calabi-Yau geometries, and we give examples of finite four-dimensional Feynman integrals in massless $\\phi^4$ theory that saturate our predicted bound in rigidity at al","authors_text":"Andrew J. McLeod, Jacob L. Bourjaily, Matthias Wilhelm, Matt von Hippel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-10-17T17:59:59Z","title":"A (Bounded) Bestiary of Feynman Integral Calabi-Yau Geometries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07689","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":"sha256:604b06a065b9ada337a056365534336e52d9d758d9f395a72cb0d1ee16e694f0","target":"record","created_at":"2026-05-17T23:55:11Z","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":"4d206de3d93ef7642b78ee54fc7edb44a2d3b9cae1516813341947f04ad8f9e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-10-17T17:59:59Z","title_canon_sha256":"f529182f7c2c392c9f5057d27e655f66410301623e5bd662f104eb7397ea6869"},"schema_version":"1.0","source":{"id":"1810.07689","kind":"arxiv","version":2}},"canonical_sha256":"9b1a12f7ddfa713efc993cdad6c83b14d4328f4e9d0d4ce7aa36fc15c6fd0965","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b1a12f7ddfa713efc993cdad6c83b14d4328f4e9d0d4ce7aa36fc15c6fd0965","first_computed_at":"2026-05-17T23:55:11.354938Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:11.354938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VfSRKsyEZLprkDy/McQeFIELG6tYn7/XkewlkiABSdwM+fP67nC8ZDOpCaQ7dJ39qpEBSxjCFUY+q7XuENrKCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:11.355379Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.07689","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:604b06a065b9ada337a056365534336e52d9d758d9f395a72cb0d1ee16e694f0","sha256:0b55fd6f12e49c939d7f98324b8c90139eff8ea0cf70d384c4c5bdf0649a163a"],"state_sha256":"00ac3ca0571bc61700b124e99bd0f67735f98855d4a25379d03bb829b30c1770"}