{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VI3D7JXN2EMYBYY27Y7VHGO2KJ","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":"c364c0a486b0b9c76748606fa68e1d91d7d940b915495c5291c10a9a78cc5524","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-16T19:50:26Z","title_canon_sha256":"f6e1283b8fb3eb617c53e74e2a4981a23c2737ac33aea3261b56f1f39f46fdf1"},"schema_version":"1.0","source":{"id":"1409.4750","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.4750","created_at":"2026-05-17T23:40:42Z"},{"alias_kind":"arxiv_version","alias_value":"1409.4750v2","created_at":"2026-05-17T23:40:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.4750","created_at":"2026-05-17T23:40:42Z"},{"alias_kind":"pith_short_12","alias_value":"VI3D7JXN2EMY","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VI3D7JXN2EMYBYY2","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VI3D7JXN","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:deb37b2530aea83b715866728b1516baaff86fb60ee60b85fdc8d9b323965f26","target":"graph","created_at":"2026-05-17T23:40:42Z","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 prove that the mirror map is trivial for the canonical formal families of Calabi-Yau varieties constructed by Gross and the second author. In other words, the natural coordinate in a canonical Calabi-Yau family is a canonical coordinate in the sense of Hodge theory. This implies that the higher weight periods directly carry enumerative information with no further gauging necessary as opposed to the classical case. A side result is that the canonical formal families lift to analytic families. We compute the relevant period integrals explicitly. The cycles to integrate over are constructed fr","authors_text":"Bernd Siebert, Helge Ruddat","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-16T19:50:26Z","title":"Canonical Coordinates in Toric Degenerations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4750","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":"sha256:4065df979c0cea40a2459fa2ee63323fadfaeaee69d29680a179e84744150d36","target":"record","created_at":"2026-05-17T23:40:42Z","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":"c364c0a486b0b9c76748606fa68e1d91d7d940b915495c5291c10a9a78cc5524","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-16T19:50:26Z","title_canon_sha256":"f6e1283b8fb3eb617c53e74e2a4981a23c2737ac33aea3261b56f1f39f46fdf1"},"schema_version":"1.0","source":{"id":"1409.4750","kind":"arxiv","version":2}},"canonical_sha256":"aa363fa6edd11980e31afe3f5399da52459629068ef2cdfd5f14b02369119c58","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa363fa6edd11980e31afe3f5399da52459629068ef2cdfd5f14b02369119c58","first_computed_at":"2026-05-17T23:40:42.244048Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:42.244048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uJXpeMqmZHRm1hRO+NZZABT+xrzlDDEDiEq5AE4m8klpr+SDOp2pJ+7S4Lcns2mTY9ZrAc//fOjZI2WJzX0zDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:42.244806Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.4750","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4065df979c0cea40a2459fa2ee63323fadfaeaee69d29680a179e84744150d36","sha256:deb37b2530aea83b715866728b1516baaff86fb60ee60b85fdc8d9b323965f26"],"state_sha256":"688b4bb03e103ff98f04c10a0f560b3c7004713dfc06019940484a8fec70d8e5"}