{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HWJW2ZBZ2PYV4R36TIMP6I4PEC","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":"97a4f4b2ac2d8ec433d6100884a385b167e0017ac20280e2c4d325de72e4da45","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-08-31T14:33:47Z","title_canon_sha256":"08f79945a57a708d25ad9f35f19484f75e65cc806eae460ad5ed045f0e229eaf"},"schema_version":"1.0","source":{"id":"1708.09750","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.09750","created_at":"2026-05-18T00:14:34Z"},{"alias_kind":"arxiv_version","alias_value":"1708.09750v2","created_at":"2026-05-18T00:14:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.09750","created_at":"2026-05-18T00:14:34Z"},{"alias_kind":"pith_short_12","alias_value":"HWJW2ZBZ2PYV","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"HWJW2ZBZ2PYV4R36","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"HWJW2ZBZ","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:f6ac184286cca295ee79757c89b2d72ca8052921bd80351836f8aa1a5af7cfbf","target":"graph","created_at":"2026-05-18T00:14:34Z","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 formulate a notion of stability for maps between polarised varieties which generalises Kontsevich's definition when the domain is a curve and Tian-Donaldson's definition of K-stability when the target is a point. We give some examples, such as Kodaira embeddings and fibrations. We prove the existence of a projective moduli space of canonically polarised stable maps, generalising the Kontsevich-Alexeev moduli space of stable maps in dimensions one and two. We also state an analogue of the Yau-Tian-Donaldson conjecture in this setting, relating stability of maps to the existence of certain ca","authors_text":"Julius Ross, Ruadha\\'i Dervan","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-08-31T14:33:47Z","title":"Stable maps in higher dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09750","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":"sha256:6eb17739593e3e4612cbdea75929e965c28e33964a0997152ab71850f2f19aab","target":"record","created_at":"2026-05-18T00:14:34Z","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":"97a4f4b2ac2d8ec433d6100884a385b167e0017ac20280e2c4d325de72e4da45","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-08-31T14:33:47Z","title_canon_sha256":"08f79945a57a708d25ad9f35f19484f75e65cc806eae460ad5ed045f0e229eaf"},"schema_version":"1.0","source":{"id":"1708.09750","kind":"arxiv","version":2}},"canonical_sha256":"3d936d6439d3f15e477e9a18ff238f208dae2c30b72f3cf00f858da5fe3731a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d936d6439d3f15e477e9a18ff238f208dae2c30b72f3cf00f858da5fe3731a8","first_computed_at":"2026-05-18T00:14:34.478757Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:34.478757Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bqfC2Gse31fYylmAYGidoJqrlgZhSU3pNl1I3VK/oJFEVDDpYPO4VAmae+ZVAUfqkaUGv/VT4qVfiWZJXu/JDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:34.479325Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.09750","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6eb17739593e3e4612cbdea75929e965c28e33964a0997152ab71850f2f19aab","sha256:f6ac184286cca295ee79757c89b2d72ca8052921bd80351836f8aa1a5af7cfbf"],"state_sha256":"e5e600be8e8a0c474110121509ed48dda4a89f606762e1f57a5372487fcfc7a2"}