{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HJ4S6VWSS356H4MBYXH2EAU64D","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":"9be67beb38492f2ef02ddb3c53451a04c334b9facfed8855d1e2b84a0f4840b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-02-11T20:24:41Z","title_canon_sha256":"947016964b4c7b8626263f2fed9ba3a7c8d0ba1ba3b63567344036d8d801e0bf"},"schema_version":"1.0","source":{"id":"1502.03427","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.03427","created_at":"2026-05-18T02:27:19Z"},{"alias_kind":"arxiv_version","alias_value":"1502.03427v1","created_at":"2026-05-18T02:27:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.03427","created_at":"2026-05-18T02:27:19Z"},{"alias_kind":"pith_short_12","alias_value":"HJ4S6VWSS356","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HJ4S6VWSS356H4MB","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HJ4S6VWS","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:77e0090f701648888ad5c64f056457afa8aa1d9fd82d035f7a3ee0ae985678c5","target":"graph","created_at":"2026-05-18T02:27:19Z","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 a Bonnet theorem for isometric immersions of submanifolds into the products of an arbitrary number of simply connected real space forms. Then, we prove the existence of associated families of minimal surfaces in such products. Finally, in the case of $\\mathbb{S}^2\\times\\mathbb{S}^2$, we give a complex version of the main theorem in terms of the two canonical complex structures of $\\mathbb{S}^2\\times\\mathbb{S}^2$.","authors_text":"Julien Roth, Marie-Am\\'elie Lawn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-02-11T20:24:41Z","title":"A Fundamental Theorem for submanifolds of multiproducts of real space forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03427","kind":"arxiv","version":1},"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:ef6c1fb9041f29e050ccb3a2af9d7dad99dad2b00870a597cd03755c5d928210","target":"record","created_at":"2026-05-18T02:27:19Z","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":"9be67beb38492f2ef02ddb3c53451a04c334b9facfed8855d1e2b84a0f4840b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-02-11T20:24:41Z","title_canon_sha256":"947016964b4c7b8626263f2fed9ba3a7c8d0ba1ba3b63567344036d8d801e0bf"},"schema_version":"1.0","source":{"id":"1502.03427","kind":"arxiv","version":1}},"canonical_sha256":"3a792f56d296fbe3f181c5cfa2029ee0e331b22c2b2d6805855e00232c702e76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a792f56d296fbe3f181c5cfa2029ee0e331b22c2b2d6805855e00232c702e76","first_computed_at":"2026-05-18T02:27:19.360271Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:19.360271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uEvMm061nG/dyEqHfDZxd5hDT0qV46YLC+HIrbIy+8zS45AHFMgwCXpzvYVHmtqHDD4RHJObUryCU5uNt5RDCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:19.361138Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.03427","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef6c1fb9041f29e050ccb3a2af9d7dad99dad2b00870a597cd03755c5d928210","sha256:77e0090f701648888ad5c64f056457afa8aa1d9fd82d035f7a3ee0ae985678c5"],"state_sha256":"dc13f2d127c8e2e013908cfcc8069d92a66f82d6fa4ec3e24506ccb5757d6627"}