{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:JYKMG5HGZGGDLMWJASSL475AEV","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":"0db140e154422a8d9a7ed55ee4c9dbce2fc923f8209f181bf996f49407c3cdb5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-12-06T11:51:15Z","title_canon_sha256":"88827a93e1bcc8591f1106e0509005f2f6222e4330b755d93a8f222456a9a36f"},"schema_version":"1.0","source":{"id":"1912.03073","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.03073","created_at":"2026-07-05T07:22:10Z"},{"alias_kind":"arxiv_version","alias_value":"1912.03073v5","created_at":"2026-07-05T07:22:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.03073","created_at":"2026-07-05T07:22:10Z"},{"alias_kind":"pith_short_12","alias_value":"JYKMG5HGZGGD","created_at":"2026-07-05T07:22:10Z"},{"alias_kind":"pith_short_16","alias_value":"JYKMG5HGZGGDLMWJ","created_at":"2026-07-05T07:22:10Z"},{"alias_kind":"pith_short_8","alias_value":"JYKMG5HG","created_at":"2026-07-05T07:22:10Z"}],"graph_snapshots":[{"event_id":"sha256:e2e9690f013ad611bf16ff675d3f5b1938266471efed8358e0f3f8a0aaa53676","target":"graph","created_at":"2026-07-05T07:22:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1912.03073/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Loops and cycles play an important role in computing endomorphism rings of supersingular elliptic curves and related cryptosystems. For a supersingular elliptic curve $E$ defined over $\\mathbb{F}_{p^2}$, if an imaginary quadratic order $O$ can be embedded in $\\text{End}(E)$ and a prime $L$ splits into two principal ideals in $O$, we construct loops or cycles in the supersingular $L$-isogeny graph at the vertices which are next to $j(E)$ in the supersingular $\\ell$-isogeny graph where $\\ell$ is a prime different from $L$. Next, we discuss the lengths of these cycles especially for $j(E)=1728$ a","authors_text":"Guanju Xiao, Lixia Luo, Yingpu Deng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-12-06T11:51:15Z","title":"Constructing Cycles in Isogeny Graphs of Supersingular Elliptic Curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.03073","kind":"arxiv","version":5},"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:f0643d19accb923bcd632b43f3050aa12aa9c48856c380c8df455404790303c8","target":"record","created_at":"2026-07-05T07:22:10Z","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":"0db140e154422a8d9a7ed55ee4c9dbce2fc923f8209f181bf996f49407c3cdb5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-12-06T11:51:15Z","title_canon_sha256":"88827a93e1bcc8591f1106e0509005f2f6222e4330b755d93a8f222456a9a36f"},"schema_version":"1.0","source":{"id":"1912.03073","kind":"arxiv","version":5}},"canonical_sha256":"4e14c374e6c98c35b2c904a4be7fa025414e2e3dbed0fd585c6d696e097f8c07","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e14c374e6c98c35b2c904a4be7fa025414e2e3dbed0fd585c6d696e097f8c07","first_computed_at":"2026-07-05T07:22:10.358480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:22:10.358480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K768w9sW/FcRfa/LcJ+xDqQgau4mkEcV4EL8lrU7wL9+nqnYjZsgONx5dMy7K+Pn77lY7MiyoA5QY8JxhokLBA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:22:10.359006Z","signed_message":"canonical_sha256_bytes"},"source_id":"1912.03073","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0643d19accb923bcd632b43f3050aa12aa9c48856c380c8df455404790303c8","sha256:e2e9690f013ad611bf16ff675d3f5b1938266471efed8358e0f3f8a0aaa53676"],"state_sha256":"626e0e9355e1cc724b9cfc570938a5114d2ee0a47f5eaba0ab63079e714af337"}