{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:XYBVYFWCOUCO3KMKM4ACRWK3CP","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":"00385eef0761a929e4b428855fb898b4514acfc73c4c29a07c142027f314c6b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-07-10T02:31:58Z","title_canon_sha256":"9192650e834a6ccd5263a38eae2e3e0b3fc2511fc9494912a2b0a2b1e9037aae"},"schema_version":"1.0","source":{"id":"2607.09048","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.09048","created_at":"2026-07-13T00:17:37Z"},{"alias_kind":"arxiv_version","alias_value":"2607.09048v1","created_at":"2026-07-13T00:17:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.09048","created_at":"2026-07-13T00:17:37Z"},{"alias_kind":"pith_short_12","alias_value":"XYBVYFWCOUCO","created_at":"2026-07-13T00:17:37Z"},{"alias_kind":"pith_short_16","alias_value":"XYBVYFWCOUCO3KMK","created_at":"2026-07-13T00:17:37Z"},{"alias_kind":"pith_short_8","alias_value":"XYBVYFWC","created_at":"2026-07-13T00:17:37Z"}],"graph_snapshots":[{"event_id":"sha256:1a32d19f7f58f16615305b5437b47ffc66cb772a9fda6304c3c39a6279f947fd","target":"graph","created_at":"2026-07-13T00:17:37Z","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/2607.09048/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We derive exact analytic representations for the perimeter of a Lam\\'e superellipse of degree $s>0$. The result is expressed in terms of two branches defined by series whose terms are Gauss hypergeometric functions: a negative branch for $0<s<1$ and a positive branch for $s>1$. For the positive branch, the convergence condition follows from the Leibniz test; the negative branch, although divergent in the ordinary sense, is shown to be Abel-summable. Consistently with the symmetry under interchange of the semi-axes, the formula is invariant under axis permutation. As $s$ varies, the family inte","authors_text":"R. Omar Rodriguez, Yomber Montilla","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-07-10T02:31:58Z","title":"Hypergeometric Series Representations for the Perimeter of Lam\\'e Superellipses"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09048","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:a9320c60b5ab45817253e897bd06fe63b96d13fc3ec9e4ec0d15089a14656b5b","target":"record","created_at":"2026-07-13T00:17:37Z","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":"00385eef0761a929e4b428855fb898b4514acfc73c4c29a07c142027f314c6b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-07-10T02:31:58Z","title_canon_sha256":"9192650e834a6ccd5263a38eae2e3e0b3fc2511fc9494912a2b0a2b1e9037aae"},"schema_version":"1.0","source":{"id":"2607.09048","kind":"arxiv","version":1}},"canonical_sha256":"be035c16c27504eda98a670028d95b13d6284b82867a9a7abd515583b916f624","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be035c16c27504eda98a670028d95b13d6284b82867a9a7abd515583b916f624","first_computed_at":"2026-07-13T00:17:37.621410Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-13T00:17:37.621410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XSTVmgTQOxgXGDYGTCeQsJQKPb9OYouW4/N7KhWHT9IGYAhCnA94J71k80k9TbBuqYfzQK3j7obsEAzHOmByBg==","signature_status":"signed_v1","signed_at":"2026-07-13T00:17:37.622440Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.09048","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a9320c60b5ab45817253e897bd06fe63b96d13fc3ec9e4ec0d15089a14656b5b","sha256:1a32d19f7f58f16615305b5437b47ffc66cb772a9fda6304c3c39a6279f947fd"],"state_sha256":"6ac75ce47368bc418f7223ddc2998f77ea5c15d60314578385c2ac341a73a1a4"}