{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:U574IAQEH3UQJIQDI2GNMJ2AOP","short_pith_number":"pith:U574IAQE","canonical_record":{"source":{"id":"1503.00969","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-03T15:09:53Z","cross_cats_sorted":[],"title_canon_sha256":"2d99b8b992f03194a308c9f3b2e213cb64ceedd5280c956007750c11949c003a","abstract_canon_sha256":"f4b6c74176c8a9df2fc8008d5171779acd0ef2ccc3a0d32db6752ffa49d79c46"},"schema_version":"1.0"},"canonical_sha256":"a77fc402043ee904a203468cd6274073caa6543365d4da04a0d5743d2094b651","source":{"kind":"arxiv","id":"1503.00969","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00969","created_at":"2026-05-18T01:11:03Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00969v2","created_at":"2026-05-18T01:11:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00969","created_at":"2026-05-18T01:11:03Z"},{"alias_kind":"pith_short_12","alias_value":"U574IAQEH3UQ","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"U574IAQEH3UQJIQD","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"U574IAQE","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:U574IAQEH3UQJIQDI2GNMJ2AOP","target":"record","payload":{"canonical_record":{"source":{"id":"1503.00969","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-03T15:09:53Z","cross_cats_sorted":[],"title_canon_sha256":"2d99b8b992f03194a308c9f3b2e213cb64ceedd5280c956007750c11949c003a","abstract_canon_sha256":"f4b6c74176c8a9df2fc8008d5171779acd0ef2ccc3a0d32db6752ffa49d79c46"},"schema_version":"1.0"},"canonical_sha256":"a77fc402043ee904a203468cd6274073caa6543365d4da04a0d5743d2094b651","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:03.537853Z","signature_b64":"1WEpiLooi5mpLBHmNkPwaYb7FmOP5tQqBFymCGe/xkYKw4f5bn18IHEALqIBlhisAOOD9JWKfHN6BllMhL5iBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a77fc402043ee904a203468cd6274073caa6543365d4da04a0d5743d2094b651","last_reissued_at":"2026-05-18T01:11:03.537408Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:03.537408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.00969","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u8PdrvXmp3qQlK5YBbaIFRNbylaW7x6dO1IXheeuF0n0HYxcE+cOuXyl9PcNk11MbeOMW3XYGEhndRWw25mECg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:36:28.097299Z"},"content_sha256":"2dd6999f0a55fa8a4056402a3a8e413184c5bcdcf78c622317b4a237a38a805f","schema_version":"1.0","event_id":"sha256:2dd6999f0a55fa8a4056402a3a8e413184c5bcdcf78c622317b4a237a38a805f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:U574IAQEH3UQJIQDI2GNMJ2AOP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The spectral curve theory for $(k,l)-$symmetric CMC surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Lynn Heller, Nicholas Schmitt, Sebastian Heller","submitted_at":"2015-03-03T15:09:53Z","abstract_excerpt":"Constant mean curvature surfaces in $S^3$ can be studied via their associated family of flat connections. In the case of tori this approach has led to a deep understanding of the moduli space of all CMC tori. For compact CMC surfaces of higher genus the theory is far more involved due to the non abelian nature of their fundamental group. In this paper we extend the spectral curve theory for tori developed in \\cite{Hi, PiSt} and for genus $2$ surfaces \\cite{He3} to CMC surfaces in $S^3$ of genus $g=k\\cdot l$ with commuting $\\mathbb Z_{k+1}$ and $\\mathbb Z_{l+1}$ symmetries. We determine their a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00969","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ClR+Tx0tine7iIksYP1lmgxklNeS+VOiqoO7rOV9PbDoPKIo2PsMjxnhCdDeIKkM46nt/rk7gAdIMorR2a56Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:36:28.097728Z"},"content_sha256":"68171c94ce677dc02c4fd53fb20754ef7f0c8ad04f990b646ed816542e809782","schema_version":"1.0","event_id":"sha256:68171c94ce677dc02c4fd53fb20754ef7f0c8ad04f990b646ed816542e809782"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U574IAQEH3UQJIQDI2GNMJ2AOP/bundle.json","state_url":"https://pith.science/pith/U574IAQEH3UQJIQDI2GNMJ2AOP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U574IAQEH3UQJIQDI2GNMJ2AOP/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T11:36:28Z","links":{"resolver":"https://pith.science/pith/U574IAQEH3UQJIQDI2GNMJ2AOP","bundle":"https://pith.science/pith/U574IAQEH3UQJIQDI2GNMJ2AOP/bundle.json","state":"https://pith.science/pith/U574IAQEH3UQJIQDI2GNMJ2AOP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U574IAQEH3UQJIQDI2GNMJ2AOP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:U574IAQEH3UQJIQDI2GNMJ2AOP","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":"f4b6c74176c8a9df2fc8008d5171779acd0ef2ccc3a0d32db6752ffa49d79c46","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-03T15:09:53Z","title_canon_sha256":"2d99b8b992f03194a308c9f3b2e213cb64ceedd5280c956007750c11949c003a"},"schema_version":"1.0","source":{"id":"1503.00969","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00969","created_at":"2026-05-18T01:11:03Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00969v2","created_at":"2026-05-18T01:11:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00969","created_at":"2026-05-18T01:11:03Z"},{"alias_kind":"pith_short_12","alias_value":"U574IAQEH3UQ","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"U574IAQEH3UQJIQD","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"U574IAQE","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:68171c94ce677dc02c4fd53fb20754ef7f0c8ad04f990b646ed816542e809782","target":"graph","created_at":"2026-05-18T01:11:03Z","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":"Constant mean curvature surfaces in $S^3$ can be studied via their associated family of flat connections. In the case of tori this approach has led to a deep understanding of the moduli space of all CMC tori. For compact CMC surfaces of higher genus the theory is far more involved due to the non abelian nature of their fundamental group. In this paper we extend the spectral curve theory for tori developed in \\cite{Hi, PiSt} and for genus $2$ surfaces \\cite{He3} to CMC surfaces in $S^3$ of genus $g=k\\cdot l$ with commuting $\\mathbb Z_{k+1}$ and $\\mathbb Z_{l+1}$ symmetries. We determine their a","authors_text":"Lynn Heller, Nicholas Schmitt, Sebastian Heller","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-03T15:09:53Z","title":"The spectral curve theory for $(k,l)-$symmetric CMC surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00969","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":"sha256:2dd6999f0a55fa8a4056402a3a8e413184c5bcdcf78c622317b4a237a38a805f","target":"record","created_at":"2026-05-18T01:11:03Z","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":"f4b6c74176c8a9df2fc8008d5171779acd0ef2ccc3a0d32db6752ffa49d79c46","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-03T15:09:53Z","title_canon_sha256":"2d99b8b992f03194a308c9f3b2e213cb64ceedd5280c956007750c11949c003a"},"schema_version":"1.0","source":{"id":"1503.00969","kind":"arxiv","version":2}},"canonical_sha256":"a77fc402043ee904a203468cd6274073caa6543365d4da04a0d5743d2094b651","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a77fc402043ee904a203468cd6274073caa6543365d4da04a0d5743d2094b651","first_computed_at":"2026-05-18T01:11:03.537408Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:03.537408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1WEpiLooi5mpLBHmNkPwaYb7FmOP5tQqBFymCGe/xkYKw4f5bn18IHEALqIBlhisAOOD9JWKfHN6BllMhL5iBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:03.537853Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.00969","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2dd6999f0a55fa8a4056402a3a8e413184c5bcdcf78c622317b4a237a38a805f","sha256:68171c94ce677dc02c4fd53fb20754ef7f0c8ad04f990b646ed816542e809782"],"state_sha256":"cc3300331d2a4c5248398268eeb92bff2271e3ab65198c1cee67c482d637ca6c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oGFcuRKo2b7ceEq40jN/D8XjVKUdyqfQBEd+QBgcwP65zJJ4RxR/9AnFp1JFa0ElGNLur7D0dgdskUC2W35XBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:36:28.100805Z","bundle_sha256":"7f1dc348a96af91eb927f34e5d9cf71601a76f977c026cfb1ed170d61bd8e2ea"}}