{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:AO2NCWQSB3HCJQQWTAKPFWRHUI","short_pith_number":"pith:AO2NCWQS","canonical_record":{"source":{"id":"2405.19742","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DG","submitted_at":"2024-05-30T06:40:40Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"c39b088f86a39c6bc10ac0c5380ef82ba0a6bd0db88dac236a5baa5af77f592d","abstract_canon_sha256":"5da20b3cd8ba99391e04a501b09df3ab9d9a04e340d4c5b43d4c24e922db4302"},"schema_version":"1.0"},"canonical_sha256":"03b4d15a120ece24c2169814f2da27a2276349390eb95e08e0821a8c3dd2d567","source":{"kind":"arxiv","id":"2405.19742","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.19742","created_at":"2026-07-05T08:38:38Z"},{"alias_kind":"arxiv_version","alias_value":"2405.19742v2","created_at":"2026-07-05T08:38:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.19742","created_at":"2026-07-05T08:38:38Z"},{"alias_kind":"pith_short_12","alias_value":"AO2NCWQSB3HC","created_at":"2026-07-05T08:38:38Z"},{"alias_kind":"pith_short_16","alias_value":"AO2NCWQSB3HCJQQW","created_at":"2026-07-05T08:38:38Z"},{"alias_kind":"pith_short_8","alias_value":"AO2NCWQS","created_at":"2026-07-05T08:38:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:AO2NCWQSB3HCJQQWTAKPFWRHUI","target":"record","payload":{"canonical_record":{"source":{"id":"2405.19742","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DG","submitted_at":"2024-05-30T06:40:40Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"c39b088f86a39c6bc10ac0c5380ef82ba0a6bd0db88dac236a5baa5af77f592d","abstract_canon_sha256":"5da20b3cd8ba99391e04a501b09df3ab9d9a04e340d4c5b43d4c24e922db4302"},"schema_version":"1.0"},"canonical_sha256":"03b4d15a120ece24c2169814f2da27a2276349390eb95e08e0821a8c3dd2d567","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:38:38.369163Z","signature_b64":"MsX6LFs9cZ9fVRelCT0loCIMZsb47SJpIIA+xDaRGDxmmy5i2oJhpWOqF0SrwvggJ/zb6XFFzJwKa5HlNNPaAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03b4d15a120ece24c2169814f2da27a2276349390eb95e08e0821a8c3dd2d567","last_reissued_at":"2026-07-05T08:38:38.368758Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:38:38.368758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.19742","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":"2026-07-05T08:38:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iRSxeKiV7g4xWvQ16L4u+EnQQWM6fnpd7NQoiRgDBNkqgPKdkqTH5wE+YOVdBWYfkdgA0sfAQlhrS/PnUfmhBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T10:31:50.759699Z"},"content_sha256":"f08c3da28cf0cb20705255e690d4e928fb115aab4cc421e5063d02fafb76a79e","schema_version":"1.0","event_id":"sha256:f08c3da28cf0cb20705255e690d4e928fb115aab4cc421e5063d02fafb76a79e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:AO2NCWQSB3HCJQQWTAKPFWRHUI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"CMC surfaces of revolution, Elliptic curves, Weierstrass-$\\wp$ functions, and Algebraicity","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DG","authors_text":"Anantadulal Paul, Rahul Kumar Singh, Rukmini Dey","submitted_at":"2024-05-30T06:40:40Z","abstract_excerpt":"This paper establishes an interesting connection between the family of CMC surfaces of revolution in $\\mathbb E_1^3$ and some specific families of elliptic curves. As a consequence of this connection, we show in the class of spacelike CMC surfaces of revolution in the $\\mathbb E_1^3$, only spacelike cylinders and standard hyperboloids are algebraic. We also show that a similar connection exists between CMC surfaces of revolution in $\\mathbb E^3$ and elliptic curves. Further, we use this to reestablish the fact that the only CMC algebraic surfaces of revolution in $\\mathbb E^3$ are spheres and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.19742","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.19742/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T08:38:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gd0tOlVb345ebRh3yIfiuRLqfshEhz/ibE/PI3twkkIzV+eBU9n1DVxSBo65jdIgeg23+bpgceSd+VuWTIO5Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T10:31:50.760241Z"},"content_sha256":"20925bc18b47824c00535839cd9488cc6d9509baed7560d58a8b2e9cd7bf656e","schema_version":"1.0","event_id":"sha256:20925bc18b47824c00535839cd9488cc6d9509baed7560d58a8b2e9cd7bf656e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AO2NCWQSB3HCJQQWTAKPFWRHUI/bundle.json","state_url":"https://pith.science/pith/AO2NCWQSB3HCJQQWTAKPFWRHUI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AO2NCWQSB3HCJQQWTAKPFWRHUI/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":"2026-08-04T10:31:50Z","links":{"resolver":"https://pith.science/pith/AO2NCWQSB3HCJQQWTAKPFWRHUI","bundle":"https://pith.science/pith/AO2NCWQSB3HCJQQWTAKPFWRHUI/bundle.json","state":"https://pith.science/pith/AO2NCWQSB3HCJQQWTAKPFWRHUI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AO2NCWQSB3HCJQQWTAKPFWRHUI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:AO2NCWQSB3HCJQQWTAKPFWRHUI","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":"5da20b3cd8ba99391e04a501b09df3ab9d9a04e340d4c5b43d4c24e922db4302","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DG","submitted_at":"2024-05-30T06:40:40Z","title_canon_sha256":"c39b088f86a39c6bc10ac0c5380ef82ba0a6bd0db88dac236a5baa5af77f592d"},"schema_version":"1.0","source":{"id":"2405.19742","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.19742","created_at":"2026-07-05T08:38:38Z"},{"alias_kind":"arxiv_version","alias_value":"2405.19742v2","created_at":"2026-07-05T08:38:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.19742","created_at":"2026-07-05T08:38:38Z"},{"alias_kind":"pith_short_12","alias_value":"AO2NCWQSB3HC","created_at":"2026-07-05T08:38:38Z"},{"alias_kind":"pith_short_16","alias_value":"AO2NCWQSB3HCJQQW","created_at":"2026-07-05T08:38:38Z"},{"alias_kind":"pith_short_8","alias_value":"AO2NCWQS","created_at":"2026-07-05T08:38:38Z"}],"graph_snapshots":[{"event_id":"sha256:20925bc18b47824c00535839cd9488cc6d9509baed7560d58a8b2e9cd7bf656e","target":"graph","created_at":"2026-07-05T08:38:38Z","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/2405.19742/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper establishes an interesting connection between the family of CMC surfaces of revolution in $\\mathbb E_1^3$ and some specific families of elliptic curves. As a consequence of this connection, we show in the class of spacelike CMC surfaces of revolution in the $\\mathbb E_1^3$, only spacelike cylinders and standard hyperboloids are algebraic. We also show that a similar connection exists between CMC surfaces of revolution in $\\mathbb E^3$ and elliptic curves. Further, we use this to reestablish the fact that the only CMC algebraic surfaces of revolution in $\\mathbb E^3$ are spheres and ","authors_text":"Anantadulal Paul, Rahul Kumar Singh, Rukmini Dey","cross_cats":["math.NT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DG","submitted_at":"2024-05-30T06:40:40Z","title":"CMC surfaces of revolution, Elliptic curves, Weierstrass-$\\wp$ functions, and Algebraicity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.19742","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:f08c3da28cf0cb20705255e690d4e928fb115aab4cc421e5063d02fafb76a79e","target":"record","created_at":"2026-07-05T08:38:38Z","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":"5da20b3cd8ba99391e04a501b09df3ab9d9a04e340d4c5b43d4c24e922db4302","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DG","submitted_at":"2024-05-30T06:40:40Z","title_canon_sha256":"c39b088f86a39c6bc10ac0c5380ef82ba0a6bd0db88dac236a5baa5af77f592d"},"schema_version":"1.0","source":{"id":"2405.19742","kind":"arxiv","version":2}},"canonical_sha256":"03b4d15a120ece24c2169814f2da27a2276349390eb95e08e0821a8c3dd2d567","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03b4d15a120ece24c2169814f2da27a2276349390eb95e08e0821a8c3dd2d567","first_computed_at":"2026-07-05T08:38:38.368758Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:38:38.368758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MsX6LFs9cZ9fVRelCT0loCIMZsb47SJpIIA+xDaRGDxmmy5i2oJhpWOqF0SrwvggJ/zb6XFFzJwKa5HlNNPaAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:38:38.369163Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.19742","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f08c3da28cf0cb20705255e690d4e928fb115aab4cc421e5063d02fafb76a79e","sha256:20925bc18b47824c00535839cd9488cc6d9509baed7560d58a8b2e9cd7bf656e"],"state_sha256":"6bc1930250a115d45703808d70aba89b24b0fa2b03e039c62bdf53c7311e22e7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4eSroLy+bqZO80nXau8Ij/YS8PSepGF9oEzgt3M1/J8P3uTrXSa14CI94pI6BVtcZsYSzbRTbYgo2AvgqXCeAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T10:31:50.769664Z","bundle_sha256":"f498273fd9be1b712784ba14179fa10aacd10ecf384af89716eb2e62891e2729"}}