{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:UYMDT6WEIH6EOMXQMYTPBH2CSD","short_pith_number":"pith:UYMDT6WE","canonical_record":{"source":{"id":"1709.08495","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-25T14:01:50Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"f55f0fabcbf6d0bc67926e7cbf4e2f375993de93ce511dad2e243dbbc0faf23b","abstract_canon_sha256":"4ae4fbdf48b78a4161373a9803c3cb0707ae2eef49ee291095a0ef0e8e465ded"},"schema_version":"1.0"},"canonical_sha256":"a61839fac441fc4732f06626f09f4290d8bfdd7d1c9f76a8459ac7baeb25bc96","source":{"kind":"arxiv","id":"1709.08495","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.08495","created_at":"2026-05-18T00:03:24Z"},{"alias_kind":"arxiv_version","alias_value":"1709.08495v2","created_at":"2026-05-18T00:03:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.08495","created_at":"2026-05-18T00:03:24Z"},{"alias_kind":"pith_short_12","alias_value":"UYMDT6WEIH6E","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"UYMDT6WEIH6EOMXQ","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"UYMDT6WE","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:UYMDT6WEIH6EOMXQMYTPBH2CSD","target":"record","payload":{"canonical_record":{"source":{"id":"1709.08495","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-25T14:01:50Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"f55f0fabcbf6d0bc67926e7cbf4e2f375993de93ce511dad2e243dbbc0faf23b","abstract_canon_sha256":"4ae4fbdf48b78a4161373a9803c3cb0707ae2eef49ee291095a0ef0e8e465ded"},"schema_version":"1.0"},"canonical_sha256":"a61839fac441fc4732f06626f09f4290d8bfdd7d1c9f76a8459ac7baeb25bc96","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:24.951126Z","signature_b64":"0RN0qu0rOzXURzbGL1MZjTOLiNvufPfj5xG4cSYeco8UBRswsS7ht4LDOaXfJJCOCdXzvuNf1T6YlFIfOw7eDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a61839fac441fc4732f06626f09f4290d8bfdd7d1c9f76a8459ac7baeb25bc96","last_reissued_at":"2026-05-18T00:03:24.950682Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:24.950682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.08495","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":"2026-05-18T00:03:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g70VQQp7BsUHMsLPa2QJSuaD81NUi1Q/cxgAyTXhY5kihnyGhHkXQckwYmfl5RVxrvad1vT9yjdmw6nrQ8s7Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:45:54.517119Z"},"content_sha256":"437af58d575998a65fd88719f285a4fa1e6a61a9f7eeb77761f2b8a9e92ff0f9","schema_version":"1.0","event_id":"sha256:437af58d575998a65fd88719f285a4fa1e6a61a9f7eeb77761f2b8a9e92ff0f9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:UYMDT6WEIH6EOMXQMYTPBH2CSD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Embedded tori with prescribed mean curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Monica Musso, Paolo Caldiroli","submitted_at":"2017-09-25T14:01:50Z","abstract_excerpt":"We construct a sequence of compact, oriented, embedded, two-dimensional surfaces of genus one into Euclidean 3-space with prescribed, almost constant, mean curvature of the form $H(X)=1+{A}{|X|^{-\\gamma}}$ for $|X|$ large, when $A<0$ and $\\gamma\\in(0,2)$. Such surfaces are close to sections of unduloids with small necksize, folded along circumferences centered at the origin and with larger and larger radii. The construction involves a deep study of the corresponding Jacobi operators, an application of the Lyapunov-Schmidt reduction method and some variational argument."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08495","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":"2026-05-18T00:03:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kWBTEvSPGSdeaeDw/PEAM/HhpoSOY+OC+RwiWORYsJpPmBJPorbeInLPKOoYhMnoMmN9ZLlnMeEYGM/G6W2EDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:45:54.517472Z"},"content_sha256":"ea8a3076b20c0262dab711e4d029f09746972da283fc5fb174eaad635c8fbe65","schema_version":"1.0","event_id":"sha256:ea8a3076b20c0262dab711e4d029f09746972da283fc5fb174eaad635c8fbe65"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UYMDT6WEIH6EOMXQMYTPBH2CSD/bundle.json","state_url":"https://pith.science/pith/UYMDT6WEIH6EOMXQMYTPBH2CSD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UYMDT6WEIH6EOMXQMYTPBH2CSD/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":"2026-05-28T06:45:54Z","links":{"resolver":"https://pith.science/pith/UYMDT6WEIH6EOMXQMYTPBH2CSD","bundle":"https://pith.science/pith/UYMDT6WEIH6EOMXQMYTPBH2CSD/bundle.json","state":"https://pith.science/pith/UYMDT6WEIH6EOMXQMYTPBH2CSD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UYMDT6WEIH6EOMXQMYTPBH2CSD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UYMDT6WEIH6EOMXQMYTPBH2CSD","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":"4ae4fbdf48b78a4161373a9803c3cb0707ae2eef49ee291095a0ef0e8e465ded","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-25T14:01:50Z","title_canon_sha256":"f55f0fabcbf6d0bc67926e7cbf4e2f375993de93ce511dad2e243dbbc0faf23b"},"schema_version":"1.0","source":{"id":"1709.08495","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.08495","created_at":"2026-05-18T00:03:24Z"},{"alias_kind":"arxiv_version","alias_value":"1709.08495v2","created_at":"2026-05-18T00:03:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.08495","created_at":"2026-05-18T00:03:24Z"},{"alias_kind":"pith_short_12","alias_value":"UYMDT6WEIH6E","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"UYMDT6WEIH6EOMXQ","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"UYMDT6WE","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:ea8a3076b20c0262dab711e4d029f09746972da283fc5fb174eaad635c8fbe65","target":"graph","created_at":"2026-05-18T00:03:24Z","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 construct a sequence of compact, oriented, embedded, two-dimensional surfaces of genus one into Euclidean 3-space with prescribed, almost constant, mean curvature of the form $H(X)=1+{A}{|X|^{-\\gamma}}$ for $|X|$ large, when $A<0$ and $\\gamma\\in(0,2)$. Such surfaces are close to sections of unduloids with small necksize, folded along circumferences centered at the origin and with larger and larger radii. The construction involves a deep study of the corresponding Jacobi operators, an application of the Lyapunov-Schmidt reduction method and some variational argument.","authors_text":"Monica Musso, Paolo Caldiroli","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-25T14:01:50Z","title":"Embedded tori with prescribed mean curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08495","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":"sha256:437af58d575998a65fd88719f285a4fa1e6a61a9f7eeb77761f2b8a9e92ff0f9","target":"record","created_at":"2026-05-18T00:03:24Z","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":"4ae4fbdf48b78a4161373a9803c3cb0707ae2eef49ee291095a0ef0e8e465ded","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-25T14:01:50Z","title_canon_sha256":"f55f0fabcbf6d0bc67926e7cbf4e2f375993de93ce511dad2e243dbbc0faf23b"},"schema_version":"1.0","source":{"id":"1709.08495","kind":"arxiv","version":2}},"canonical_sha256":"a61839fac441fc4732f06626f09f4290d8bfdd7d1c9f76a8459ac7baeb25bc96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a61839fac441fc4732f06626f09f4290d8bfdd7d1c9f76a8459ac7baeb25bc96","first_computed_at":"2026-05-18T00:03:24.950682Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:24.950682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0RN0qu0rOzXURzbGL1MZjTOLiNvufPfj5xG4cSYeco8UBRswsS7ht4LDOaXfJJCOCdXzvuNf1T6YlFIfOw7eDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:24.951126Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.08495","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:437af58d575998a65fd88719f285a4fa1e6a61a9f7eeb77761f2b8a9e92ff0f9","sha256:ea8a3076b20c0262dab711e4d029f09746972da283fc5fb174eaad635c8fbe65"],"state_sha256":"d8052837e279e4bedc8660d927c7f57e35c4402fea48ad3c8398e90fdd1e49e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q7om8suv/QETpKnlMEfkhlz+Wyh75ueCaRX+5dIx4oh+8ObFwyt/sgnxjtvs6Q0Qt9xJSP5vosK4ioE+O6yrAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T06:45:54.519465Z","bundle_sha256":"22cfd161f4075f0966a1d1df57ea7f5c166b2e332292e40f57a92b358cf606bb"}}