{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:2A6K6MQ3YSHE45HNZZNS3STMZV","short_pith_number":"pith:2A6K6MQ3","canonical_record":{"source":{"id":"1710.09283","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2017-10-24T03:21:08Z","cross_cats_sorted":["math-ph","math.MP","physics.bio-ph"],"title_canon_sha256":"d2cf127f6e957b5bc6de979aa63de8d07915835430b343efdd73a8ec62f311dc","abstract_canon_sha256":"b6fd64f1a9922dc6dba3010ef8be013828079e58370afb3b65610c872f7ae938"},"schema_version":"1.0"},"canonical_sha256":"d03caf321bc48e4e74edce5b2dca6ccd67eb75701a35c3b336567265c59bac1e","source":{"kind":"arxiv","id":"1710.09283","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.09283","created_at":"2026-05-18T00:12:56Z"},{"alias_kind":"arxiv_version","alias_value":"1710.09283v4","created_at":"2026-05-18T00:12:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.09283","created_at":"2026-05-18T00:12:56Z"},{"alias_kind":"pith_short_12","alias_value":"2A6K6MQ3YSHE","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2A6K6MQ3YSHE45HN","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2A6K6MQ3","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:2A6K6MQ3YSHE45HNZZNS3STMZV","target":"record","payload":{"canonical_record":{"source":{"id":"1710.09283","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2017-10-24T03:21:08Z","cross_cats_sorted":["math-ph","math.MP","physics.bio-ph"],"title_canon_sha256":"d2cf127f6e957b5bc6de979aa63de8d07915835430b343efdd73a8ec62f311dc","abstract_canon_sha256":"b6fd64f1a9922dc6dba3010ef8be013828079e58370afb3b65610c872f7ae938"},"schema_version":"1.0"},"canonical_sha256":"d03caf321bc48e4e74edce5b2dca6ccd67eb75701a35c3b336567265c59bac1e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:56.324552Z","signature_b64":"HcIkw6/+Ja51pIGPxXRGODeHRS6ZZVTWKiPa86Bm5WzHiMoAfZsxPOm40nt1aE3Gmo7pBGUADU3IajkLtRS8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d03caf321bc48e4e74edce5b2dca6ccd67eb75701a35c3b336567265c59bac1e","last_reissued_at":"2026-05-18T00:12:56.323995Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:56.323995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.09283","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:12:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TaAoWPRQ7KT2nA8yUsIul2rtiJgz01w4R3MF42pndaguojXfiNLBq+m1wmn1Zmo677Zb/36PgmlS3QKCceDWAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:47:29.308933Z"},"content_sha256":"649f5c913806fee0e4af44dbbd76a3e9f0ce4e34aae39e0b67bd78d8d8909aff","schema_version":"1.0","event_id":"sha256:649f5c913806fee0e4af44dbbd76a3e9f0ce4e34aae39e0b67bd78d8d8909aff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:2A6K6MQ3YSHE45HNZZNS3STMZV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological Bounds of Bending Energy for Lipid Vesicles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.bio-ph"],"primary_cat":"cond-mat.soft","authors_text":"Yisong Yang","submitted_at":"2017-10-24T03:21:08Z","abstract_excerpt":"The Helfrich bending energy plays an important role in providing a mechanism for the conformation of a lipid vesicle in theoretical biophysics, which is governed by the principle of energy minimization over configurations of appropriate topological characteristics. We will show that the presence of a quantity called the spontaneous curvature obstructs the existence of a minimizer of the Helfrich energy over the set of embedded ring tori. Besides, despite the well-realized knowledge that lipid vesicles may present themselves in a variety of shapes of complicated topology, there is a lack of top"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09283","kind":"arxiv","version":4},"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":"2026-05-18T00:12:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sYN5DcXKObqgaR7HB7VS1S1T1ggD2er9aM1npYGzRdOYYJ6Q3kEPqeNXPAlQHFsewz5pwomv/MuQKPlK3i4GBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:47:29.309283Z"},"content_sha256":"8864591d719bb2ad82cc3c487a600fc29f34e91ddc480f4f86b2b7618ad0a2af","schema_version":"1.0","event_id":"sha256:8864591d719bb2ad82cc3c487a600fc29f34e91ddc480f4f86b2b7618ad0a2af"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2A6K6MQ3YSHE45HNZZNS3STMZV/bundle.json","state_url":"https://pith.science/pith/2A6K6MQ3YSHE45HNZZNS3STMZV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2A6K6MQ3YSHE45HNZZNS3STMZV/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":"2026-06-03T01:47:29Z","links":{"resolver":"https://pith.science/pith/2A6K6MQ3YSHE45HNZZNS3STMZV","bundle":"https://pith.science/pith/2A6K6MQ3YSHE45HNZZNS3STMZV/bundle.json","state":"https://pith.science/pith/2A6K6MQ3YSHE45HNZZNS3STMZV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2A6K6MQ3YSHE45HNZZNS3STMZV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2A6K6MQ3YSHE45HNZZNS3STMZV","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":"b6fd64f1a9922dc6dba3010ef8be013828079e58370afb3b65610c872f7ae938","cross_cats_sorted":["math-ph","math.MP","physics.bio-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2017-10-24T03:21:08Z","title_canon_sha256":"d2cf127f6e957b5bc6de979aa63de8d07915835430b343efdd73a8ec62f311dc"},"schema_version":"1.0","source":{"id":"1710.09283","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.09283","created_at":"2026-05-18T00:12:56Z"},{"alias_kind":"arxiv_version","alias_value":"1710.09283v4","created_at":"2026-05-18T00:12:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.09283","created_at":"2026-05-18T00:12:56Z"},{"alias_kind":"pith_short_12","alias_value":"2A6K6MQ3YSHE","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2A6K6MQ3YSHE45HN","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2A6K6MQ3","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:8864591d719bb2ad82cc3c487a600fc29f34e91ddc480f4f86b2b7618ad0a2af","target":"graph","created_at":"2026-05-18T00:12:56Z","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":"The Helfrich bending energy plays an important role in providing a mechanism for the conformation of a lipid vesicle in theoretical biophysics, which is governed by the principle of energy minimization over configurations of appropriate topological characteristics. We will show that the presence of a quantity called the spontaneous curvature obstructs the existence of a minimizer of the Helfrich energy over the set of embedded ring tori. Besides, despite the well-realized knowledge that lipid vesicles may present themselves in a variety of shapes of complicated topology, there is a lack of top","authors_text":"Yisong Yang","cross_cats":["math-ph","math.MP","physics.bio-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2017-10-24T03:21:08Z","title":"Topological Bounds of Bending Energy for Lipid Vesicles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09283","kind":"arxiv","version":4},"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":"sha256:649f5c913806fee0e4af44dbbd76a3e9f0ce4e34aae39e0b67bd78d8d8909aff","target":"record","created_at":"2026-05-18T00:12:56Z","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":"b6fd64f1a9922dc6dba3010ef8be013828079e58370afb3b65610c872f7ae938","cross_cats_sorted":["math-ph","math.MP","physics.bio-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2017-10-24T03:21:08Z","title_canon_sha256":"d2cf127f6e957b5bc6de979aa63de8d07915835430b343efdd73a8ec62f311dc"},"schema_version":"1.0","source":{"id":"1710.09283","kind":"arxiv","version":4}},"canonical_sha256":"d03caf321bc48e4e74edce5b2dca6ccd67eb75701a35c3b336567265c59bac1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d03caf321bc48e4e74edce5b2dca6ccd67eb75701a35c3b336567265c59bac1e","first_computed_at":"2026-05-18T00:12:56.323995Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:56.323995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HcIkw6/+Ja51pIGPxXRGODeHRS6ZZVTWKiPa86Bm5WzHiMoAfZsxPOm40nt1aE3Gmo7pBGUADU3IajkLtRS8Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:56.324552Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.09283","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:649f5c913806fee0e4af44dbbd76a3e9f0ce4e34aae39e0b67bd78d8d8909aff","sha256:8864591d719bb2ad82cc3c487a600fc29f34e91ddc480f4f86b2b7618ad0a2af"],"state_sha256":"4224db08f3751f933f39d2e509e19ccf6c780cfce9e22f65e95b741fda8065b1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QWlLlKvF0Wi+4q0OkOOC0v9RlluCox3SsewkA3ru3obz6piBW5hFWNT9a7dTIKewdSb4ETXSQE95QTFv45P0CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T01:47:29.311192Z","bundle_sha256":"520823b6bce3292c4ce24df2503158dc04cc0e75b608a06443445ee67189bf27"}}