{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:I2JEGWIFVBN5CBES74EDTU7BDD","short_pith_number":"pith:I2JEGWIF","canonical_record":{"source":{"id":"1108.2942","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-08-15T06:40:13Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1187f40c1787207b2c4cf1a98fb08a9eb026dfc873f82da702bd0132677c11f8","abstract_canon_sha256":"369a8e17ba117758992fcdd669b7f453f66e68005c0dffd4a86f2c755f8a0f23"},"schema_version":"1.0"},"canonical_sha256":"4692435905a85bd10492ff0839d3e118e0a999851953ae40d9c08c3c89db93b8","source":{"kind":"arxiv","id":"1108.2942","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2942","created_at":"2026-05-18T04:15:28Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2942v1","created_at":"2026-05-18T04:15:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2942","created_at":"2026-05-18T04:15:28Z"},{"alias_kind":"pith_short_12","alias_value":"I2JEGWIFVBN5","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"I2JEGWIFVBN5CBES","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"I2JEGWIF","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:I2JEGWIFVBN5CBES74EDTU7BDD","target":"record","payload":{"canonical_record":{"source":{"id":"1108.2942","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-08-15T06:40:13Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1187f40c1787207b2c4cf1a98fb08a9eb026dfc873f82da702bd0132677c11f8","abstract_canon_sha256":"369a8e17ba117758992fcdd669b7f453f66e68005c0dffd4a86f2c755f8a0f23"},"schema_version":"1.0"},"canonical_sha256":"4692435905a85bd10492ff0839d3e118e0a999851953ae40d9c08c3c89db93b8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:15:28.942147Z","signature_b64":"qDLoi6Drt5cZRMz0yURkygOexCjyqhpgyg9s4I1smIED8GU5Nmz+tuYjxBX8YA5jNIvv7bOvrYaisSvGgrLvBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4692435905a85bd10492ff0839d3e118e0a999851953ae40d9c08c3c89db93b8","last_reissued_at":"2026-05-18T04:15:28.941675Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:15:28.941675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.2942","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:15:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FNz1GVwogbuOb/z/6wrY4+4iNR6VT5JRthkLtrr2birVP79nr8jMwDMXkO9PeoDJ7S2rMwzfxt81wivJOkf2CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:06:59.552502Z"},"content_sha256":"810a67ce582efcdeedef18d60a505dfdc8bfe10ca116349d63e220f84e7cfe1f","schema_version":"1.0","event_id":"sha256:810a67ce582efcdeedef18d60a505dfdc8bfe10ca116349d63e220f84e7cfe1f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:I2JEGWIFVBN5CBES74EDTU7BDD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regular Submanifolds in the Conformal Space ${\\mathbb Q}^n_p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Changxiong Nie","submitted_at":"2011-08-15T06:40:13Z","abstract_excerpt":"There is a Lorenzian group acting on the conformal space ${\\mathbb Q}^n_p$. We study the regular submanifolds in the conformal space ${\\mathbb Q}^n_p$ and construct general submanifold theory in the conformal space ${\\mathbb Q}^n_p$. Finally we give the first variation formula of the Willmore volume functional of submanifolds in the conformal space ${\\mathbb Q}^n_p$ and classify the conformal isotropic submanifolds in the conformal space ${\\mathbb Q}^n_p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2942","kind":"arxiv","version":1},"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":"2026-05-18T04:15:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6svtztSOe+YyViY3erbm09bUYpBbdol3ifIRj9Wk4uJB61Xss1bq1RHm1I0Y4/Z0zdEuj4TxH4LdK4L9ufqGBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:06:59.553219Z"},"content_sha256":"1eb4993c9ae08fe231df4817a11568cbd7c6280e15514d551b0d709f926e6f91","schema_version":"1.0","event_id":"sha256:1eb4993c9ae08fe231df4817a11568cbd7c6280e15514d551b0d709f926e6f91"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I2JEGWIFVBN5CBES74EDTU7BDD/bundle.json","state_url":"https://pith.science/pith/I2JEGWIFVBN5CBES74EDTU7BDD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I2JEGWIFVBN5CBES74EDTU7BDD/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":"2026-06-11T22:06:59Z","links":{"resolver":"https://pith.science/pith/I2JEGWIFVBN5CBES74EDTU7BDD","bundle":"https://pith.science/pith/I2JEGWIFVBN5CBES74EDTU7BDD/bundle.json","state":"https://pith.science/pith/I2JEGWIFVBN5CBES74EDTU7BDD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I2JEGWIFVBN5CBES74EDTU7BDD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:I2JEGWIFVBN5CBES74EDTU7BDD","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":"369a8e17ba117758992fcdd669b7f453f66e68005c0dffd4a86f2c755f8a0f23","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-08-15T06:40:13Z","title_canon_sha256":"1187f40c1787207b2c4cf1a98fb08a9eb026dfc873f82da702bd0132677c11f8"},"schema_version":"1.0","source":{"id":"1108.2942","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2942","created_at":"2026-05-18T04:15:28Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2942v1","created_at":"2026-05-18T04:15:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2942","created_at":"2026-05-18T04:15:28Z"},{"alias_kind":"pith_short_12","alias_value":"I2JEGWIFVBN5","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"I2JEGWIFVBN5CBES","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"I2JEGWIF","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:1eb4993c9ae08fe231df4817a11568cbd7c6280e15514d551b0d709f926e6f91","target":"graph","created_at":"2026-05-18T04:15:28Z","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":"There is a Lorenzian group acting on the conformal space ${\\mathbb Q}^n_p$. We study the regular submanifolds in the conformal space ${\\mathbb Q}^n_p$ and construct general submanifold theory in the conformal space ${\\mathbb Q}^n_p$. Finally we give the first variation formula of the Willmore volume functional of submanifolds in the conformal space ${\\mathbb Q}^n_p$ and classify the conformal isotropic submanifolds in the conformal space ${\\mathbb Q}^n_p$.","authors_text":"Changxiong Nie","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-08-15T06:40:13Z","title":"Regular Submanifolds in the Conformal Space ${\\mathbb Q}^n_p$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2942","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":"sha256:810a67ce582efcdeedef18d60a505dfdc8bfe10ca116349d63e220f84e7cfe1f","target":"record","created_at":"2026-05-18T04:15:28Z","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":"369a8e17ba117758992fcdd669b7f453f66e68005c0dffd4a86f2c755f8a0f23","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-08-15T06:40:13Z","title_canon_sha256":"1187f40c1787207b2c4cf1a98fb08a9eb026dfc873f82da702bd0132677c11f8"},"schema_version":"1.0","source":{"id":"1108.2942","kind":"arxiv","version":1}},"canonical_sha256":"4692435905a85bd10492ff0839d3e118e0a999851953ae40d9c08c3c89db93b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4692435905a85bd10492ff0839d3e118e0a999851953ae40d9c08c3c89db93b8","first_computed_at":"2026-05-18T04:15:28.941675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:28.941675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qDLoi6Drt5cZRMz0yURkygOexCjyqhpgyg9s4I1smIED8GU5Nmz+tuYjxBX8YA5jNIvv7bOvrYaisSvGgrLvBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:28.942147Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.2942","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:810a67ce582efcdeedef18d60a505dfdc8bfe10ca116349d63e220f84e7cfe1f","sha256:1eb4993c9ae08fe231df4817a11568cbd7c6280e15514d551b0d709f926e6f91"],"state_sha256":"78dce84a092c40bf596a20a8fe10e524234b45d9d4eba429978557741643c220"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3lu2dkpLywJbnvXFSGESPUlGJI06HIFtbtGF803iH49+DHk7nh8I/lu8YuVRz6fMAi8cyTByOF4URk1YqK5RAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T22:06:59.557113Z","bundle_sha256":"c785b755e2071d627b7e2991def35127a79b8b1f68748b7acc63c970bdef576d"}}