{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:I4DFA4OTNW6BYJCFQFZJYFY2KF","short_pith_number":"pith:I4DFA4OT","canonical_record":{"source":{"id":"1011.2168","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-11-09T18:27:53Z","cross_cats_sorted":["math-ph","math.MP","math.RT"],"title_canon_sha256":"b512e7ad84b067b1c1e0f8a42419cc77edcb4b346460ece60d91c856f2c8822c","abstract_canon_sha256":"e47fc4448705ffb636fa6fb83cc088e5ff756ca0da21565a9a50b98de858613d"},"schema_version":"1.0"},"canonical_sha256":"47065071d36dbc1c244581729c171a516cf95f6c3d51e1289ac1396ef7d4b56b","source":{"kind":"arxiv","id":"1011.2168","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2168","created_at":"2026-05-18T02:04:49Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2168v1","created_at":"2026-05-18T02:04:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2168","created_at":"2026-05-18T02:04:49Z"},{"alias_kind":"pith_short_12","alias_value":"I4DFA4OTNW6B","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"I4DFA4OTNW6BYJCF","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"I4DFA4OT","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:I4DFA4OTNW6BYJCFQFZJYFY2KF","target":"record","payload":{"canonical_record":{"source":{"id":"1011.2168","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-11-09T18:27:53Z","cross_cats_sorted":["math-ph","math.MP","math.RT"],"title_canon_sha256":"b512e7ad84b067b1c1e0f8a42419cc77edcb4b346460ece60d91c856f2c8822c","abstract_canon_sha256":"e47fc4448705ffb636fa6fb83cc088e5ff756ca0da21565a9a50b98de858613d"},"schema_version":"1.0"},"canonical_sha256":"47065071d36dbc1c244581729c171a516cf95f6c3d51e1289ac1396ef7d4b56b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:49.675197Z","signature_b64":"v/3LZHTRS9yG5p2wByHTxbOWiB7hkIyKWQ2MAUDz9RlWYS19XVfFbRY/znc/oGrdZa8G9IwaZAD4rxRfUsaRBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47065071d36dbc1c244581729c171a516cf95f6c3d51e1289ac1396ef7d4b56b","last_reissued_at":"2026-05-18T02:04:49.674500Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:49.674500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.2168","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":"2026-05-18T02:04:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KuOKtcdJKtnRJsSFJAS8bMBeI8GArCgG7OgP8q+6i1xDC+VdQJMxkMQFzdX8aEIYWhyt3f4fl2KEt8/yKyV2DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T14:41:13.289641Z"},"content_sha256":"1946f1d85d75728e436abb4ec0e77de56ee034c8f4dfe894b694d447d79a30b8","schema_version":"1.0","event_id":"sha256:1946f1d85d75728e436abb4ec0e77de56ee034c8f4dfe894b694d447d79a30b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:I4DFA4OTNW6BYJCFQFZJYFY2KF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"BKM Lie superalgebra for the Z_5 orbifolded CHL string","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RT"],"primary_cat":"hep-th","authors_text":"K. Gopala Krishna","submitted_at":"2010-11-09T18:27:53Z","abstract_excerpt":"We study the Z_5-orbifolding of the CHL string theory by explicitly constructing the modular form tilde{Phi}_2 generating the degeneracies of the 1/4-BPS states in the theory. Since the additive seed for the sum form is a weak Jacobi form in this case, a mismatch is found between the modular forms generated from the additive lift and the product form derived from threshold corrections. We also construct the BKM Lie superalgebra, tilde{G}_5, corresponding to the modular form tilde{Delta}_1 (Z) = tilde{Phi}_2 (Z)^{1/2} which happens to be a hyperbolic algebra. This is the first occurrence of a h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2168","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":"2026-05-18T02:04:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+qiDo5P431D4SbNneCWz6wnkU4RV1/7R4fn0K7d15hAfjtMHxrfrCNKCSxEMyFVWQPZUF2BxN0SRXTY49+6FDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T14:41:13.289990Z"},"content_sha256":"29dcb185c6e2b93939d84364a4f623f2854764beaa42ef66f634a7f44b9e0b7f","schema_version":"1.0","event_id":"sha256:29dcb185c6e2b93939d84364a4f623f2854764beaa42ef66f634a7f44b9e0b7f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I4DFA4OTNW6BYJCFQFZJYFY2KF/bundle.json","state_url":"https://pith.science/pith/I4DFA4OTNW6BYJCFQFZJYFY2KF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I4DFA4OTNW6BYJCFQFZJYFY2KF/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":"2026-06-05T14:41:13Z","links":{"resolver":"https://pith.science/pith/I4DFA4OTNW6BYJCFQFZJYFY2KF","bundle":"https://pith.science/pith/I4DFA4OTNW6BYJCFQFZJYFY2KF/bundle.json","state":"https://pith.science/pith/I4DFA4OTNW6BYJCFQFZJYFY2KF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I4DFA4OTNW6BYJCFQFZJYFY2KF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:I4DFA4OTNW6BYJCFQFZJYFY2KF","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":"e47fc4448705ffb636fa6fb83cc088e5ff756ca0da21565a9a50b98de858613d","cross_cats_sorted":["math-ph","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-11-09T18:27:53Z","title_canon_sha256":"b512e7ad84b067b1c1e0f8a42419cc77edcb4b346460ece60d91c856f2c8822c"},"schema_version":"1.0","source":{"id":"1011.2168","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2168","created_at":"2026-05-18T02:04:49Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2168v1","created_at":"2026-05-18T02:04:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2168","created_at":"2026-05-18T02:04:49Z"},{"alias_kind":"pith_short_12","alias_value":"I4DFA4OTNW6B","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"I4DFA4OTNW6BYJCF","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"I4DFA4OT","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:29dcb185c6e2b93939d84364a4f623f2854764beaa42ef66f634a7f44b9e0b7f","target":"graph","created_at":"2026-05-18T02:04:49Z","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 study the Z_5-orbifolding of the CHL string theory by explicitly constructing the modular form tilde{Phi}_2 generating the degeneracies of the 1/4-BPS states in the theory. Since the additive seed for the sum form is a weak Jacobi form in this case, a mismatch is found between the modular forms generated from the additive lift and the product form derived from threshold corrections. We also construct the BKM Lie superalgebra, tilde{G}_5, corresponding to the modular form tilde{Delta}_1 (Z) = tilde{Phi}_2 (Z)^{1/2} which happens to be a hyperbolic algebra. This is the first occurrence of a h","authors_text":"K. Gopala Krishna","cross_cats":["math-ph","math.MP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-11-09T18:27:53Z","title":"BKM Lie superalgebra for the Z_5 orbifolded CHL string"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2168","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":"sha256:1946f1d85d75728e436abb4ec0e77de56ee034c8f4dfe894b694d447d79a30b8","target":"record","created_at":"2026-05-18T02:04:49Z","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":"e47fc4448705ffb636fa6fb83cc088e5ff756ca0da21565a9a50b98de858613d","cross_cats_sorted":["math-ph","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-11-09T18:27:53Z","title_canon_sha256":"b512e7ad84b067b1c1e0f8a42419cc77edcb4b346460ece60d91c856f2c8822c"},"schema_version":"1.0","source":{"id":"1011.2168","kind":"arxiv","version":1}},"canonical_sha256":"47065071d36dbc1c244581729c171a516cf95f6c3d51e1289ac1396ef7d4b56b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47065071d36dbc1c244581729c171a516cf95f6c3d51e1289ac1396ef7d4b56b","first_computed_at":"2026-05-18T02:04:49.674500Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:04:49.674500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v/3LZHTRS9yG5p2wByHTxbOWiB7hkIyKWQ2MAUDz9RlWYS19XVfFbRY/znc/oGrdZa8G9IwaZAD4rxRfUsaRBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:04:49.675197Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.2168","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1946f1d85d75728e436abb4ec0e77de56ee034c8f4dfe894b694d447d79a30b8","sha256:29dcb185c6e2b93939d84364a4f623f2854764beaa42ef66f634a7f44b9e0b7f"],"state_sha256":"d52efb12bb13d6d7b3c467d6d73ea18e4b900728dc1dbab691b0cb5f49af146c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N31rxmfWSd2aeGgxP9IiL+KzWYEf3+q97KAlPPjzEFKWoXLl7V1ic19y2h4d83vXZwyn7wf8FRwz1uRtatanCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T14:41:13.291960Z","bundle_sha256":"4d9a342b46ba0040f1fdba5038ff4908e6360259b9d59a3f63b764a975c900d0"}}