{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KTQPZY24GJW6EPSX5IXUZZWRL4","short_pith_number":"pith:KTQPZY24","canonical_record":{"source":{"id":"1303.4390","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-03-18T20:00:01Z","cross_cats_sorted":["cond-mat.str-el"],"title_canon_sha256":"d2f984c38226d8e420c910dba8a3263bc8acfbb444f6689e7879abef7058f041","abstract_canon_sha256":"c50178bffed1476445ce0cc9c2b099c22a6eff646e8d85323b7a72d86b4f2e2c"},"schema_version":"1.0"},"canonical_sha256":"54e0fce35c326de23e57ea2f4ce6d15f0de0abeb8fe691cde77aafea2ec5075e","source":{"kind":"arxiv","id":"1303.4390","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4390","created_at":"2026-05-18T03:16:26Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4390v2","created_at":"2026-05-18T03:16:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4390","created_at":"2026-05-18T03:16:26Z"},{"alias_kind":"pith_short_12","alias_value":"KTQPZY24GJW6","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KTQPZY24GJW6EPSX","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KTQPZY24","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KTQPZY24GJW6EPSX5IXUZZWRL4","target":"record","payload":{"canonical_record":{"source":{"id":"1303.4390","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-03-18T20:00:01Z","cross_cats_sorted":["cond-mat.str-el"],"title_canon_sha256":"d2f984c38226d8e420c910dba8a3263bc8acfbb444f6689e7879abef7058f041","abstract_canon_sha256":"c50178bffed1476445ce0cc9c2b099c22a6eff646e8d85323b7a72d86b4f2e2c"},"schema_version":"1.0"},"canonical_sha256":"54e0fce35c326de23e57ea2f4ce6d15f0de0abeb8fe691cde77aafea2ec5075e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:26.735080Z","signature_b64":"TZynNBbCFJ+iKWVP9sJJlp0aPIQ7q6i3Z1+d7DkbnckPAci/R6tgdfqeDqpB1IqVCzIXvTqVLWaIpI6z35jcCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54e0fce35c326de23e57ea2f4ce6d15f0de0abeb8fe691cde77aafea2ec5075e","last_reissued_at":"2026-05-18T03:16:26.734585Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:26.734585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.4390","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":"2026-05-18T03:16:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wQtWSzslDEm9sGH+aOpbU+bMZxrCjeFE2l/eBs4byh2ptlNLAZrAi8gjdR3MCvXXWBJ4t0RfuXYf0QFCLxXMCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:03:27.081823Z"},"content_sha256":"904031b5f40d288889d06135013b7dbdc44882127aa54d8bac369fd24c4718d6","schema_version":"1.0","event_id":"sha256:904031b5f40d288889d06135013b7dbdc44882127aa54d8bac369fd24c4718d6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KTQPZY24GJW6EPSX5IXUZZWRL4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vortex Lattices and Crystalline Geometries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el"],"primary_cat":"hep-th","authors_text":"Ning Bao, Sarah Harrison, Shamit Kachru, Subir Sachdev","submitted_at":"2013-03-18T20:00:01Z","abstract_excerpt":"We consider $AdS_2 \\times R^2$ solutions supported by a magnetic field, such as those which arise in the near-horizon limit of magnetically charged $AdS_4$ Reissner-Nordstrom black branes. In the presence of an electrically charged scalar field, such magnetic solutions can be unstable to spontaneous formation of a vortex lattice. We solve the coupled partial differential equations which govern the charged scalar, gauge field, and metric degrees of freedom to lowest non-trivial order in an expansion around the critical point, and discuss the corrections to the free energy and thermodynamic func"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4390","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":"2026-05-18T03:16:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nCJELjoADbH3t1rqVSoXESAPZiWA6PcS9r0aJ1lrNf7Zv+Q3XBtyMs6hbpP5+luTm4oNzBhXHjGATpNoRMozAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:03:27.082181Z"},"content_sha256":"97f8e89a124e207516f3e30826fb0f870a69dac54553fe59f4a3104c230aca61","schema_version":"1.0","event_id":"sha256:97f8e89a124e207516f3e30826fb0f870a69dac54553fe59f4a3104c230aca61"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KTQPZY24GJW6EPSX5IXUZZWRL4/bundle.json","state_url":"https://pith.science/pith/KTQPZY24GJW6EPSX5IXUZZWRL4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KTQPZY24GJW6EPSX5IXUZZWRL4/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":"2026-06-05T15:03:27Z","links":{"resolver":"https://pith.science/pith/KTQPZY24GJW6EPSX5IXUZZWRL4","bundle":"https://pith.science/pith/KTQPZY24GJW6EPSX5IXUZZWRL4/bundle.json","state":"https://pith.science/pith/KTQPZY24GJW6EPSX5IXUZZWRL4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KTQPZY24GJW6EPSX5IXUZZWRL4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KTQPZY24GJW6EPSX5IXUZZWRL4","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":"c50178bffed1476445ce0cc9c2b099c22a6eff646e8d85323b7a72d86b4f2e2c","cross_cats_sorted":["cond-mat.str-el"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-03-18T20:00:01Z","title_canon_sha256":"d2f984c38226d8e420c910dba8a3263bc8acfbb444f6689e7879abef7058f041"},"schema_version":"1.0","source":{"id":"1303.4390","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4390","created_at":"2026-05-18T03:16:26Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4390v2","created_at":"2026-05-18T03:16:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4390","created_at":"2026-05-18T03:16:26Z"},{"alias_kind":"pith_short_12","alias_value":"KTQPZY24GJW6","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KTQPZY24GJW6EPSX","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KTQPZY24","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:97f8e89a124e207516f3e30826fb0f870a69dac54553fe59f4a3104c230aca61","target":"graph","created_at":"2026-05-18T03:16:26Z","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 consider $AdS_2 \\times R^2$ solutions supported by a magnetic field, such as those which arise in the near-horizon limit of magnetically charged $AdS_4$ Reissner-Nordstrom black branes. In the presence of an electrically charged scalar field, such magnetic solutions can be unstable to spontaneous formation of a vortex lattice. We solve the coupled partial differential equations which govern the charged scalar, gauge field, and metric degrees of freedom to lowest non-trivial order in an expansion around the critical point, and discuss the corrections to the free energy and thermodynamic func","authors_text":"Ning Bao, Sarah Harrison, Shamit Kachru, Subir Sachdev","cross_cats":["cond-mat.str-el"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-03-18T20:00:01Z","title":"Vortex Lattices and Crystalline Geometries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4390","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":"sha256:904031b5f40d288889d06135013b7dbdc44882127aa54d8bac369fd24c4718d6","target":"record","created_at":"2026-05-18T03:16:26Z","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":"c50178bffed1476445ce0cc9c2b099c22a6eff646e8d85323b7a72d86b4f2e2c","cross_cats_sorted":["cond-mat.str-el"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-03-18T20:00:01Z","title_canon_sha256":"d2f984c38226d8e420c910dba8a3263bc8acfbb444f6689e7879abef7058f041"},"schema_version":"1.0","source":{"id":"1303.4390","kind":"arxiv","version":2}},"canonical_sha256":"54e0fce35c326de23e57ea2f4ce6d15f0de0abeb8fe691cde77aafea2ec5075e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54e0fce35c326de23e57ea2f4ce6d15f0de0abeb8fe691cde77aafea2ec5075e","first_computed_at":"2026-05-18T03:16:26.734585Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:26.734585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TZynNBbCFJ+iKWVP9sJJlp0aPIQ7q6i3Z1+d7DkbnckPAci/R6tgdfqeDqpB1IqVCzIXvTqVLWaIpI6z35jcCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:26.735080Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.4390","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:904031b5f40d288889d06135013b7dbdc44882127aa54d8bac369fd24c4718d6","sha256:97f8e89a124e207516f3e30826fb0f870a69dac54553fe59f4a3104c230aca61"],"state_sha256":"f10048f21d3dbfe394f2f97cab4b2fd2711c5a8722640dbf82c05ba673146bea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oZ2QJi8dNmsdJaXqx7bj5iCNNozBIRFR0Fn+m9FGdJkusC0itTrk+YmE2wb8fDu8sx2xKpM/JC3gFKOGLrG+Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T15:03:27.084601Z","bundle_sha256":"49a4f055bff3d44245801c4c513f946c9bffb5ed59a79b6c4f9ba739d413a421"}}