{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:JGN7ZWA44L2Y22QVG24S5TPYOP","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":"44646b114d1611fd3212b390bc0a55798d9c66d78b4332e29ba6d2e1385bbf36","cross_cats_sorted":["hep-ph"],"license":"","primary_cat":"hep-th","submitted_at":"2002-12-12T17:53:10Z","title_canon_sha256":"db3e0dcebb7800f81f813c21f2d115e6dd74205e336cc72dc2e974a83fa59fe4"},"schema_version":"1.0","source":{"id":"hep-th/0212144","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0212144","created_at":"2026-05-18T02:35:53Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0212144v2","created_at":"2026-05-18T02:35:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0212144","created_at":"2026-05-18T02:35:53Z"},{"alias_kind":"pith_short_12","alias_value":"JGN7ZWA44L2Y","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"JGN7ZWA44L2Y22QV","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"JGN7ZWA4","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:bc3a9d0a1d08bed5bd299c2f6d9ac82e0b27e582b804c3dc4e86961f3ebf0f2d","target":"graph","created_at":"2026-05-18T02:35:53Z","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":"Compactifying a higher-dimensional theory defined in R^{1,3+n} on an n-dimensional manifold {\\cal M} results in a spectrum of four-dimensional (bosonic) fields with masses m^2_i = \\lambda_i, where - \\lambda_i are the eigenvalues of the Laplacian on the compact manifold. The question we address in this paper is the inverse: given the masses of the Kaluza-Klein fields in four dimensions, what can we say about the size and shape (i.e. the topology and the metric) of the compact manifold? We present some examples of isospectral manifolds (i.e., different manifolds which give rise to the same Kaluz","authors_text":"Gary Shiu, Raul Rabadan","cross_cats":["hep-ph"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2002-12-12T17:53:10Z","title":"(Re)constructing Dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0212144","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":"sha256:34d485e5de2571b0a10c5da889edc9c5aae44c9966d7d7a53f1246dc452424d6","target":"record","created_at":"2026-05-18T02:35:53Z","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":"44646b114d1611fd3212b390bc0a55798d9c66d78b4332e29ba6d2e1385bbf36","cross_cats_sorted":["hep-ph"],"license":"","primary_cat":"hep-th","submitted_at":"2002-12-12T17:53:10Z","title_canon_sha256":"db3e0dcebb7800f81f813c21f2d115e6dd74205e336cc72dc2e974a83fa59fe4"},"schema_version":"1.0","source":{"id":"hep-th/0212144","kind":"arxiv","version":2}},"canonical_sha256":"499bfcd81ce2f58d6a1536b92ecdf873ed0b9616f5de507045e7609ee9ede9b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"499bfcd81ce2f58d6a1536b92ecdf873ed0b9616f5de507045e7609ee9ede9b7","first_computed_at":"2026-05-18T02:35:53.303985Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:35:53.303985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uCsiTlUXqsCnXt0CqvlkEm9DyKG25f3fuN58rqAtL/rlfNBjoppdMZHNY1hhX0VT74vCBRku9UxBXKfpNauCAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:35:53.304471Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0212144","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34d485e5de2571b0a10c5da889edc9c5aae44c9966d7d7a53f1246dc452424d6","sha256:bc3a9d0a1d08bed5bd299c2f6d9ac82e0b27e582b804c3dc4e86961f3ebf0f2d"],"state_sha256":"10983df4e12af0f90b277e97a4f22b54355d0627154d0b01b339678e710b2542"}