{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:FMCOLGB7HSWW2MNBNJSX43BR33","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":"4c9644675a1be294860e6a0f927908b15a9fab8e354ff076dfa5a87ceace798d","cross_cats_sorted":["gr-qc","hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-16T06:37:28Z","title_canon_sha256":"fc94a3eff683ba2148df66b434d5e3aa6105d4db367bffe6378e40a0bf5bcafa"},"schema_version":"1.0","source":{"id":"1012.3520","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.3520","created_at":"2026-05-18T04:33:06Z"},{"alias_kind":"arxiv_version","alias_value":"1012.3520v1","created_at":"2026-05-18T04:33:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3520","created_at":"2026-05-18T04:33:06Z"},{"alias_kind":"pith_short_12","alias_value":"FMCOLGB7HSWW","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"FMCOLGB7HSWW2MNB","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"FMCOLGB7","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:014bd94ceb641a0c41e7e1251ee6b87242c845ee02dba529de3738ee7cc8f421","target":"graph","created_at":"2026-05-18T04:33:06Z","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":"This rather technical paper presents some generalization of the results of recent publications \\cite{Shirkov2010, DVPF2010, PFDV2010} where toy models of dimensional reduction of space-time were considered. Here we introduce and consider a specific type of multidimensional space-times with nontrivial topology and nontrivial Riemannian metric, which admit a reduction of the dimension $d$ of the space to any lower one $d_{low} = 1, 2,..., d-1$. The variable geometry is described by several variable radii of compactification of part of space dimensions. We succeed once more in transforming the sh","authors_text":"Plamen Fiziev","cross_cats":["gr-qc","hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-16T06:37:28Z","title":"Riemannian $\\mathbf{(1+d)}$-Dim Space-Time Manifolds with Nonstandard Topology which Admit Dimensional Reduction to Any Lower Dimension and Transformation of the Klein-Gordon Equation to the $\\mathbf{1}$-Dim Schr\\\"odinger Like Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3520","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":"sha256:49ab800f321d720e0f0249c62f0227d47aba2e172ab81e7446e6c5d57f68f49b","target":"record","created_at":"2026-05-18T04:33:06Z","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":"4c9644675a1be294860e6a0f927908b15a9fab8e354ff076dfa5a87ceace798d","cross_cats_sorted":["gr-qc","hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-16T06:37:28Z","title_canon_sha256":"fc94a3eff683ba2148df66b434d5e3aa6105d4db367bffe6378e40a0bf5bcafa"},"schema_version":"1.0","source":{"id":"1012.3520","kind":"arxiv","version":1}},"canonical_sha256":"2b04e5983f3cad6d31a16a657e6c31ded714cd687a5037d04e85791423f7fd02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b04e5983f3cad6d31a16a657e6c31ded714cd687a5037d04e85791423f7fd02","first_computed_at":"2026-05-18T04:33:06.471855Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:06.471855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kIw1xe0nfzAAhNw2mg80enTTWoV81mNaeXm1GPWzOliO7NCRW35Gq/kET/4TosJB5gcpbO5oXEBHvYAzWvZXDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:06.472483Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.3520","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49ab800f321d720e0f0249c62f0227d47aba2e172ab81e7446e6c5d57f68f49b","sha256:014bd94ceb641a0c41e7e1251ee6b87242c845ee02dba529de3738ee7cc8f421"],"state_sha256":"432fecf77ff54ee536c00d67b7106fe8a9872d582f8831ce6cf428b4781588f3"}