{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:FMCOLGB7HSWW2MNBNJSX43BR33","short_pith_number":"pith:FMCOLGB7","canonical_record":{"source":{"id":"1012.3520","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-16T06:37:28Z","cross_cats_sorted":["gr-qc","hep-th","math.MP"],"title_canon_sha256":"fc94a3eff683ba2148df66b434d5e3aa6105d4db367bffe6378e40a0bf5bcafa","abstract_canon_sha256":"4c9644675a1be294860e6a0f927908b15a9fab8e354ff076dfa5a87ceace798d"},"schema_version":"1.0"},"canonical_sha256":"2b04e5983f3cad6d31a16a657e6c31ded714cd687a5037d04e85791423f7fd02","source":{"kind":"arxiv","id":"1012.3520","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:FMCOLGB7HSWW2MNBNJSX43BR33","target":"record","payload":{"canonical_record":{"source":{"id":"1012.3520","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-16T06:37:28Z","cross_cats_sorted":["gr-qc","hep-th","math.MP"],"title_canon_sha256":"fc94a3eff683ba2148df66b434d5e3aa6105d4db367bffe6378e40a0bf5bcafa","abstract_canon_sha256":"4c9644675a1be294860e6a0f927908b15a9fab8e354ff076dfa5a87ceace798d"},"schema_version":"1.0"},"canonical_sha256":"2b04e5983f3cad6d31a16a657e6c31ded714cd687a5037d04e85791423f7fd02","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:06.472483Z","signature_b64":"kIw1xe0nfzAAhNw2mg80enTTWoV81mNaeXm1GPWzOliO7NCRW35Gq/kET/4TosJB5gcpbO5oXEBHvYAzWvZXDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b04e5983f3cad6d31a16a657e6c31ded714cd687a5037d04e85791423f7fd02","last_reissued_at":"2026-05-18T04:33:06.471855Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:06.471855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.3520","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":"2026-05-18T04:33:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ReBExNH/X07mOa80eUTgJpAZE8KdhrbmEIfa7Es/sFRm4azh9HJbqFcjiWQL1FyKCcouUjvHwPcYoFX4Ip87AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:45:03.311778Z"},"content_sha256":"49ab800f321d720e0f0249c62f0227d47aba2e172ab81e7446e6c5d57f68f49b","schema_version":"1.0","event_id":"sha256:49ab800f321d720e0f0249c62f0227d47aba2e172ab81e7446e6c5d57f68f49b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:FMCOLGB7HSWW2MNBNJSX43BR33","target":"graph","payload":{"graph_snapshot":{"paper":{"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","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Plamen Fiziev","submitted_at":"2010-12-16T06:37:28Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3520","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":"2026-05-18T04:33:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q1C8mdSJBxh0KRuRAbALbp5StWuk3kq7Me+zz0FugLouzXUd7Ev7Vz+FgAG9Mya8uM4Am9URNQJ8RPLc4sptBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:45:03.312498Z"},"content_sha256":"014bd94ceb641a0c41e7e1251ee6b87242c845ee02dba529de3738ee7cc8f421","schema_version":"1.0","event_id":"sha256:014bd94ceb641a0c41e7e1251ee6b87242c845ee02dba529de3738ee7cc8f421"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FMCOLGB7HSWW2MNBNJSX43BR33/bundle.json","state_url":"https://pith.science/pith/FMCOLGB7HSWW2MNBNJSX43BR33/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FMCOLGB7HSWW2MNBNJSX43BR33/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":"2026-06-04T20:45:03Z","links":{"resolver":"https://pith.science/pith/FMCOLGB7HSWW2MNBNJSX43BR33","bundle":"https://pith.science/pith/FMCOLGB7HSWW2MNBNJSX43BR33/bundle.json","state":"https://pith.science/pith/FMCOLGB7HSWW2MNBNJSX43BR33/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FMCOLGB7HSWW2MNBNJSX43BR33/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8fA64PINYYfmpyEGCpPrefdFL/F8AgzJzWEKLAyyPM2dxtu1v6XUI4bKpc69IrKSXr+Xwqg0DGO5dcQwfSa/BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T20:45:03.316173Z","bundle_sha256":"9be647e51c7e78b00ab1b65bbf614608fce73110ec994a64fc894506c6c2c79c"}}