{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MDXX6YDRF6KY3MHW4PT5P5L2AV","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":"e869ef5a14c207cc9271e2e763bf3eb3c7d1af820f9a5b6e61fee391e8b1124a","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-24T07:45:52Z","title_canon_sha256":"84b577094fe88d6349092fb946947fcffb426ff83b60970ad8786fc7f28542d8"},"schema_version":"1.0","source":{"id":"1202.5383","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.5383","created_at":"2026-05-18T02:21:17Z"},{"alias_kind":"arxiv_version","alias_value":"1202.5383v3","created_at":"2026-05-18T02:21:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5383","created_at":"2026-05-18T02:21:17Z"},{"alias_kind":"pith_short_12","alias_value":"MDXX6YDRF6KY","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MDXX6YDRF6KY3MHW","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MDXX6YDR","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:859597dbfd306a9be69b79129b5dbc5128c5575bb56f0a4a6c4fb7c7634a534e","target":"graph","created_at":"2026-05-18T02:21:17Z","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 define an infinite class of unitary transformations between position and momentum fractional spaces, thus generalizing the Fourier transform to a special class of fractal geometries. Each transform diagonalizes a unique Laplacian operator. We also introduce a new version of fractional spaces, where coordinates and momenta span the whole real line. In one topological dimension, these results are extended to more general measures.","authors_text":"Gianluca Calcagni, Giuseppe Nardelli","cross_cats":["hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-24T07:45:52Z","title":"Momentum transforms and Laplacians in fractional spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5383","kind":"arxiv","version":3},"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":"sha256:36f401130122a9aaeaa940cc5c07e89918e1f2d6aaf7a283fd557a9c308cba5c","target":"record","created_at":"2026-05-18T02:21:17Z","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":"e869ef5a14c207cc9271e2e763bf3eb3c7d1af820f9a5b6e61fee391e8b1124a","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-24T07:45:52Z","title_canon_sha256":"84b577094fe88d6349092fb946947fcffb426ff83b60970ad8786fc7f28542d8"},"schema_version":"1.0","source":{"id":"1202.5383","kind":"arxiv","version":3}},"canonical_sha256":"60ef7f60712f958db0f6e3e7d7f57a056c8a81b961d08dd02deb0dfa25e3cd99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60ef7f60712f958db0f6e3e7d7f57a056c8a81b961d08dd02deb0dfa25e3cd99","first_computed_at":"2026-05-18T02:21:17.582036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:17.582036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qiYRnWGoywmr2Da7RcxJ1eHBufKlb49YDRK9Z7+pUT0J0053Z4WFo/cQKIm0pZCbFlhiZSOPhz6R3FNUwVxnBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:17.582727Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.5383","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36f401130122a9aaeaa940cc5c07e89918e1f2d6aaf7a283fd557a9c308cba5c","sha256:859597dbfd306a9be69b79129b5dbc5128c5575bb56f0a4a6c4fb7c7634a534e"],"state_sha256":"e5d786a4b5d58b469a222bb028f60ff573d484be242410752acf021b8e7b1982"}