{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:72US2BZSWVPRWCMVI2AE4A52SG","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":"f8e79cd9a0072d2ce936a6de82705fb414cc2e49649041d49910b55f1dd1e1da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-01-04T16:27:16Z","title_canon_sha256":"1bb8e5642672594dfb2cade9592a862d8e20867590b8a485b7f46fcf928872ac"},"schema_version":"1.0","source":{"id":"1201.0934","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.0934","created_at":"2026-05-18T03:28:54Z"},{"alias_kind":"arxiv_version","alias_value":"1201.0934v1","created_at":"2026-05-18T03:28:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0934","created_at":"2026-05-18T03:28:54Z"},{"alias_kind":"pith_short_12","alias_value":"72US2BZSWVPR","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"72US2BZSWVPRWCMV","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"72US2BZS","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:cf54829adfc52756536fbd173512312d05fdd32b1150c4b4f65b73d11246ba72","target":"graph","created_at":"2026-05-18T03:28:54Z","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":"In this article we define the continuous Gabor transform for second countable, non-abelian, unimodular and type I groups and also we investigate a Plancherel formula and an inversion formula for our definition. As an example we show that how these formulas work for the Heisenberg group and also the matrix group ${SL(2,\\mathbb{R})}$.","authors_text":"Arash Ghaani Farashahi, Rajabali Kamyabi-Gol","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-01-04T16:27:16Z","title":"Continuous Gabor transform for a class of non-Abelian groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0934","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:bfbb30d79578e707acda041e7a4fd7cfa7ce98b444da71c20dca924cd8658004","target":"record","created_at":"2026-05-18T03:28:54Z","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":"f8e79cd9a0072d2ce936a6de82705fb414cc2e49649041d49910b55f1dd1e1da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-01-04T16:27:16Z","title_canon_sha256":"1bb8e5642672594dfb2cade9592a862d8e20867590b8a485b7f46fcf928872ac"},"schema_version":"1.0","source":{"id":"1201.0934","kind":"arxiv","version":1}},"canonical_sha256":"fea92d0732b55f1b099546804e03ba91952fdf62df503e796efa90675f095281","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fea92d0732b55f1b099546804e03ba91952fdf62df503e796efa90675f095281","first_computed_at":"2026-05-18T03:28:54.063730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:54.063730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BKY4lqqp0EUQBnPb6scpUdwxpP/q78o0S6q/sR2dvVsIECnWwgOobkbvYOo9K861dzgWXITQgtk8DzPIlylxAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:54.064422Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.0934","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bfbb30d79578e707acda041e7a4fd7cfa7ce98b444da71c20dca924cd8658004","sha256:cf54829adfc52756536fbd173512312d05fdd32b1150c4b4f65b73d11246ba72"],"state_sha256":"402e3ea1eb0e77ac0b102ff3e0372cb7c495fffdc12f8da85320a4e003a4a289"}