{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LEPPWZNMM3NKD6AVSBU2ALYGFU","short_pith_number":"pith:LEPPWZNM","canonical_record":{"source":{"id":"1604.06686","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2016-04-19T21:54:03Z","cross_cats_sorted":[],"title_canon_sha256":"24cdbf828305309b6b1d96a8d733aa237c7f5bb3dffd881de4cf308cdac9c587","abstract_canon_sha256":"b95e6b7c1515a81258886cf7c4c575a210422e693caa7c3157148cc6ed7813da"},"schema_version":"1.0"},"canonical_sha256":"591efb65ac66daa1f8159069a02f062d318ad4f2a67868416692a068797acba9","source":{"kind":"arxiv","id":"1604.06686","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06686","created_at":"2026-05-18T01:16:28Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06686v1","created_at":"2026-05-18T01:16:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06686","created_at":"2026-05-18T01:16:28Z"},{"alias_kind":"pith_short_12","alias_value":"LEPPWZNMM3NK","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LEPPWZNMM3NKD6AV","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LEPPWZNM","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LEPPWZNMM3NKD6AVSBU2ALYGFU","target":"record","payload":{"canonical_record":{"source":{"id":"1604.06686","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2016-04-19T21:54:03Z","cross_cats_sorted":[],"title_canon_sha256":"24cdbf828305309b6b1d96a8d733aa237c7f5bb3dffd881de4cf308cdac9c587","abstract_canon_sha256":"b95e6b7c1515a81258886cf7c4c575a210422e693caa7c3157148cc6ed7813da"},"schema_version":"1.0"},"canonical_sha256":"591efb65ac66daa1f8159069a02f062d318ad4f2a67868416692a068797acba9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:28.427518Z","signature_b64":"Cx1aNWZCzW+oDo6mYJ1Cxtq7zU5VHvaJcc/D4y9WYb5yV1jrz7BMZ7OZVi29CCcpNMh19cBqgPpr6hMtfRnCBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"591efb65ac66daa1f8159069a02f062d318ad4f2a67868416692a068797acba9","last_reissued_at":"2026-05-18T01:16:28.426656Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:28.426656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.06686","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":"2026-05-18T01:16:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VRSaX648dPbSpIm/zAtO4nlMsPPJy7GylxA2zUt0vZs2slNqMnQseXV9qDD/gGdWNerjHYa4ueEPIpMrg6JyAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:02:53.783448Z"},"content_sha256":"530490226c0b0a1a3ef00da29feb1a51529cd5d9a926a7c3f5f91a88faa80f3b","schema_version":"1.0","event_id":"sha256:530490226c0b0a1a3ef00da29feb1a51529cd5d9a926a7c3f5f91a88faa80f3b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LEPPWZNMM3NKD6AVSBU2ALYGFU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Discrete fractional Fourier transform: Vandermonde approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Francisco Soto-Eguibar, H\\'ector M. Moya-Cessa","submitted_at":"2016-04-19T21:54:03Z","abstract_excerpt":"Based on the definition of the Fourier transform in terms of the number operator of the quantum harmonic oscillator and in the corresponding definition of the fractional Fourier transform, we have obtained the discrete fractional Fourier transform from the discrete Fourier transform in a completely analogous manner. To achieve this, we have used a very simple method based on the Vandermonde matrices, to obtain rational and irrational powers of the discrete Fourier transform matrices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06686","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":"2026-05-18T01:16:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BURQSCheWVJy3qx1L58guaAI3gGS6yQ8UJ2/TXBmRgX/tKSp7WZm9k9a4aBnoAtcL5m3bHAQztjbSCLtRtnjCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:02:53.784071Z"},"content_sha256":"fff5947ca06b71fc3fc338fd83459f2b69bcef526efa995b43238e466cf682c5","schema_version":"1.0","event_id":"sha256:fff5947ca06b71fc3fc338fd83459f2b69bcef526efa995b43238e466cf682c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LEPPWZNMM3NKD6AVSBU2ALYGFU/bundle.json","state_url":"https://pith.science/pith/LEPPWZNMM3NKD6AVSBU2ALYGFU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LEPPWZNMM3NKD6AVSBU2ALYGFU/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":"2026-05-28T00:02:53Z","links":{"resolver":"https://pith.science/pith/LEPPWZNMM3NKD6AVSBU2ALYGFU","bundle":"https://pith.science/pith/LEPPWZNMM3NKD6AVSBU2ALYGFU/bundle.json","state":"https://pith.science/pith/LEPPWZNMM3NKD6AVSBU2ALYGFU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LEPPWZNMM3NKD6AVSBU2ALYGFU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LEPPWZNMM3NKD6AVSBU2ALYGFU","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":"b95e6b7c1515a81258886cf7c4c575a210422e693caa7c3157148cc6ed7813da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2016-04-19T21:54:03Z","title_canon_sha256":"24cdbf828305309b6b1d96a8d733aa237c7f5bb3dffd881de4cf308cdac9c587"},"schema_version":"1.0","source":{"id":"1604.06686","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06686","created_at":"2026-05-18T01:16:28Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06686v1","created_at":"2026-05-18T01:16:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06686","created_at":"2026-05-18T01:16:28Z"},{"alias_kind":"pith_short_12","alias_value":"LEPPWZNMM3NK","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LEPPWZNMM3NKD6AV","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LEPPWZNM","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:fff5947ca06b71fc3fc338fd83459f2b69bcef526efa995b43238e466cf682c5","target":"graph","created_at":"2026-05-18T01:16:28Z","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":"Based on the definition of the Fourier transform in terms of the number operator of the quantum harmonic oscillator and in the corresponding definition of the fractional Fourier transform, we have obtained the discrete fractional Fourier transform from the discrete Fourier transform in a completely analogous manner. To achieve this, we have used a very simple method based on the Vandermonde matrices, to obtain rational and irrational powers of the discrete Fourier transform matrices.","authors_text":"Francisco Soto-Eguibar, H\\'ector M. Moya-Cessa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2016-04-19T21:54:03Z","title":"Discrete fractional Fourier transform: Vandermonde approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06686","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":"sha256:530490226c0b0a1a3ef00da29feb1a51529cd5d9a926a7c3f5f91a88faa80f3b","target":"record","created_at":"2026-05-18T01:16:28Z","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":"b95e6b7c1515a81258886cf7c4c575a210422e693caa7c3157148cc6ed7813da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2016-04-19T21:54:03Z","title_canon_sha256":"24cdbf828305309b6b1d96a8d733aa237c7f5bb3dffd881de4cf308cdac9c587"},"schema_version":"1.0","source":{"id":"1604.06686","kind":"arxiv","version":1}},"canonical_sha256":"591efb65ac66daa1f8159069a02f062d318ad4f2a67868416692a068797acba9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"591efb65ac66daa1f8159069a02f062d318ad4f2a67868416692a068797acba9","first_computed_at":"2026-05-18T01:16:28.426656Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:28.426656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cx1aNWZCzW+oDo6mYJ1Cxtq7zU5VHvaJcc/D4y9WYb5yV1jrz7BMZ7OZVi29CCcpNMh19cBqgPpr6hMtfRnCBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:28.427518Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.06686","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:530490226c0b0a1a3ef00da29feb1a51529cd5d9a926a7c3f5f91a88faa80f3b","sha256:fff5947ca06b71fc3fc338fd83459f2b69bcef526efa995b43238e466cf682c5"],"state_sha256":"8786d3604c489625ba0830add4b147059fe49ce4e2a10949ff750e3c0237eebf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ILU7trCNsqfcAS51j0FaFBtwCLUNUmJXXNT93Pp/XxJXV1rHQuHio+bk/0dbiv1n6RtsPDjwAzObeKBgKelnBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T00:02:53.787691Z","bundle_sha256":"c496060032d7b867ac9852af997df2b883b54bfe228fe1ba4635cfe684c378b5"}}