{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:RUCL66QSRPS4TVJ3XHKFOR5MTG","short_pith_number":"pith:RUCL66QS","canonical_record":{"source":{"id":"1504.06106","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-04-23T09:37:28Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"daca711cfcdca71385616006ae5941c4b7699ca69becda56350d5f8fd4788114","abstract_canon_sha256":"d58572e0cff51fc39ffbef8992fa212f70cfe416393e80f3ce30d94516ea72cd"},"schema_version":"1.0"},"canonical_sha256":"8d04bf7a128be5c9d53bb9d45747ac9995df6afbf2d3fa721563b474747aa952","source":{"kind":"arxiv","id":"1504.06106","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06106","created_at":"2026-05-18T01:18:25Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06106v1","created_at":"2026-05-18T01:18:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06106","created_at":"2026-05-18T01:18:25Z"},{"alias_kind":"pith_short_12","alias_value":"RUCL66QSRPS4","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RUCL66QSRPS4TVJ3","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RUCL66QS","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:RUCL66QSRPS4TVJ3XHKFOR5MTG","target":"record","payload":{"canonical_record":{"source":{"id":"1504.06106","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-04-23T09:37:28Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"daca711cfcdca71385616006ae5941c4b7699ca69becda56350d5f8fd4788114","abstract_canon_sha256":"d58572e0cff51fc39ffbef8992fa212f70cfe416393e80f3ce30d94516ea72cd"},"schema_version":"1.0"},"canonical_sha256":"8d04bf7a128be5c9d53bb9d45747ac9995df6afbf2d3fa721563b474747aa952","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:25.533018Z","signature_b64":"uHlPclaOsWMzXsRAagBp9Ko376L40ceGsViBp/Jw5niPq7NBjik9NCLCvGJ+AwV5YPsop03hJYl/u7SbK2ubBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d04bf7a128be5c9d53bb9d45747ac9995df6afbf2d3fa721563b474747aa952","last_reissued_at":"2026-05-18T01:18:25.532425Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:25.532425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.06106","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":"2026-05-18T01:18:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gq8Cns9UQOWhmo69jHkowV0T0oLdwSkV+AFT0GSGpW9lN7SEkyQmWKYNOcQhpDkTlgY244BMYXloqjfehLlvAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T07:19:44.488241Z"},"content_sha256":"cfd32984f9e0ae5ae4fe5c470d45e90b4d42369baa6af5935f80e56bf6c5763b","schema_version":"1.0","event_id":"sha256:cfd32984f9e0ae5ae4fe5c470d45e90b4d42369baa6af5935f80e56bf6c5763b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:RUCL66QSRPS4TVJ3XHKFOR5MTG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Short Survey on Arithmetic Transforms and the Arithmetic Hartley Transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.CA","authors_text":"H. M. de Oliveira, R. J. Cintra","submitted_at":"2015-04-23T09:37:28Z","abstract_excerpt":"Arithmetic complexity has a main role in the performance of algorithms for spectrum evaluation. Arithmetic transform theory offers a method for computing trigonometrical transforms with minimal number of multiplications. In this paper, the proposed algorithms for the arithmetic Fourier transform are surveyed. A new arithmetic transform for computing the discrete Hartley transform is introduced: the Arithmetic Hartley transform. The interpolation process is shown to be the key element of the arithmetic transform theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06106","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":"2026-05-18T01:18:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iS5Ua2Ot8LvQVNZfFMVzD6IJSxDs03ilx//tAI+P1QPFMtUcoYAYh7JMf3l0Flh5m7MIjmx3sZ1NjUb1vtZXBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T07:19:44.488607Z"},"content_sha256":"747e67aa6c4849ccf7d2e25b7b10c96fe3efc1ee5ecfe3e7714792392ceadbae","schema_version":"1.0","event_id":"sha256:747e67aa6c4849ccf7d2e25b7b10c96fe3efc1ee5ecfe3e7714792392ceadbae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RUCL66QSRPS4TVJ3XHKFOR5MTG/bundle.json","state_url":"https://pith.science/pith/RUCL66QSRPS4TVJ3XHKFOR5MTG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RUCL66QSRPS4TVJ3XHKFOR5MTG/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":"2026-06-27T07:19:44Z","links":{"resolver":"https://pith.science/pith/RUCL66QSRPS4TVJ3XHKFOR5MTG","bundle":"https://pith.science/pith/RUCL66QSRPS4TVJ3XHKFOR5MTG/bundle.json","state":"https://pith.science/pith/RUCL66QSRPS4TVJ3XHKFOR5MTG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RUCL66QSRPS4TVJ3XHKFOR5MTG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RUCL66QSRPS4TVJ3XHKFOR5MTG","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":"d58572e0cff51fc39ffbef8992fa212f70cfe416393e80f3ce30d94516ea72cd","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-04-23T09:37:28Z","title_canon_sha256":"daca711cfcdca71385616006ae5941c4b7699ca69becda56350d5f8fd4788114"},"schema_version":"1.0","source":{"id":"1504.06106","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06106","created_at":"2026-05-18T01:18:25Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06106v1","created_at":"2026-05-18T01:18:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06106","created_at":"2026-05-18T01:18:25Z"},{"alias_kind":"pith_short_12","alias_value":"RUCL66QSRPS4","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RUCL66QSRPS4TVJ3","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RUCL66QS","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:747e67aa6c4849ccf7d2e25b7b10c96fe3efc1ee5ecfe3e7714792392ceadbae","target":"graph","created_at":"2026-05-18T01:18:25Z","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":"Arithmetic complexity has a main role in the performance of algorithms for spectrum evaluation. Arithmetic transform theory offers a method for computing trigonometrical transforms with minimal number of multiplications. In this paper, the proposed algorithms for the arithmetic Fourier transform are surveyed. A new arithmetic transform for computing the discrete Hartley transform is introduced: the Arithmetic Hartley transform. The interpolation process is shown to be the key element of the arithmetic transform theory.","authors_text":"H. M. de Oliveira, R. J. Cintra","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-04-23T09:37:28Z","title":"A Short Survey on Arithmetic Transforms and the Arithmetic Hartley Transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06106","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:cfd32984f9e0ae5ae4fe5c470d45e90b4d42369baa6af5935f80e56bf6c5763b","target":"record","created_at":"2026-05-18T01:18:25Z","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":"d58572e0cff51fc39ffbef8992fa212f70cfe416393e80f3ce30d94516ea72cd","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-04-23T09:37:28Z","title_canon_sha256":"daca711cfcdca71385616006ae5941c4b7699ca69becda56350d5f8fd4788114"},"schema_version":"1.0","source":{"id":"1504.06106","kind":"arxiv","version":1}},"canonical_sha256":"8d04bf7a128be5c9d53bb9d45747ac9995df6afbf2d3fa721563b474747aa952","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d04bf7a128be5c9d53bb9d45747ac9995df6afbf2d3fa721563b474747aa952","first_computed_at":"2026-05-18T01:18:25.532425Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:25.532425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uHlPclaOsWMzXsRAagBp9Ko376L40ceGsViBp/Jw5niPq7NBjik9NCLCvGJ+AwV5YPsop03hJYl/u7SbK2ubBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:25.533018Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.06106","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfd32984f9e0ae5ae4fe5c470d45e90b4d42369baa6af5935f80e56bf6c5763b","sha256:747e67aa6c4849ccf7d2e25b7b10c96fe3efc1ee5ecfe3e7714792392ceadbae"],"state_sha256":"d0066a4ca7d6b3b1be8c89fd2419b4f7e62bf7aad846868056b4fd834eedeee7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"we2ZNxIcFlP4r7mLLPaKYh3ZDd6acU7D+OUkffn6asOkCvki/pYIi/FXyeVlRUnlGVSAkQlvp+mZmtA5yiioBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T07:19:44.490451Z","bundle_sha256":"29da460039ff2bd68800b4ebe0f8f7635318cb9c939a784562152e7913dd4a8e"}}