{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:IH56Q34WACH53RRGADWU72OUHM","short_pith_number":"pith:IH56Q34W","canonical_record":{"source":{"id":"1502.01377","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-02-04T22:10:21Z","cross_cats_sorted":["math.NA","stat.AP","stat.CO","stat.ME"],"title_canon_sha256":"8a4241d03a3c090388e8ad15a7e973bf6fb1e3f1b9d2ce0ebd7aab8e5abafe05","abstract_canon_sha256":"02261a66da4c4ed8c0380c7046db078b60552fd27b5eb2ec9182c78a8c0150d5"},"schema_version":"1.0"},"canonical_sha256":"41fbe86f96008fddc62600ed4fe9d43b06fd42015d6e2b08240328b70271bfb0","source":{"kind":"arxiv","id":"1502.01377","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.01377","created_at":"2026-05-18T02:27:56Z"},{"alias_kind":"arxiv_version","alias_value":"1502.01377v1","created_at":"2026-05-18T02:27:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01377","created_at":"2026-05-18T02:27:56Z"},{"alias_kind":"pith_short_12","alias_value":"IH56Q34WACH5","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IH56Q34WACH53RRG","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IH56Q34W","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:IH56Q34WACH53RRGADWU72OUHM","target":"record","payload":{"canonical_record":{"source":{"id":"1502.01377","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-02-04T22:10:21Z","cross_cats_sorted":["math.NA","stat.AP","stat.CO","stat.ME"],"title_canon_sha256":"8a4241d03a3c090388e8ad15a7e973bf6fb1e3f1b9d2ce0ebd7aab8e5abafe05","abstract_canon_sha256":"02261a66da4c4ed8c0380c7046db078b60552fd27b5eb2ec9182c78a8c0150d5"},"schema_version":"1.0"},"canonical_sha256":"41fbe86f96008fddc62600ed4fe9d43b06fd42015d6e2b08240328b70271bfb0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:56.654667Z","signature_b64":"GqVXaleXS1yYsdtrDqYfc3dcsXwD9wYz947+/h827Y3ADGd+DsI24gBvYODblFoLl4LViNJ9Q77ekpfZn+CRCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41fbe86f96008fddc62600ed4fe9d43b06fd42015d6e2b08240328b70271bfb0","last_reissued_at":"2026-05-18T02:27:56.654247Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:56.654247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.01377","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":"2026-05-18T02:27:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WTsgp4taDN2Ya7k6Lp3pK2vH0GjMYH75D8vOXlMN+p81sfS/XIdTkrc356h3uBKEYEzjEx27h6T0qlloMnXfCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:58:44.098658Z"},"content_sha256":"914de5007b11ad9b776dd7fd03091f9907dec3e662f7ae22828477fca8915423","schema_version":"1.0","event_id":"sha256:914de5007b11ad9b776dd7fd03091f9907dec3e662f7ae22828477fca8915423"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:IH56Q34WACH53RRGADWU72OUHM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Arithmetic Cosine Transform: Exact and Approximate Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","stat.AP","stat.CO","stat.ME"],"primary_cat":"cs.NA","authors_text":"R. J. Cintra, V. S. Dimitrov","submitted_at":"2015-02-04T22:10:21Z","abstract_excerpt":"In this paper, we introduce a new class of transform method --- the arithmetic cosine transform (ACT). We provide the central mathematical properties of the ACT, necessary in designing efficient and accurate implementations of the new transform method. The key mathematical tools used in the paper come from analytic number theory, in particular the properties of the Riemann zeta function. Additionally, we demonstrate that an exact signal interpolation is achievable for any block-length. Approximate calculations were also considered. The numerical examples provided show the potential of the ACT "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01377","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":"2026-05-18T02:27:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ak+ofD4rqKP+Nm1bXYHFWdxYfNPfvuVMrTgYsaOdDW+1KteIiHDaYaoP6ibve9s4cHg2tAg67dWlfJg8dwfpAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:58:44.099004Z"},"content_sha256":"4cbf8b6ddfdfef6401850dc223fed1dd9e2670d685c121d82872eb0d9a0ae160","schema_version":"1.0","event_id":"sha256:4cbf8b6ddfdfef6401850dc223fed1dd9e2670d685c121d82872eb0d9a0ae160"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IH56Q34WACH53RRGADWU72OUHM/bundle.json","state_url":"https://pith.science/pith/IH56Q34WACH53RRGADWU72OUHM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IH56Q34WACH53RRGADWU72OUHM/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":"2026-06-27T16:58:44Z","links":{"resolver":"https://pith.science/pith/IH56Q34WACH53RRGADWU72OUHM","bundle":"https://pith.science/pith/IH56Q34WACH53RRGADWU72OUHM/bundle.json","state":"https://pith.science/pith/IH56Q34WACH53RRGADWU72OUHM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IH56Q34WACH53RRGADWU72OUHM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IH56Q34WACH53RRGADWU72OUHM","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":"02261a66da4c4ed8c0380c7046db078b60552fd27b5eb2ec9182c78a8c0150d5","cross_cats_sorted":["math.NA","stat.AP","stat.CO","stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-02-04T22:10:21Z","title_canon_sha256":"8a4241d03a3c090388e8ad15a7e973bf6fb1e3f1b9d2ce0ebd7aab8e5abafe05"},"schema_version":"1.0","source":{"id":"1502.01377","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.01377","created_at":"2026-05-18T02:27:56Z"},{"alias_kind":"arxiv_version","alias_value":"1502.01377v1","created_at":"2026-05-18T02:27:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01377","created_at":"2026-05-18T02:27:56Z"},{"alias_kind":"pith_short_12","alias_value":"IH56Q34WACH5","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IH56Q34WACH53RRG","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IH56Q34W","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:4cbf8b6ddfdfef6401850dc223fed1dd9e2670d685c121d82872eb0d9a0ae160","target":"graph","created_at":"2026-05-18T02:27:56Z","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 paper, we introduce a new class of transform method --- the arithmetic cosine transform (ACT). We provide the central mathematical properties of the ACT, necessary in designing efficient and accurate implementations of the new transform method. The key mathematical tools used in the paper come from analytic number theory, in particular the properties of the Riemann zeta function. Additionally, we demonstrate that an exact signal interpolation is achievable for any block-length. Approximate calculations were also considered. The numerical examples provided show the potential of the ACT ","authors_text":"R. J. Cintra, V. S. Dimitrov","cross_cats":["math.NA","stat.AP","stat.CO","stat.ME"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-02-04T22:10:21Z","title":"The Arithmetic Cosine Transform: Exact and Approximate Algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01377","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":"sha256:914de5007b11ad9b776dd7fd03091f9907dec3e662f7ae22828477fca8915423","target":"record","created_at":"2026-05-18T02:27:56Z","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":"02261a66da4c4ed8c0380c7046db078b60552fd27b5eb2ec9182c78a8c0150d5","cross_cats_sorted":["math.NA","stat.AP","stat.CO","stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-02-04T22:10:21Z","title_canon_sha256":"8a4241d03a3c090388e8ad15a7e973bf6fb1e3f1b9d2ce0ebd7aab8e5abafe05"},"schema_version":"1.0","source":{"id":"1502.01377","kind":"arxiv","version":1}},"canonical_sha256":"41fbe86f96008fddc62600ed4fe9d43b06fd42015d6e2b08240328b70271bfb0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41fbe86f96008fddc62600ed4fe9d43b06fd42015d6e2b08240328b70271bfb0","first_computed_at":"2026-05-18T02:27:56.654247Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:56.654247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GqVXaleXS1yYsdtrDqYfc3dcsXwD9wYz947+/h827Y3ADGd+DsI24gBvYODblFoLl4LViNJ9Q77ekpfZn+CRCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:56.654667Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.01377","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:914de5007b11ad9b776dd7fd03091f9907dec3e662f7ae22828477fca8915423","sha256:4cbf8b6ddfdfef6401850dc223fed1dd9e2670d685c121d82872eb0d9a0ae160"],"state_sha256":"01aa3b5ac661e3ac314c33c96679f583c1dc75c62740add29201b8d745e0f0f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eGqyGnkf5YpjSN8U8k4cDcbaF6kWJ6eGVun3HFQi1fHzjDZilkdR8K3v1kI7bC/uHaf422AmnV5M0pDFWtxTDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T16:58:44.100857Z","bundle_sha256":"9eec4d1eb3b8812558a5b2fe5702287233b8b9f924d9f518234d96b22046188c"}}