{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:45PO3GPS66LU7WRJVOGXB3BMLU","short_pith_number":"pith:45PO3GPS","canonical_record":{"source":{"id":"1501.01652","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-01-07T21:25:10Z","cross_cats_sorted":[],"title_canon_sha256":"5677f370fbc09b4d16a1d746cd05d3a84bb8cd4f7222c04b811663c82968f5d4","abstract_canon_sha256":"04274935aee1eb10fd327e19cb5429f3474b212b9ed26b6089924ff877425f21"},"schema_version":"1.0"},"canonical_sha256":"e75eed99f2f7974fda29ab8d70ec2c5d2818cd6ed17085fd1a605c006d50c52d","source":{"kind":"arxiv","id":"1501.01652","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01652","created_at":"2026-05-18T02:03:59Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01652v2","created_at":"2026-05-18T02:03:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01652","created_at":"2026-05-18T02:03:59Z"},{"alias_kind":"pith_short_12","alias_value":"45PO3GPS66LU","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"45PO3GPS66LU7WRJ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"45PO3GPS","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:45PO3GPS66LU7WRJVOGXB3BMLU","target":"record","payload":{"canonical_record":{"source":{"id":"1501.01652","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-01-07T21:25:10Z","cross_cats_sorted":[],"title_canon_sha256":"5677f370fbc09b4d16a1d746cd05d3a84bb8cd4f7222c04b811663c82968f5d4","abstract_canon_sha256":"04274935aee1eb10fd327e19cb5429f3474b212b9ed26b6089924ff877425f21"},"schema_version":"1.0"},"canonical_sha256":"e75eed99f2f7974fda29ab8d70ec2c5d2818cd6ed17085fd1a605c006d50c52d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:59.979401Z","signature_b64":"3QNgccIU/fDyufQGFWwyJ429jgo9eycH8vqTk8iBenfZvky/LHLwlcAX53yH0GqaLnwzmaYs6FoDeGtvMZ4YCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e75eed99f2f7974fda29ab8d70ec2c5d2818cd6ed17085fd1a605c006d50c52d","last_reissued_at":"2026-05-18T02:03:59.978650Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:59.978650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.01652","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:03:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W4v3BoS4AtiA6HwFxhiXgKTBj4uHyE261Ct6Fw/SiFd9C8AWyiFll322dSpeMH0dxQBlGTPAMrWi4MYaHgL7Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:49:46.949988Z"},"content_sha256":"803c2d237de19c96d85dd654c2219e8adeabf12414da17a66fd4cdcd24cf447b","schema_version":"1.0","event_id":"sha256:803c2d237de19c96d85dd654c2219e8adeabf12414da17a66fd4cdcd24cf447b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:45PO3GPS66LU7WRJVOGXB3BMLU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A fast analysis-based discrete Hankel transform using asymptotic expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alex Townsend","submitted_at":"2015-01-07T21:25:10Z","abstract_excerpt":"A fast and numerically stable algorithm is described for computing the discrete Hankel transform of order $0$ as well as evaluating Schl\\\"{o}milch and Fourier--Bessel expansions in $\\mathcal{O}(N(\\log N)^2/\\log\\!\\log N)$ operations. The algorithm is based on an asymptotic expansion for Bessel functions of large arguments, the fast Fourier transform, and the Neumann addition formula. All the algorithmic parameters are selected from error bounds to achieve a near-optimal computational cost for any accuracy goal. Numerical results demonstrate the efficiency of the resulting algorithm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01652","kind":"arxiv","version":2},"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":"2026-05-18T02:03:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MtU7I2DmEay8TjSkFeWwMe4Q18BPog8N34R/SeaJ2a9GETfEqJUbtjcRtq8kIp1JCUZz6evFwD091xljRYjMDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:49:46.950409Z"},"content_sha256":"737e7b176633bf9794a95b4a86abad99c0aeaa9e58171560398cf74eda8f9177","schema_version":"1.0","event_id":"sha256:737e7b176633bf9794a95b4a86abad99c0aeaa9e58171560398cf74eda8f9177"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/45PO3GPS66LU7WRJVOGXB3BMLU/bundle.json","state_url":"https://pith.science/pith/45PO3GPS66LU7WRJVOGXB3BMLU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/45PO3GPS66LU7WRJVOGXB3BMLU/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":"2026-05-27T05:49:46Z","links":{"resolver":"https://pith.science/pith/45PO3GPS66LU7WRJVOGXB3BMLU","bundle":"https://pith.science/pith/45PO3GPS66LU7WRJVOGXB3BMLU/bundle.json","state":"https://pith.science/pith/45PO3GPS66LU7WRJVOGXB3BMLU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/45PO3GPS66LU7WRJVOGXB3BMLU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:45PO3GPS66LU7WRJVOGXB3BMLU","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":"04274935aee1eb10fd327e19cb5429f3474b212b9ed26b6089924ff877425f21","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-01-07T21:25:10Z","title_canon_sha256":"5677f370fbc09b4d16a1d746cd05d3a84bb8cd4f7222c04b811663c82968f5d4"},"schema_version":"1.0","source":{"id":"1501.01652","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01652","created_at":"2026-05-18T02:03:59Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01652v2","created_at":"2026-05-18T02:03:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01652","created_at":"2026-05-18T02:03:59Z"},{"alias_kind":"pith_short_12","alias_value":"45PO3GPS66LU","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"45PO3GPS66LU7WRJ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"45PO3GPS","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:737e7b176633bf9794a95b4a86abad99c0aeaa9e58171560398cf74eda8f9177","target":"graph","created_at":"2026-05-18T02:03:59Z","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":"A fast and numerically stable algorithm is described for computing the discrete Hankel transform of order $0$ as well as evaluating Schl\\\"{o}milch and Fourier--Bessel expansions in $\\mathcal{O}(N(\\log N)^2/\\log\\!\\log N)$ operations. The algorithm is based on an asymptotic expansion for Bessel functions of large arguments, the fast Fourier transform, and the Neumann addition formula. All the algorithmic parameters are selected from error bounds to achieve a near-optimal computational cost for any accuracy goal. Numerical results demonstrate the efficiency of the resulting algorithm.","authors_text":"Alex Townsend","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-01-07T21:25:10Z","title":"A fast analysis-based discrete Hankel transform using asymptotic expansions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01652","kind":"arxiv","version":2},"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":"sha256:803c2d237de19c96d85dd654c2219e8adeabf12414da17a66fd4cdcd24cf447b","target":"record","created_at":"2026-05-18T02:03:59Z","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":"04274935aee1eb10fd327e19cb5429f3474b212b9ed26b6089924ff877425f21","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-01-07T21:25:10Z","title_canon_sha256":"5677f370fbc09b4d16a1d746cd05d3a84bb8cd4f7222c04b811663c82968f5d4"},"schema_version":"1.0","source":{"id":"1501.01652","kind":"arxiv","version":2}},"canonical_sha256":"e75eed99f2f7974fda29ab8d70ec2c5d2818cd6ed17085fd1a605c006d50c52d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e75eed99f2f7974fda29ab8d70ec2c5d2818cd6ed17085fd1a605c006d50c52d","first_computed_at":"2026-05-18T02:03:59.978650Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:59.978650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3QNgccIU/fDyufQGFWwyJ429jgo9eycH8vqTk8iBenfZvky/LHLwlcAX53yH0GqaLnwzmaYs6FoDeGtvMZ4YCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:59.979401Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.01652","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:803c2d237de19c96d85dd654c2219e8adeabf12414da17a66fd4cdcd24cf447b","sha256:737e7b176633bf9794a95b4a86abad99c0aeaa9e58171560398cf74eda8f9177"],"state_sha256":"8fc8d061ce91c67a7bf3b22cc4839586d75d3adb465adb5aca16f7e27dd6c20a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tBp1vPyjY2CGpe6HrXjhuGhgQIavJXMZ6gdttx2UtEvpgIG5TJId+whcJlnCRS/aP15VoFP7TdrLYRtgH5rjBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T05:49:46.953132Z","bundle_sha256":"2ad60e054e0ad553729a567f0dda763b93f03e6702c2c40b211dbdba2636ddea"}}