{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:QM3J5DXHTXUJRLYV354EXEEYWX","short_pith_number":"pith:QM3J5DXH","canonical_record":{"source":{"id":"1308.0643","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-08-03T00:04:49Z","cross_cats_sorted":[],"title_canon_sha256":"b4bbc9a985c3c715e72deeec15cbd005c441100fce2a00de21d3d3d150751c94","abstract_canon_sha256":"4435ac29ceb0e12618f81837ba544476f8dbc6fd2c961c00f1001c2c2a0170fc"},"schema_version":"1.0"},"canonical_sha256":"83369e8ee79de898af15df784b9098b5dd8d6e44db7cd3527c304577249671f3","source":{"kind":"arxiv","id":"1308.0643","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0643","created_at":"2026-05-18T01:48:24Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0643v1","created_at":"2026-05-18T01:48:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0643","created_at":"2026-05-18T01:48:24Z"},{"alias_kind":"pith_short_12","alias_value":"QM3J5DXHTXUJ","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QM3J5DXHTXUJRLYV","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QM3J5DXH","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:QM3J5DXHTXUJRLYV354EXEEYWX","target":"record","payload":{"canonical_record":{"source":{"id":"1308.0643","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-08-03T00:04:49Z","cross_cats_sorted":[],"title_canon_sha256":"b4bbc9a985c3c715e72deeec15cbd005c441100fce2a00de21d3d3d150751c94","abstract_canon_sha256":"4435ac29ceb0e12618f81837ba544476f8dbc6fd2c961c00f1001c2c2a0170fc"},"schema_version":"1.0"},"canonical_sha256":"83369e8ee79de898af15df784b9098b5dd8d6e44db7cd3527c304577249671f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:48:24.334261Z","signature_b64":"N5LR1z6sPcsmk8WSXrALG+7C26kB5jMwCR75slZJI5mTXBKam8th1zHMpv/aUOX+9ESmxQZo6iMzFjd0mSHYBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83369e8ee79de898af15df784b9098b5dd8d6e44db7cd3527c304577249671f3","last_reissued_at":"2026-05-18T01:48:24.333634Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:48:24.333634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.0643","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":"2026-05-18T01:48:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T04NWw9HeYQc7qWSr9xLAp2UnQYHcb7CdUmYR+VfCCH2apzQfRq2jYuijiMsCHlioxQGt6kMOAT5Hcb3lgHpBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T10:41:47.162290Z"},"content_sha256":"3060f6d3cf7a5b4bb8a729f469946cbc4615b3e033ef9c306463cbc12f3e9a87","schema_version":"1.0","event_id":"sha256:3060f6d3cf7a5b4bb8a729f469946cbc4615b3e033ef9c306463cbc12f3e9a87"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:QM3J5DXHTXUJRLYV354EXEEYWX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The solution of the scalar wave equation in the exterior of a sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Leslie Greengard, Shidong Jiang, Thomas Hagstrom","submitted_at":"2013-08-03T00:04:49Z","abstract_excerpt":"We derive new, explicit representations for the solution to the scalar wave equation in the exterior of a sphere, subject to either Dirichlet or Robin boundary conditions. Our formula leads to a stable and high-order numerical scheme that permits the evaluation of the solution at an arbitrary target, without the use of a spatial grid and without numerical dispersion error. In the process, we correct some errors in the analytic literature concerning the asymptotic behavior of the logarithmic derivative of the spherical modified Hankel function. We illustrate the performance of the method with s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0643","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":"2026-05-18T01:48:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bMgInfOe/OsvDtr1Y/5Y529a4bAY/VAj+fy0o9z/tyMLhbx6pVVZoH4cW6jjODsjUoL/OScmQUwZRZ+LjIMFCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T10:41:47.162650Z"},"content_sha256":"20f7872166a72ceea4b4ea60e392226465c9d8b587c013f58dcb3fd9c2414019","schema_version":"1.0","event_id":"sha256:20f7872166a72ceea4b4ea60e392226465c9d8b587c013f58dcb3fd9c2414019"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QM3J5DXHTXUJRLYV354EXEEYWX/bundle.json","state_url":"https://pith.science/pith/QM3J5DXHTXUJRLYV354EXEEYWX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QM3J5DXHTXUJRLYV354EXEEYWX/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":"2026-06-08T10:41:47Z","links":{"resolver":"https://pith.science/pith/QM3J5DXHTXUJRLYV354EXEEYWX","bundle":"https://pith.science/pith/QM3J5DXHTXUJRLYV354EXEEYWX/bundle.json","state":"https://pith.science/pith/QM3J5DXHTXUJRLYV354EXEEYWX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QM3J5DXHTXUJRLYV354EXEEYWX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QM3J5DXHTXUJRLYV354EXEEYWX","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":"4435ac29ceb0e12618f81837ba544476f8dbc6fd2c961c00f1001c2c2a0170fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-08-03T00:04:49Z","title_canon_sha256":"b4bbc9a985c3c715e72deeec15cbd005c441100fce2a00de21d3d3d150751c94"},"schema_version":"1.0","source":{"id":"1308.0643","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0643","created_at":"2026-05-18T01:48:24Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0643v1","created_at":"2026-05-18T01:48:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0643","created_at":"2026-05-18T01:48:24Z"},{"alias_kind":"pith_short_12","alias_value":"QM3J5DXHTXUJ","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QM3J5DXHTXUJRLYV","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QM3J5DXH","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:20f7872166a72ceea4b4ea60e392226465c9d8b587c013f58dcb3fd9c2414019","target":"graph","created_at":"2026-05-18T01:48:24Z","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":"We derive new, explicit representations for the solution to the scalar wave equation in the exterior of a sphere, subject to either Dirichlet or Robin boundary conditions. Our formula leads to a stable and high-order numerical scheme that permits the evaluation of the solution at an arbitrary target, without the use of a spatial grid and without numerical dispersion error. In the process, we correct some errors in the analytic literature concerning the asymptotic behavior of the logarithmic derivative of the spherical modified Hankel function. We illustrate the performance of the method with s","authors_text":"Leslie Greengard, Shidong Jiang, Thomas Hagstrom","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-08-03T00:04:49Z","title":"The solution of the scalar wave equation in the exterior of a sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0643","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":"sha256:3060f6d3cf7a5b4bb8a729f469946cbc4615b3e033ef9c306463cbc12f3e9a87","target":"record","created_at":"2026-05-18T01:48:24Z","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":"4435ac29ceb0e12618f81837ba544476f8dbc6fd2c961c00f1001c2c2a0170fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-08-03T00:04:49Z","title_canon_sha256":"b4bbc9a985c3c715e72deeec15cbd005c441100fce2a00de21d3d3d150751c94"},"schema_version":"1.0","source":{"id":"1308.0643","kind":"arxiv","version":1}},"canonical_sha256":"83369e8ee79de898af15df784b9098b5dd8d6e44db7cd3527c304577249671f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83369e8ee79de898af15df784b9098b5dd8d6e44db7cd3527c304577249671f3","first_computed_at":"2026-05-18T01:48:24.333634Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:48:24.333634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N5LR1z6sPcsmk8WSXrALG+7C26kB5jMwCR75slZJI5mTXBKam8th1zHMpv/aUOX+9ESmxQZo6iMzFjd0mSHYBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:48:24.334261Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.0643","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3060f6d3cf7a5b4bb8a729f469946cbc4615b3e033ef9c306463cbc12f3e9a87","sha256:20f7872166a72ceea4b4ea60e392226465c9d8b587c013f58dcb3fd9c2414019"],"state_sha256":"90fbf0f34bf5c397db40c98997854eba881bc0adc102f8c62fc2c2f428a5b2fb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f2F8ag0UuaYjTOVcoyBqfcfDK+mCzo1Dr3Y2z3QlW4SgOcP+E7I2K0P3Q46LDAzr6TBTboOTHNThh7mS9YxvCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T10:41:47.164668Z","bundle_sha256":"28cd27e956d9e20fda9e4cd0130f2a316ec6d7cae98e1315aae406eab072b8ac"}}