{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:VYK6BIWHWT4TSOLLESBSSE27FW","short_pith_number":"pith:VYK6BIWH","canonical_record":{"source":{"id":"2606.31380","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-30T09:09:48Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"ae68adefc9828a19c913fa8f911840d8c62dc29d3ee40195b4dd79ad17590d82","abstract_canon_sha256":"9ab818ab79a6d16199dcc7f548287a58660c040760bb75d2c64379e5c9f89df3"},"schema_version":"1.0"},"canonical_sha256":"ae15e0a2c7b4f939396b248329135f2d93aa3d6da6adb29f8734fb863a878602","source":{"kind":"arxiv","id":"2606.31380","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.31380","created_at":"2026-07-01T01:18:01Z"},{"alias_kind":"arxiv_version","alias_value":"2606.31380v1","created_at":"2026-07-01T01:18:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.31380","created_at":"2026-07-01T01:18:01Z"},{"alias_kind":"pith_short_12","alias_value":"VYK6BIWHWT4T","created_at":"2026-07-01T01:18:01Z"},{"alias_kind":"pith_short_16","alias_value":"VYK6BIWHWT4TSOLL","created_at":"2026-07-01T01:18:01Z"},{"alias_kind":"pith_short_8","alias_value":"VYK6BIWH","created_at":"2026-07-01T01:18:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:VYK6BIWHWT4TSOLLESBSSE27FW","target":"record","payload":{"canonical_record":{"source":{"id":"2606.31380","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-30T09:09:48Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"ae68adefc9828a19c913fa8f911840d8c62dc29d3ee40195b4dd79ad17590d82","abstract_canon_sha256":"9ab818ab79a6d16199dcc7f548287a58660c040760bb75d2c64379e5c9f89df3"},"schema_version":"1.0"},"canonical_sha256":"ae15e0a2c7b4f939396b248329135f2d93aa3d6da6adb29f8734fb863a878602","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-01T01:18:01.334200Z","signature_b64":"mDf3GC4+W8sLm9mKulZ1ExRwLiN3bxsEgsEMYStmN6ZGiR1VvxRVll9Ke/kfTCrRR/iADk9JfKx5DK79qipzBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae15e0a2c7b4f939396b248329135f2d93aa3d6da6adb29f8734fb863a878602","last_reissued_at":"2026-07-01T01:18:01.333664Z","signature_status":"signed_v1","first_computed_at":"2026-07-01T01:18:01.333664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.31380","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":"2026-07-01T01:18:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5LDvTxXLn4ImJ2yNE7X+OD2XMxe9MCWKhfHSsI9OQl0BIXXdXGm4Ay1axLkLjzbJRGDLRwDY/S/XSk5g+R0TDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-16T06:56:41.968312Z"},"content_sha256":"f6224ecd2b69de758b3d151687f66e8f70b209e0f4f0d4d12e66c8f847d88345","schema_version":"1.0","event_id":"sha256:f6224ecd2b69de758b3d151687f66e8f70b209e0f4f0d4d12e66c8f847d88345"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:VYK6BIWHWT4TSOLLESBSSE27FW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Spectral Solver for Acoustic Scattering by Multiple Quasi-Axisymmetric Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Jun Lai, Yuxin Li","submitted_at":"2026-06-30T09:09:48Z","abstract_excerpt":"Acoustic scattering arises in a wide range of applications, including medical imaging, geophysical exploration, acoustic metamaterials, etc. In this paper, we develop a fast and highly accurate algorithm for acoustic scattering by multiple quasi-axisymmetric objects, whose axis of rotation is an arbitrary curve. The method is based on a Nystr\\\"om discretization that combines Gauss-Legendre quadrature with the trapezoidal rule. To treat the singular integrals that occur when target points are close to or coincide with source points, we reformulate them as evaluations of the modal Green's functi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31380","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.31380/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-01T01:18:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ycEygn5K0u8AkzMLric3FIPFYueiOhFWJ8nDLX9k04dkbdTI49MSe2NkzPj/C8AjvIRwYX6M4xb3YJqs9z+nBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-16T06:56:41.968715Z"},"content_sha256":"51ce0b22939951c578dd6d14638257f94202131eae06cfdb8589565f3c05b9d8","schema_version":"1.0","event_id":"sha256:51ce0b22939951c578dd6d14638257f94202131eae06cfdb8589565f3c05b9d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VYK6BIWHWT4TSOLLESBSSE27FW/bundle.json","state_url":"https://pith.science/pith/VYK6BIWHWT4TSOLLESBSSE27FW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VYK6BIWHWT4TSOLLESBSSE27FW/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":"2026-07-16T06:56:41Z","links":{"resolver":"https://pith.science/pith/VYK6BIWHWT4TSOLLESBSSE27FW","bundle":"https://pith.science/pith/VYK6BIWHWT4TSOLLESBSSE27FW/bundle.json","state":"https://pith.science/pith/VYK6BIWHWT4TSOLLESBSSE27FW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VYK6BIWHWT4TSOLLESBSSE27FW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:VYK6BIWHWT4TSOLLESBSSE27FW","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":"9ab818ab79a6d16199dcc7f548287a58660c040760bb75d2c64379e5c9f89df3","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-30T09:09:48Z","title_canon_sha256":"ae68adefc9828a19c913fa8f911840d8c62dc29d3ee40195b4dd79ad17590d82"},"schema_version":"1.0","source":{"id":"2606.31380","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.31380","created_at":"2026-07-01T01:18:01Z"},{"alias_kind":"arxiv_version","alias_value":"2606.31380v1","created_at":"2026-07-01T01:18:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.31380","created_at":"2026-07-01T01:18:01Z"},{"alias_kind":"pith_short_12","alias_value":"VYK6BIWHWT4T","created_at":"2026-07-01T01:18:01Z"},{"alias_kind":"pith_short_16","alias_value":"VYK6BIWHWT4TSOLL","created_at":"2026-07-01T01:18:01Z"},{"alias_kind":"pith_short_8","alias_value":"VYK6BIWH","created_at":"2026-07-01T01:18:01Z"}],"graph_snapshots":[{"event_id":"sha256:51ce0b22939951c578dd6d14638257f94202131eae06cfdb8589565f3c05b9d8","target":"graph","created_at":"2026-07-01T01:18:01Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.31380/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Acoustic scattering arises in a wide range of applications, including medical imaging, geophysical exploration, acoustic metamaterials, etc. In this paper, we develop a fast and highly accurate algorithm for acoustic scattering by multiple quasi-axisymmetric objects, whose axis of rotation is an arbitrary curve. The method is based on a Nystr\\\"om discretization that combines Gauss-Legendre quadrature with the trapezoidal rule. To treat the singular integrals that occur when target points are close to or coincide with source points, we reformulate them as evaluations of the modal Green's functi","authors_text":"Jun Lai, Yuxin Li","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-30T09:09:48Z","title":"A Spectral Solver for Acoustic Scattering by Multiple Quasi-Axisymmetric Structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31380","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:f6224ecd2b69de758b3d151687f66e8f70b209e0f4f0d4d12e66c8f847d88345","target":"record","created_at":"2026-07-01T01:18:01Z","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":"9ab818ab79a6d16199dcc7f548287a58660c040760bb75d2c64379e5c9f89df3","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-30T09:09:48Z","title_canon_sha256":"ae68adefc9828a19c913fa8f911840d8c62dc29d3ee40195b4dd79ad17590d82"},"schema_version":"1.0","source":{"id":"2606.31380","kind":"arxiv","version":1}},"canonical_sha256":"ae15e0a2c7b4f939396b248329135f2d93aa3d6da6adb29f8734fb863a878602","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae15e0a2c7b4f939396b248329135f2d93aa3d6da6adb29f8734fb863a878602","first_computed_at":"2026-07-01T01:18:01.333664Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-01T01:18:01.333664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mDf3GC4+W8sLm9mKulZ1ExRwLiN3bxsEgsEMYStmN6ZGiR1VvxRVll9Ke/kfTCrRR/iADk9JfKx5DK79qipzBQ==","signature_status":"signed_v1","signed_at":"2026-07-01T01:18:01.334200Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.31380","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6224ecd2b69de758b3d151687f66e8f70b209e0f4f0d4d12e66c8f847d88345","sha256:51ce0b22939951c578dd6d14638257f94202131eae06cfdb8589565f3c05b9d8"],"state_sha256":"ee74194c1a7587be95acb417a78d7994220b353f390209b29f31130cce2934c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FQpLOTGBl6tOwnNi1dQcKY2P4x7819+ujb9uyG30YwVrZUQqoOX1CQlhvx6pLu/sIHoTSVEqJbU54BZwlp2RBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-16T06:56:41.972030Z","bundle_sha256":"a1939b5c3d104fb08c87c93f5e5516b13e89293f0cd6788158fb7da6f3b3564f"}}