{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:YVKUW6EVW3XLPJGN7O3FAKUPHU","short_pith_number":"pith:YVKUW6EV","canonical_record":{"source":{"id":"2605.15825","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-15T10:25:22Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"69cb8be92d0d7872998d00a38fd5c4d737e037c724c076a94737389cf5121374","abstract_canon_sha256":"3a799cfc84c3a4bbc9b2a3614b61a2351581d5ea08639d5d1a71222ebf76ec16"},"schema_version":"1.0"},"canonical_sha256":"c5554b7895b6eeb7a4cdfbb6502a8f3d2180ba284c9be896199f181a92e45909","source":{"kind":"arxiv","id":"2605.15825","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.15825","created_at":"2026-05-20T00:01:20Z"},{"alias_kind":"arxiv_version","alias_value":"2605.15825v1","created_at":"2026-05-20T00:01:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.15825","created_at":"2026-05-20T00:01:20Z"},{"alias_kind":"pith_short_12","alias_value":"YVKUW6EVW3XL","created_at":"2026-05-20T00:01:20Z"},{"alias_kind":"pith_short_16","alias_value":"YVKUW6EVW3XLPJGN","created_at":"2026-05-20T00:01:20Z"},{"alias_kind":"pith_short_8","alias_value":"YVKUW6EV","created_at":"2026-05-20T00:01:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:YVKUW6EVW3XLPJGN7O3FAKUPHU","target":"record","payload":{"canonical_record":{"source":{"id":"2605.15825","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-15T10:25:22Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"69cb8be92d0d7872998d00a38fd5c4d737e037c724c076a94737389cf5121374","abstract_canon_sha256":"3a799cfc84c3a4bbc9b2a3614b61a2351581d5ea08639d5d1a71222ebf76ec16"},"schema_version":"1.0"},"canonical_sha256":"c5554b7895b6eeb7a4cdfbb6502a8f3d2180ba284c9be896199f181a92e45909","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:01:20.462376Z","signature_b64":"J6JclEQ9IDfNwDHslQttpiV6S0jd5DSQ2J0WoroIIB1+9WJk1biRTSsMe0hnDiCCVUxSCiRYX9ErLLgWisqzCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5554b7895b6eeb7a4cdfbb6502a8f3d2180ba284c9be896199f181a92e45909","last_reissued_at":"2026-05-20T00:01:20.461611Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:01:20.461611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.15825","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":"2026-05-20T00:01:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"06CY80043GiDTutLrysOZki+5/g1SNP2nqtNXx1qMroPRKh4RE5PLXdvWwoiwkJI91rzJajxHe94lHcXlFu5Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T12:42:58.710606Z"},"content_sha256":"f6fa0eb07fdad8441956f6c4132f0f66b8995d0cafd25bd39c14b046bf29da85","schema_version":"1.0","event_id":"sha256:f6fa0eb07fdad8441956f6c4132f0f66b8995d0cafd25bd39c14b046bf29da85"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:YVKUW6EVW3XLPJGN7O3FAKUPHU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Endpoint-singularity-preserving spectral approximation theory for weakly singular integral equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Composing Jacobi polynomials with an endpoint algebraic mapping yields bases that preserve terminal singularities for high-order spectral approximations.","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Mahmoud A. Zaky","submitted_at":"2026-05-15T10:25:22Z","abstract_excerpt":"We introduce a fractional approximation framework for functions with limited regularity near the terminal point. The proposed basis is constructed by composing classical Jacobi polynomials with an endpoint algebraic mapping, thereby incorporating the terminal singular structure directly into the approximation space. The main structural properties of the fractional polynomials are established, including orthogonality relations, derivative identities, and a singular Sturm--Liouville eigenvalue formulation. We then introduce the associated weighted Sobolev spaces and prove projection and Gauss-ty"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The resulting theory provides a rigorous foundation for high-order spectral and collocation approximations of endpoint-singular and weakly regular problems, including terminal value problems, fractional differential equations, and weakly singular Volterra integral equations.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That composing classical Jacobi polynomials with an endpoint algebraic mapping directly incorporates the terminal singular structure into the approximation space and thereby yields the claimed orthogonality, derivative identities, and weighted error estimates for functions with limited regularity near the terminal point.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Introduces fractional Jacobi polynomials via endpoint algebraic mapping and derives projection, interpolation, and embedding estimates for spectral approximations of endpoint-singular problems.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Composing Jacobi polynomials with an endpoint algebraic mapping yields bases that preserve terminal singularities for high-order spectral approximations.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"03aa7ecccbd9c7ceabab925099fed0ad54934fec38ff6b2eeb38f61bba313ff6"},"source":{"id":"2605.15825","kind":"arxiv","version":1},"verdict":{"id":"79f8885c-fdd8-4e3a-a212-03dfbd57c296","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T22:20:42.210057Z","strongest_claim":"The resulting theory provides a rigorous foundation for high-order spectral and collocation approximations of endpoint-singular and weakly regular problems, including terminal value problems, fractional differential equations, and weakly singular Volterra integral equations.","one_line_summary":"Introduces fractional Jacobi polynomials via endpoint algebraic mapping and derives projection, interpolation, and embedding estimates for spectral approximations of endpoint-singular problems.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That composing classical Jacobi polynomials with an endpoint algebraic mapping directly incorporates the terminal singular structure into the approximation space and thereby yields the claimed orthogonality, derivative identities, and weighted error estimates for functions with limited regularity near the terminal point.","pith_extraction_headline":"Composing Jacobi polynomials with an endpoint algebraic mapping yields bases that preserve terminal singularities for high-order spectral approximations."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15825/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T22:31:19.656773Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T22:31:19.648094Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:48.722227Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:21:55.866865Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"43cd6de478f51c6f84303feb08b1d3babb2b7fb76f21b44b557c145ce374c4ad"},"references":{"count":16,"sample":[{"doi":"","year":2021,"title":"I. G. Ameen, M. A. Zaky, E. H. Doha, Singularity preservin g spectral collocation method for nonlinear systems of fractional di fferential equations with the right-sided Caputo fractional derivative, J","work_id":"18e6132e-a60e-4a65-a249-6a617b5ba5fb","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1997,"title":"C. Bernardi, Y . Maday, Spectral methods, Handbook of num erical analysis 5 (1997) 209–485","work_id":"e56934ef-a05f-444a-9449-2b60c299b0fb","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2016,"title":"S. Chen, J. Shen, L.-L. Wang, Generalized Jacobi functio ns and their applications to fractional di fferential equa- tions, Mathematics of Computation 85 (300) (2016) 1603–163 8","work_id":"ad55b38b-b711-44f0-a41c-5e7c160797f0","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2013,"title":"Y . Chen, X. Li, T. Tang, A note on Jacobi spectral-colloca tion methods for weakly singular Volterra integral equations with smooth solutions, Journal of Computational Mathematics (2013) 47–56","work_id":"6de7f99d-ed2d-4867-83f7-35f756ccdf12","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"K. Diethelm, R. Garrappa, M. Stynes, Good (and not so good ) practices in computational methods for fractional calculus, Mathematics 8 (3) (2020) 324","work_id":"04a5c057-5c48-46e9-b7e1-43e97451ec93","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":16,"snapshot_sha256":"f60c10644ee8812c90757a3c9363090e99c4a6ef98542f8b7b22d10b104bbf28","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"e24a6a45ba2d4e651298e2cca8387025e3752fe037c6dc64f13d5284bb6d662a"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"79f8885c-fdd8-4e3a-a212-03dfbd57c296"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:01:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GHJn6mavVGhFIXDGUcyHOWnIZNVI5v0jJdsEfm5SVZx5aAL8ZLEINlujox9gFCupzkoJ2eyc4v7G6Guja2eVAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T12:42:58.712160Z"},"content_sha256":"1ca045f92fe9d983a168d98d0e61d7bdf07896ec4aff319c8488cd4f1d383d0e","schema_version":"1.0","event_id":"sha256:1ca045f92fe9d983a168d98d0e61d7bdf07896ec4aff319c8488cd4f1d383d0e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YVKUW6EVW3XLPJGN7O3FAKUPHU/bundle.json","state_url":"https://pith.science/pith/YVKUW6EVW3XLPJGN7O3FAKUPHU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YVKUW6EVW3XLPJGN7O3FAKUPHU/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":"2026-06-10T12:42:58Z","links":{"resolver":"https://pith.science/pith/YVKUW6EVW3XLPJGN7O3FAKUPHU","bundle":"https://pith.science/pith/YVKUW6EVW3XLPJGN7O3FAKUPHU/bundle.json","state":"https://pith.science/pith/YVKUW6EVW3XLPJGN7O3FAKUPHU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YVKUW6EVW3XLPJGN7O3FAKUPHU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YVKUW6EVW3XLPJGN7O3FAKUPHU","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":"3a799cfc84c3a4bbc9b2a3614b61a2351581d5ea08639d5d1a71222ebf76ec16","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-15T10:25:22Z","title_canon_sha256":"69cb8be92d0d7872998d00a38fd5c4d737e037c724c076a94737389cf5121374"},"schema_version":"1.0","source":{"id":"2605.15825","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.15825","created_at":"2026-05-20T00:01:20Z"},{"alias_kind":"arxiv_version","alias_value":"2605.15825v1","created_at":"2026-05-20T00:01:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.15825","created_at":"2026-05-20T00:01:20Z"},{"alias_kind":"pith_short_12","alias_value":"YVKUW6EVW3XL","created_at":"2026-05-20T00:01:20Z"},{"alias_kind":"pith_short_16","alias_value":"YVKUW6EVW3XLPJGN","created_at":"2026-05-20T00:01:20Z"},{"alias_kind":"pith_short_8","alias_value":"YVKUW6EV","created_at":"2026-05-20T00:01:20Z"}],"graph_snapshots":[{"event_id":"sha256:1ca045f92fe9d983a168d98d0e61d7bdf07896ec4aff319c8488cd4f1d383d0e","target":"graph","created_at":"2026-05-20T00:01:20Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"The resulting theory provides a rigorous foundation for high-order spectral and collocation approximations of endpoint-singular and weakly regular problems, including terminal value problems, fractional differential equations, and weakly singular Volterra integral equations."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That composing classical Jacobi polynomials with an endpoint algebraic mapping directly incorporates the terminal singular structure into the approximation space and thereby yields the claimed orthogonality, derivative identities, and weighted error estimates for functions with limited regularity near the terminal point."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Introduces fractional Jacobi polynomials via endpoint algebraic mapping and derives projection, interpolation, and embedding estimates for spectral approximations of endpoint-singular problems."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Composing Jacobi polynomials with an endpoint algebraic mapping yields bases that preserve terminal singularities for high-order spectral approximations."}],"snapshot_sha256":"03aa7ecccbd9c7ceabab925099fed0ad54934fec38ff6b2eeb38f61bba313ff6"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"e24a6a45ba2d4e651298e2cca8387025e3752fe037c6dc64f13d5284bb6d662a"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T22:31:19.656773Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T22:31:19.648094Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:48.722227Z","status":"skipped","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T17:21:55.866865Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.15825/integrity.json","findings":[],"snapshot_sha256":"43cd6de478f51c6f84303feb08b1d3babb2b7fb76f21b44b557c145ce374c4ad","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a fractional approximation framework for functions with limited regularity near the terminal point. The proposed basis is constructed by composing classical Jacobi polynomials with an endpoint algebraic mapping, thereby incorporating the terminal singular structure directly into the approximation space. The main structural properties of the fractional polynomials are established, including orthogonality relations, derivative identities, and a singular Sturm--Liouville eigenvalue formulation. We then introduce the associated weighted Sobolev spaces and prove projection and Gauss-ty","authors_text":"Mahmoud A. Zaky","cross_cats":["cs.NA"],"headline":"Composing Jacobi polynomials with an endpoint algebraic mapping yields bases that preserve terminal singularities for high-order spectral approximations.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-15T10:25:22Z","title":"Endpoint-singularity-preserving spectral approximation theory for weakly singular integral equations"},"references":{"count":16,"internal_anchors":0,"resolved_work":16,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"I. G. Ameen, M. A. Zaky, E. H. Doha, Singularity preservin g spectral collocation method for nonlinear systems of fractional di fferential equations with the right-sided Caputo fractional derivative, J","work_id":"18e6132e-a60e-4a65-a249-6a617b5ba5fb","year":2021},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"C. Bernardi, Y . Maday, Spectral methods, Handbook of num erical analysis 5 (1997) 209–485","work_id":"e56934ef-a05f-444a-9449-2b60c299b0fb","year":1997},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"S. Chen, J. Shen, L.-L. Wang, Generalized Jacobi functio ns and their applications to fractional di fferential equa- tions, Mathematics of Computation 85 (300) (2016) 1603–163 8","work_id":"ad55b38b-b711-44f0-a41c-5e7c160797f0","year":2016},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"Y . Chen, X. Li, T. Tang, A note on Jacobi spectral-colloca tion methods for weakly singular Volterra integral equations with smooth solutions, Journal of Computational Mathematics (2013) 47–56","work_id":"6de7f99d-ed2d-4867-83f7-35f756ccdf12","year":2013},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"K. Diethelm, R. Garrappa, M. Stynes, Good (and not so good ) practices in computational methods for fractional calculus, Mathematics 8 (3) (2020) 324","work_id":"04a5c057-5c48-46e9-b7e1-43e97451ec93","year":2020}],"snapshot_sha256":"f60c10644ee8812c90757a3c9363090e99c4a6ef98542f8b7b22d10b104bbf28"},"source":{"id":"2605.15825","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T22:20:42.210057Z","id":"79f8885c-fdd8-4e3a-a212-03dfbd57c296","model_set":{"reader":"grok-4.3"},"one_line_summary":"Introduces fractional Jacobi polynomials via endpoint algebraic mapping and derives projection, interpolation, and embedding estimates for spectral approximations of endpoint-singular problems.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Composing Jacobi polynomials with an endpoint algebraic mapping yields bases that preserve terminal singularities for high-order spectral approximations.","strongest_claim":"The resulting theory provides a rigorous foundation for high-order spectral and collocation approximations of endpoint-singular and weakly regular problems, including terminal value problems, fractional differential equations, and weakly singular Volterra integral equations.","weakest_assumption":"That composing classical Jacobi polynomials with an endpoint algebraic mapping directly incorporates the terminal singular structure into the approximation space and thereby yields the claimed orthogonality, derivative identities, and weighted error estimates for functions with limited regularity near the terminal point."}},"verdict_id":"79f8885c-fdd8-4e3a-a212-03dfbd57c296"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f6fa0eb07fdad8441956f6c4132f0f66b8995d0cafd25bd39c14b046bf29da85","target":"record","created_at":"2026-05-20T00:01:20Z","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":"3a799cfc84c3a4bbc9b2a3614b61a2351581d5ea08639d5d1a71222ebf76ec16","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-15T10:25:22Z","title_canon_sha256":"69cb8be92d0d7872998d00a38fd5c4d737e037c724c076a94737389cf5121374"},"schema_version":"1.0","source":{"id":"2605.15825","kind":"arxiv","version":1}},"canonical_sha256":"c5554b7895b6eeb7a4cdfbb6502a8f3d2180ba284c9be896199f181a92e45909","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5554b7895b6eeb7a4cdfbb6502a8f3d2180ba284c9be896199f181a92e45909","first_computed_at":"2026-05-20T00:01:20.461611Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:20.461611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J6JclEQ9IDfNwDHslQttpiV6S0jd5DSQ2J0WoroIIB1+9WJk1biRTSsMe0hnDiCCVUxSCiRYX9ErLLgWisqzCQ==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:20.462376Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.15825","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6fa0eb07fdad8441956f6c4132f0f66b8995d0cafd25bd39c14b046bf29da85","sha256:1ca045f92fe9d983a168d98d0e61d7bdf07896ec4aff319c8488cd4f1d383d0e"],"state_sha256":"24a61350fc368e29c7cd5cd9ad1e9c60cb7e3c8596cbfafe5797755b7c48df74"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hQJr1fSsxrnNfTmsXsPj+l2l8L1aI2tTYh28cteAFjsx3YoklLIrUAx0G8XBQgHK/HoRE//7XUCEMrNFOOBDAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T12:42:58.718230Z","bundle_sha256":"c0739e13daa0a8cac53b7c1f2b07255dd041c275ac8ffd00abca3818fe1084ff"}}