{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:7NKFLYMP3AK6GWSK24EGKZ4OJD","short_pith_number":"pith:7NKFLYMP","canonical_record":{"source":{"id":"2605.30037","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-28T14:56:40Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"5f7671b06274bf9295cab948fb452e732438b5a0ce3e9b8ff12538c74892baed","abstract_canon_sha256":"8d14dd82291ec45b3c35b3f1d38a78230fe5931ded3027a967b196f450ccfa21"},"schema_version":"1.0"},"canonical_sha256":"fb5455e18fd815e35a4ad70865678e48de62587da720764dabaf66a1d70aec1e","source":{"kind":"arxiv","id":"2605.30037","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.30037","created_at":"2026-05-29T02:06:07Z"},{"alias_kind":"arxiv_version","alias_value":"2605.30037v1","created_at":"2026-05-29T02:06:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.30037","created_at":"2026-05-29T02:06:07Z"},{"alias_kind":"pith_short_12","alias_value":"7NKFLYMP3AK6","created_at":"2026-05-29T02:06:07Z"},{"alias_kind":"pith_short_16","alias_value":"7NKFLYMP3AK6GWSK","created_at":"2026-05-29T02:06:07Z"},{"alias_kind":"pith_short_8","alias_value":"7NKFLYMP","created_at":"2026-05-29T02:06:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:7NKFLYMP3AK6GWSK24EGKZ4OJD","target":"record","payload":{"canonical_record":{"source":{"id":"2605.30037","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-28T14:56:40Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"5f7671b06274bf9295cab948fb452e732438b5a0ce3e9b8ff12538c74892baed","abstract_canon_sha256":"8d14dd82291ec45b3c35b3f1d38a78230fe5931ded3027a967b196f450ccfa21"},"schema_version":"1.0"},"canonical_sha256":"fb5455e18fd815e35a4ad70865678e48de62587da720764dabaf66a1d70aec1e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T02:06:07.992462Z","signature_b64":"THtEFpXBwiVnf8HRLQVCXXrzKdPvCIsDrnx5xZ6doTf4f8OddniIt0VkpXLO/+AovPpkvUUsEpkIfKH4wwWkAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb5455e18fd815e35a4ad70865678e48de62587da720764dabaf66a1d70aec1e","last_reissued_at":"2026-05-29T02:06:07.992011Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T02:06:07.992011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.30037","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":"2026-05-29T02:06:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zBg63OKh1GLf5CN3yNS8bZaUBUXWJ1TOt+NO9OhjqODo+5LkPH3R/9MrwfLaoxlBm3ZN9YITvRc9kQASta2hCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:39:40.485401Z"},"content_sha256":"fdaf69c10b902bbaa9bba6126d8226ee18f59e874159be2c040f8878ddb81f99","schema_version":"1.0","event_id":"sha256:fdaf69c10b902bbaa9bba6126d8226ee18f59e874159be2c040f8878ddb81f99"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:7NKFLYMP3AK6GWSK24EGKZ4OJD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A novel mixed spectral method with ball polynomials for the Biharmonic equation on a unit ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Bing Su, Jianwei Zhou, Mengxue Gao","submitted_at":"2026-05-28T14:56:40Z","abstract_excerpt":"A novel mixed spectral-Galerkin method based on generalized ball polynomials is proposed for solving the biharmonic equation on a unit ball. By introducing an auxiliary variable to decouple the biharmonic equation into a system of second-order equations, the corresponding discrete scheme yields a strictly diagonal stiffness matrix, which significantly enhances the computational efficiency. Rigorous a-priori error estimates are established to demonstrate the exponential convergence rates in both the $L^2$- and $H^1$-norms. Extensive numerical experiments are conducted to verify the theoretical "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30037","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/2605.30037/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":"2026-05-29T02:06:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ImQaofP83QPGtQxgLFsmwQ/dBqbgdJ8SrRExuCxq/3S60aggjTrmGaeONfFRscOxDfOUj5nbeA3vwgh/eafCBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:39:40.485787Z"},"content_sha256":"785efc306c8f402f35aa9c8b382195ff3f28376247771fce5a4350f6693db62e","schema_version":"1.0","event_id":"sha256:785efc306c8f402f35aa9c8b382195ff3f28376247771fce5a4350f6693db62e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7NKFLYMP3AK6GWSK24EGKZ4OJD/bundle.json","state_url":"https://pith.science/pith/7NKFLYMP3AK6GWSK24EGKZ4OJD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7NKFLYMP3AK6GWSK24EGKZ4OJD/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":"2026-06-05T12:39:40Z","links":{"resolver":"https://pith.science/pith/7NKFLYMP3AK6GWSK24EGKZ4OJD","bundle":"https://pith.science/pith/7NKFLYMP3AK6GWSK24EGKZ4OJD/bundle.json","state":"https://pith.science/pith/7NKFLYMP3AK6GWSK24EGKZ4OJD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7NKFLYMP3AK6GWSK24EGKZ4OJD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:7NKFLYMP3AK6GWSK24EGKZ4OJD","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":"8d14dd82291ec45b3c35b3f1d38a78230fe5931ded3027a967b196f450ccfa21","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-28T14:56:40Z","title_canon_sha256":"5f7671b06274bf9295cab948fb452e732438b5a0ce3e9b8ff12538c74892baed"},"schema_version":"1.0","source":{"id":"2605.30037","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.30037","created_at":"2026-05-29T02:06:07Z"},{"alias_kind":"arxiv_version","alias_value":"2605.30037v1","created_at":"2026-05-29T02:06:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.30037","created_at":"2026-05-29T02:06:07Z"},{"alias_kind":"pith_short_12","alias_value":"7NKFLYMP3AK6","created_at":"2026-05-29T02:06:07Z"},{"alias_kind":"pith_short_16","alias_value":"7NKFLYMP3AK6GWSK","created_at":"2026-05-29T02:06:07Z"},{"alias_kind":"pith_short_8","alias_value":"7NKFLYMP","created_at":"2026-05-29T02:06:07Z"}],"graph_snapshots":[{"event_id":"sha256:785efc306c8f402f35aa9c8b382195ff3f28376247771fce5a4350f6693db62e","target":"graph","created_at":"2026-05-29T02:06:07Z","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/2605.30037/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A novel mixed spectral-Galerkin method based on generalized ball polynomials is proposed for solving the biharmonic equation on a unit ball. By introducing an auxiliary variable to decouple the biharmonic equation into a system of second-order equations, the corresponding discrete scheme yields a strictly diagonal stiffness matrix, which significantly enhances the computational efficiency. Rigorous a-priori error estimates are established to demonstrate the exponential convergence rates in both the $L^2$- and $H^1$-norms. Extensive numerical experiments are conducted to verify the theoretical ","authors_text":"Bing Su, Jianwei Zhou, Mengxue Gao","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-28T14:56:40Z","title":"A novel mixed spectral method with ball polynomials for the Biharmonic equation on a unit ball"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30037","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:fdaf69c10b902bbaa9bba6126d8226ee18f59e874159be2c040f8878ddb81f99","target":"record","created_at":"2026-05-29T02:06:07Z","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":"8d14dd82291ec45b3c35b3f1d38a78230fe5931ded3027a967b196f450ccfa21","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-28T14:56:40Z","title_canon_sha256":"5f7671b06274bf9295cab948fb452e732438b5a0ce3e9b8ff12538c74892baed"},"schema_version":"1.0","source":{"id":"2605.30037","kind":"arxiv","version":1}},"canonical_sha256":"fb5455e18fd815e35a4ad70865678e48de62587da720764dabaf66a1d70aec1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb5455e18fd815e35a4ad70865678e48de62587da720764dabaf66a1d70aec1e","first_computed_at":"2026-05-29T02:06:07.992011Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T02:06:07.992011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"THtEFpXBwiVnf8HRLQVCXXrzKdPvCIsDrnx5xZ6doTf4f8OddniIt0VkpXLO/+AovPpkvUUsEpkIfKH4wwWkAg==","signature_status":"signed_v1","signed_at":"2026-05-29T02:06:07.992462Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.30037","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fdaf69c10b902bbaa9bba6126d8226ee18f59e874159be2c040f8878ddb81f99","sha256:785efc306c8f402f35aa9c8b382195ff3f28376247771fce5a4350f6693db62e"],"state_sha256":"a8ecb4ad168484f11485af0f9b7ac3b296d6a83499c09e697a0a17c86435c6ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L0khaBXBgt5TYcrkbGvqTFS9MUQSvbXTp3mJ/0icKzbasgSEY7UkPW1l84yQ1E9YPzcYnrEdJmmhaIRnvQ8qBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T12:39:40.487830Z","bundle_sha256":"58c8a426a8f7fdff7dd2c165b8acb395d562a663c3df65ee0e4ebb912a655716"}}