{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:IXZL4BIFIYLMYT3H5YXCHIYBMY","short_pith_number":"pith:IXZL4BIF","canonical_record":{"source":{"id":"1711.02519","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-11-04T16:42:04Z","cross_cats_sorted":[],"title_canon_sha256":"7ccc5acbf79abafc255af70d370b60f73eeb235dc7d5c444e027bfd7dbb7b6e2","abstract_canon_sha256":"373e9248b9b39315327fddd76f3b143c2bf0f8b431af868b753640e1919214a3"},"schema_version":"1.0"},"canonical_sha256":"45f2be05054616cc4f67ee2e23a3016635be55503857197b91f9d1eef55f4150","source":{"kind":"arxiv","id":"1711.02519","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02519","created_at":"2026-05-18T00:28:22Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02519v2","created_at":"2026-05-18T00:28:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02519","created_at":"2026-05-18T00:28:22Z"},{"alias_kind":"pith_short_12","alias_value":"IXZL4BIFIYLM","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IXZL4BIFIYLMYT3H","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IXZL4BIF","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:IXZL4BIFIYLMYT3H5YXCHIYBMY","target":"record","payload":{"canonical_record":{"source":{"id":"1711.02519","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-11-04T16:42:04Z","cross_cats_sorted":[],"title_canon_sha256":"7ccc5acbf79abafc255af70d370b60f73eeb235dc7d5c444e027bfd7dbb7b6e2","abstract_canon_sha256":"373e9248b9b39315327fddd76f3b143c2bf0f8b431af868b753640e1919214a3"},"schema_version":"1.0"},"canonical_sha256":"45f2be05054616cc4f67ee2e23a3016635be55503857197b91f9d1eef55f4150","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:22.292171Z","signature_b64":"JVo8N8Q84TjZswLioxxPwohfvEnt/OCnvGxWVI3iVvjosft2udwMisfGBAHz4x/nxY1ovQj959/rfHahFJh1DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"45f2be05054616cc4f67ee2e23a3016635be55503857197b91f9d1eef55f4150","last_reissued_at":"2026-05-18T00:28:22.291461Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:22.291461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.02519","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":"2026-05-18T00:28:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h2MryWeIL8Mrq10DRTwwLukOyG8qbNSSwwf7wo/mdo68bM+G5D/yXZsH/ob4LgBggk66Rp12dGaUY4C0EF+SDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:59:31.142512Z"},"content_sha256":"4fdf74da61db8a6dc0e9e965218385e1c2ec18ea777a44ab7328fb6c76962966","schema_version":"1.0","event_id":"sha256:4fdf74da61db8a6dc0e9e965218385e1c2ec18ea777a44ab7328fb6c76962966"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:IXZL4BIFIYLMYT3H5YXCHIYBMY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Efficient Multigrid Method for Ground State Solution of Bose-Einstein Condensates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Fei Xu, Hehu Xie, Ning Zhang","submitted_at":"2017-11-04T16:42:04Z","abstract_excerpt":"An efficient multigrid method is proposed to compute the ground state solution of Bose-Einstein condensations by the finite element method based on the combination of the multigrid method for nonlinear eigenvalue problem and an efficient implementation for the nonlinear iteration. The proposed numerical method not only has the optimal convergence rate, but also has the asymptotically optimal computational work which is independent from the nonlinearity of the problem. The independence from the nonlinearity means that the asymptotic estimate of the computational work can reach almost the same a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02519","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":"2026-05-18T00:28:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P2/ScZcUU3bMpfK+dfOWRdxiFC0sfca5Mho9ApZw3QnAvV/6jLOhvLaPBHc8aWyWztB4ezNQdoPEgutKrvBjAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:59:31.143149Z"},"content_sha256":"a8f969bbb3ae45a7b20ecc46f1859f5f23c050f46eccbd57c8f6f549a2683bc9","schema_version":"1.0","event_id":"sha256:a8f969bbb3ae45a7b20ecc46f1859f5f23c050f46eccbd57c8f6f549a2683bc9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IXZL4BIFIYLMYT3H5YXCHIYBMY/bundle.json","state_url":"https://pith.science/pith/IXZL4BIFIYLMYT3H5YXCHIYBMY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IXZL4BIFIYLMYT3H5YXCHIYBMY/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":"2026-05-27T10:59:31Z","links":{"resolver":"https://pith.science/pith/IXZL4BIFIYLMYT3H5YXCHIYBMY","bundle":"https://pith.science/pith/IXZL4BIFIYLMYT3H5YXCHIYBMY/bundle.json","state":"https://pith.science/pith/IXZL4BIFIYLMYT3H5YXCHIYBMY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IXZL4BIFIYLMYT3H5YXCHIYBMY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IXZL4BIFIYLMYT3H5YXCHIYBMY","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":"373e9248b9b39315327fddd76f3b143c2bf0f8b431af868b753640e1919214a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-11-04T16:42:04Z","title_canon_sha256":"7ccc5acbf79abafc255af70d370b60f73eeb235dc7d5c444e027bfd7dbb7b6e2"},"schema_version":"1.0","source":{"id":"1711.02519","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02519","created_at":"2026-05-18T00:28:22Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02519v2","created_at":"2026-05-18T00:28:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02519","created_at":"2026-05-18T00:28:22Z"},{"alias_kind":"pith_short_12","alias_value":"IXZL4BIFIYLM","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IXZL4BIFIYLMYT3H","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IXZL4BIF","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:a8f969bbb3ae45a7b20ecc46f1859f5f23c050f46eccbd57c8f6f549a2683bc9","target":"graph","created_at":"2026-05-18T00:28:22Z","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":"An efficient multigrid method is proposed to compute the ground state solution of Bose-Einstein condensations by the finite element method based on the combination of the multigrid method for nonlinear eigenvalue problem and an efficient implementation for the nonlinear iteration. The proposed numerical method not only has the optimal convergence rate, but also has the asymptotically optimal computational work which is independent from the nonlinearity of the problem. The independence from the nonlinearity means that the asymptotic estimate of the computational work can reach almost the same a","authors_text":"Fei Xu, Hehu Xie, Ning Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-11-04T16:42:04Z","title":"An Efficient Multigrid Method for Ground State Solution of Bose-Einstein Condensates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02519","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":"sha256:4fdf74da61db8a6dc0e9e965218385e1c2ec18ea777a44ab7328fb6c76962966","target":"record","created_at":"2026-05-18T00:28:22Z","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":"373e9248b9b39315327fddd76f3b143c2bf0f8b431af868b753640e1919214a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-11-04T16:42:04Z","title_canon_sha256":"7ccc5acbf79abafc255af70d370b60f73eeb235dc7d5c444e027bfd7dbb7b6e2"},"schema_version":"1.0","source":{"id":"1711.02519","kind":"arxiv","version":2}},"canonical_sha256":"45f2be05054616cc4f67ee2e23a3016635be55503857197b91f9d1eef55f4150","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"45f2be05054616cc4f67ee2e23a3016635be55503857197b91f9d1eef55f4150","first_computed_at":"2026-05-18T00:28:22.291461Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:22.291461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JVo8N8Q84TjZswLioxxPwohfvEnt/OCnvGxWVI3iVvjosft2udwMisfGBAHz4x/nxY1ovQj959/rfHahFJh1DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:22.292171Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.02519","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4fdf74da61db8a6dc0e9e965218385e1c2ec18ea777a44ab7328fb6c76962966","sha256:a8f969bbb3ae45a7b20ecc46f1859f5f23c050f46eccbd57c8f6f549a2683bc9"],"state_sha256":"696a2189983321213462440402510257776bdcf982d36e89cf2ea0b49c7e7775"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jie8Hq56ybP/rZ+8aZm8hS4HRo2Oeky5dmLntaYSNd0NQfC3rNehGsLlapOITf62ujGlRIOrTJz3h6dGVF57Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T10:59:31.146253Z","bundle_sha256":"c79ba4b7222e69f3efca4d705da5102ec069741ec577b7497ca5fe44d054217a"}}