{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:52YKHKNOBQM7AFDFWEQPFAR6BR","short_pith_number":"pith:52YKHKNO","canonical_record":{"source":{"id":"1702.02242","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-02-08T01:10:40Z","cross_cats_sorted":[],"title_canon_sha256":"2acf083e104e83e0b92f89e86363a487ead0289e329329fdcf9b6d9bc06161ca","abstract_canon_sha256":"94dd3ed90f9235db3f7e45bc02f99fb7b0bef7a77f2f565bd391b6d73accbe23"},"schema_version":"1.0"},"canonical_sha256":"eeb0a3a9ae0c19f01465b120f2823e0c4197c03b339fd7b299d85af4b106ea86","source":{"kind":"arxiv","id":"1702.02242","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.02242","created_at":"2026-05-18T00:11:44Z"},{"alias_kind":"arxiv_version","alias_value":"1702.02242v3","created_at":"2026-05-18T00:11:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.02242","created_at":"2026-05-18T00:11:44Z"},{"alias_kind":"pith_short_12","alias_value":"52YKHKNOBQM7","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"52YKHKNOBQM7AFDF","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"52YKHKNO","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:52YKHKNOBQM7AFDFWEQPFAR6BR","target":"record","payload":{"canonical_record":{"source":{"id":"1702.02242","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-02-08T01:10:40Z","cross_cats_sorted":[],"title_canon_sha256":"2acf083e104e83e0b92f89e86363a487ead0289e329329fdcf9b6d9bc06161ca","abstract_canon_sha256":"94dd3ed90f9235db3f7e45bc02f99fb7b0bef7a77f2f565bd391b6d73accbe23"},"schema_version":"1.0"},"canonical_sha256":"eeb0a3a9ae0c19f01465b120f2823e0c4197c03b339fd7b299d85af4b106ea86","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:44.039942Z","signature_b64":"hESIKq83bdHP/DFM8wMe4hDITgO1MpYU9NqKC37Cu+Q+hdeYTiXr6nSRz3VpVjnZiZoFf+xxUjz+TosQzpfiDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eeb0a3a9ae0c19f01465b120f2823e0c4197c03b339fd7b299d85af4b106ea86","last_reissued_at":"2026-05-18T00:11:44.039171Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:44.039171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.02242","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:11:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PuwXfzJEKnBDG72GQr6p8RHU2AYezUKs28CF2RuOabvvE+se0LtPltFqh9d/L8VwxvhD0RaWxgQ9q6wZiD0/CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T04:15:39.000463Z"},"content_sha256":"cf885c093f91034e238749e6c008da64ebc519f15aa9db5e23647d6b70ea254d","schema_version":"1.0","event_id":"sha256:cf885c093f91034e238749e6c008da64ebc519f15aa9db5e23647d6b70ea254d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:52YKHKNOBQM7AFDFWEQPFAR6BR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Equation-By-Equation Method for Solving the Multidimensional Moment Constrained Maximum Entropy Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"John Harlim, Wenrui Hao","submitted_at":"2017-02-08T01:10:40Z","abstract_excerpt":"An equation-by-equation (EBE) method is proposed to solve a system of nonlinear equations arising from the moment constrained maximum entropy problem of multidimensional variables. The design of the EBE method combines ideas from homotopy continuation and Newton's iterative methods. Theoretically, we establish the local convergence under appropriate conditions and show that the proposed method, geometrically, finds the solution by searching along the surface corresponding to one component of the nonlinear problem. We will demonstrate the robustness of the method on various numerical examples, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02242","kind":"arxiv","version":3},"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":"2026-05-18T00:11:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZcRtsLyddN7CRuYUYx41qchY+gsc9IdKJBA+RtGKcX9ju6Z8zbNfneY8RtBNy0A0FR+qu5s5ogdY20KnHj4ACg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T04:15:39.000848Z"},"content_sha256":"25d4d84654798b456d3afdc09aab6d2c7b54248306890604adda6244fe95b443","schema_version":"1.0","event_id":"sha256:25d4d84654798b456d3afdc09aab6d2c7b54248306890604adda6244fe95b443"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/52YKHKNOBQM7AFDFWEQPFAR6BR/bundle.json","state_url":"https://pith.science/pith/52YKHKNOBQM7AFDFWEQPFAR6BR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/52YKHKNOBQM7AFDFWEQPFAR6BR/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":"2026-05-30T04:15:39Z","links":{"resolver":"https://pith.science/pith/52YKHKNOBQM7AFDFWEQPFAR6BR","bundle":"https://pith.science/pith/52YKHKNOBQM7AFDFWEQPFAR6BR/bundle.json","state":"https://pith.science/pith/52YKHKNOBQM7AFDFWEQPFAR6BR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/52YKHKNOBQM7AFDFWEQPFAR6BR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:52YKHKNOBQM7AFDFWEQPFAR6BR","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":"94dd3ed90f9235db3f7e45bc02f99fb7b0bef7a77f2f565bd391b6d73accbe23","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-02-08T01:10:40Z","title_canon_sha256":"2acf083e104e83e0b92f89e86363a487ead0289e329329fdcf9b6d9bc06161ca"},"schema_version":"1.0","source":{"id":"1702.02242","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.02242","created_at":"2026-05-18T00:11:44Z"},{"alias_kind":"arxiv_version","alias_value":"1702.02242v3","created_at":"2026-05-18T00:11:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.02242","created_at":"2026-05-18T00:11:44Z"},{"alias_kind":"pith_short_12","alias_value":"52YKHKNOBQM7","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"52YKHKNOBQM7AFDF","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"52YKHKNO","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:25d4d84654798b456d3afdc09aab6d2c7b54248306890604adda6244fe95b443","target":"graph","created_at":"2026-05-18T00:11:44Z","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 equation-by-equation (EBE) method is proposed to solve a system of nonlinear equations arising from the moment constrained maximum entropy problem of multidimensional variables. The design of the EBE method combines ideas from homotopy continuation and Newton's iterative methods. Theoretically, we establish the local convergence under appropriate conditions and show that the proposed method, geometrically, finds the solution by searching along the surface corresponding to one component of the nonlinear problem. We will demonstrate the robustness of the method on various numerical examples, ","authors_text":"John Harlim, Wenrui Hao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-02-08T01:10:40Z","title":"An Equation-By-Equation Method for Solving the Multidimensional Moment Constrained Maximum Entropy Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02242","kind":"arxiv","version":3},"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:cf885c093f91034e238749e6c008da64ebc519f15aa9db5e23647d6b70ea254d","target":"record","created_at":"2026-05-18T00:11:44Z","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":"94dd3ed90f9235db3f7e45bc02f99fb7b0bef7a77f2f565bd391b6d73accbe23","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-02-08T01:10:40Z","title_canon_sha256":"2acf083e104e83e0b92f89e86363a487ead0289e329329fdcf9b6d9bc06161ca"},"schema_version":"1.0","source":{"id":"1702.02242","kind":"arxiv","version":3}},"canonical_sha256":"eeb0a3a9ae0c19f01465b120f2823e0c4197c03b339fd7b299d85af4b106ea86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eeb0a3a9ae0c19f01465b120f2823e0c4197c03b339fd7b299d85af4b106ea86","first_computed_at":"2026-05-18T00:11:44.039171Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:44.039171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hESIKq83bdHP/DFM8wMe4hDITgO1MpYU9NqKC37Cu+Q+hdeYTiXr6nSRz3VpVjnZiZoFf+xxUjz+TosQzpfiDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:44.039942Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.02242","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf885c093f91034e238749e6c008da64ebc519f15aa9db5e23647d6b70ea254d","sha256:25d4d84654798b456d3afdc09aab6d2c7b54248306890604adda6244fe95b443"],"state_sha256":"a876822ef1bc4d0daf7f61ab2145d52eeab91cc6d2c9e1d84d86006ed106c739"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E+AAaDSmTgnrHfVJ85yke3njmVuyn1He67qltBsdgKpCTpnjVcRQTDPtWI+CRghtbsad5ynILk1oWbFtX87cBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T04:15:39.003290Z","bundle_sha256":"22bf64d502f25d9bd3ee5af9fe1e488c8b57d9f940f70367a56844978ce2ced2"}}