{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5NKKJHZULGFN6YDVV32PBISE4W","short_pith_number":"pith:5NKKJHZU","canonical_record":{"source":{"id":"1610.06519","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-10-20T17:49:21Z","cross_cats_sorted":["cs.CE","math.NA"],"title_canon_sha256":"6b1078ae673209448dfcd660beef4962badac2547d74c997b8f6db9c56da2e45","abstract_canon_sha256":"8335ed19af7be3debcdd51462f164eee45ad98c4152b26a055c371c574a4deb0"},"schema_version":"1.0"},"canonical_sha256":"eb54a49f34598adf6075aef4f0a244e5a2c64323363a348ad8ef487abd078ce7","source":{"kind":"arxiv","id":"1610.06519","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06519","created_at":"2026-05-17T23:54:26Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06519v2","created_at":"2026-05-17T23:54:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06519","created_at":"2026-05-17T23:54:26Z"},{"alias_kind":"pith_short_12","alias_value":"5NKKJHZULGFN","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5NKKJHZULGFN6YDV","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5NKKJHZU","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5NKKJHZULGFN6YDVV32PBISE4W","target":"record","payload":{"canonical_record":{"source":{"id":"1610.06519","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-10-20T17:49:21Z","cross_cats_sorted":["cs.CE","math.NA"],"title_canon_sha256":"6b1078ae673209448dfcd660beef4962badac2547d74c997b8f6db9c56da2e45","abstract_canon_sha256":"8335ed19af7be3debcdd51462f164eee45ad98c4152b26a055c371c574a4deb0"},"schema_version":"1.0"},"canonical_sha256":"eb54a49f34598adf6075aef4f0a244e5a2c64323363a348ad8ef487abd078ce7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:26.966271Z","signature_b64":"k/Qcq66ys76ESs5VcN36TTrb2q5KNkngVxSECL4WnMLeYxEzLXiYo+upgfYOnIWFYn/9DFnxsu2H5jVouvErAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb54a49f34598adf6075aef4f0a244e5a2c64323363a348ad8ef487abd078ce7","last_reissued_at":"2026-05-17T23:54:26.965656Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:26.965656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.06519","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":"2026-05-17T23:54:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vee6BJr4YJbOEugF68Uy+rcWwxhYrb2jOsZ1tjGphekW+c9kBLkKNgcr6YR3ezOo2RsUEbT+Eiq+oPlf4bc1AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:51:01.111902Z"},"content_sha256":"68bf8e706aaa1af27c3d8efda0d7bfa75704cc7845e0d3a7e60c1606bc5d38fe","schema_version":"1.0","event_id":"sha256:68bf8e706aaa1af27c3d8efda0d7bfa75704cc7845e0d3a7e60c1606bc5d38fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5NKKJHZULGFN6YDVV32PBISE4W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CE","math.NA"],"primary_cat":"math.OC","authors_text":"Bernhard Schmitzer","submitted_at":"2016-10-20T17:49:21Z","abstract_excerpt":"Scaling algorithms for entropic transport-type problems have become a very popular numerical method, encompassing Wasserstein barycenters, multi-marginal problems, gradient flows and unbalanced transport. However, a standard implementation of the scaling algorithm has several numerical limitations: the scaling factors diverge and convergence becomes impractically slow as the entropy regularization approaches zero. Moreover, handling the dense kernel matrix becomes unfeasible for large problems. To address this, we combine several modifications: A log-domain stabilized formulation, the well-kno"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06519","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":"2026-05-17T23:54:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sep1q+4OfeWiMhXrvycyr8TxDsUo9APcsyQjOsc4iy3W9QcfX9JoeL4JwNJ8brrLyj7hrEFmDxzibjaocDn6BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:51:01.112242Z"},"content_sha256":"ffca5f0e6572978718a82183a391d3657dba01e5cac277e4cc67ad54c1ce34a5","schema_version":"1.0","event_id":"sha256:ffca5f0e6572978718a82183a391d3657dba01e5cac277e4cc67ad54c1ce34a5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5NKKJHZULGFN6YDVV32PBISE4W/bundle.json","state_url":"https://pith.science/pith/5NKKJHZULGFN6YDVV32PBISE4W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5NKKJHZULGFN6YDVV32PBISE4W/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":"2026-05-31T05:51:01Z","links":{"resolver":"https://pith.science/pith/5NKKJHZULGFN6YDVV32PBISE4W","bundle":"https://pith.science/pith/5NKKJHZULGFN6YDVV32PBISE4W/bundle.json","state":"https://pith.science/pith/5NKKJHZULGFN6YDVV32PBISE4W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5NKKJHZULGFN6YDVV32PBISE4W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5NKKJHZULGFN6YDVV32PBISE4W","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":"8335ed19af7be3debcdd51462f164eee45ad98c4152b26a055c371c574a4deb0","cross_cats_sorted":["cs.CE","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-10-20T17:49:21Z","title_canon_sha256":"6b1078ae673209448dfcd660beef4962badac2547d74c997b8f6db9c56da2e45"},"schema_version":"1.0","source":{"id":"1610.06519","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06519","created_at":"2026-05-17T23:54:26Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06519v2","created_at":"2026-05-17T23:54:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06519","created_at":"2026-05-17T23:54:26Z"},{"alias_kind":"pith_short_12","alias_value":"5NKKJHZULGFN","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5NKKJHZULGFN6YDV","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5NKKJHZU","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:ffca5f0e6572978718a82183a391d3657dba01e5cac277e4cc67ad54c1ce34a5","target":"graph","created_at":"2026-05-17T23:54:26Z","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":"Scaling algorithms for entropic transport-type problems have become a very popular numerical method, encompassing Wasserstein barycenters, multi-marginal problems, gradient flows and unbalanced transport. However, a standard implementation of the scaling algorithm has several numerical limitations: the scaling factors diverge and convergence becomes impractically slow as the entropy regularization approaches zero. Moreover, handling the dense kernel matrix becomes unfeasible for large problems. To address this, we combine several modifications: A log-domain stabilized formulation, the well-kno","authors_text":"Bernhard Schmitzer","cross_cats":["cs.CE","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-10-20T17:49:21Z","title":"Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06519","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":"sha256:68bf8e706aaa1af27c3d8efda0d7bfa75704cc7845e0d3a7e60c1606bc5d38fe","target":"record","created_at":"2026-05-17T23:54:26Z","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":"8335ed19af7be3debcdd51462f164eee45ad98c4152b26a055c371c574a4deb0","cross_cats_sorted":["cs.CE","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-10-20T17:49:21Z","title_canon_sha256":"6b1078ae673209448dfcd660beef4962badac2547d74c997b8f6db9c56da2e45"},"schema_version":"1.0","source":{"id":"1610.06519","kind":"arxiv","version":2}},"canonical_sha256":"eb54a49f34598adf6075aef4f0a244e5a2c64323363a348ad8ef487abd078ce7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb54a49f34598adf6075aef4f0a244e5a2c64323363a348ad8ef487abd078ce7","first_computed_at":"2026-05-17T23:54:26.965656Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:26.965656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k/Qcq66ys76ESs5VcN36TTrb2q5KNkngVxSECL4WnMLeYxEzLXiYo+upgfYOnIWFYn/9DFnxsu2H5jVouvErAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:26.966271Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.06519","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68bf8e706aaa1af27c3d8efda0d7bfa75704cc7845e0d3a7e60c1606bc5d38fe","sha256:ffca5f0e6572978718a82183a391d3657dba01e5cac277e4cc67ad54c1ce34a5"],"state_sha256":"1ab406bcddd57256aef6007b499758f6b1bdbfbc0f296effa0da7770a118a1b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TVXM+ks1QNPde5/6vJd0ddTby1gST+8L03ES+RGRV3flPfkDZ8rrTYpsHhZ+FpbkTde3lpXbtiyGP3rJ3NzRDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T05:51:01.114152Z","bundle_sha256":"63e936d3723d0445e2863c8f07f5f6ab07f73e9f905595d58255f0aea4737f06"}}