{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:P5ILGSJCVSJX5DWGEYVKI5HMPR","short_pith_number":"pith:P5ILGSJC","canonical_record":{"source":{"id":"1609.06349","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-20T20:41:04Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"4613d4d857ad666cadede745c295e4fa9110726001cec8cc468ca27678b37752","abstract_canon_sha256":"e2c578c00fd41aa9b71967c7d144d1ece678a3b52a67a27d446a555ad58e2194"},"schema_version":"1.0"},"canonical_sha256":"7f50b34922ac937e8ec6262aa474ec7c55f3d7d20f4217279fb2001ae1512cb8","source":{"kind":"arxiv","id":"1609.06349","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.06349","created_at":"2026-05-18T01:04:08Z"},{"alias_kind":"arxiv_version","alias_value":"1609.06349v1","created_at":"2026-05-18T01:04:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06349","created_at":"2026-05-18T01:04:08Z"},{"alias_kind":"pith_short_12","alias_value":"P5ILGSJCVSJX","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"P5ILGSJCVSJX5DWG","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"P5ILGSJC","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:P5ILGSJCVSJX5DWGEYVKI5HMPR","target":"record","payload":{"canonical_record":{"source":{"id":"1609.06349","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-20T20:41:04Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"4613d4d857ad666cadede745c295e4fa9110726001cec8cc468ca27678b37752","abstract_canon_sha256":"e2c578c00fd41aa9b71967c7d144d1ece678a3b52a67a27d446a555ad58e2194"},"schema_version":"1.0"},"canonical_sha256":"7f50b34922ac937e8ec6262aa474ec7c55f3d7d20f4217279fb2001ae1512cb8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:08.517324Z","signature_b64":"CF190MTGZHRq/2ik351tg14tYXj3maWnod+ei4LszH2kqPyTD9dxKiT2vA+ajPmMcJBEw5wrdDTwaaj/N9n6Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f50b34922ac937e8ec6262aa474ec7c55f3d7d20f4217279fb2001ae1512cb8","last_reissued_at":"2026-05-18T01:04:08.516540Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:08.516540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.06349","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":"2026-05-18T01:04:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"789JD+pZbeEKLWm6eFhFRzXbgKE0ArARPtQS2VFTz6Ecf+Tdp2gjmhvAAL5TXgRau4jzBjYalG8ro5OPPKVvAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:40:04.556594Z"},"content_sha256":"8c5f8b539841f2607ca88e1859714282588324a98bf490d8bbb968f8c866acaf","schema_version":"1.0","event_id":"sha256:8c5f8b539841f2607ca88e1859714282588324a98bf490d8bbb968f8c866acaf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:P5ILGSJCVSJX5DWGEYVKI5HMPR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A review of matrix scaling and Sinkhorn's normal form for matrices and positive maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.RA","authors_text":"Martin Idel","submitted_at":"2016-09-20T20:41:04Z","abstract_excerpt":"Given a nonnegative matrix $A$, can you find diagonal matrices $D_1,~D_2$ such that $D_1AD_2$ is doubly stochastic? The answer to this question is known as Sinkhorn's theorem. It has been proved with a wide variety of methods, each presenting a variety of possible generalisations. Recently, generalisations such as to positive maps between matrix algebras have become more and more interesting for applications. This text gives a review of over 70 years of matrix scaling. The focus lies on the mathematical landscape surrounding the problem and its solution as well as the generalisation to positiv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06349","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":""},"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":"2026-05-18T01:04:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ktSVHmdHc92ND0Mu2EZfKb+dx4bsB6Ft2GAKZ4DswCS80+ZzYeKuOXmy2NdYSd1rJqePF0XSOeL+ypI/dBVrDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:40:04.557247Z"},"content_sha256":"3b7027650dc17fc89e28a235861756f7c15b1f22e320a735d166de968126545f","schema_version":"1.0","event_id":"sha256:3b7027650dc17fc89e28a235861756f7c15b1f22e320a735d166de968126545f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P5ILGSJCVSJX5DWGEYVKI5HMPR/bundle.json","state_url":"https://pith.science/pith/P5ILGSJCVSJX5DWGEYVKI5HMPR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P5ILGSJCVSJX5DWGEYVKI5HMPR/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":"2026-05-25T18:40:04Z","links":{"resolver":"https://pith.science/pith/P5ILGSJCVSJX5DWGEYVKI5HMPR","bundle":"https://pith.science/pith/P5ILGSJCVSJX5DWGEYVKI5HMPR/bundle.json","state":"https://pith.science/pith/P5ILGSJCVSJX5DWGEYVKI5HMPR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P5ILGSJCVSJX5DWGEYVKI5HMPR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:P5ILGSJCVSJX5DWGEYVKI5HMPR","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":"e2c578c00fd41aa9b71967c7d144d1ece678a3b52a67a27d446a555ad58e2194","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-20T20:41:04Z","title_canon_sha256":"4613d4d857ad666cadede745c295e4fa9110726001cec8cc468ca27678b37752"},"schema_version":"1.0","source":{"id":"1609.06349","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.06349","created_at":"2026-05-18T01:04:08Z"},{"alias_kind":"arxiv_version","alias_value":"1609.06349v1","created_at":"2026-05-18T01:04:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06349","created_at":"2026-05-18T01:04:08Z"},{"alias_kind":"pith_short_12","alias_value":"P5ILGSJCVSJX","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"P5ILGSJCVSJX5DWG","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"P5ILGSJC","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:3b7027650dc17fc89e28a235861756f7c15b1f22e320a735d166de968126545f","target":"graph","created_at":"2026-05-18T01:04:08Z","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":"Given a nonnegative matrix $A$, can you find diagonal matrices $D_1,~D_2$ such that $D_1AD_2$ is doubly stochastic? The answer to this question is known as Sinkhorn's theorem. It has been proved with a wide variety of methods, each presenting a variety of possible generalisations. Recently, generalisations such as to positive maps between matrix algebras have become more and more interesting for applications. This text gives a review of over 70 years of matrix scaling. The focus lies on the mathematical landscape surrounding the problem and its solution as well as the generalisation to positiv","authors_text":"Martin Idel","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-20T20:41:04Z","title":"A review of matrix scaling and Sinkhorn's normal form for matrices and positive maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06349","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":"sha256:8c5f8b539841f2607ca88e1859714282588324a98bf490d8bbb968f8c866acaf","target":"record","created_at":"2026-05-18T01:04:08Z","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":"e2c578c00fd41aa9b71967c7d144d1ece678a3b52a67a27d446a555ad58e2194","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-20T20:41:04Z","title_canon_sha256":"4613d4d857ad666cadede745c295e4fa9110726001cec8cc468ca27678b37752"},"schema_version":"1.0","source":{"id":"1609.06349","kind":"arxiv","version":1}},"canonical_sha256":"7f50b34922ac937e8ec6262aa474ec7c55f3d7d20f4217279fb2001ae1512cb8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f50b34922ac937e8ec6262aa474ec7c55f3d7d20f4217279fb2001ae1512cb8","first_computed_at":"2026-05-18T01:04:08.516540Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:08.516540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CF190MTGZHRq/2ik351tg14tYXj3maWnod+ei4LszH2kqPyTD9dxKiT2vA+ajPmMcJBEw5wrdDTwaaj/N9n6Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:08.517324Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.06349","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c5f8b539841f2607ca88e1859714282588324a98bf490d8bbb968f8c866acaf","sha256:3b7027650dc17fc89e28a235861756f7c15b1f22e320a735d166de968126545f"],"state_sha256":"44050926f18d5dcbdc44b6cb74389c8e448f03251986150f9a75db3ec6cc41ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iHiL0BO4ZinuIfnBuqd0ha7LS5VrAVQHH4JqiKKgN/6rLzHy8zX92/nMf/bAHTmevqCHDdC6uJ6y+lHwkM32Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T18:40:04.561142Z","bundle_sha256":"8452c03900c2de5fa9adb0a2ca6492505b8e338e4710100fc473d732d6cd8011"}}