{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:FUVNP7NA4IC3XHBCDP3E3AVGSH","short_pith_number":"pith:FUVNP7NA","canonical_record":{"source":{"id":"1907.08306","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-07-18T22:04:21Z","cross_cats_sorted":["stat.CO"],"title_canon_sha256":"98ee6ea8911db42761591906a7d25a6bdf1539e1ec12c4e7b854493811768109","abstract_canon_sha256":"51117a68e552537cd674d920ae6c4bce4892376cee092b9d0dfcee678d36eb1f"},"schema_version":"1.0"},"canonical_sha256":"2d2ad7fda0e205bb9c221bf64d82a691c65ec932b9985dfa0ae51c0f1e7cc5d1","source":{"kind":"arxiv","id":"1907.08306","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.08306","created_at":"2026-05-17T23:40:10Z"},{"alias_kind":"arxiv_version","alias_value":"1907.08306v1","created_at":"2026-05-17T23:40:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.08306","created_at":"2026-05-17T23:40:10Z"},{"alias_kind":"pith_short_12","alias_value":"FUVNP7NA4IC3","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"FUVNP7NA4IC3XHBC","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"FUVNP7NA","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:FUVNP7NA4IC3XHBCDP3E3AVGSH","target":"record","payload":{"canonical_record":{"source":{"id":"1907.08306","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-07-18T22:04:21Z","cross_cats_sorted":["stat.CO"],"title_canon_sha256":"98ee6ea8911db42761591906a7d25a6bdf1539e1ec12c4e7b854493811768109","abstract_canon_sha256":"51117a68e552537cd674d920ae6c4bce4892376cee092b9d0dfcee678d36eb1f"},"schema_version":"1.0"},"canonical_sha256":"2d2ad7fda0e205bb9c221bf64d82a691c65ec932b9985dfa0ae51c0f1e7cc5d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:10.273562Z","signature_b64":"b0qJStaUO/o8on2Lhl7RFKpf4KqWmrDBIHf9T5cXI4VB/rIa68CFPcbmE+eieMtGNO4oKo73zMV8K9gK3tYKCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d2ad7fda0e205bb9c221bf64d82a691c65ec932b9985dfa0ae51c0f1e7cc5d1","last_reissued_at":"2026-05-17T23:40:10.273048Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:10.273048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.08306","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":"2026-05-17T23:40:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NypY5bRHhm90AGhCN0dQyEYIyFmO2+/iaJur9C5k65fDSbiEj5CEy7gyHK7eEwXQoqyVcCNBwbuLH7/PxKu7AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:57:45.376367Z"},"content_sha256":"47e4e0b53878902ee566afb6b1b5f633bf0870d44098139bff891b1591662a59","schema_version":"1.0","event_id":"sha256:47e4e0b53878902ee566afb6b1b5f633bf0870d44098139bff891b1591662a59"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:FUVNP7NA4IC3XHBCDP3E3AVGSH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Polynomial Time Algorithm for Log-Concave Maximum Likelihood via Locally Exponential Families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.CO"],"primary_cat":"cs.DS","authors_text":"Alistair Stewart, Anastasios Sidiropoulos, Brian Axelrod, Gregory Valiant, Ilias Diakonikolas","submitted_at":"2019-07-18T22:04:21Z","abstract_excerpt":"We consider the problem of computing the maximum likelihood multivariate log-concave distribution for a set of points. Specifically, we present an algorithm which, given $n$ points in $\\mathbb{R}^d$ and an accuracy parameter $\\epsilon>0$, runs in time $poly(n,d,1/\\epsilon),$ and returns a log-concave distribution which, with high probability, has the property that the likelihood of the $n$ points under the returned distribution is at most an additive $\\epsilon$ less than the maximum likelihood that could be achieved via any log-concave distribution. This is the first computationally efficient "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08306","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":"2026-05-17T23:40:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JIocVXbr/uYHARG4BtWDvi1k/kD3YWHGvoCz39/u7ACzM82yIT21eZjGytjU5eaYRJckYjxlGIrNWczcN0c3Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:57:45.377038Z"},"content_sha256":"c5233ddea9905c1110ff2b8f671608a5ded97920b57f8429ac4ba2ce928ee4b4","schema_version":"1.0","event_id":"sha256:c5233ddea9905c1110ff2b8f671608a5ded97920b57f8429ac4ba2ce928ee4b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FUVNP7NA4IC3XHBCDP3E3AVGSH/bundle.json","state_url":"https://pith.science/pith/FUVNP7NA4IC3XHBCDP3E3AVGSH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FUVNP7NA4IC3XHBCDP3E3AVGSH/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":"2026-05-26T21:57:45Z","links":{"resolver":"https://pith.science/pith/FUVNP7NA4IC3XHBCDP3E3AVGSH","bundle":"https://pith.science/pith/FUVNP7NA4IC3XHBCDP3E3AVGSH/bundle.json","state":"https://pith.science/pith/FUVNP7NA4IC3XHBCDP3E3AVGSH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FUVNP7NA4IC3XHBCDP3E3AVGSH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:FUVNP7NA4IC3XHBCDP3E3AVGSH","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":"51117a68e552537cd674d920ae6c4bce4892376cee092b9d0dfcee678d36eb1f","cross_cats_sorted":["stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-07-18T22:04:21Z","title_canon_sha256":"98ee6ea8911db42761591906a7d25a6bdf1539e1ec12c4e7b854493811768109"},"schema_version":"1.0","source":{"id":"1907.08306","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.08306","created_at":"2026-05-17T23:40:10Z"},{"alias_kind":"arxiv_version","alias_value":"1907.08306v1","created_at":"2026-05-17T23:40:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.08306","created_at":"2026-05-17T23:40:10Z"},{"alias_kind":"pith_short_12","alias_value":"FUVNP7NA4IC3","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"FUVNP7NA4IC3XHBC","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"FUVNP7NA","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:c5233ddea9905c1110ff2b8f671608a5ded97920b57f8429ac4ba2ce928ee4b4","target":"graph","created_at":"2026-05-17T23:40:10Z","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":"We consider the problem of computing the maximum likelihood multivariate log-concave distribution for a set of points. Specifically, we present an algorithm which, given $n$ points in $\\mathbb{R}^d$ and an accuracy parameter $\\epsilon>0$, runs in time $poly(n,d,1/\\epsilon),$ and returns a log-concave distribution which, with high probability, has the property that the likelihood of the $n$ points under the returned distribution is at most an additive $\\epsilon$ less than the maximum likelihood that could be achieved via any log-concave distribution. This is the first computationally efficient ","authors_text":"Alistair Stewart, Anastasios Sidiropoulos, Brian Axelrod, Gregory Valiant, Ilias Diakonikolas","cross_cats":["stat.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-07-18T22:04:21Z","title":"A Polynomial Time Algorithm for Log-Concave Maximum Likelihood via Locally Exponential Families"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08306","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":"sha256:47e4e0b53878902ee566afb6b1b5f633bf0870d44098139bff891b1591662a59","target":"record","created_at":"2026-05-17T23:40:10Z","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":"51117a68e552537cd674d920ae6c4bce4892376cee092b9d0dfcee678d36eb1f","cross_cats_sorted":["stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-07-18T22:04:21Z","title_canon_sha256":"98ee6ea8911db42761591906a7d25a6bdf1539e1ec12c4e7b854493811768109"},"schema_version":"1.0","source":{"id":"1907.08306","kind":"arxiv","version":1}},"canonical_sha256":"2d2ad7fda0e205bb9c221bf64d82a691c65ec932b9985dfa0ae51c0f1e7cc5d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d2ad7fda0e205bb9c221bf64d82a691c65ec932b9985dfa0ae51c0f1e7cc5d1","first_computed_at":"2026-05-17T23:40:10.273048Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:10.273048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b0qJStaUO/o8on2Lhl7RFKpf4KqWmrDBIHf9T5cXI4VB/rIa68CFPcbmE+eieMtGNO4oKo73zMV8K9gK3tYKCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:10.273562Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.08306","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47e4e0b53878902ee566afb6b1b5f633bf0870d44098139bff891b1591662a59","sha256:c5233ddea9905c1110ff2b8f671608a5ded97920b57f8429ac4ba2ce928ee4b4"],"state_sha256":"209176639428b1bc9ed637b8fa3f08aa610ffaf6c508c40dcada936c39bf7a49"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x+wTpjBhZE+v4ZO/EjY1KrYYONfM6HIl6zCIhwfcuer2QEsi1p2CzU7Wmrx7BGE1eYid1ppFLHd89YqZuuoBCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T21:57:45.380617Z","bundle_sha256":"492d7356393d5889281aa110b6530a7df1007a5cb3f365e623c414a0f2ecc7d6"}}