{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:VA3MBRFAFZHLMU6LXMRIEH3JNI","short_pith_number":"pith:VA3MBRFA","canonical_record":{"source":{"id":"1904.04559","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-09T09:24:48Z","cross_cats_sorted":[],"title_canon_sha256":"7b930bfedf93893bbf68453bb0af745dbe8f942e336b386ed54a83184ccf5609","abstract_canon_sha256":"dd36b1d4d59ed54671ddb70909e3a7f575aa537571431c2bf5c320adb164e84a"},"schema_version":"1.0"},"canonical_sha256":"a836c0c4a02e4eb653cbbb22821f696a0a475743b65449fea3d32f9a18285c15","source":{"kind":"arxiv","id":"1904.04559","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.04559","created_at":"2026-05-17T23:48:58Z"},{"alias_kind":"arxiv_version","alias_value":"1904.04559v1","created_at":"2026-05-17T23:48:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.04559","created_at":"2026-05-17T23:48:58Z"},{"alias_kind":"pith_short_12","alias_value":"VA3MBRFAFZHL","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VA3MBRFAFZHLMU6L","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VA3MBRFA","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:VA3MBRFAFZHLMU6LXMRIEH3JNI","target":"record","payload":{"canonical_record":{"source":{"id":"1904.04559","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-09T09:24:48Z","cross_cats_sorted":[],"title_canon_sha256":"7b930bfedf93893bbf68453bb0af745dbe8f942e336b386ed54a83184ccf5609","abstract_canon_sha256":"dd36b1d4d59ed54671ddb70909e3a7f575aa537571431c2bf5c320adb164e84a"},"schema_version":"1.0"},"canonical_sha256":"a836c0c4a02e4eb653cbbb22821f696a0a475743b65449fea3d32f9a18285c15","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:58.754775Z","signature_b64":"bHwpYhSV5pJtPey4HC7DJLknv3whB0heFzfo23g9P9raWN3qE2rfriSicjZMJLuf1NwAK5JglzNfJb+f0f0CAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a836c0c4a02e4eb653cbbb22821f696a0a475743b65449fea3d32f9a18285c15","last_reissued_at":"2026-05-17T23:48:58.754381Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:58.754381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.04559","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":"2026-05-17T23:48:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lCl9dSbeNwYqiDKhg0iYQxB22pPfU4YShOiMdNjjvV8L/T0Wewsh/GazpTwHaZgqO9r4w8b9nxYrPAweBhr6Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T20:23:20.373233Z"},"content_sha256":"97d8bb49591c77fe46da2d7ce0653c211f0c36e1a775cfb1d2177e9bbc9bdce1","schema_version":"1.0","event_id":"sha256:97d8bb49591c77fe46da2d7ce0653c211f0c36e1a775cfb1d2177e9bbc9bdce1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:VA3MBRFAFZHLMU6LXMRIEH3JNI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positive solutions for large random linear systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jamal Najim (LIGM), Pierre Bizeul (ENS Paris Saclay)","submitted_at":"2019-04-09T09:24:48Z","abstract_excerpt":"Consider a large linear system where $A_n$ is a $n\\times n$ matrix with independent real standard Gaussian entries, $\\boldsymbol{1}_n$ is a $n\\times 1$ vector of ones and with unknown the $n\\times 1$ vector $\\boldsymbol{x}_n$ satisfying$$\\boldsymbol{x}_n = \\boldsymbol{1}_n +\\frac 1{\\alpha_n\\sqrt{n}} A_n \\boldsymbol{x}_n\\, .$$We investigate the (componentwise) positivity of the solution $\\boldsymbol{x}_n$ depending on the scaling factor $\\alpha_n$ as the dimension $n$ goes to $\\infty$. We prove that there is a sharp phase transition at the threshold $\\alpha^*_n =\\sqrt{2\\log n}$: below the thres"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04559","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":"2026-05-17T23:48:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ctu5v9+1btI0p3E1WxJ0OV934wXloWfMqpXhuPE7hLXusa4ceTS9xAd2bnltV+yFWZnuNL3pb4MJsRc7c2ohAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T20:23:20.373725Z"},"content_sha256":"b746c9fb731f5a7393a786083e31e998f0881fc8f54c2deba0d6c84fece542be","schema_version":"1.0","event_id":"sha256:b746c9fb731f5a7393a786083e31e998f0881fc8f54c2deba0d6c84fece542be"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VA3MBRFAFZHLMU6LXMRIEH3JNI/bundle.json","state_url":"https://pith.science/pith/VA3MBRFAFZHLMU6LXMRIEH3JNI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VA3MBRFAFZHLMU6LXMRIEH3JNI/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":"2026-07-01T20:23:20Z","links":{"resolver":"https://pith.science/pith/VA3MBRFAFZHLMU6LXMRIEH3JNI","bundle":"https://pith.science/pith/VA3MBRFAFZHLMU6LXMRIEH3JNI/bundle.json","state":"https://pith.science/pith/VA3MBRFAFZHLMU6LXMRIEH3JNI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VA3MBRFAFZHLMU6LXMRIEH3JNI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VA3MBRFAFZHLMU6LXMRIEH3JNI","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":"dd36b1d4d59ed54671ddb70909e3a7f575aa537571431c2bf5c320adb164e84a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-09T09:24:48Z","title_canon_sha256":"7b930bfedf93893bbf68453bb0af745dbe8f942e336b386ed54a83184ccf5609"},"schema_version":"1.0","source":{"id":"1904.04559","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.04559","created_at":"2026-05-17T23:48:58Z"},{"alias_kind":"arxiv_version","alias_value":"1904.04559v1","created_at":"2026-05-17T23:48:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.04559","created_at":"2026-05-17T23:48:58Z"},{"alias_kind":"pith_short_12","alias_value":"VA3MBRFAFZHL","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VA3MBRFAFZHLMU6L","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VA3MBRFA","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:b746c9fb731f5a7393a786083e31e998f0881fc8f54c2deba0d6c84fece542be","target":"graph","created_at":"2026-05-17T23:48:58Z","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":"Consider a large linear system where $A_n$ is a $n\\times n$ matrix with independent real standard Gaussian entries, $\\boldsymbol{1}_n$ is a $n\\times 1$ vector of ones and with unknown the $n\\times 1$ vector $\\boldsymbol{x}_n$ satisfying$$\\boldsymbol{x}_n = \\boldsymbol{1}_n +\\frac 1{\\alpha_n\\sqrt{n}} A_n \\boldsymbol{x}_n\\, .$$We investigate the (componentwise) positivity of the solution $\\boldsymbol{x}_n$ depending on the scaling factor $\\alpha_n$ as the dimension $n$ goes to $\\infty$. We prove that there is a sharp phase transition at the threshold $\\alpha^*_n =\\sqrt{2\\log n}$: below the thres","authors_text":"Jamal Najim (LIGM), Pierre Bizeul (ENS Paris Saclay)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-09T09:24:48Z","title":"Positive solutions for large random linear systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04559","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":"sha256:97d8bb49591c77fe46da2d7ce0653c211f0c36e1a775cfb1d2177e9bbc9bdce1","target":"record","created_at":"2026-05-17T23:48:58Z","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":"dd36b1d4d59ed54671ddb70909e3a7f575aa537571431c2bf5c320adb164e84a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-09T09:24:48Z","title_canon_sha256":"7b930bfedf93893bbf68453bb0af745dbe8f942e336b386ed54a83184ccf5609"},"schema_version":"1.0","source":{"id":"1904.04559","kind":"arxiv","version":1}},"canonical_sha256":"a836c0c4a02e4eb653cbbb22821f696a0a475743b65449fea3d32f9a18285c15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a836c0c4a02e4eb653cbbb22821f696a0a475743b65449fea3d32f9a18285c15","first_computed_at":"2026-05-17T23:48:58.754381Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:58.754381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bHwpYhSV5pJtPey4HC7DJLknv3whB0heFzfo23g9P9raWN3qE2rfriSicjZMJLuf1NwAK5JglzNfJb+f0f0CAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:58.754775Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.04559","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97d8bb49591c77fe46da2d7ce0653c211f0c36e1a775cfb1d2177e9bbc9bdce1","sha256:b746c9fb731f5a7393a786083e31e998f0881fc8f54c2deba0d6c84fece542be"],"state_sha256":"cc34677f33e53395b34b19603ec871ec4f076a58b60fa512e6408c6cf9bd24f1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GV1FNF5OXT0U/3CH8tyw2cj645MZrXFk9qXhG7KAcY/WmmxzfMdbHbtFQPkYHBSvIjlJ6caevLTkPqKUdS5vDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T20:23:20.380354Z","bundle_sha256":"ff430c116011735428389387830fd2c28fb3bd46f1f87e7c235892187f69257a"}}