{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:GNIZQ34D7RHODHDQME3SZWZZUD","short_pith_number":"pith:GNIZQ34D","canonical_record":{"source":{"id":"2406.09851","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-06-14T09:01:25Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"26781e99ee2a618666069c5ff4ce9ef55287b50fd49f9d3e5d95b1659fd6d615","abstract_canon_sha256":"11c84b5bee9b2b9643c08b2fa324ea211d712ba6932ddae63a2151f434945007"},"schema_version":"1.0"},"canonical_sha256":"3351986f83fc4ee19c7061372cdb39a0e4852f55c0a2c2c894b990e96830482b","source":{"kind":"arxiv","id":"2406.09851","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.09851","created_at":"2026-07-05T08:32:43Z"},{"alias_kind":"arxiv_version","alias_value":"2406.09851v2","created_at":"2026-07-05T08:32:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.09851","created_at":"2026-07-05T08:32:43Z"},{"alias_kind":"pith_short_12","alias_value":"GNIZQ34D7RHO","created_at":"2026-07-05T08:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"GNIZQ34D7RHODHDQ","created_at":"2026-07-05T08:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"GNIZQ34D","created_at":"2026-07-05T08:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:GNIZQ34D7RHODHDQME3SZWZZUD","target":"record","payload":{"canonical_record":{"source":{"id":"2406.09851","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-06-14T09:01:25Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"26781e99ee2a618666069c5ff4ce9ef55287b50fd49f9d3e5d95b1659fd6d615","abstract_canon_sha256":"11c84b5bee9b2b9643c08b2fa324ea211d712ba6932ddae63a2151f434945007"},"schema_version":"1.0"},"canonical_sha256":"3351986f83fc4ee19c7061372cdb39a0e4852f55c0a2c2c894b990e96830482b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:32:43.024577Z","signature_b64":"Mmn3YybDSS3g4FalvhxTQydyJ97wIFuKItqhcPrXqWnINd7fNqTuu9lYKk9eE6Z0cU6O8Q5foMJDuZJBiVszDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3351986f83fc4ee19c7061372cdb39a0e4852f55c0a2c2c894b990e96830482b","last_reissued_at":"2026-07-05T08:32:43.024051Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:32:43.024051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.09851","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":"2026-07-05T08:32:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P8c4YF5/FiXTaY5rCfMomlRKLOC+2a2JPoM/s94d5BbtlnUFXuawL8y+dYHt23buEMr6M+SIGVHVUFH2duyABw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T04:29:36.606399Z"},"content_sha256":"aa0354f95f098b2585b58cda76fc58adb2e5e1e913068e21dd3f86b240674a23","schema_version":"1.0","event_id":"sha256:aa0354f95f098b2585b58cda76fc58adb2e5e1e913068e21dd3f86b240674a23"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:GNIZQ34D7RHODHDQME3SZWZZUD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large deviations for the largest singular value of sparse non-Hermitian matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Hyungwon Han","submitted_at":"2024-06-14T09:01:25Z","abstract_excerpt":"We prove a large deviation principle for the largest singular value of sparse non-Hermitian random matrices, or directed Erd\\H{o}s-R\\'enyi networks in the constant average degree regime $p =\\frac{d}{n}$ where $d$ is fixed. Entries are assumed to have Weibull distributions with tail decaying at rate $e^{-t^{\\alpha}}$ for $\\alpha >0$. While the law of large number results agree with the largest eigenvalue of sparse Hermitian matrices given in (Ganguly and Nam, '22) and (Ganguly, Hiesmayr and Nam, '22), large deviation results are surprisingly simpler, exhibiting a single transition at $\\alpha =2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.09851","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.09851/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T08:32:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wZwScAqSX3dwup009iK9QH+c7xEHVhPAiD/OjAJXC5OXJ7w6J81dGFOWcUfgA8VQA3HP+o8SR90SZtY0RyA6AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T04:29:36.606909Z"},"content_sha256":"1be3b39ba07a337f5c7c40a5a43224bab6e066e43b1886e8615b985144a03d8c","schema_version":"1.0","event_id":"sha256:1be3b39ba07a337f5c7c40a5a43224bab6e066e43b1886e8615b985144a03d8c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GNIZQ34D7RHODHDQME3SZWZZUD/bundle.json","state_url":"https://pith.science/pith/GNIZQ34D7RHODHDQME3SZWZZUD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GNIZQ34D7RHODHDQME3SZWZZUD/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":"2026-08-13T04:29:36Z","links":{"resolver":"https://pith.science/pith/GNIZQ34D7RHODHDQME3SZWZZUD","bundle":"https://pith.science/pith/GNIZQ34D7RHODHDQME3SZWZZUD/bundle.json","state":"https://pith.science/pith/GNIZQ34D7RHODHDQME3SZWZZUD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GNIZQ34D7RHODHDQME3SZWZZUD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:GNIZQ34D7RHODHDQME3SZWZZUD","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":"11c84b5bee9b2b9643c08b2fa324ea211d712ba6932ddae63a2151f434945007","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-06-14T09:01:25Z","title_canon_sha256":"26781e99ee2a618666069c5ff4ce9ef55287b50fd49f9d3e5d95b1659fd6d615"},"schema_version":"1.0","source":{"id":"2406.09851","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.09851","created_at":"2026-07-05T08:32:43Z"},{"alias_kind":"arxiv_version","alias_value":"2406.09851v2","created_at":"2026-07-05T08:32:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.09851","created_at":"2026-07-05T08:32:43Z"},{"alias_kind":"pith_short_12","alias_value":"GNIZQ34D7RHO","created_at":"2026-07-05T08:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"GNIZQ34D7RHODHDQ","created_at":"2026-07-05T08:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"GNIZQ34D","created_at":"2026-07-05T08:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:1be3b39ba07a337f5c7c40a5a43224bab6e066e43b1886e8615b985144a03d8c","target":"graph","created_at":"2026-07-05T08:32:43Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2406.09851/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a large deviation principle for the largest singular value of sparse non-Hermitian random matrices, or directed Erd\\H{o}s-R\\'enyi networks in the constant average degree regime $p =\\frac{d}{n}$ where $d$ is fixed. Entries are assumed to have Weibull distributions with tail decaying at rate $e^{-t^{\\alpha}}$ for $\\alpha >0$. While the law of large number results agree with the largest eigenvalue of sparse Hermitian matrices given in (Ganguly and Nam, '22) and (Ganguly, Hiesmayr and Nam, '22), large deviation results are surprisingly simpler, exhibiting a single transition at $\\alpha =2","authors_text":"Hyungwon Han","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-06-14T09:01:25Z","title":"Large deviations for the largest singular value of sparse non-Hermitian matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.09851","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:aa0354f95f098b2585b58cda76fc58adb2e5e1e913068e21dd3f86b240674a23","target":"record","created_at":"2026-07-05T08:32:43Z","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":"11c84b5bee9b2b9643c08b2fa324ea211d712ba6932ddae63a2151f434945007","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-06-14T09:01:25Z","title_canon_sha256":"26781e99ee2a618666069c5ff4ce9ef55287b50fd49f9d3e5d95b1659fd6d615"},"schema_version":"1.0","source":{"id":"2406.09851","kind":"arxiv","version":2}},"canonical_sha256":"3351986f83fc4ee19c7061372cdb39a0e4852f55c0a2c2c894b990e96830482b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3351986f83fc4ee19c7061372cdb39a0e4852f55c0a2c2c894b990e96830482b","first_computed_at":"2026-07-05T08:32:43.024051Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:32:43.024051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Mmn3YybDSS3g4FalvhxTQydyJ97wIFuKItqhcPrXqWnINd7fNqTuu9lYKk9eE6Z0cU6O8Q5foMJDuZJBiVszDw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:32:43.024577Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.09851","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa0354f95f098b2585b58cda76fc58adb2e5e1e913068e21dd3f86b240674a23","sha256:1be3b39ba07a337f5c7c40a5a43224bab6e066e43b1886e8615b985144a03d8c"],"state_sha256":"8f850289db8c4b0301c36e82cb303d0fddf837c229aa1ed5240744b56c8b808a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r/0Z5M+P9HaFYhcoyPhojlbz5DgJVyCQYnHyV+dhjxWewOaLWiwNq65ufm691eX1ku04qOiUK4kqk3+d2gZuBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T04:29:36.611859Z","bundle_sha256":"8af29d8a256b46318e5b94607da2d76c4a1a8a2a6863c4ad1c62f64ba3aa889e"}}