{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:I37QP66T7TYPHHF6J3IBA72MYT","short_pith_number":"pith:I37QP66T","canonical_record":{"source":{"id":"1906.05368","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-12T20:29:11Z","cross_cats_sorted":[],"title_canon_sha256":"ab7cea449516b6fabf24bf78e04653f28c781a93cd5a6f38987d938196b1c299","abstract_canon_sha256":"970e079aca5a858fc7c97137960b199342d37d5460202aaf98f6a787725ced5e"},"schema_version":"1.0"},"canonical_sha256":"46ff07fbd3fcf0f39cbe4ed0107f4cc4d3a081af5920cae99204ef2b356884c7","source":{"kind":"arxiv","id":"1906.05368","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.05368","created_at":"2026-05-17T23:43:25Z"},{"alias_kind":"arxiv_version","alias_value":"1906.05368v1","created_at":"2026-05-17T23:43:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.05368","created_at":"2026-05-17T23:43:25Z"},{"alias_kind":"pith_short_12","alias_value":"I37QP66T7TYP","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"I37QP66T7TYPHHF6","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"I37QP66T","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:I37QP66T7TYPHHF6J3IBA72MYT","target":"record","payload":{"canonical_record":{"source":{"id":"1906.05368","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-12T20:29:11Z","cross_cats_sorted":[],"title_canon_sha256":"ab7cea449516b6fabf24bf78e04653f28c781a93cd5a6f38987d938196b1c299","abstract_canon_sha256":"970e079aca5a858fc7c97137960b199342d37d5460202aaf98f6a787725ced5e"},"schema_version":"1.0"},"canonical_sha256":"46ff07fbd3fcf0f39cbe4ed0107f4cc4d3a081af5920cae99204ef2b356884c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:25.463372Z","signature_b64":"jw2f8x8gXkWn2I/HKfBn29ILXwGxH2dnNVLfBNM0xhle/mXaXZctjqpyUzljA9wlf+1DxnLlUQe5v9YL6+4EDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46ff07fbd3fcf0f39cbe4ed0107f4cc4d3a081af5920cae99204ef2b356884c7","last_reissued_at":"2026-05-17T23:43:25.462843Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:25.462843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.05368","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":"2026-05-17T23:43:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X09xEeShpBfdEoB7sbnwxr4hmILgMyl7dZa8i1IEb+3jJT4lCfwZc9uLVJnXHShPGrC2I0z5RAZJkHvsVXaeAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T04:27:07.100058Z"},"content_sha256":"3af123f028f76ded58b6d3d49ac8098c4df733b16744376a05d195c7ba2cdbc5","schema_version":"1.0","event_id":"sha256:3af123f028f76ded58b6d3d49ac8098c4df733b16744376a05d195c7ba2cdbc5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:I37QP66T7TYPHHF6J3IBA72MYT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Brouwer's conjecture holds asymptotically almost surely","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Israel Rocha","submitted_at":"2019-06-12T20:29:11Z","abstract_excerpt":"We show that for a sequence of random graphs Brouwer's conjecture holds true with probability tending to one as the number of vertices tends to infinity. Surprisingly, it was found that a similar statement holds true for weighted graphs with possible negative weights as well. For graphs with a fixed number of vertices, the result implies that there are constants $C>0$ and $n_{0}$ such that if $n\\geq n_{0}$ then among all $2^{{n \\choose 2}}$ graphs with $n$ vertices, at least $\\left(1-\\exp\\left(-Cn\\right)\\right)2^{{n \\choose 2}}$ graphs satisfy Brouwer's conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.05368","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":"2026-05-17T23:43:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lfT9nKVZot77pjUo3KLjwWoXaX6XC0pRxGma7MWgiq+CPCIehLawv8WZJdjP4c8K/crZ+nX0LO99Fh/epeklBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T04:27:07.100729Z"},"content_sha256":"ace93c093d6bb770d886ecb959d3f149f2a826575e24e7c3b9ca7d5ea5a4d9eb","schema_version":"1.0","event_id":"sha256:ace93c093d6bb770d886ecb959d3f149f2a826575e24e7c3b9ca7d5ea5a4d9eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I37QP66T7TYPHHF6J3IBA72MYT/bundle.json","state_url":"https://pith.science/pith/I37QP66T7TYPHHF6J3IBA72MYT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I37QP66T7TYPHHF6J3IBA72MYT/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":"2026-06-09T04:27:07Z","links":{"resolver":"https://pith.science/pith/I37QP66T7TYPHHF6J3IBA72MYT","bundle":"https://pith.science/pith/I37QP66T7TYPHHF6J3IBA72MYT/bundle.json","state":"https://pith.science/pith/I37QP66T7TYPHHF6J3IBA72MYT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I37QP66T7TYPHHF6J3IBA72MYT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:I37QP66T7TYPHHF6J3IBA72MYT","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":"970e079aca5a858fc7c97137960b199342d37d5460202aaf98f6a787725ced5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-12T20:29:11Z","title_canon_sha256":"ab7cea449516b6fabf24bf78e04653f28c781a93cd5a6f38987d938196b1c299"},"schema_version":"1.0","source":{"id":"1906.05368","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.05368","created_at":"2026-05-17T23:43:25Z"},{"alias_kind":"arxiv_version","alias_value":"1906.05368v1","created_at":"2026-05-17T23:43:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.05368","created_at":"2026-05-17T23:43:25Z"},{"alias_kind":"pith_short_12","alias_value":"I37QP66T7TYP","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"I37QP66T7TYPHHF6","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"I37QP66T","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:ace93c093d6bb770d886ecb959d3f149f2a826575e24e7c3b9ca7d5ea5a4d9eb","target":"graph","created_at":"2026-05-17T23:43:25Z","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 show that for a sequence of random graphs Brouwer's conjecture holds true with probability tending to one as the number of vertices tends to infinity. Surprisingly, it was found that a similar statement holds true for weighted graphs with possible negative weights as well. For graphs with a fixed number of vertices, the result implies that there are constants $C>0$ and $n_{0}$ such that if $n\\geq n_{0}$ then among all $2^{{n \\choose 2}}$ graphs with $n$ vertices, at least $\\left(1-\\exp\\left(-Cn\\right)\\right)2^{{n \\choose 2}}$ graphs satisfy Brouwer's conjecture.","authors_text":"Israel Rocha","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-12T20:29:11Z","title":"Brouwer's conjecture holds asymptotically almost surely"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.05368","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":"sha256:3af123f028f76ded58b6d3d49ac8098c4df733b16744376a05d195c7ba2cdbc5","target":"record","created_at":"2026-05-17T23:43:25Z","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":"970e079aca5a858fc7c97137960b199342d37d5460202aaf98f6a787725ced5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-12T20:29:11Z","title_canon_sha256":"ab7cea449516b6fabf24bf78e04653f28c781a93cd5a6f38987d938196b1c299"},"schema_version":"1.0","source":{"id":"1906.05368","kind":"arxiv","version":1}},"canonical_sha256":"46ff07fbd3fcf0f39cbe4ed0107f4cc4d3a081af5920cae99204ef2b356884c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46ff07fbd3fcf0f39cbe4ed0107f4cc4d3a081af5920cae99204ef2b356884c7","first_computed_at":"2026-05-17T23:43:25.462843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:25.462843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jw2f8x8gXkWn2I/HKfBn29ILXwGxH2dnNVLfBNM0xhle/mXaXZctjqpyUzljA9wlf+1DxnLlUQe5v9YL6+4EDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:25.463372Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.05368","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3af123f028f76ded58b6d3d49ac8098c4df733b16744376a05d195c7ba2cdbc5","sha256:ace93c093d6bb770d886ecb959d3f149f2a826575e24e7c3b9ca7d5ea5a4d9eb"],"state_sha256":"a410a11d26db7c7f06379a58052fb79f10ddbfa19d84f8c6566964e7dfc9a9db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aN4jCa+T3bnjeEsgCdiITS799kywfmvK+JqanD69LMpAiiRlE/JjrYmW+OkvGhuWHBU+raYzWuLP3MGafG4tAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T04:27:07.104349Z","bundle_sha256":"30ee83984384fd656808630362eac15beb1d6e0f7837db672f521590724f4a66"}}