{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:MWJSW32RWV534YUTZ2HHSL7PT5","short_pith_number":"pith:MWJSW32R","canonical_record":{"source":{"id":"1908.08534","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-22T20:42:51Z","cross_cats_sorted":[],"title_canon_sha256":"7ae70edd1d429b905a8f11c1e065339d5ee97415eef9431cf97d6a05887ff84d","abstract_canon_sha256":"0d88d13b9e30168d4ff3b4242380d6c235169e7f400c6356a620fe1f6f694b3f"},"schema_version":"1.0"},"canonical_sha256":"65932b6f51b57bbe6293ce8e792fef9f4d4bca67479103a627d1e82a9e6c90ab","source":{"kind":"arxiv","id":"1908.08534","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.08534","created_at":"2026-07-05T10:52:07Z"},{"alias_kind":"arxiv_version","alias_value":"1908.08534v7","created_at":"2026-07-05T10:52:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08534","created_at":"2026-07-05T10:52:07Z"},{"alias_kind":"pith_short_12","alias_value":"MWJSW32RWV53","created_at":"2026-07-05T10:52:07Z"},{"alias_kind":"pith_short_16","alias_value":"MWJSW32RWV534YUT","created_at":"2026-07-05T10:52:07Z"},{"alias_kind":"pith_short_8","alias_value":"MWJSW32R","created_at":"2026-07-05T10:52:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:MWJSW32RWV534YUTZ2HHSL7PT5","target":"record","payload":{"canonical_record":{"source":{"id":"1908.08534","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-22T20:42:51Z","cross_cats_sorted":[],"title_canon_sha256":"7ae70edd1d429b905a8f11c1e065339d5ee97415eef9431cf97d6a05887ff84d","abstract_canon_sha256":"0d88d13b9e30168d4ff3b4242380d6c235169e7f400c6356a620fe1f6f694b3f"},"schema_version":"1.0"},"canonical_sha256":"65932b6f51b57bbe6293ce8e792fef9f4d4bca67479103a627d1e82a9e6c90ab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:52:07.213601Z","signature_b64":"a+rprF0HsoPMt6xQ5aGGLqms3JOU56yfSuYquTuio/aUIm1gas2BnLeDfgmb1IVJ44lDGcNAanjMK6JnWYAtAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65932b6f51b57bbe6293ce8e792fef9f4d4bca67479103a627d1e82a9e6c90ab","last_reissued_at":"2026-07-05T10:52:07.213114Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:52:07.213114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.08534","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:52:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l1CN+sRpXuIMb4Inv7qEmv5Sm5saQ4ANPECbbtUPWFrkVadjUocKuMZOeCrfrh3EKQsFH7RzChMg9lwci8+sCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T20:44:11.944459Z"},"content_sha256":"6094549fe5946bffbfb0aa32724d4a289b2c6e2d96a55b36e53e43e1048c104e","schema_version":"1.0","event_id":"sha256:6094549fe5946bffbfb0aa32724d4a289b2c6e2d96a55b36e53e43e1048c104e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:MWJSW32RWV534YUTZ2HHSL7PT5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Proof of Brouwers Conjecture (BC) for all graphs with number of vertices n > n_0 assuming that BC holds for n< n_0 for some n_0","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexander Pchelintsev, Llohann D. Speran\\c{c}a, Vladimir Blinovsky","submitted_at":"2019-08-22T20:42:51Z","abstract_excerpt":"Assuming that Brouwers Conjecture the upper bound for the sum of t< n largest eigenvalues of Laplacian graph on n vertices true for n <n_0, we prove the Brouwers Conjecture BC for n > n_0 for some fixed n_0"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08534","kind":"arxiv","version":7},"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/1908.08534/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":"2026-07-05T10:52:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vd27/WrID7ytF+PASFYrzKo5S/UTFOZymXS1o8ph09mCJc/w9szA++Xcfc+gyOksRRE73ZYjLV0tSzU9xrsADA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T20:44:11.945286Z"},"content_sha256":"4be8cfeb2dd03859099c28bb052685885da20d95da207efd85cec2aae36250d7","schema_version":"1.0","event_id":"sha256:4be8cfeb2dd03859099c28bb052685885da20d95da207efd85cec2aae36250d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MWJSW32RWV534YUTZ2HHSL7PT5/bundle.json","state_url":"https://pith.science/pith/MWJSW32RWV534YUTZ2HHSL7PT5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MWJSW32RWV534YUTZ2HHSL7PT5/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":"2026-08-15T20:44:11Z","links":{"resolver":"https://pith.science/pith/MWJSW32RWV534YUTZ2HHSL7PT5","bundle":"https://pith.science/pith/MWJSW32RWV534YUTZ2HHSL7PT5/bundle.json","state":"https://pith.science/pith/MWJSW32RWV534YUTZ2HHSL7PT5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MWJSW32RWV534YUTZ2HHSL7PT5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MWJSW32RWV534YUTZ2HHSL7PT5","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":"0d88d13b9e30168d4ff3b4242380d6c235169e7f400c6356a620fe1f6f694b3f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-22T20:42:51Z","title_canon_sha256":"7ae70edd1d429b905a8f11c1e065339d5ee97415eef9431cf97d6a05887ff84d"},"schema_version":"1.0","source":{"id":"1908.08534","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.08534","created_at":"2026-07-05T10:52:07Z"},{"alias_kind":"arxiv_version","alias_value":"1908.08534v7","created_at":"2026-07-05T10:52:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08534","created_at":"2026-07-05T10:52:07Z"},{"alias_kind":"pith_short_12","alias_value":"MWJSW32RWV53","created_at":"2026-07-05T10:52:07Z"},{"alias_kind":"pith_short_16","alias_value":"MWJSW32RWV534YUT","created_at":"2026-07-05T10:52:07Z"},{"alias_kind":"pith_short_8","alias_value":"MWJSW32R","created_at":"2026-07-05T10:52:07Z"}],"graph_snapshots":[{"event_id":"sha256:4be8cfeb2dd03859099c28bb052685885da20d95da207efd85cec2aae36250d7","target":"graph","created_at":"2026-07-05T10:52:07Z","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/1908.08534/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Assuming that Brouwers Conjecture the upper bound for the sum of t< n largest eigenvalues of Laplacian graph on n vertices true for n <n_0, we prove the Brouwers Conjecture BC for n > n_0 for some fixed n_0","authors_text":"Alexander Pchelintsev, Llohann D. Speran\\c{c}a, Vladimir Blinovsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-22T20:42:51Z","title":"Proof of Brouwers Conjecture (BC) for all graphs with number of vertices n > n_0 assuming that BC holds for n< n_0 for some n_0"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08534","kind":"arxiv","version":7},"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":"sha256:6094549fe5946bffbfb0aa32724d4a289b2c6e2d96a55b36e53e43e1048c104e","target":"record","created_at":"2026-07-05T10:52:07Z","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":"0d88d13b9e30168d4ff3b4242380d6c235169e7f400c6356a620fe1f6f694b3f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-22T20:42:51Z","title_canon_sha256":"7ae70edd1d429b905a8f11c1e065339d5ee97415eef9431cf97d6a05887ff84d"},"schema_version":"1.0","source":{"id":"1908.08534","kind":"arxiv","version":7}},"canonical_sha256":"65932b6f51b57bbe6293ce8e792fef9f4d4bca67479103a627d1e82a9e6c90ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65932b6f51b57bbe6293ce8e792fef9f4d4bca67479103a627d1e82a9e6c90ab","first_computed_at":"2026-07-05T10:52:07.213114Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:52:07.213114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a+rprF0HsoPMt6xQ5aGGLqms3JOU56yfSuYquTuio/aUIm1gas2BnLeDfgmb1IVJ44lDGcNAanjMK6JnWYAtAA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:52:07.213601Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.08534","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6094549fe5946bffbfb0aa32724d4a289b2c6e2d96a55b36e53e43e1048c104e","sha256:4be8cfeb2dd03859099c28bb052685885da20d95da207efd85cec2aae36250d7"],"state_sha256":"1fa26c2dc4ec5c004b2bae2a0edd2105fd30f41e98006e8649f5e8cb33d21993"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fMSLRLlPujrI85umfoh2thwKKw5CrrwrfRHXa8FSVYRuY0Ifb78WwYApp7194A01kR/3mqQkjwjUmrPfuEn0Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T20:44:11.951290Z","bundle_sha256":"9e5b67fdd98800a3acf9e30a94a1f808a4f291eeb0285175dbbcc7cfa3dc713d"}}