{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:33RNGDLM262JLKTS55Y3VOQYWP","short_pith_number":"pith:33RNGDLM","canonical_record":{"source":{"id":"2605.26707","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-26T08:47:25Z","cross_cats_sorted":[],"title_canon_sha256":"117f456dbcc0a13a0c496021e36aa7733176bb6b03a54484f5a2c6c6b791f25b","abstract_canon_sha256":"b36b54ff1309a1810abfe6a679a3d9923e3cda8b94926533aa5ecbe710faa2f0"},"schema_version":"1.0"},"canonical_sha256":"dee2d30d6cd7b495aa72ef71baba18b3f87a24e02a717b680a3cb1a47c106bc6","source":{"kind":"arxiv","id":"2605.26707","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.26707","created_at":"2026-05-27T01:06:08Z"},{"alias_kind":"arxiv_version","alias_value":"2605.26707v1","created_at":"2026-05-27T01:06:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.26707","created_at":"2026-05-27T01:06:08Z"},{"alias_kind":"pith_short_12","alias_value":"33RNGDLM262J","created_at":"2026-05-27T01:06:08Z"},{"alias_kind":"pith_short_16","alias_value":"33RNGDLM262JLKTS","created_at":"2026-05-27T01:06:08Z"},{"alias_kind":"pith_short_8","alias_value":"33RNGDLM","created_at":"2026-05-27T01:06:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:33RNGDLM262JLKTS55Y3VOQYWP","target":"record","payload":{"canonical_record":{"source":{"id":"2605.26707","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-26T08:47:25Z","cross_cats_sorted":[],"title_canon_sha256":"117f456dbcc0a13a0c496021e36aa7733176bb6b03a54484f5a2c6c6b791f25b","abstract_canon_sha256":"b36b54ff1309a1810abfe6a679a3d9923e3cda8b94926533aa5ecbe710faa2f0"},"schema_version":"1.0"},"canonical_sha256":"dee2d30d6cd7b495aa72ef71baba18b3f87a24e02a717b680a3cb1a47c106bc6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T01:06:08.460402Z","signature_b64":"fseVgRnQVz7KggzBwteKON69ZRbPDcWaFl2u18/BJbQ2jwRcPOyD6iR66CIVHG8F7CVUA0eOrjpo9/kXNwDUCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dee2d30d6cd7b495aa72ef71baba18b3f87a24e02a717b680a3cb1a47c106bc6","last_reissued_at":"2026-05-27T01:06:08.459535Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T01:06:08.459535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.26707","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":"2026-05-27T01:06:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CcxyddmM1YvFo5Ksv3SCcr5aMZeFwapsZYgHWLJQUXm9IImcJZE2KM0QsFh0EElemlcX/90JjomuM1xm83eIDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:33:54.895244Z"},"content_sha256":"2d12adc977ddab8abed5520ec05160499fe076d59bf1c75cb6a3d0a1cf221bc6","schema_version":"1.0","event_id":"sha256:2d12adc977ddab8abed5520ec05160499fe076d59bf1c75cb6a3d0a1cf221bc6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:33RNGDLM262JLKTS55Y3VOQYWP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kinkar Chandra Das, Shaowei Sun, Yaping Min","submitted_at":"2026-05-26T08:47:25Z","abstract_excerpt":"This paper establishes new upper bounds for the sum of the $k$ largest eigenvalues of symmetric matrices. When applied to the adjacency matrix of a graph, our results improve upon a related bound due to Mohar {\\bf [On the sum of k largest eigenvalues of graphs and symmetric matrices, J. Combin. Theory Ser. B 99 (2009) 306--313]}. Furthermore, in the case of the Laplacian matrix, we prove that the well-known Brouwer's conjecture {\\bf [Spectra of Graphs, Springer, New York, 2012]} holds for small values of $k$ for almost all graphs, thereby taking a significant step toward its complete resolutio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26707","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.26707/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":"2026-05-27T01:06:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RbG3U7Z2dtdmjfN78GmB7MtychsP6mRJpq8yjBq51Nhiteu795FrjEpy0CVGjG8YnOi1FtN6t6NNfY0e5YvoBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:33:54.895644Z"},"content_sha256":"91842b701d1f90bc9ebaf235d693ddfa96ce3c0413e0dc825304f55053c392ee","schema_version":"1.0","event_id":"sha256:91842b701d1f90bc9ebaf235d693ddfa96ce3c0413e0dc825304f55053c392ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/33RNGDLM262JLKTS55Y3VOQYWP/bundle.json","state_url":"https://pith.science/pith/33RNGDLM262JLKTS55Y3VOQYWP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/33RNGDLM262JLKTS55Y3VOQYWP/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":"2026-06-23T14:33:54Z","links":{"resolver":"https://pith.science/pith/33RNGDLM262JLKTS55Y3VOQYWP","bundle":"https://pith.science/pith/33RNGDLM262JLKTS55Y3VOQYWP/bundle.json","state":"https://pith.science/pith/33RNGDLM262JLKTS55Y3VOQYWP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/33RNGDLM262JLKTS55Y3VOQYWP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:33RNGDLM262JLKTS55Y3VOQYWP","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":"b36b54ff1309a1810abfe6a679a3d9923e3cda8b94926533aa5ecbe710faa2f0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-26T08:47:25Z","title_canon_sha256":"117f456dbcc0a13a0c496021e36aa7733176bb6b03a54484f5a2c6c6b791f25b"},"schema_version":"1.0","source":{"id":"2605.26707","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.26707","created_at":"2026-05-27T01:06:08Z"},{"alias_kind":"arxiv_version","alias_value":"2605.26707v1","created_at":"2026-05-27T01:06:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.26707","created_at":"2026-05-27T01:06:08Z"},{"alias_kind":"pith_short_12","alias_value":"33RNGDLM262J","created_at":"2026-05-27T01:06:08Z"},{"alias_kind":"pith_short_16","alias_value":"33RNGDLM262JLKTS","created_at":"2026-05-27T01:06:08Z"},{"alias_kind":"pith_short_8","alias_value":"33RNGDLM","created_at":"2026-05-27T01:06:08Z"}],"graph_snapshots":[{"event_id":"sha256:91842b701d1f90bc9ebaf235d693ddfa96ce3c0413e0dc825304f55053c392ee","target":"graph","created_at":"2026-05-27T01:06:08Z","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/2605.26707/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper establishes new upper bounds for the sum of the $k$ largest eigenvalues of symmetric matrices. When applied to the adjacency matrix of a graph, our results improve upon a related bound due to Mohar {\\bf [On the sum of k largest eigenvalues of graphs and symmetric matrices, J. Combin. Theory Ser. B 99 (2009) 306--313]}. Furthermore, in the case of the Laplacian matrix, we prove that the well-known Brouwer's conjecture {\\bf [Spectra of Graphs, Springer, New York, 2012]} holds for small values of $k$ for almost all graphs, thereby taking a significant step toward its complete resolutio","authors_text":"Kinkar Chandra Das, Shaowei Sun, Yaping Min","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-26T08:47:25Z","title":"Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26707","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":"sha256:2d12adc977ddab8abed5520ec05160499fe076d59bf1c75cb6a3d0a1cf221bc6","target":"record","created_at":"2026-05-27T01:06:08Z","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":"b36b54ff1309a1810abfe6a679a3d9923e3cda8b94926533aa5ecbe710faa2f0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-26T08:47:25Z","title_canon_sha256":"117f456dbcc0a13a0c496021e36aa7733176bb6b03a54484f5a2c6c6b791f25b"},"schema_version":"1.0","source":{"id":"2605.26707","kind":"arxiv","version":1}},"canonical_sha256":"dee2d30d6cd7b495aa72ef71baba18b3f87a24e02a717b680a3cb1a47c106bc6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dee2d30d6cd7b495aa72ef71baba18b3f87a24e02a717b680a3cb1a47c106bc6","first_computed_at":"2026-05-27T01:06:08.459535Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-27T01:06:08.459535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fseVgRnQVz7KggzBwteKON69ZRbPDcWaFl2u18/BJbQ2jwRcPOyD6iR66CIVHG8F7CVUA0eOrjpo9/kXNwDUCA==","signature_status":"signed_v1","signed_at":"2026-05-27T01:06:08.460402Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.26707","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d12adc977ddab8abed5520ec05160499fe076d59bf1c75cb6a3d0a1cf221bc6","sha256:91842b701d1f90bc9ebaf235d693ddfa96ce3c0413e0dc825304f55053c392ee"],"state_sha256":"163baeccd9a3b770e49098dc55df2484df714c5655c8100e226db9b09c6bbeb1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q0Pmvkzt3Y+TpQsYYRmlbKbxEYaMpEL1Oag8iwu/zu+w/XOR1c1VqIXJooRcvgKZkXfxKcrIBh5SJ6mMWcUrCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T14:33:54.897889Z","bundle_sha256":"baf7104a44e1ca357806b1ae92ffc645a97466f03940c9097b720ed36de22476"}}