{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:23L567BXIGX5722AAIVX7F6XJI","short_pith_number":"pith:23L567BX","canonical_record":{"source":{"id":"2607.29191","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2026-07-31T09:12:45Z","cross_cats_sorted":[],"title_canon_sha256":"d29be65c76b863dbbb0849bb0e36341bc07739e794b6653f930b9b0e53b5c54f","abstract_canon_sha256":"0914c7da064dab2c9facc1c6d64db7b18f1af1bfd4a2b04a2c7787d8fca735d1"},"schema_version":"1.0"},"canonical_sha256":"d6d7df7c3741afdfeb40022b7f97d74a04f080baf0001bc59503ec50310e4f0f","source":{"kind":"arxiv","id":"2607.29191","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.29191","created_at":"2026-08-03T01:20:47Z"},{"alias_kind":"arxiv_version","alias_value":"2607.29191v1","created_at":"2026-08-03T01:20:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.29191","created_at":"2026-08-03T01:20:47Z"},{"alias_kind":"pith_short_12","alias_value":"23L567BXIGX5","created_at":"2026-08-03T01:20:47Z"},{"alias_kind":"pith_short_16","alias_value":"23L567BXIGX5722A","created_at":"2026-08-03T01:20:47Z"},{"alias_kind":"pith_short_8","alias_value":"23L567BX","created_at":"2026-08-03T01:20:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:23L567BXIGX5722AAIVX7F6XJI","target":"record","payload":{"canonical_record":{"source":{"id":"2607.29191","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2026-07-31T09:12:45Z","cross_cats_sorted":[],"title_canon_sha256":"d29be65c76b863dbbb0849bb0e36341bc07739e794b6653f930b9b0e53b5c54f","abstract_canon_sha256":"0914c7da064dab2c9facc1c6d64db7b18f1af1bfd4a2b04a2c7787d8fca735d1"},"schema_version":"1.0"},"canonical_sha256":"d6d7df7c3741afdfeb40022b7f97d74a04f080baf0001bc59503ec50310e4f0f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-03T01:20:47.635418Z","signature_b64":"GXC7wUGE3jC6C90KvTcT3SQQtt7VOvDJBlYye/MAbdc44LyYy8m4Kh0gnoZqXAR+B455+4PzglTBOVC0ftg1Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6d7df7c3741afdfeb40022b7f97d74a04f080baf0001bc59503ec50310e4f0f","last_reissued_at":"2026-08-03T01:20:47.633912Z","signature_status":"signed_v1","first_computed_at":"2026-08-03T01:20:47.633912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.29191","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":"2026-08-03T01:20:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xSLJUx2gbEIvmhbBmLkICcAyU4m73Te9bBdUm98vNKJVMM1U1J6cTBFwKNWOvHVcO2x+IR/jTRs6W1wkglygAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T12:23:08.652846Z"},"content_sha256":"903d3e540d71d0e6b19d28c05259c2edcdca4aca9a49182b09bb26641cc2ae0d","schema_version":"1.0","event_id":"sha256:903d3e540d71d0e6b19d28c05259c2edcdca4aca9a49182b09bb26641cc2ae0d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:23L567BXIGX5722AAIVX7F6XJI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Proof of the Dittert Conjecture in Dimension 4 via an Agent-Guided Exact Sum-of-Squares Certificate","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Beibei Xiong, Jinhui Li, Zhengfeng Yang","submitted_at":"2026-07-31T09:12:45Z","abstract_excerpt":"The Dittert conjecture states that the Dittert functional on nonnegative $n\\times n$ matrices whose entries sum to $n$ is uniquely maximized by the uniform matrix. We prove the conjecture in dimension $4$. More precisely, let $K_4$ be the simplex of nonnegative $4\\times4$ real matrices whose entries sum to $4$, let $U_4$ be the uniform matrix, and let $\\phi$ denote the Dittert functional. We establish $\\frac{61}{32}-\\phi(A)\\geq \\frac{1}{52}\\lVert A-U_4\\rVert_F^2$ for every $A\\in K_4$. Consequently, $U_4$ is the unique maximizer of $\\phi$ on $K_4$. The proof reduces to certifying the nonnegativ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.29191","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/2607.29191/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":"2026-08-03T01:20:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"47nDRkdfWd41lbnFdZKJ/mcPkIlro6XzNMRNJkfgqP5ars4s5nWAZhJ75OtyPwLUgakePaUGMsKAlvmgrCAKDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T12:23:08.653564Z"},"content_sha256":"0b2d31c8dac3ca42bdb725cb865f058a794110840852b7953878ba7deed055a3","schema_version":"1.0","event_id":"sha256:0b2d31c8dac3ca42bdb725cb865f058a794110840852b7953878ba7deed055a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/23L567BXIGX5722AAIVX7F6XJI/bundle.json","state_url":"https://pith.science/pith/23L567BXIGX5722AAIVX7F6XJI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/23L567BXIGX5722AAIVX7F6XJI/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":"2026-08-04T12:23:08Z","links":{"resolver":"https://pith.science/pith/23L567BXIGX5722AAIVX7F6XJI","bundle":"https://pith.science/pith/23L567BXIGX5722AAIVX7F6XJI/bundle.json","state":"https://pith.science/pith/23L567BXIGX5722AAIVX7F6XJI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/23L567BXIGX5722AAIVX7F6XJI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:23L567BXIGX5722AAIVX7F6XJI","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":"0914c7da064dab2c9facc1c6d64db7b18f1af1bfd4a2b04a2c7787d8fca735d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2026-07-31T09:12:45Z","title_canon_sha256":"d29be65c76b863dbbb0849bb0e36341bc07739e794b6653f930b9b0e53b5c54f"},"schema_version":"1.0","source":{"id":"2607.29191","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.29191","created_at":"2026-08-03T01:20:47Z"},{"alias_kind":"arxiv_version","alias_value":"2607.29191v1","created_at":"2026-08-03T01:20:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.29191","created_at":"2026-08-03T01:20:47Z"},{"alias_kind":"pith_short_12","alias_value":"23L567BXIGX5","created_at":"2026-08-03T01:20:47Z"},{"alias_kind":"pith_short_16","alias_value":"23L567BXIGX5722A","created_at":"2026-08-03T01:20:47Z"},{"alias_kind":"pith_short_8","alias_value":"23L567BX","created_at":"2026-08-03T01:20:47Z"}],"graph_snapshots":[{"event_id":"sha256:0b2d31c8dac3ca42bdb725cb865f058a794110840852b7953878ba7deed055a3","target":"graph","created_at":"2026-08-03T01:20:47Z","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/2607.29191/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Dittert conjecture states that the Dittert functional on nonnegative $n\\times n$ matrices whose entries sum to $n$ is uniquely maximized by the uniform matrix. We prove the conjecture in dimension $4$. More precisely, let $K_4$ be the simplex of nonnegative $4\\times4$ real matrices whose entries sum to $4$, let $U_4$ be the uniform matrix, and let $\\phi$ denote the Dittert functional. We establish $\\frac{61}{32}-\\phi(A)\\geq \\frac{1}{52}\\lVert A-U_4\\rVert_F^2$ for every $A\\in K_4$. Consequently, $U_4$ is the unique maximizer of $\\phi$ on $K_4$. The proof reduces to certifying the nonnegativ","authors_text":"Beibei Xiong, Jinhui Li, Zhengfeng Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2026-07-31T09:12:45Z","title":"A Proof of the Dittert Conjecture in Dimension 4 via an Agent-Guided Exact Sum-of-Squares Certificate"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.29191","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":"sha256:903d3e540d71d0e6b19d28c05259c2edcdca4aca9a49182b09bb26641cc2ae0d","target":"record","created_at":"2026-08-03T01:20:47Z","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":"0914c7da064dab2c9facc1c6d64db7b18f1af1bfd4a2b04a2c7787d8fca735d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2026-07-31T09:12:45Z","title_canon_sha256":"d29be65c76b863dbbb0849bb0e36341bc07739e794b6653f930b9b0e53b5c54f"},"schema_version":"1.0","source":{"id":"2607.29191","kind":"arxiv","version":1}},"canonical_sha256":"d6d7df7c3741afdfeb40022b7f97d74a04f080baf0001bc59503ec50310e4f0f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6d7df7c3741afdfeb40022b7f97d74a04f080baf0001bc59503ec50310e4f0f","first_computed_at":"2026-08-03T01:20:47.633912Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-03T01:20:47.633912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GXC7wUGE3jC6C90KvTcT3SQQtt7VOvDJBlYye/MAbdc44LyYy8m4Kh0gnoZqXAR+B455+4PzglTBOVC0ftg1Cg==","signature_status":"signed_v1","signed_at":"2026-08-03T01:20:47.635418Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.29191","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:903d3e540d71d0e6b19d28c05259c2edcdca4aca9a49182b09bb26641cc2ae0d","sha256:0b2d31c8dac3ca42bdb725cb865f058a794110840852b7953878ba7deed055a3"],"state_sha256":"953ba715929c6c0a081c7eb1c744f1660b37af6dfda16717f2fa956c96a8615c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H9uPIWe8rh5/t4QpfXw0/B+IvfrZiXialPcsXfsLCPFXCOXDEoDWE6KQQKpLBRTyukkG3qr7o76NF/+iOdqjDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T12:23:08.658681Z","bundle_sha256":"18b4c47fcf5ed975a22f64227e84350c7de7e377794631a356c02f0a76a3afae"}}