{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:QE4GV3AADHX3F4W7TU7MUYYBKJ","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":"2d821e2496a2e0a3d52b915710b74c695f42efa9e32f5a5dc88dc7167ef8df58","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-08-13T12:14:55Z","title_canon_sha256":"eb022b6921470d9e2e9743e28c4cc583dddc917c7e68f46e995428b67e71540f"},"schema_version":"1.0","source":{"id":"2608.13139","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.13139","created_at":"2026-08-14T01:00:28Z"},{"alias_kind":"arxiv_version","alias_value":"2608.13139v1","created_at":"2026-08-14T01:00:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.13139","created_at":"2026-08-14T01:00:28Z"},{"alias_kind":"pith_short_12","alias_value":"QE4GV3AADHX3","created_at":"2026-08-14T01:00:28Z"},{"alias_kind":"pith_short_16","alias_value":"QE4GV3AADHX3F4W7","created_at":"2026-08-14T01:00:28Z"},{"alias_kind":"pith_short_8","alias_value":"QE4GV3AA","created_at":"2026-08-14T01:00:28Z"}],"graph_snapshots":[{"event_id":"sha256:934d4ec37eeaad0f7308947f896cfcbab57f4384ed4d6ee7f23e1a4605773a17","target":"graph","created_at":"2026-08-14T01:00:28Z","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/2608.13139/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recent work established a sharp graph-distance lower bound for the Haraux function of maximally monotone operators on reflexive Banach spaces and raised the question of its extension beyond reflexivity. We prove that the sharp constant $1/2$ remains valid for every maximally monotone operator of type~(NI) on an arbitrary real Banach space and for every positive weight. The result is generated by an exact energy decomposition: the Haraux contribution of a graph point and its weighted quasidensity residual are complementary terms whose sum is one half of the weighted squared graph displacement. ","authors_text":"Weifeng Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-08-13T12:14:55Z","title":"Sharp Lower Bounds on the Haraux Function Beyond Reflexivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.13139","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":"sha256:067ad1b779681698110b56d72a817d5bad4696d02d6286c89fb55ffd6c2b0757","target":"record","created_at":"2026-08-14T01:00:28Z","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":"2d821e2496a2e0a3d52b915710b74c695f42efa9e32f5a5dc88dc7167ef8df58","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-08-13T12:14:55Z","title_canon_sha256":"eb022b6921470d9e2e9743e28c4cc583dddc917c7e68f46e995428b67e71540f"},"schema_version":"1.0","source":{"id":"2608.13139","kind":"arxiv","version":1}},"canonical_sha256":"81386aec0019efb2f2df9d3eca63015245c2ae6e718a6924b75da33e7a32db76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81386aec0019efb2f2df9d3eca63015245c2ae6e718a6924b75da33e7a32db76","first_computed_at":"2026-08-14T01:00:28.061820Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-14T01:00:28.061820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"anPPLPHeH8OzusZNhXSpDAjZV7lMeuCfYRCG7aCrNeKyS1v/ENGQHklX99Td0iY3iW78HW9Yw0o+xCc5a/sGBw==","signature_status":"signed_v1","signed_at":"2026-08-14T01:00:28.063878Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.13139","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:067ad1b779681698110b56d72a817d5bad4696d02d6286c89fb55ffd6c2b0757","sha256:934d4ec37eeaad0f7308947f896cfcbab57f4384ed4d6ee7f23e1a4605773a17"],"state_sha256":"e9cdbd1b69aacfd86d9dbbe98c8117b71ddacd9dd2dfecd4c02c9b8e6cf3250c"}