{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:M5MVXKW2TDWGAFZEFVDD36XVUC","short_pith_number":"pith:M5MVXKW2","canonical_record":{"source":{"id":"2602.16810","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2026-02-18T19:15:22Z","cross_cats_sorted":[],"title_canon_sha256":"a1fa9c6b4bab036e579aed4db49eead82bfa9998ec83243cd9f92d3d9bab7b11","abstract_canon_sha256":"45445223581db97c1e312fb9727d39cdc87cd76e5e91fd3675ea20876960893d"},"schema_version":"1.0"},"canonical_sha256":"67595baada98ec6017242d463dfaf5a0920e6992dc82df25edd83b638d75075d","source":{"kind":"arxiv","id":"2602.16810","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.16810","created_at":"2026-05-26T01:02:32Z"},{"alias_kind":"arxiv_version","alias_value":"2602.16810v2","created_at":"2026-05-26T01:02:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.16810","created_at":"2026-05-26T01:02:32Z"},{"alias_kind":"pith_short_12","alias_value":"M5MVXKW2TDWG","created_at":"2026-05-26T01:02:32Z"},{"alias_kind":"pith_short_16","alias_value":"M5MVXKW2TDWGAFZE","created_at":"2026-05-26T01:02:32Z"},{"alias_kind":"pith_short_8","alias_value":"M5MVXKW2","created_at":"2026-05-26T01:02:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:M5MVXKW2TDWGAFZEFVDD36XVUC","target":"record","payload":{"canonical_record":{"source":{"id":"2602.16810","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2026-02-18T19:15:22Z","cross_cats_sorted":[],"title_canon_sha256":"a1fa9c6b4bab036e579aed4db49eead82bfa9998ec83243cd9f92d3d9bab7b11","abstract_canon_sha256":"45445223581db97c1e312fb9727d39cdc87cd76e5e91fd3675ea20876960893d"},"schema_version":"1.0"},"canonical_sha256":"67595baada98ec6017242d463dfaf5a0920e6992dc82df25edd83b638d75075d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T01:02:32.413180Z","signature_b64":"CUrRQxZ2dQeHPR/ayuNK235msTsfGM+Me2WvkOStqxT2l/usdUx/daNZw0AkzT7V/d0donX9JpskwKhcvkDqBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67595baada98ec6017242d463dfaf5a0920e6992dc82df25edd83b638d75075d","last_reissued_at":"2026-05-26T01:02:32.412253Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T01:02:32.412253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2602.16810","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-26T01:02:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rtYbTeA/keRTICLH+ccyhXOD82cnmLwV7LUBdLXxgeu11jMlekt/+HOB3lekjlTMVmQUecbyc1reoGPAF0T5Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:18:25.204722Z"},"content_sha256":"e0b5bb1727880d1c7be5d26b232282c281b3f2c671494f463cc293d032f2de0d","schema_version":"1.0","event_id":"sha256:e0b5bb1727880d1c7be5d26b232282c281b3f2c671494f463cc293d032f2de0d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:M5MVXKW2TDWGAFZEFVDD36XVUC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Separations above TFNP from Sherali-Adams Lower Bounds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Anna Gal, Christophe Marciot, Deniz Imrek, Noah Fleming","submitted_at":"2026-02-18T19:15:22Z","abstract_excerpt":"Unlike in TFNP, for which there is an abundance of problems capturing natural existence principles which are incomparable (in the black-box setting), Kleinberg et al. [KKMP21] observed that many of the natural problems considered so far in the second level of the total function polynomial hierarchy (TF$\\Sigma_2$) reduce to the Strong Avoid problem. In this work, we prove that the Linear Ordering Principle does not reduce to Strong Avoid in the black-box setting, exhibiting the first TF$\\Sigma_2$ problem that lies outside of the class of problems reducible to Strong Avoid.\n  The proof of our se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.16810","kind":"arxiv","version":2},"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/2602.16810/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":"2026-05-26T01:02:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ObA6iomCyVsj9fMv4z97cSGvAdSXRUdiIVmp/zOK385sVm//nDNl9C3YwnSEQhK3suMRmJwXrnXizqknOjE6BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:18:25.205101Z"},"content_sha256":"44ad5f833412d6aa426f568bb8dc4eb5ef5b5fa1e9919bf30a44a34677d0722b","schema_version":"1.0","event_id":"sha256:44ad5f833412d6aa426f568bb8dc4eb5ef5b5fa1e9919bf30a44a34677d0722b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M5MVXKW2TDWGAFZEFVDD36XVUC/bundle.json","state_url":"https://pith.science/pith/M5MVXKW2TDWGAFZEFVDD36XVUC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M5MVXKW2TDWGAFZEFVDD36XVUC/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":"2026-06-02T22:18:25Z","links":{"resolver":"https://pith.science/pith/M5MVXKW2TDWGAFZEFVDD36XVUC","bundle":"https://pith.science/pith/M5MVXKW2TDWGAFZEFVDD36XVUC/bundle.json","state":"https://pith.science/pith/M5MVXKW2TDWGAFZEFVDD36XVUC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M5MVXKW2TDWGAFZEFVDD36XVUC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:M5MVXKW2TDWGAFZEFVDD36XVUC","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":"45445223581db97c1e312fb9727d39cdc87cd76e5e91fd3675ea20876960893d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2026-02-18T19:15:22Z","title_canon_sha256":"a1fa9c6b4bab036e579aed4db49eead82bfa9998ec83243cd9f92d3d9bab7b11"},"schema_version":"1.0","source":{"id":"2602.16810","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.16810","created_at":"2026-05-26T01:02:32Z"},{"alias_kind":"arxiv_version","alias_value":"2602.16810v2","created_at":"2026-05-26T01:02:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.16810","created_at":"2026-05-26T01:02:32Z"},{"alias_kind":"pith_short_12","alias_value":"M5MVXKW2TDWG","created_at":"2026-05-26T01:02:32Z"},{"alias_kind":"pith_short_16","alias_value":"M5MVXKW2TDWGAFZE","created_at":"2026-05-26T01:02:32Z"},{"alias_kind":"pith_short_8","alias_value":"M5MVXKW2","created_at":"2026-05-26T01:02:32Z"}],"graph_snapshots":[{"event_id":"sha256:44ad5f833412d6aa426f568bb8dc4eb5ef5b5fa1e9919bf30a44a34677d0722b","target":"graph","created_at":"2026-05-26T01:02:32Z","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/2602.16810/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Unlike in TFNP, for which there is an abundance of problems capturing natural existence principles which are incomparable (in the black-box setting), Kleinberg et al. [KKMP21] observed that many of the natural problems considered so far in the second level of the total function polynomial hierarchy (TF$\\Sigma_2$) reduce to the Strong Avoid problem. In this work, we prove that the Linear Ordering Principle does not reduce to Strong Avoid in the black-box setting, exhibiting the first TF$\\Sigma_2$ problem that lies outside of the class of problems reducible to Strong Avoid.\n  The proof of our se","authors_text":"Anna Gal, Christophe Marciot, Deniz Imrek, Noah Fleming","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2026-02-18T19:15:22Z","title":"Separations above TFNP from Sherali-Adams Lower Bounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.16810","kind":"arxiv","version":2},"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:e0b5bb1727880d1c7be5d26b232282c281b3f2c671494f463cc293d032f2de0d","target":"record","created_at":"2026-05-26T01:02:32Z","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":"45445223581db97c1e312fb9727d39cdc87cd76e5e91fd3675ea20876960893d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2026-02-18T19:15:22Z","title_canon_sha256":"a1fa9c6b4bab036e579aed4db49eead82bfa9998ec83243cd9f92d3d9bab7b11"},"schema_version":"1.0","source":{"id":"2602.16810","kind":"arxiv","version":2}},"canonical_sha256":"67595baada98ec6017242d463dfaf5a0920e6992dc82df25edd83b638d75075d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67595baada98ec6017242d463dfaf5a0920e6992dc82df25edd83b638d75075d","first_computed_at":"2026-05-26T01:02:32.412253Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T01:02:32.412253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CUrRQxZ2dQeHPR/ayuNK235msTsfGM+Me2WvkOStqxT2l/usdUx/daNZw0AkzT7V/d0donX9JpskwKhcvkDqBw==","signature_status":"signed_v1","signed_at":"2026-05-26T01:02:32.413180Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.16810","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0b5bb1727880d1c7be5d26b232282c281b3f2c671494f463cc293d032f2de0d","sha256:44ad5f833412d6aa426f568bb8dc4eb5ef5b5fa1e9919bf30a44a34677d0722b"],"state_sha256":"b8e034411083400c2b298c09b8f000b635f799dcd0e2bc10d4c51877a8dbe408"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GDCAccYat43+XYmZUA+nl3sfXssMvC5TcEdVy6RRH5Jx81bl55EYY+Vs6FuoLCnfZzqI8fcdb3HdYbjKL63kCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T22:18:25.207244Z","bundle_sha256":"e5a921d31b608f9a5da4f6ec97c084dc1236201e5a078594f15f38254f17c3ec"}}