{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:PKRP77PBFBLZPU6SV5IFGDWXOH","short_pith_number":"pith:PKRP77PB","canonical_record":{"source":{"id":"2606.02257","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-01T13:44:32Z","cross_cats_sorted":[],"title_canon_sha256":"396ea339b70d70ca0d0363b64e1ad88bb91622fc4253c8dca5dfadb1d29d26d8","abstract_canon_sha256":"0f51aa63fddb8725e4f392126cfa83cce4aaa1547bc88e97f71ac607d223bdce"},"schema_version":"1.0"},"canonical_sha256":"7aa2fffde1285797d3d2af50530ed771f6c79d56f1ced5bddfacb71937dc80ae","source":{"kind":"arxiv","id":"2606.02257","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.02257","created_at":"2026-06-02T03:04:54Z"},{"alias_kind":"arxiv_version","alias_value":"2606.02257v1","created_at":"2026-06-02T03:04:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.02257","created_at":"2026-06-02T03:04:54Z"},{"alias_kind":"pith_short_12","alias_value":"PKRP77PBFBLZ","created_at":"2026-06-02T03:04:54Z"},{"alias_kind":"pith_short_16","alias_value":"PKRP77PBFBLZPU6S","created_at":"2026-06-02T03:04:54Z"},{"alias_kind":"pith_short_8","alias_value":"PKRP77PB","created_at":"2026-06-02T03:04:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:PKRP77PBFBLZPU6SV5IFGDWXOH","target":"record","payload":{"canonical_record":{"source":{"id":"2606.02257","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-01T13:44:32Z","cross_cats_sorted":[],"title_canon_sha256":"396ea339b70d70ca0d0363b64e1ad88bb91622fc4253c8dca5dfadb1d29d26d8","abstract_canon_sha256":"0f51aa63fddb8725e4f392126cfa83cce4aaa1547bc88e97f71ac607d223bdce"},"schema_version":"1.0"},"canonical_sha256":"7aa2fffde1285797d3d2af50530ed771f6c79d56f1ced5bddfacb71937dc80ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T03:04:54.334679Z","signature_b64":"5tIIqvsEe/gLtUG0rRGi0yfuI6OvftQH21HaL1vg3Uh0++Mll4d6JmKNXopAxS1YIzRH2K75yt5i6orWEdgiDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7aa2fffde1285797d3d2af50530ed771f6c79d56f1ced5bddfacb71937dc80ae","last_reissued_at":"2026-06-02T03:04:54.334333Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T03:04:54.334333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.02257","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":"2026-06-02T03:04:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IKL8TT723Dr2amY/XJy11clZw2qmtsuXVy8nLobnCBz3q/r7Vix1kVyqhpN2YNoYTT+MkFe0M+u6n54QilvHDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:55:35.645486Z"},"content_sha256":"057fbe2165bf8f50e6a707d9d18f75f8d74b3a0708ef41a7cbba29936bdc2379","schema_version":"1.0","event_id":"sha256:057fbe2165bf8f50e6a707d9d18f75f8d74b3a0708ef41a7cbba29936bdc2379"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:PKRP77PBFBLZPU6SV5IFGDWXOH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counterexamples to Robichaux's conjecture for Grothendieck polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Avery St. Dizier","submitted_at":"2026-06-01T13:44:32Z","abstract_excerpt":"Ross and Yong conjectured a $K$-theoretic Kohnert rule for Grothendieck polynomials. Robichaux exhibited a counterexample to the Ross--Yong rule and proposed a revised ghost $K$-Kohnert rule, proving both rules hold for 321-avoiding permutations. We provide counterexamples to Robichaux's rule and give an explicit bijection showing that both the Ross--Yong and Robichaux rules hold for 1432-avoiding permutations. As an application, we provide a Kohnert-theoretic characterization of 1432-avoidance."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02257","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/2606.02257/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":"2026-06-02T03:04:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nNVordNrpmrfAdSvyVC9lVwoe47JWUTt4yHZWRsFTC64Th0JsXDJ+70J0jEVDJimjNTsZ7xYOGJ56bp6UP91Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:55:35.645849Z"},"content_sha256":"dcbcce8df1f7903a2565ed39a620e3a96fdb3d14de69ec8492a9807a80951df0","schema_version":"1.0","event_id":"sha256:dcbcce8df1f7903a2565ed39a620e3a96fdb3d14de69ec8492a9807a80951df0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PKRP77PBFBLZPU6SV5IFGDWXOH/bundle.json","state_url":"https://pith.science/pith/PKRP77PBFBLZPU6SV5IFGDWXOH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PKRP77PBFBLZPU6SV5IFGDWXOH/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":"2026-06-03T06:55:35Z","links":{"resolver":"https://pith.science/pith/PKRP77PBFBLZPU6SV5IFGDWXOH","bundle":"https://pith.science/pith/PKRP77PBFBLZPU6SV5IFGDWXOH/bundle.json","state":"https://pith.science/pith/PKRP77PBFBLZPU6SV5IFGDWXOH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PKRP77PBFBLZPU6SV5IFGDWXOH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PKRP77PBFBLZPU6SV5IFGDWXOH","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":"0f51aa63fddb8725e4f392126cfa83cce4aaa1547bc88e97f71ac607d223bdce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-01T13:44:32Z","title_canon_sha256":"396ea339b70d70ca0d0363b64e1ad88bb91622fc4253c8dca5dfadb1d29d26d8"},"schema_version":"1.0","source":{"id":"2606.02257","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.02257","created_at":"2026-06-02T03:04:54Z"},{"alias_kind":"arxiv_version","alias_value":"2606.02257v1","created_at":"2026-06-02T03:04:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.02257","created_at":"2026-06-02T03:04:54Z"},{"alias_kind":"pith_short_12","alias_value":"PKRP77PBFBLZ","created_at":"2026-06-02T03:04:54Z"},{"alias_kind":"pith_short_16","alias_value":"PKRP77PBFBLZPU6S","created_at":"2026-06-02T03:04:54Z"},{"alias_kind":"pith_short_8","alias_value":"PKRP77PB","created_at":"2026-06-02T03:04:54Z"}],"graph_snapshots":[{"event_id":"sha256:dcbcce8df1f7903a2565ed39a620e3a96fdb3d14de69ec8492a9807a80951df0","target":"graph","created_at":"2026-06-02T03:04:54Z","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/2606.02257/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Ross and Yong conjectured a $K$-theoretic Kohnert rule for Grothendieck polynomials. Robichaux exhibited a counterexample to the Ross--Yong rule and proposed a revised ghost $K$-Kohnert rule, proving both rules hold for 321-avoiding permutations. We provide counterexamples to Robichaux's rule and give an explicit bijection showing that both the Ross--Yong and Robichaux rules hold for 1432-avoiding permutations. As an application, we provide a Kohnert-theoretic characterization of 1432-avoidance.","authors_text":"Avery St. Dizier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-01T13:44:32Z","title":"Counterexamples to Robichaux's conjecture for Grothendieck polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02257","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":"sha256:057fbe2165bf8f50e6a707d9d18f75f8d74b3a0708ef41a7cbba29936bdc2379","target":"record","created_at":"2026-06-02T03:04:54Z","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":"0f51aa63fddb8725e4f392126cfa83cce4aaa1547bc88e97f71ac607d223bdce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-01T13:44:32Z","title_canon_sha256":"396ea339b70d70ca0d0363b64e1ad88bb91622fc4253c8dca5dfadb1d29d26d8"},"schema_version":"1.0","source":{"id":"2606.02257","kind":"arxiv","version":1}},"canonical_sha256":"7aa2fffde1285797d3d2af50530ed771f6c79d56f1ced5bddfacb71937dc80ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7aa2fffde1285797d3d2af50530ed771f6c79d56f1ced5bddfacb71937dc80ae","first_computed_at":"2026-06-02T03:04:54.334333Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T03:04:54.334333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5tIIqvsEe/gLtUG0rRGi0yfuI6OvftQH21HaL1vg3Uh0++Mll4d6JmKNXopAxS1YIzRH2K75yt5i6orWEdgiDQ==","signature_status":"signed_v1","signed_at":"2026-06-02T03:04:54.334679Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.02257","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:057fbe2165bf8f50e6a707d9d18f75f8d74b3a0708ef41a7cbba29936bdc2379","sha256:dcbcce8df1f7903a2565ed39a620e3a96fdb3d14de69ec8492a9807a80951df0"],"state_sha256":"3215e77e6c228f572b94b33a9882f7d8813b1ff17718eef60ed31a01756d0204"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KH6eb6KgrQM/IyU9FZBVbd7MidKGx3FfNtj2A/v4LF1S0+01/KuvqHuZX/chgD/PwiooFGPbJFgv3KGqSrKRCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T06:55:35.648814Z","bundle_sha256":"4a1c64cf3fbcd78d875c5a315ca2934a17a2d2861f8378506aac08a1e30d6a5b"}}