{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JB4MBD72HWL2INBWDUAXD2U4NM","short_pith_number":"pith:JB4MBD72","canonical_record":{"source":{"id":"1509.07058","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-23T16:50:21Z","cross_cats_sorted":[],"title_canon_sha256":"e25183c83371fa92ba1d43b0885f6cff28d145a13cfc165b3bf7e514851796b3","abstract_canon_sha256":"0e0220fb8516769c860edcf84694ff21d446c2726f436adb932ba788e4f1fec6"},"schema_version":"1.0"},"canonical_sha256":"4878c08ffa3d97a434361d0171ea9c6b396edb24eb59d246d93285c6e90abf88","source":{"kind":"arxiv","id":"1509.07058","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.07058","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"1509.07058v4","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07058","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"JB4MBD72HWL2","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JB4MBD72HWL2INBW","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JB4MBD72","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JB4MBD72HWL2INBWDUAXD2U4NM","target":"record","payload":{"canonical_record":{"source":{"id":"1509.07058","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-23T16:50:21Z","cross_cats_sorted":[],"title_canon_sha256":"e25183c83371fa92ba1d43b0885f6cff28d145a13cfc165b3bf7e514851796b3","abstract_canon_sha256":"0e0220fb8516769c860edcf84694ff21d446c2726f436adb932ba788e4f1fec6"},"schema_version":"1.0"},"canonical_sha256":"4878c08ffa3d97a434361d0171ea9c6b396edb24eb59d246d93285c6e90abf88","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:55.821908Z","signature_b64":"BgGzcwcH8iUH9dRZomwCbrfiOtgQVwenDt/TudEtKkhlWiZNEXapgfs8fKX+IG/F5fBM1L/us42CeFSwBkflCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4878c08ffa3d97a434361d0171ea9c6b396edb24eb59d246d93285c6e90abf88","last_reissued_at":"2026-05-18T00:35:55.821547Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:55.821547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.07058","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:35:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pglOMKTriPVlBpNHgS8Kr2XoDIgE/XB5aBarMBBQ1yQKQuGbu2fQ87+7ShCVCUGfS3ck6mhmkcM9o+w0glBTDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:18:13.776293Z"},"content_sha256":"fce5844374f59ce8d2009b9f2754e09ebaa6b0cadac8ed2cd95a1e94c84964d9","schema_version":"1.0","event_id":"sha256:fce5844374f59ce8d2009b9f2754e09ebaa6b0cadac8ed2cd95a1e94c84964d9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JB4MBD72HWL2INBWDUAXD2U4NM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Delta Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrew Timothy Wilson, James Haglund, Jeffrey Remmel","submitted_at":"2015-09-23T16:50:21Z","abstract_excerpt":"We conjecture two combinatorial interpretations for the symmetric function $\\Delta_{e_k} e_n$, where $\\Delta_f$ is an eigenoperator for the modified Macdonald polynomials defined by Bergeron, Garsia, Haiman, and Tesler. Both interpretations can be seen as generalizations of the Shuffle Conjecture of Haglund, Haiman, Remmel, Loehr, and Ulyanov, which was proved recently by Carlsson and Mellit. We show how previous work of the third author on Tesler matrices and ordered set partitions can be used to verify several cases of our conjectures. Furthermore, we use a reciprocity identity and LLT polyn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07058","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:35:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UXDCGlwtZZN1mOnkq4arsmpq78vFBxnE3+wvZYQbPbcZZgW1EOCjQWi0saiDFuHJCx0pUduDkIo26HNJoNOoBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:18:13.776667Z"},"content_sha256":"d87dedeb588c23bac5d8f8a5a9eb91e9149f78b75bea739770eb59674ebd99f1","schema_version":"1.0","event_id":"sha256:d87dedeb588c23bac5d8f8a5a9eb91e9149f78b75bea739770eb59674ebd99f1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JB4MBD72HWL2INBWDUAXD2U4NM/bundle.json","state_url":"https://pith.science/pith/JB4MBD72HWL2INBWDUAXD2U4NM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JB4MBD72HWL2INBWDUAXD2U4NM/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":"2026-06-03T00:18:13Z","links":{"resolver":"https://pith.science/pith/JB4MBD72HWL2INBWDUAXD2U4NM","bundle":"https://pith.science/pith/JB4MBD72HWL2INBWDUAXD2U4NM/bundle.json","state":"https://pith.science/pith/JB4MBD72HWL2INBWDUAXD2U4NM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JB4MBD72HWL2INBWDUAXD2U4NM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JB4MBD72HWL2INBWDUAXD2U4NM","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":"0e0220fb8516769c860edcf84694ff21d446c2726f436adb932ba788e4f1fec6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-23T16:50:21Z","title_canon_sha256":"e25183c83371fa92ba1d43b0885f6cff28d145a13cfc165b3bf7e514851796b3"},"schema_version":"1.0","source":{"id":"1509.07058","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.07058","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"1509.07058v4","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07058","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"JB4MBD72HWL2","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JB4MBD72HWL2INBW","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JB4MBD72","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:d87dedeb588c23bac5d8f8a5a9eb91e9149f78b75bea739770eb59674ebd99f1","target":"graph","created_at":"2026-05-18T00:35:55Z","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"},"paper":{"abstract_excerpt":"We conjecture two combinatorial interpretations for the symmetric function $\\Delta_{e_k} e_n$, where $\\Delta_f$ is an eigenoperator for the modified Macdonald polynomials defined by Bergeron, Garsia, Haiman, and Tesler. Both interpretations can be seen as generalizations of the Shuffle Conjecture of Haglund, Haiman, Remmel, Loehr, and Ulyanov, which was proved recently by Carlsson and Mellit. We show how previous work of the third author on Tesler matrices and ordered set partitions can be used to verify several cases of our conjectures. Furthermore, we use a reciprocity identity and LLT polyn","authors_text":"Andrew Timothy Wilson, James Haglund, Jeffrey Remmel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-23T16:50:21Z","title":"The Delta Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07058","kind":"arxiv","version":4},"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:fce5844374f59ce8d2009b9f2754e09ebaa6b0cadac8ed2cd95a1e94c84964d9","target":"record","created_at":"2026-05-18T00:35:55Z","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":"0e0220fb8516769c860edcf84694ff21d446c2726f436adb932ba788e4f1fec6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-23T16:50:21Z","title_canon_sha256":"e25183c83371fa92ba1d43b0885f6cff28d145a13cfc165b3bf7e514851796b3"},"schema_version":"1.0","source":{"id":"1509.07058","kind":"arxiv","version":4}},"canonical_sha256":"4878c08ffa3d97a434361d0171ea9c6b396edb24eb59d246d93285c6e90abf88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4878c08ffa3d97a434361d0171ea9c6b396edb24eb59d246d93285c6e90abf88","first_computed_at":"2026-05-18T00:35:55.821547Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:55.821547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BgGzcwcH8iUH9dRZomwCbrfiOtgQVwenDt/TudEtKkhlWiZNEXapgfs8fKX+IG/F5fBM1L/us42CeFSwBkflCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:55.821908Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.07058","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fce5844374f59ce8d2009b9f2754e09ebaa6b0cadac8ed2cd95a1e94c84964d9","sha256:d87dedeb588c23bac5d8f8a5a9eb91e9149f78b75bea739770eb59674ebd99f1"],"state_sha256":"ea8fbd5fef873e81510b66556129d55ae5a7159f43aa9c95454eb8ba94c184b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M/nL6LlPOGn5qIYqQ/JmOx0aPUCcxdUVzF59X51Vgj7FXErg7ab0rJ8C+NIK5aEzMtYQk+iQJ3U3FBvoQcfWCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T00:18:13.778726Z","bundle_sha256":"45394fa50086af6547cab10f7e63abec6d365e8b85c7a602bacec34d7bb9e765"}}