{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:FPMB2BTOFQXXLHUQHFCHXVW33W","short_pith_number":"pith:FPMB2BTO","canonical_record":{"source":{"id":"1812.03445","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-12-09T08:27:39Z","cross_cats_sorted":[],"title_canon_sha256":"8bb04fffa2c69b4c6bf64681eb437cf30f945d156cda827254ae00d492ca43e3","abstract_canon_sha256":"20f1b8b3cbae4080a6a8476663ba3147d3c0be14ed0b022a29ea92e7dc42fb0e"},"schema_version":"1.0"},"canonical_sha256":"2bd81d066e2c2f759e9039447bd6dbdda70ab8db2da5c3cf9b454bfada35b29f","source":{"kind":"arxiv","id":"1812.03445","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.03445","created_at":"2026-05-17T23:58:46Z"},{"alias_kind":"arxiv_version","alias_value":"1812.03445v1","created_at":"2026-05-17T23:58:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.03445","created_at":"2026-05-17T23:58:46Z"},{"alias_kind":"pith_short_12","alias_value":"FPMB2BTOFQXX","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FPMB2BTOFQXXLHUQ","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FPMB2BTO","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:FPMB2BTOFQXXLHUQHFCHXVW33W","target":"record","payload":{"canonical_record":{"source":{"id":"1812.03445","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-12-09T08:27:39Z","cross_cats_sorted":[],"title_canon_sha256":"8bb04fffa2c69b4c6bf64681eb437cf30f945d156cda827254ae00d492ca43e3","abstract_canon_sha256":"20f1b8b3cbae4080a6a8476663ba3147d3c0be14ed0b022a29ea92e7dc42fb0e"},"schema_version":"1.0"},"canonical_sha256":"2bd81d066e2c2f759e9039447bd6dbdda70ab8db2da5c3cf9b454bfada35b29f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:46.244859Z","signature_b64":"t9TuEpxWP2hJE8QyagSisbr43Pp7K07X5FcRuQgKheTC12ZcKKFSJbpA+bKNRHqaTt/dWSI9dFZAMxVbL5oUDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2bd81d066e2c2f759e9039447bd6dbdda70ab8db2da5c3cf9b454bfada35b29f","last_reissued_at":"2026-05-17T23:58:46.244464Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:46.244464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.03445","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":"2026-05-17T23:58:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XVGw0fqPPj3R/8rFfkRfUSDE08Hkm9DYIr/+AEndZs2lXW6uS7oDy+l2KCP5Vr1kH6HSIWvN2xUWcjgF0FOtDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:13:55.999345Z"},"content_sha256":"e9cad55f3fce77a976f9c3a99e469d827bbbcb7c2a7be40fd8ed2fa5d814c302","schema_version":"1.0","event_id":"sha256:e9cad55f3fce77a976f9c3a99e469d827bbbcb7c2a7be40fd8ed2fa5d814c302"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:FPMB2BTOFQXXLHUQHFCHXVW33W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Melting lollipop chromatic quasisymmetric functions and Schur expansion of unicellular LLT polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"JiSun Huh, Meesue Yoo, Sun-Young Nam","submitted_at":"2018-12-09T08:27:39Z","abstract_excerpt":"In this work, we generalize and utilize the linear relations of LLT polynomials introduced by Lee \\cite{Lee}. By using the fact that the chromatic quasisymmetric functions and the unicellular LLT polynomials are related via plethystic substitution and thus they satisfy the same linear relations, we can apply the linear relations to both sets of functions.\n  As a result, in the chromatic quasisymmetric function side, we find a class of $e$-positive graphs, called \\emph{melting lollipop graphs}, and explicitly prove the $e$-unimodality. In the unicellular LLT side, we obtain Schur expansion form"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03445","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":""},"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":"2026-05-17T23:58:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m31WMhQ0n3DD7sUz4hNP9jG3i7DKpyrjJjq73O/NNaRLzukpOTv/RCeM03UsT4P5ZZ2hZdHpHAULXjRBc5PtBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:13:55.999737Z"},"content_sha256":"f2b145e75a300d8071a71e4f6e96de0fef841269b40d2ebe4767c672da547a01","schema_version":"1.0","event_id":"sha256:f2b145e75a300d8071a71e4f6e96de0fef841269b40d2ebe4767c672da547a01"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FPMB2BTOFQXXLHUQHFCHXVW33W/bundle.json","state_url":"https://pith.science/pith/FPMB2BTOFQXXLHUQHFCHXVW33W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FPMB2BTOFQXXLHUQHFCHXVW33W/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":"2026-05-28T08:13:56Z","links":{"resolver":"https://pith.science/pith/FPMB2BTOFQXXLHUQHFCHXVW33W","bundle":"https://pith.science/pith/FPMB2BTOFQXXLHUQHFCHXVW33W/bundle.json","state":"https://pith.science/pith/FPMB2BTOFQXXLHUQHFCHXVW33W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FPMB2BTOFQXXLHUQHFCHXVW33W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FPMB2BTOFQXXLHUQHFCHXVW33W","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":"20f1b8b3cbae4080a6a8476663ba3147d3c0be14ed0b022a29ea92e7dc42fb0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-12-09T08:27:39Z","title_canon_sha256":"8bb04fffa2c69b4c6bf64681eb437cf30f945d156cda827254ae00d492ca43e3"},"schema_version":"1.0","source":{"id":"1812.03445","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.03445","created_at":"2026-05-17T23:58:46Z"},{"alias_kind":"arxiv_version","alias_value":"1812.03445v1","created_at":"2026-05-17T23:58:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.03445","created_at":"2026-05-17T23:58:46Z"},{"alias_kind":"pith_short_12","alias_value":"FPMB2BTOFQXX","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FPMB2BTOFQXXLHUQ","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FPMB2BTO","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:f2b145e75a300d8071a71e4f6e96de0fef841269b40d2ebe4767c672da547a01","target":"graph","created_at":"2026-05-17T23:58:46Z","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":"In this work, we generalize and utilize the linear relations of LLT polynomials introduced by Lee \\cite{Lee}. By using the fact that the chromatic quasisymmetric functions and the unicellular LLT polynomials are related via plethystic substitution and thus they satisfy the same linear relations, we can apply the linear relations to both sets of functions.\n  As a result, in the chromatic quasisymmetric function side, we find a class of $e$-positive graphs, called \\emph{melting lollipop graphs}, and explicitly prove the $e$-unimodality. In the unicellular LLT side, we obtain Schur expansion form","authors_text":"JiSun Huh, Meesue Yoo, Sun-Young Nam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-12-09T08:27:39Z","title":"Melting lollipop chromatic quasisymmetric functions and Schur expansion of unicellular LLT polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03445","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:e9cad55f3fce77a976f9c3a99e469d827bbbcb7c2a7be40fd8ed2fa5d814c302","target":"record","created_at":"2026-05-17T23:58:46Z","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":"20f1b8b3cbae4080a6a8476663ba3147d3c0be14ed0b022a29ea92e7dc42fb0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-12-09T08:27:39Z","title_canon_sha256":"8bb04fffa2c69b4c6bf64681eb437cf30f945d156cda827254ae00d492ca43e3"},"schema_version":"1.0","source":{"id":"1812.03445","kind":"arxiv","version":1}},"canonical_sha256":"2bd81d066e2c2f759e9039447bd6dbdda70ab8db2da5c3cf9b454bfada35b29f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2bd81d066e2c2f759e9039447bd6dbdda70ab8db2da5c3cf9b454bfada35b29f","first_computed_at":"2026-05-17T23:58:46.244464Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:46.244464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t9TuEpxWP2hJE8QyagSisbr43Pp7K07X5FcRuQgKheTC12ZcKKFSJbpA+bKNRHqaTt/dWSI9dFZAMxVbL5oUDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:46.244859Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.03445","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9cad55f3fce77a976f9c3a99e469d827bbbcb7c2a7be40fd8ed2fa5d814c302","sha256:f2b145e75a300d8071a71e4f6e96de0fef841269b40d2ebe4767c672da547a01"],"state_sha256":"e97fb7f7b3ff45ca40c78e0bc8efa9a16cb26ff4a109da6df2c628266104a171"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fj5e+jPe07GWVVDeVKnrvzfuYJzntYbXCgWQvpeMg4jq9S3kYVcc64BTnlNjW0WRQ49TF42LtdGckrc7EA/BDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T08:13:56.001764Z","bundle_sha256":"bda2279d29778158023fe4a369252a0d4b5e090163fe7dac2e38d4c4b0ba622b"}}