{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:H5D5L2PPAH5TW4H2ZLVXG7N4QV","short_pith_number":"pith:H5D5L2PP","canonical_record":{"source":{"id":"1705.10353","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-29T18:35:33Z","cross_cats_sorted":[],"title_canon_sha256":"061382de7fc9f5b833ee8e668bdd35dc04323eae4947707a300c2ff134edc828","abstract_canon_sha256":"f3291eaaf32be414a38e4fee8d19c4ed4aa5ede0ec02cfb97f16cb8aa4927005"},"schema_version":"1.0"},"canonical_sha256":"3f47d5e9ef01fb3b70facaeb737dbc8574f6854a9ecffb3737644030a656f3e4","source":{"kind":"arxiv","id":"1705.10353","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.10353","created_at":"2026-05-18T00:05:00Z"},{"alias_kind":"arxiv_version","alias_value":"1705.10353v2","created_at":"2026-05-18T00:05:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.10353","created_at":"2026-05-18T00:05:00Z"},{"alias_kind":"pith_short_12","alias_value":"H5D5L2PPAH5T","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"H5D5L2PPAH5TW4H2","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"H5D5L2PP","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:H5D5L2PPAH5TW4H2ZLVXG7N4QV","target":"record","payload":{"canonical_record":{"source":{"id":"1705.10353","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-29T18:35:33Z","cross_cats_sorted":[],"title_canon_sha256":"061382de7fc9f5b833ee8e668bdd35dc04323eae4947707a300c2ff134edc828","abstract_canon_sha256":"f3291eaaf32be414a38e4fee8d19c4ed4aa5ede0ec02cfb97f16cb8aa4927005"},"schema_version":"1.0"},"canonical_sha256":"3f47d5e9ef01fb3b70facaeb737dbc8574f6854a9ecffb3737644030a656f3e4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:00.592378Z","signature_b64":"WTFhieXJ5p/JapXNWz96KTUjJHF7fSX4tn1Ae3Y0qkmLkIgq2wPyXB2BOKeGefpbUDX2VndNQvjQdpzEQz/yBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f47d5e9ef01fb3b70facaeb737dbc8574f6854a9ecffb3737644030a656f3e4","last_reissued_at":"2026-05-18T00:05:00.591968Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:00.591968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.10353","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":"2026-05-18T00:05:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5SvEb7UWmGPvkshQldtHfOEjeTBmqvFnKMY0x/Qz7+5pbvftvbqgKn5AjHxsV71VFEkcDzpdhdeFp+dkzc2ABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:14:14.672451Z"},"content_sha256":"443002994df4292e4ab602c3e669a00ec5429375ffe97fec8e590725d72fc190","schema_version":"1.0","event_id":"sha256:443002994df4292e4ab602c3e669a00ec5429375ffe97fec8e590725d72fc190"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:H5D5L2PPAH5TW4H2ZLVXG7N4QV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"LLT polynomials, chromatic quasisymmetric functions and graphs with cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Greta Panova, Per Alexandersson","submitted_at":"2017-05-29T18:35:33Z","abstract_excerpt":"We use a Dyck path model for unit-interval graphs to study the chromatic quasisymmetric functions introduced by Shareshian and Wachs, as well as vertical strip --- in particular, unicellular LLT polynomials.\n  We show that there are parallel phenomena regarding $e$-positivity of these two families of polynomials. In particular, we give several examples where the LLT polynomials behave like a \"mirror image\" of the chromatic quasisymmetric counterpart.\n  The Dyck path model is also extended to circular arc digraphs to obtain larger families of polynomials. This circular extensions of LLT polynom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10353","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":""},"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":"2026-05-18T00:05:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3ttigLArRpJA/GSgX4bywWsDljagX4GuTD7TFgv1Rfv4uofvtvA10BcO0T6yvvzazySop1BiRVUoan4wRIbKAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:14:14.672900Z"},"content_sha256":"86abe9e6fc47d02c9ee1c8fdce7df0377f8f9f96ad975fad9f2f6c2206f3d49d","schema_version":"1.0","event_id":"sha256:86abe9e6fc47d02c9ee1c8fdce7df0377f8f9f96ad975fad9f2f6c2206f3d49d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H5D5L2PPAH5TW4H2ZLVXG7N4QV/bundle.json","state_url":"https://pith.science/pith/H5D5L2PPAH5TW4H2ZLVXG7N4QV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H5D5L2PPAH5TW4H2ZLVXG7N4QV/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":"2026-05-31T15:14:14Z","links":{"resolver":"https://pith.science/pith/H5D5L2PPAH5TW4H2ZLVXG7N4QV","bundle":"https://pith.science/pith/H5D5L2PPAH5TW4H2ZLVXG7N4QV/bundle.json","state":"https://pith.science/pith/H5D5L2PPAH5TW4H2ZLVXG7N4QV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H5D5L2PPAH5TW4H2ZLVXG7N4QV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:H5D5L2PPAH5TW4H2ZLVXG7N4QV","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":"f3291eaaf32be414a38e4fee8d19c4ed4aa5ede0ec02cfb97f16cb8aa4927005","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-29T18:35:33Z","title_canon_sha256":"061382de7fc9f5b833ee8e668bdd35dc04323eae4947707a300c2ff134edc828"},"schema_version":"1.0","source":{"id":"1705.10353","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.10353","created_at":"2026-05-18T00:05:00Z"},{"alias_kind":"arxiv_version","alias_value":"1705.10353v2","created_at":"2026-05-18T00:05:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.10353","created_at":"2026-05-18T00:05:00Z"},{"alias_kind":"pith_short_12","alias_value":"H5D5L2PPAH5T","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"H5D5L2PPAH5TW4H2","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"H5D5L2PP","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:86abe9e6fc47d02c9ee1c8fdce7df0377f8f9f96ad975fad9f2f6c2206f3d49d","target":"graph","created_at":"2026-05-18T00:05:00Z","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 use a Dyck path model for unit-interval graphs to study the chromatic quasisymmetric functions introduced by Shareshian and Wachs, as well as vertical strip --- in particular, unicellular LLT polynomials.\n  We show that there are parallel phenomena regarding $e$-positivity of these two families of polynomials. In particular, we give several examples where the LLT polynomials behave like a \"mirror image\" of the chromatic quasisymmetric counterpart.\n  The Dyck path model is also extended to circular arc digraphs to obtain larger families of polynomials. This circular extensions of LLT polynom","authors_text":"Greta Panova, Per Alexandersson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-29T18:35:33Z","title":"LLT polynomials, chromatic quasisymmetric functions and graphs with cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10353","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":"sha256:443002994df4292e4ab602c3e669a00ec5429375ffe97fec8e590725d72fc190","target":"record","created_at":"2026-05-18T00:05:00Z","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":"f3291eaaf32be414a38e4fee8d19c4ed4aa5ede0ec02cfb97f16cb8aa4927005","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-29T18:35:33Z","title_canon_sha256":"061382de7fc9f5b833ee8e668bdd35dc04323eae4947707a300c2ff134edc828"},"schema_version":"1.0","source":{"id":"1705.10353","kind":"arxiv","version":2}},"canonical_sha256":"3f47d5e9ef01fb3b70facaeb737dbc8574f6854a9ecffb3737644030a656f3e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f47d5e9ef01fb3b70facaeb737dbc8574f6854a9ecffb3737644030a656f3e4","first_computed_at":"2026-05-18T00:05:00.591968Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:00.591968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WTFhieXJ5p/JapXNWz96KTUjJHF7fSX4tn1Ae3Y0qkmLkIgq2wPyXB2BOKeGefpbUDX2VndNQvjQdpzEQz/yBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:00.592378Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.10353","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:443002994df4292e4ab602c3e669a00ec5429375ffe97fec8e590725d72fc190","sha256:86abe9e6fc47d02c9ee1c8fdce7df0377f8f9f96ad975fad9f2f6c2206f3d49d"],"state_sha256":"09dfd0356c39ed83bdaba7c4af9aaead49dd9adfb2299b81d59544ccf97fa4df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zSNeBv8PN/YLEkltNX0z8DlTpw1Of8jjdZ7pnSBdkO/BPO0cj8DXNxvUtcySLC7UN3HBfA+MG9lb25yobeCzAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T15:14:14.676704Z","bundle_sha256":"e152e114a2fc61f0db1d70978fe18dd80900b0145f806f61bbee038159f69ac4"}}