{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:57EUC2OFPHTIRZHPWBXA2S3TH6","short_pith_number":"pith:57EUC2OF","canonical_record":{"source":{"id":"1508.01301","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-06T07:44:40Z","cross_cats_sorted":[],"title_canon_sha256":"c9d3432f57a8cb05d2fb9d6d52c686b262da90160648eab36c5d0db98499fabe","abstract_canon_sha256":"2254953a76cab7fd73ab28cdc33a5af2566cfd100319f235d8579e29a811d806"},"schema_version":"1.0"},"canonical_sha256":"efc94169c579e688e4efb06e0d4b733f935b59b0070fa4b1ae9aa67d5fa4cb34","source":{"kind":"arxiv","id":"1508.01301","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01301","created_at":"2026-05-18T00:52:09Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01301v1","created_at":"2026-05-18T00:52:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01301","created_at":"2026-05-18T00:52:09Z"},{"alias_kind":"pith_short_12","alias_value":"57EUC2OFPHTI","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"57EUC2OFPHTIRZHP","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"57EUC2OF","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:57EUC2OFPHTIRZHPWBXA2S3TH6","target":"record","payload":{"canonical_record":{"source":{"id":"1508.01301","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-06T07:44:40Z","cross_cats_sorted":[],"title_canon_sha256":"c9d3432f57a8cb05d2fb9d6d52c686b262da90160648eab36c5d0db98499fabe","abstract_canon_sha256":"2254953a76cab7fd73ab28cdc33a5af2566cfd100319f235d8579e29a811d806"},"schema_version":"1.0"},"canonical_sha256":"efc94169c579e688e4efb06e0d4b733f935b59b0070fa4b1ae9aa67d5fa4cb34","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:09.592856Z","signature_b64":"ZgF9tzSnlFK6UGsRJlGQjudCgp2hT6xvBAhB2JzLgS/TKq1MRIObN/j3SuTiPiH4na6rsfvaVwjB3iym9inGBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"efc94169c579e688e4efb06e0d4b733f935b59b0070fa4b1ae9aa67d5fa4cb34","last_reissued_at":"2026-05-18T00:52:09.592225Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:09.592225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.01301","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":"2026-05-18T00:52:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dSsYXD7thxr/LPe+sSnYPylKRyBX0vV6YH+jjqwpZpTZku/VYV3azwJFf80Vm9N687pSsusSAT4WK0MbOaoFAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:04:02.449913Z"},"content_sha256":"1b4396987df51bd22cc43aea0acab795b16fe0636576c6042c1a4d639e37589c","schema_version":"1.0","event_id":"sha256:1b4396987df51bd22cc43aea0acab795b16fe0636576c6042c1a4d639e37589c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:57EUC2OFPHTIRZHPWBXA2S3TH6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Calculating Greene's function via root polytopes and subdivision algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Karola Meszaros","submitted_at":"2015-08-06T07:44:40Z","abstract_excerpt":"Greene's rational function $\\Psi_P({\\bf x})$ is a sum of certain rational functions in ${\\bf x}=(x_1, \\ldots, x_n)$ over the linear extensions of the poset $P$ (which has $n$ elements), which he introduced in his study of the Murnaghan-Nakayama formula for the characters of the symmetric group. In recent work Boussicault, F\\'eray, Lascoux and Reiner showed that $\\Psi_P({\\bf x})$ equals a valuation on a cone and calculated $\\Psi_P({\\bf x})$ for several posets this way. In this paper we give an expression for $\\Psi_P({\\bf x})$ for any poset $P$. We obtain such a formula using dissections of root"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01301","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":"2026-05-18T00:52:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XqhQ+HYCSQ9Ul7RpoAKqtt6n9pUSmHoLNlXZr5KR53uirl8zrUizupqpxavcA7z7EH3Wh05QMxZdE2hI3QhHAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:04:02.450374Z"},"content_sha256":"a382ddb69e1457638153e4644248952131845fb3ba41d95b095dd9ddc8e0e2b2","schema_version":"1.0","event_id":"sha256:a382ddb69e1457638153e4644248952131845fb3ba41d95b095dd9ddc8e0e2b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/57EUC2OFPHTIRZHPWBXA2S3TH6/bundle.json","state_url":"https://pith.science/pith/57EUC2OFPHTIRZHPWBXA2S3TH6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/57EUC2OFPHTIRZHPWBXA2S3TH6/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":"2026-05-26T16:04:02Z","links":{"resolver":"https://pith.science/pith/57EUC2OFPHTIRZHPWBXA2S3TH6","bundle":"https://pith.science/pith/57EUC2OFPHTIRZHPWBXA2S3TH6/bundle.json","state":"https://pith.science/pith/57EUC2OFPHTIRZHPWBXA2S3TH6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/57EUC2OFPHTIRZHPWBXA2S3TH6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:57EUC2OFPHTIRZHPWBXA2S3TH6","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":"2254953a76cab7fd73ab28cdc33a5af2566cfd100319f235d8579e29a811d806","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-06T07:44:40Z","title_canon_sha256":"c9d3432f57a8cb05d2fb9d6d52c686b262da90160648eab36c5d0db98499fabe"},"schema_version":"1.0","source":{"id":"1508.01301","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01301","created_at":"2026-05-18T00:52:09Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01301v1","created_at":"2026-05-18T00:52:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01301","created_at":"2026-05-18T00:52:09Z"},{"alias_kind":"pith_short_12","alias_value":"57EUC2OFPHTI","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"57EUC2OFPHTIRZHP","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"57EUC2OF","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:a382ddb69e1457638153e4644248952131845fb3ba41d95b095dd9ddc8e0e2b2","target":"graph","created_at":"2026-05-18T00:52:09Z","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":"Greene's rational function $\\Psi_P({\\bf x})$ is a sum of certain rational functions in ${\\bf x}=(x_1, \\ldots, x_n)$ over the linear extensions of the poset $P$ (which has $n$ elements), which he introduced in his study of the Murnaghan-Nakayama formula for the characters of the symmetric group. In recent work Boussicault, F\\'eray, Lascoux and Reiner showed that $\\Psi_P({\\bf x})$ equals a valuation on a cone and calculated $\\Psi_P({\\bf x})$ for several posets this way. In this paper we give an expression for $\\Psi_P({\\bf x})$ for any poset $P$. We obtain such a formula using dissections of root","authors_text":"Karola Meszaros","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-06T07:44:40Z","title":"Calculating Greene's function via root polytopes and subdivision algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01301","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":"sha256:1b4396987df51bd22cc43aea0acab795b16fe0636576c6042c1a4d639e37589c","target":"record","created_at":"2026-05-18T00:52:09Z","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":"2254953a76cab7fd73ab28cdc33a5af2566cfd100319f235d8579e29a811d806","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-06T07:44:40Z","title_canon_sha256":"c9d3432f57a8cb05d2fb9d6d52c686b262da90160648eab36c5d0db98499fabe"},"schema_version":"1.0","source":{"id":"1508.01301","kind":"arxiv","version":1}},"canonical_sha256":"efc94169c579e688e4efb06e0d4b733f935b59b0070fa4b1ae9aa67d5fa4cb34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"efc94169c579e688e4efb06e0d4b733f935b59b0070fa4b1ae9aa67d5fa4cb34","first_computed_at":"2026-05-18T00:52:09.592225Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:09.592225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZgF9tzSnlFK6UGsRJlGQjudCgp2hT6xvBAhB2JzLgS/TKq1MRIObN/j3SuTiPiH4na6rsfvaVwjB3iym9inGBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:09.592856Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.01301","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b4396987df51bd22cc43aea0acab795b16fe0636576c6042c1a4d639e37589c","sha256:a382ddb69e1457638153e4644248952131845fb3ba41d95b095dd9ddc8e0e2b2"],"state_sha256":"3fef7cf9f7d0be5f25028f1568ad81776d6cf5c9e4cabccde9472592968b5e41"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uFxzmXBrGVSgKAURZL392Quk3nWnLmpQXPpBd1NsUoQR+/tl2cWPfgjEONYqlciJrV+OZJWz7T8lgz97JLHWDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T16:04:02.453001Z","bundle_sha256":"bfb61af625782150c8a0acca79cf1c67ff3c0c92e0455641475a976a1e680fdf"}}