{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:IDICVZ6D47UNIV4PVF2BOEGMYZ","short_pith_number":"pith:IDICVZ6D","canonical_record":{"source":{"id":"1501.04742","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-01-20T09:11:42Z","cross_cats_sorted":[],"title_canon_sha256":"da08e9a8f9e1260e0c44f6bd5894677e973ad8ec4c6d681cfcc49f610232c2fe","abstract_canon_sha256":"c50fcd288a850d4e6cfe5820d4a65056272475684cac60ff589edccd0bda29a5"},"schema_version":"1.0"},"canonical_sha256":"40d02ae7c3e7e8d4578fa9741710ccc64c07373e0cddcf54ce8cbd946b231afd","source":{"kind":"arxiv","id":"1501.04742","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04742","created_at":"2026-05-18T01:04:33Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04742v2","created_at":"2026-05-18T01:04:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04742","created_at":"2026-05-18T01:04:33Z"},{"alias_kind":"pith_short_12","alias_value":"IDICVZ6D47UN","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IDICVZ6D47UNIV4P","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IDICVZ6D","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:IDICVZ6D47UNIV4PVF2BOEGMYZ","target":"record","payload":{"canonical_record":{"source":{"id":"1501.04742","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-01-20T09:11:42Z","cross_cats_sorted":[],"title_canon_sha256":"da08e9a8f9e1260e0c44f6bd5894677e973ad8ec4c6d681cfcc49f610232c2fe","abstract_canon_sha256":"c50fcd288a850d4e6cfe5820d4a65056272475684cac60ff589edccd0bda29a5"},"schema_version":"1.0"},"canonical_sha256":"40d02ae7c3e7e8d4578fa9741710ccc64c07373e0cddcf54ce8cbd946b231afd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:33.451554Z","signature_b64":"niUQOjGkZJzx/JSOu4ei+vNTZCC22qAVzGbl1wrjrh+m2cUP+Iat8VV6ij5htWrsmhEsoE6McKflNZ2qSXDcCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40d02ae7c3e7e8d4578fa9741710ccc64c07373e0cddcf54ce8cbd946b231afd","last_reissued_at":"2026-05-18T01:04:33.450813Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:33.450813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.04742","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":"2026-05-18T01:04:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AlZdptzk84VsTJtSHdOS52hScWlyYQ1XMd68gcYh064XHFwawwlFPtXOv7QVshUh1MQ1F+8LZjnDz1FOqu1aBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:57:46.836746Z"},"content_sha256":"5183bd95069dcce4a4a35bae75a610a76009109b8036743f972794a632c8edb1","schema_version":"1.0","event_id":"sha256:5183bd95069dcce4a4a35bae75a610a76009109b8036743f972794a632c8edb1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:IDICVZ6D47UNIV4PVF2BOEGMYZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Poincar\\'e duality of wonderful compactifications and tautological rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dan Petersen","submitted_at":"2015-01-20T09:11:42Z","abstract_excerpt":"Let $g \\geq 2$. Let $M_{g,n}^{rt}$ be the moduli space of $n$-pointed genus $g$ curves with rational tails. Let $C_g^n$ be the $n$-fold fibered power of the universal curve over $M_g$. We prove that the tautological ring of $M_{g,n}^{rt}$ has Poincar\\'e duality if and only if the same holds for the tautological ring of $C_g^n$. We also obtain a presentation of the tautological ring of $M_{g,n}^{rt}$ as an algebra over the tautological ring of $C_g^n$. This proves a conjecture of Tavakol. Our results are valid in the more general setting of wonderful compactifications."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04742","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":"2026-05-18T01:04:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tM0Ho2VJ1RkZxRi3WufrVnliVMO5MUrJpAX+r+Bstfavhya0Y4HL+gucq1Eyjvjq4s3u1Fggm3gSbDdsRJP3Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:57:46.837086Z"},"content_sha256":"d11b86cf691e4991bb592cd47d9aecef3c43c8a89488b793cbfb7a21cb88acd5","schema_version":"1.0","event_id":"sha256:d11b86cf691e4991bb592cd47d9aecef3c43c8a89488b793cbfb7a21cb88acd5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IDICVZ6D47UNIV4PVF2BOEGMYZ/bundle.json","state_url":"https://pith.science/pith/IDICVZ6D47UNIV4PVF2BOEGMYZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IDICVZ6D47UNIV4PVF2BOEGMYZ/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":"2026-06-04T17:57:46Z","links":{"resolver":"https://pith.science/pith/IDICVZ6D47UNIV4PVF2BOEGMYZ","bundle":"https://pith.science/pith/IDICVZ6D47UNIV4PVF2BOEGMYZ/bundle.json","state":"https://pith.science/pith/IDICVZ6D47UNIV4PVF2BOEGMYZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IDICVZ6D47UNIV4PVF2BOEGMYZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IDICVZ6D47UNIV4PVF2BOEGMYZ","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":"c50fcd288a850d4e6cfe5820d4a65056272475684cac60ff589edccd0bda29a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-01-20T09:11:42Z","title_canon_sha256":"da08e9a8f9e1260e0c44f6bd5894677e973ad8ec4c6d681cfcc49f610232c2fe"},"schema_version":"1.0","source":{"id":"1501.04742","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04742","created_at":"2026-05-18T01:04:33Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04742v2","created_at":"2026-05-18T01:04:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04742","created_at":"2026-05-18T01:04:33Z"},{"alias_kind":"pith_short_12","alias_value":"IDICVZ6D47UN","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IDICVZ6D47UNIV4P","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IDICVZ6D","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:d11b86cf691e4991bb592cd47d9aecef3c43c8a89488b793cbfb7a21cb88acd5","target":"graph","created_at":"2026-05-18T01:04:33Z","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":"Let $g \\geq 2$. Let $M_{g,n}^{rt}$ be the moduli space of $n$-pointed genus $g$ curves with rational tails. Let $C_g^n$ be the $n$-fold fibered power of the universal curve over $M_g$. We prove that the tautological ring of $M_{g,n}^{rt}$ has Poincar\\'e duality if and only if the same holds for the tautological ring of $C_g^n$. We also obtain a presentation of the tautological ring of $M_{g,n}^{rt}$ as an algebra over the tautological ring of $C_g^n$. This proves a conjecture of Tavakol. Our results are valid in the more general setting of wonderful compactifications.","authors_text":"Dan Petersen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-01-20T09:11:42Z","title":"Poincar\\'e duality of wonderful compactifications and tautological rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04742","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":"sha256:5183bd95069dcce4a4a35bae75a610a76009109b8036743f972794a632c8edb1","target":"record","created_at":"2026-05-18T01:04:33Z","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":"c50fcd288a850d4e6cfe5820d4a65056272475684cac60ff589edccd0bda29a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-01-20T09:11:42Z","title_canon_sha256":"da08e9a8f9e1260e0c44f6bd5894677e973ad8ec4c6d681cfcc49f610232c2fe"},"schema_version":"1.0","source":{"id":"1501.04742","kind":"arxiv","version":2}},"canonical_sha256":"40d02ae7c3e7e8d4578fa9741710ccc64c07373e0cddcf54ce8cbd946b231afd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40d02ae7c3e7e8d4578fa9741710ccc64c07373e0cddcf54ce8cbd946b231afd","first_computed_at":"2026-05-18T01:04:33.450813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:33.450813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"niUQOjGkZJzx/JSOu4ei+vNTZCC22qAVzGbl1wrjrh+m2cUP+Iat8VV6ij5htWrsmhEsoE6McKflNZ2qSXDcCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:33.451554Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.04742","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5183bd95069dcce4a4a35bae75a610a76009109b8036743f972794a632c8edb1","sha256:d11b86cf691e4991bb592cd47d9aecef3c43c8a89488b793cbfb7a21cb88acd5"],"state_sha256":"8deef0675475f1456964789780fb654e9d811b1ea758c830d6eaefb3032a15a6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4IUJ2KuUe+kIofBxqIWLpCvMPX89l55iifNNqMh89wWlEeDepR5mJrZXBaK48AABhf9KpuxY8J8nn1dyv8iTCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T17:57:46.839041Z","bundle_sha256":"129d4e675c4424c20bd81a75a033c017e76fa142427735030ffd08ce86b973a6"}}