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Using the canonical $S_n$-equivariant isomorphisms $\\widetilde{H}^{i-1}(\\Delta_{g,n};\\mathbb{Q}) \\cong W_0 H^i_c(\\mathcal{M}_{g,n};\\mathbb{Q})$, we calculate the weight $0$, compactly supported rational cohomology of the moduli spaces $\\mathcal{M}_{g,n}$ in the range"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2307.01960","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-07-04T23:50:30Z","cross_cats_sorted":["math.AT","math.CO"],"title_canon_sha256":"1afd8f15ca6969cdb44f4b12f35a30a4db64ec022f365b68865d822748bd9269","abstract_canon_sha256":"a99fae07325ff14e24f177cb13d3136e672e49ed665c6d3280d6e506cd258bd5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:07:57.107141Z","signature_b64":"tT+GpubVF/MPOxG3oQak2FqKnNqbpm5oxHw2w+6p7Q9cz1cWomoj9FQpySaQjm6PzI+3W6Re+4dmACBCjamkDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"756409cee31fd92f3e88c35af20495968a94e4108024faf3f20d464f931deac8","last_reissued_at":"2026-07-05T08:07:57.106502Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:07:57.106502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Serre spectral sequence for the moduli space of tropical curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CO"],"primary_cat":"math.AG","authors_text":"Christin Bibby, Claudia He Yun, Melody Chan, Nir Gadish","submitted_at":"2023-07-04T23:50:30Z","abstract_excerpt":"We construct, for all $g\\geq 2$ and $n\\geq 0$, a spectral sequence of rational $S_n$-representations which computes the $S_n$-equivariant reduced rational cohomology of the tropical moduli spaces of curves $\\Delta_{g,n}$ in terms of compactly supported cohomology groups of configuration spaces of $n$ points on graphs of genus $g$. 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