{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:MFHNYNCBWHNGKD46ARCVNBYA2C","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":"74e7bb871f6d05cdc01c14fa3081f3ec7153ec4df69afdeda20483a46ce46481","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-04T19:25:23Z","title_canon_sha256":"eede5c57951030597e67e4cfb80e23f2756d3d23c5d8da5ef3336c23d480cc55"},"schema_version":"1.0","source":{"id":"2605.03097","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.03097","created_at":"2026-06-02T02:04:18Z"},{"alias_kind":"arxiv_version","alias_value":"2605.03097v2","created_at":"2026-06-02T02:04:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.03097","created_at":"2026-06-02T02:04:18Z"},{"alias_kind":"pith_short_12","alias_value":"MFHNYNCBWHNG","created_at":"2026-06-02T02:04:18Z"},{"alias_kind":"pith_short_16","alias_value":"MFHNYNCBWHNGKD46","created_at":"2026-06-02T02:04:18Z"},{"alias_kind":"pith_short_8","alias_value":"MFHNYNCB","created_at":"2026-06-02T02:04:18Z"}],"graph_snapshots":[{"event_id":"sha256:dba17003bfe0aaba9ccfea323972d5c13541bca8c697ca176f6a3bfed3201c8f","target":"graph","created_at":"2026-06-02T02:04:18Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We prove a full support theorem for the relative good moduli space of the universal compactified Jacobian π̄ : J̄_{g,n}^{d,φ} → M̄_{g,n}, showing that every direct summand appearing in the BBDG decomposition of Rπ̄_* IC(J̄_{g,n}^{d,φ}) has full support on the base M̄_{g,n}."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The stability condition φ and degree d are chosen so that the good moduli space morphism exists and the intersection cohomology sheaf behaves well under the cited decomposition and support theorems; the abstract does not specify the precise range of (g,n,d,φ) for which this holds."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Every direct summand in the BBDG decomposition of Rπ_* IC of the universal compactified Jacobian has full support on the base moduli space of curves, with the decomposition governed by the pushforward of the constant sheaf on the universal curve."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Every summand in the decomposition of the pushforward of the intersection cohomology sheaf from the universal compactified Jacobian has full support over the moduli space of curves."}],"snapshot_sha256":"e7767a53e0af04ac5d4d1a0ae7c122f7a4703c20af3ecb02455f96c7aff0cf36"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-20T14:37:08.345748Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-20T02:01:21.875696Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T15:43:42.925900Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.03097/integrity.json","findings":[],"snapshot_sha256":"ab02d4210299bc8ae698a9814c61429131d704f27759c73f9a59d8fb1daade34","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a full support theorem for the relative good moduli space of the universal compactified Jacobian $\\bar{\\pi}\\colon \\overline{J}_{g,n}^{d,\\phi}\\to \\overline{\\mathcal{M}}_{g,n}$, showing that every direct summand appearing in the BBDG decomposition of $\\mathrm{R}\\bar{\\pi}_*\\mathrm{IC}(\\overline{J}_{g,n}^{d,\\phi})$ has full support on the base $\\overline{\\mathcal{M}}_{g,n}$. Moreover, we explicitly describe this decomposition governed by the derived pushforward of the constant sheaf on the universal curve.\n  The first proof synthesizes Maulik and Shen's generalization of Ng\\^{o}'s support","authors_text":"Yifan Wu","cross_cats":[],"headline":"Every summand in the decomposition of the pushforward of the intersection cohomology sheaf from the universal compactified Jacobian has full support over the moduli space of curves.","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-04T19:25:23Z","title":"Support theorem of universal compactified Jacobians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.03097","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-07T02:08:10.112378Z","id":"7aca147f-a9f2-4b36-a267-c9e337c8b399","model_set":{"reader":"grok-4.3"},"one_line_summary":"Every direct summand in the BBDG decomposition of Rπ_* IC of the universal compactified Jacobian has full support on the base moduli space of curves, with the decomposition governed by the pushforward of the constant sheaf on the universal curve.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Every summand in the decomposition of the pushforward of the intersection cohomology sheaf from the universal compactified Jacobian has full support over the moduli space of curves.","strongest_claim":"We prove a full support theorem for the relative good moduli space of the universal compactified Jacobian π̄ : J̄_{g,n}^{d,φ} → M̄_{g,n}, showing that every direct summand appearing in the BBDG decomposition of Rπ̄_* IC(J̄_{g,n}^{d,φ}) has full support on the base M̄_{g,n}.","weakest_assumption":"The stability condition φ and degree d are chosen so that the good moduli space morphism exists and the intersection cohomology sheaf behaves well under the cited decomposition and support theorems; the abstract does not specify the precise range of (g,n,d,φ) for which this holds."}},"verdict_id":"7aca147f-a9f2-4b36-a267-c9e337c8b399"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f5a71f1e51d4ccaf1c018ccfdfef23264ce5acfb472301a3ce5a631b8c6c77cb","target":"record","created_at":"2026-06-02T02:04:18Z","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":"74e7bb871f6d05cdc01c14fa3081f3ec7153ec4df69afdeda20483a46ce46481","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-04T19:25:23Z","title_canon_sha256":"eede5c57951030597e67e4cfb80e23f2756d3d23c5d8da5ef3336c23d480cc55"},"schema_version":"1.0","source":{"id":"2605.03097","kind":"arxiv","version":2}},"canonical_sha256":"614edc3441b1da650f9e0445568700d0a56e9e24c3f935cc2333bbf03c8d4029","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"614edc3441b1da650f9e0445568700d0a56e9e24c3f935cc2333bbf03c8d4029","first_computed_at":"2026-06-02T02:04:18.482606Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T02:04:18.482606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gl6Rlu0Vzl4ih1WE4NfiELRLnWZrN7+9z5GeKNyoqlMKa9hbJmZq4FIS4u1tqFp1zj94ZexbOJV+/Q7rl/rOAg==","signature_status":"signed_v1","signed_at":"2026-06-02T02:04:18.483114Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.03097","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5a71f1e51d4ccaf1c018ccfdfef23264ce5acfb472301a3ce5a631b8c6c77cb","sha256:dba17003bfe0aaba9ccfea323972d5c13541bca8c697ca176f6a3bfed3201c8f"],"state_sha256":"ef93d3a96a3c2432c015bd5c483321371950c4c9fc48d555842c4446ed85ee9b"}