{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:OSYLPBIN3ZL4V3AKWIZO5QZF6X","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":"f04e0a2684d562f8af7aadd68f381b8b9bc6bcabff39dbd735172d6cae5ad471","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-05-28T20:07:45Z","title_canon_sha256":"d123b04b073413f27a558f52f476a9af27f3959f0d3dd1dc402f7022ab39c4b0"},"schema_version":"1.0","source":{"id":"2605.30530","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.30530","created_at":"2026-06-01T01:02:59Z"},{"alias_kind":"arxiv_version","alias_value":"2605.30530v1","created_at":"2026-06-01T01:02:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.30530","created_at":"2026-06-01T01:02:59Z"},{"alias_kind":"pith_short_12","alias_value":"OSYLPBIN3ZL4","created_at":"2026-06-01T01:02:59Z"},{"alias_kind":"pith_short_16","alias_value":"OSYLPBIN3ZL4V3AK","created_at":"2026-06-01T01:02:59Z"},{"alias_kind":"pith_short_8","alias_value":"OSYLPBIN","created_at":"2026-06-01T01:02:59Z"}],"graph_snapshots":[{"event_id":"sha256:6d31d722eaf32eaac4dfd67b88da3100f4ce08719431207b582a7b44802bb397","target":"graph","created_at":"2026-06-01T01:02:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.30530/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For an abelian variety $X$ and $\\alpha \\in Br(X)$, we propose a new invariance $Ind_{SH}(\\alpha)$ that refines the known period index relations. It is closely related to the geometry of $\\mathcal{X}$, the $\\mathbb{G}_m$-gerbe over $X$ that corresponds to $\\alpha$: we study the minimal trivializing isogenies for $\\mathcal{X}$ via its $\\mu_n$-lifts and the $1-$twisted semi-homogeneous vector bundles on $\\mathcal{X}$. As an application, we show that the period index conjecture holds true for products of elliptic curves of any dimension.","authors_text":"Ruoxi Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-05-28T20:07:45Z","title":"Minimal Trivializing Isogenies of $\\mathbb{G}_m$-gerbes over Abelian Varieties and Period-Index Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30530","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":"sha256:0f439f9633f0eaa6dab4d74423873e30cf7186b43ba3e02eafdb0216ddf81e06","target":"record","created_at":"2026-06-01T01:02:59Z","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":"f04e0a2684d562f8af7aadd68f381b8b9bc6bcabff39dbd735172d6cae5ad471","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-05-28T20:07:45Z","title_canon_sha256":"d123b04b073413f27a558f52f476a9af27f3959f0d3dd1dc402f7022ab39c4b0"},"schema_version":"1.0","source":{"id":"2605.30530","kind":"arxiv","version":1}},"canonical_sha256":"74b0b7850dde57caec0ab232eec325f5e40132de880bf77787286317192b1cbe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74b0b7850dde57caec0ab232eec325f5e40132de880bf77787286317192b1cbe","first_computed_at":"2026-06-01T01:02:59.380114Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-01T01:02:59.380114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1EqfEAD3lm4oWVJYCCuOS8ng4yIP23P+sXWcXVwfqtBED8bTUXUmIZELs2QZEIv4KYV6kG5lzamPdSzUlseFDw==","signature_status":"signed_v1","signed_at":"2026-06-01T01:02:59.380987Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.30530","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f439f9633f0eaa6dab4d74423873e30cf7186b43ba3e02eafdb0216ddf81e06","sha256:6d31d722eaf32eaac4dfd67b88da3100f4ce08719431207b582a7b44802bb397"],"state_sha256":"634095481d74125695cf79e3f68993b0c3aaca92b967da17074f37120c35a23e"}