{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:W4QGX4JNREM6EGS2WASNQ3OMOZ","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":"11ba2358467cf214d7310d320940d722883fe06cd77480b4a51354d93c01106f","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-06-28T00:47:13Z","title_canon_sha256":"63d87fc9afca835a376c9f6952d310d15b34a1b2dc51ce7d3f80eebc348a3866"},"schema_version":"1.0","source":{"id":"2606.29135","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.29135","created_at":"2026-06-30T01:17:53Z"},{"alias_kind":"arxiv_version","alias_value":"2606.29135v1","created_at":"2026-06-30T01:17:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.29135","created_at":"2026-06-30T01:17:53Z"},{"alias_kind":"pith_short_12","alias_value":"W4QGX4JNREM6","created_at":"2026-06-30T01:17:53Z"},{"alias_kind":"pith_short_16","alias_value":"W4QGX4JNREM6EGS2","created_at":"2026-06-30T01:17:53Z"},{"alias_kind":"pith_short_8","alias_value":"W4QGX4JN","created_at":"2026-06-30T01:17:53Z"}],"graph_snapshots":[{"event_id":"sha256:b0cb3470bd8451d5b01192d6e391c80a7db14d9953539c85bb1a9f335c883d70","target":"graph","created_at":"2026-06-30T01:17:53Z","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/2606.29135/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Gromov's simplicial volume is a fundamental invariant measuring the topological complexity of a manifold. A conjecture of Gromov predicts that every closed manifold admitting a metric of positive scalar curvature has vanishing simplicial volume. In this paper, we prove this conjecture under a natural weakening of the classical rapid decay (RD) property for the fundamental group.","authors_text":"Guoliang Yu, Qiaochu Ma","cross_cats":["math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-06-28T00:47:13Z","title":"Gromov's Conjecture on Positive Scalar Curvature and Simplicial Volume under a Fundamental Group Decay Property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29135","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":"sha256:781b24efe2e402eba93207fee6f4af4684138edfc6d22f18d5d1517b5009d2fa","target":"record","created_at":"2026-06-30T01:17:53Z","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":"11ba2358467cf214d7310d320940d722883fe06cd77480b4a51354d93c01106f","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-06-28T00:47:13Z","title_canon_sha256":"63d87fc9afca835a376c9f6952d310d15b34a1b2dc51ce7d3f80eebc348a3866"},"schema_version":"1.0","source":{"id":"2606.29135","kind":"arxiv","version":1}},"canonical_sha256":"b7206bf12d8919e21a5ab024d86dcc76579bc6a938e15fc43d5d84e4f77e89c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7206bf12d8919e21a5ab024d86dcc76579bc6a938e15fc43d5d84e4f77e89c7","first_computed_at":"2026-06-30T01:17:53.990990Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T01:17:53.990990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eC02ocArA8iC8/iZMuyXXDdSkjKbi9/m4YoQ4d2MYl4HYTXJYiy5wr0H07aGsdFqXG0SGUFFQbQ+70DHE/dgDw==","signature_status":"signed_v1","signed_at":"2026-06-30T01:17:53.991470Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.29135","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:781b24efe2e402eba93207fee6f4af4684138edfc6d22f18d5d1517b5009d2fa","sha256:b0cb3470bd8451d5b01192d6e391c80a7db14d9953539c85bb1a9f335c883d70"],"state_sha256":"10a6c8d9958ad14d7139cf07644cec52fc338c2c5d84fc0446e1a636560c563d"}