{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:VZ27VCNQCRYIM74HXUVJ6BTZBA","short_pith_number":"pith:VZ27VCNQ","canonical_record":{"source":{"id":"2504.09603","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-04-13T14:39:53Z","cross_cats_sorted":[],"title_canon_sha256":"c0b86c639d3e9b89373c3cd82416193c46fcef27c7bbbd9c76872ce9414adeb1","abstract_canon_sha256":"410b9a42e273bd9f67cbbb109f1b8199cf7fc379e27a6842de2c06c9dad167b8"},"schema_version":"1.0"},"canonical_sha256":"ae75fa89b01470867f87bd2a9f06790830f3220f16aa8e10407a806d515d8ae9","source":{"kind":"arxiv","id":"2504.09603","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.09603","created_at":"2026-05-29T02:05:34Z"},{"alias_kind":"arxiv_version","alias_value":"2504.09603v2","created_at":"2026-05-29T02:05:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.09603","created_at":"2026-05-29T02:05:34Z"},{"alias_kind":"pith_short_12","alias_value":"VZ27VCNQCRYI","created_at":"2026-05-29T02:05:34Z"},{"alias_kind":"pith_short_16","alias_value":"VZ27VCNQCRYIM74H","created_at":"2026-05-29T02:05:34Z"},{"alias_kind":"pith_short_8","alias_value":"VZ27VCNQ","created_at":"2026-05-29T02:05:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:VZ27VCNQCRYIM74HXUVJ6BTZBA","target":"record","payload":{"canonical_record":{"source":{"id":"2504.09603","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-04-13T14:39:53Z","cross_cats_sorted":[],"title_canon_sha256":"c0b86c639d3e9b89373c3cd82416193c46fcef27c7bbbd9c76872ce9414adeb1","abstract_canon_sha256":"410b9a42e273bd9f67cbbb109f1b8199cf7fc379e27a6842de2c06c9dad167b8"},"schema_version":"1.0"},"canonical_sha256":"ae75fa89b01470867f87bd2a9f06790830f3220f16aa8e10407a806d515d8ae9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T02:05:34.713143Z","signature_b64":"BuDdAPGAv3Fo9vPyXJdVzdRN48OkwjeWTKd31C8vKjlzwh4dI0duyQQUoFxcclq2RAdOxNlI8OdgCBOd4jlXBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae75fa89b01470867f87bd2a9f06790830f3220f16aa8e10407a806d515d8ae9","last_reissued_at":"2026-05-29T02:05:34.712565Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T02:05:34.712565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.09603","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":"2026-05-29T02:05:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2xhgrI/+hCAYvNEWXxB0wjzVzYnrP3gfHEUMU+/JFRPpSWYSsB+1z1sLGwefe/uhe53I/ib3hDISb26E4z79Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:36:29.495039Z"},"content_sha256":"c03ba914cc128f6e954dc33ca8c34f6c303b139eeeff825d52fa778e3f7530e5","schema_version":"1.0","event_id":"sha256:c03ba914cc128f6e954dc33ca8c34f6c303b139eeeff825d52fa778e3f7530e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:VZ27VCNQCRYIM74HXUVJ6BTZBA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Compact Manifolds with Unbounded Nilpotent Fundamental Groups and Positive Ricci Curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Aaron Naber, Daniele Semola, Elia Bru\\`e","submitted_at":"2025-04-13T14:39:53Z","abstract_excerpt":"It follows from the work of Kapovitch and Wilking that a closed manifold with nonnegative Ricci curvature has an almost nilpotent fundamental group. Leftover questions and conjectures have asked if in this context the fundamental group is actually uniformly almost abelian. The main goal of this work is to construct examples $(M^{9}_k, g_k)$ with uniformly positive Ricci curvature ${\\rm Ric}_{g_k}\\geq 8$ whose fundamental groups cannot be uniformly virtually abelian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.09603","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.09603/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-29T02:05:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+qGS+01Dj+mNkK6PvG7s2eBwQCkCrKW0tC8KvgfjcJc2rQpbUxBge6XBtnGSKWRvjRxtn2ZwYOZnMypCsIg+CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:36:29.495421Z"},"content_sha256":"7e4a90a1e774f68335adf29d6c73de8e5dfd815d355554501996fa1d80bf8387","schema_version":"1.0","event_id":"sha256:7e4a90a1e774f68335adf29d6c73de8e5dfd815d355554501996fa1d80bf8387"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VZ27VCNQCRYIM74HXUVJ6BTZBA/bundle.json","state_url":"https://pith.science/pith/VZ27VCNQCRYIM74HXUVJ6BTZBA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VZ27VCNQCRYIM74HXUVJ6BTZBA/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":"2026-06-20T22:36:29Z","links":{"resolver":"https://pith.science/pith/VZ27VCNQCRYIM74HXUVJ6BTZBA","bundle":"https://pith.science/pith/VZ27VCNQCRYIM74HXUVJ6BTZBA/bundle.json","state":"https://pith.science/pith/VZ27VCNQCRYIM74HXUVJ6BTZBA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VZ27VCNQCRYIM74HXUVJ6BTZBA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:VZ27VCNQCRYIM74HXUVJ6BTZBA","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":"410b9a42e273bd9f67cbbb109f1b8199cf7fc379e27a6842de2c06c9dad167b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-04-13T14:39:53Z","title_canon_sha256":"c0b86c639d3e9b89373c3cd82416193c46fcef27c7bbbd9c76872ce9414adeb1"},"schema_version":"1.0","source":{"id":"2504.09603","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.09603","created_at":"2026-05-29T02:05:34Z"},{"alias_kind":"arxiv_version","alias_value":"2504.09603v2","created_at":"2026-05-29T02:05:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.09603","created_at":"2026-05-29T02:05:34Z"},{"alias_kind":"pith_short_12","alias_value":"VZ27VCNQCRYI","created_at":"2026-05-29T02:05:34Z"},{"alias_kind":"pith_short_16","alias_value":"VZ27VCNQCRYIM74H","created_at":"2026-05-29T02:05:34Z"},{"alias_kind":"pith_short_8","alias_value":"VZ27VCNQ","created_at":"2026-05-29T02:05:34Z"}],"graph_snapshots":[{"event_id":"sha256:7e4a90a1e774f68335adf29d6c73de8e5dfd815d355554501996fa1d80bf8387","target":"graph","created_at":"2026-05-29T02:05:34Z","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/2504.09603/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It follows from the work of Kapovitch and Wilking that a closed manifold with nonnegative Ricci curvature has an almost nilpotent fundamental group. Leftover questions and conjectures have asked if in this context the fundamental group is actually uniformly almost abelian. The main goal of this work is to construct examples $(M^{9}_k, g_k)$ with uniformly positive Ricci curvature ${\\rm Ric}_{g_k}\\geq 8$ whose fundamental groups cannot be uniformly virtually abelian.","authors_text":"Aaron Naber, Daniele Semola, Elia Bru\\`e","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-04-13T14:39:53Z","title":"Compact Manifolds with Unbounded Nilpotent Fundamental Groups and Positive Ricci Curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.09603","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:c03ba914cc128f6e954dc33ca8c34f6c303b139eeeff825d52fa778e3f7530e5","target":"record","created_at":"2026-05-29T02:05:34Z","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":"410b9a42e273bd9f67cbbb109f1b8199cf7fc379e27a6842de2c06c9dad167b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-04-13T14:39:53Z","title_canon_sha256":"c0b86c639d3e9b89373c3cd82416193c46fcef27c7bbbd9c76872ce9414adeb1"},"schema_version":"1.0","source":{"id":"2504.09603","kind":"arxiv","version":2}},"canonical_sha256":"ae75fa89b01470867f87bd2a9f06790830f3220f16aa8e10407a806d515d8ae9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae75fa89b01470867f87bd2a9f06790830f3220f16aa8e10407a806d515d8ae9","first_computed_at":"2026-05-29T02:05:34.712565Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T02:05:34.712565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BuDdAPGAv3Fo9vPyXJdVzdRN48OkwjeWTKd31C8vKjlzwh4dI0duyQQUoFxcclq2RAdOxNlI8OdgCBOd4jlXBw==","signature_status":"signed_v1","signed_at":"2026-05-29T02:05:34.713143Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.09603","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c03ba914cc128f6e954dc33ca8c34f6c303b139eeeff825d52fa778e3f7530e5","sha256:7e4a90a1e774f68335adf29d6c73de8e5dfd815d355554501996fa1d80bf8387"],"state_sha256":"7dee8829610d2b6defda916b06147c84b1779d534afce68f44269528a9d36076"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vuPOb53Gu9vqUrqsybLRdiyN60dE0PpoZmw52iJWdDm0jtcKVK50cmmXyd9uHYn3qo6TfL5XID+eUCkcdV0JDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T22:36:29.497381Z","bundle_sha256":"8a0fa2fd7026dfcc42083a8196b48dbd50723e258057ea2af80fa13b55008dcb"}}