{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NLPPSTJN4LLCD35HUUVGUUGQTI","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":"610294320408c956f74240a603bf92887fff30d21906500bc2711e67106fc06f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-10-29T15:52:46Z","title_canon_sha256":"abb78e2674873962c1b21bb10ad2de756103d00d656d63919fe95fb36f2e9ffb"},"schema_version":"1.0","source":{"id":"1810.12205","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.12205","created_at":"2026-05-18T00:02:03Z"},{"alias_kind":"arxiv_version","alias_value":"1810.12205v1","created_at":"2026-05-18T00:02:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.12205","created_at":"2026-05-18T00:02:03Z"},{"alias_kind":"pith_short_12","alias_value":"NLPPSTJN4LLC","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NLPPSTJN4LLCD35H","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NLPPSTJN","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:5c7c355781dfc19667b45c34c1b3183d7a55207154b206207384c7efe33e61c4","target":"graph","created_at":"2026-05-18T00:02:03Z","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"},"paper":{"abstract_excerpt":"We derive new estimates for the first Betti number of compact Riemannian manifolds. Our approach relies on the Birman-Schwinger principle and Schatten norm estimates for semigroup differences. In contrast to previous works we do not require any a priori ultracontractivity estimates and we provide bounds which explicitly depend on suitable integral norms of the Ricci tensor.","authors_text":"Christian Rose, Marcel Hansmann, Peter Stollmann","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-10-29T15:52:46Z","title":"Bounds on the first Betti number - an approach via Schatten norm estimates on semigroup differences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12205","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:c8a39e2c7bb7aa322f67767bd072ed6529203c1300685ad3bf54f150b56bfb10","target":"record","created_at":"2026-05-18T00:02:03Z","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":"610294320408c956f74240a603bf92887fff30d21906500bc2711e67106fc06f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-10-29T15:52:46Z","title_canon_sha256":"abb78e2674873962c1b21bb10ad2de756103d00d656d63919fe95fb36f2e9ffb"},"schema_version":"1.0","source":{"id":"1810.12205","kind":"arxiv","version":1}},"canonical_sha256":"6adef94d2de2d621efa7a52a6a50d09a19146b26fd4edee80d47bf9f925e7a6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6adef94d2de2d621efa7a52a6a50d09a19146b26fd4edee80d47bf9f925e7a6c","first_computed_at":"2026-05-18T00:02:03.929033Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:03.929033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1yz/T6wPFWrlRuTkk8NWuHQZ+CXRMdGGZuUFULSfdqNpvgavxAa6wtvdLZ3IM4UU8ovKuZPqLaGHFUhs7feoCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:03.929734Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.12205","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8a39e2c7bb7aa322f67767bd072ed6529203c1300685ad3bf54f150b56bfb10","sha256:5c7c355781dfc19667b45c34c1b3183d7a55207154b206207384c7efe33e61c4"],"state_sha256":"fbf55dbb3717f27c1efeee6e718eb84c8ddbdb0147f6c9e8b5ed3556bcf768ae"}