{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZPWXPHCKDYCYYDCTPOUGK5SEGE","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":"e99de81527b4b52ca21732f41b71e462d351512169cc5428b5d5e7acdd202eea","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-12-28T13:15:08Z","title_canon_sha256":"9d6c5d22427ae689a6d1c473cbdc7fee4bd4c01ebce36300ec75f69b7ef0f0c2"},"schema_version":"1.0","source":{"id":"1512.08405","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08405","created_at":"2026-05-18T00:47:43Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08405v2","created_at":"2026-05-18T00:47:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08405","created_at":"2026-05-18T00:47:43Z"},{"alias_kind":"pith_short_12","alias_value":"ZPWXPHCKDYCY","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZPWXPHCKDYCYYDCT","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZPWXPHCK","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:bbbe4fd256dc80dc36f737e890ca2cb68eeef8ad18f35057008259d1d100c3c8","target":"graph","created_at":"2026-05-18T00:47:43Z","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":"In this paper, we consider the generalized lambda constant and the existence of ground states of the generalized Perelman's W-functional from a variational formulation. One result is concerned with the estimation of the generalized $\\lambda$ constant. The other results are about the existence of ground states of generalized $F$-functional and W-functional both on a complete non-compact Riemannian manifold $(M,g)$ with positive injectivity radius and with Ricci curvature bounded from below. Our main results are Theorems 2,3 and 7. For the existence of the ground states we use Lions' concentrati","authors_text":"Li Ma","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-12-28T13:15:08Z","title":"Lambda constant and Ground states of Perelman's W-functional"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08405","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:a58a2450089355dcfed6fc21b3cf8aef93b1178505b53d7ea3fe7810ed9e7281","target":"record","created_at":"2026-05-18T00:47:43Z","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":"e99de81527b4b52ca21732f41b71e462d351512169cc5428b5d5e7acdd202eea","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-12-28T13:15:08Z","title_canon_sha256":"9d6c5d22427ae689a6d1c473cbdc7fee4bd4c01ebce36300ec75f69b7ef0f0c2"},"schema_version":"1.0","source":{"id":"1512.08405","kind":"arxiv","version":2}},"canonical_sha256":"cbed779c4a1e058c0c537ba865764431208a2f374c66294f7c76085494d5280d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cbed779c4a1e058c0c537ba865764431208a2f374c66294f7c76085494d5280d","first_computed_at":"2026-05-18T00:47:43.154380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:43.154380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1vEf5FoYLmSfhQKW7EBKozbj3YFYCi/LWpflXLeRAPT2N4G1r9nVu6Y4PAchH5MTiqw4G1wZr720yDxsBX6vAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:43.155052Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.08405","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a58a2450089355dcfed6fc21b3cf8aef93b1178505b53d7ea3fe7810ed9e7281","sha256:bbbe4fd256dc80dc36f737e890ca2cb68eeef8ad18f35057008259d1d100c3c8"],"state_sha256":"baca0a66dc1b0173cacce8f8a3494211ae2dd98ea26dcc929d8f12b8fffeae68"}