{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CR4YMM3M3VSW5C43WYJE3KJPE7","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":"f39d0bf98c497f0fda16cfb5925652731332156e457c10919a1cf557557ad4b2","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-05-27T03:01:54Z","title_canon_sha256":"fbf7fbb7516a3c28db7f995071acc4851307354eede4cc68c70c2b2066e247d4"},"schema_version":"1.0","source":{"id":"1805.10573","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.10573","created_at":"2026-05-18T00:14:52Z"},{"alias_kind":"arxiv_version","alias_value":"1805.10573v1","created_at":"2026-05-18T00:14:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10573","created_at":"2026-05-18T00:14:52Z"},{"alias_kind":"pith_short_12","alias_value":"CR4YMM3M3VSW","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CR4YMM3M3VSW5C43","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CR4YMM3M","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:22e3cdf11e565ff7367581c6ca7cca89dca22f8fb78249e3d9b0bbcf3de3ef0a","target":"graph","created_at":"2026-05-18T00:14:52Z","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 study the geometric aspects of ball packings on $(M,\\mathcal{T})$, where $\\mathcal{T}$ is a triangulation on a 3-manifold $M$. We introduce a combinatorial Yamabe invariant $Y_{\\mathcal{T}}$, depending on the topology of $M$ and the combinatoric of $\\mathcal{T}$. We prove that $Y_{\\mathcal{T}}$ is attainable if and only if there is a constant curvature packing, and the combinatorial Yamabe problem can be solved by minimizing Cooper-Rivin-Glickenstein functional. We then study the combinatorial Yamabe flow introduced by Glickenstein \\cite{G0}-\\cite{G2}. We first prove a small ","authors_text":"Huabin Ge, Liangming Shen, Wenshuai Jiang","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-05-27T03:01:54Z","title":"On the deformation of ball packings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10573","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":"sha256:59065080e1d93dc47426b8cd47a2824698faa1d538b267186c79fba3b69c23df","target":"record","created_at":"2026-05-18T00:14:52Z","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":"f39d0bf98c497f0fda16cfb5925652731332156e457c10919a1cf557557ad4b2","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-05-27T03:01:54Z","title_canon_sha256":"fbf7fbb7516a3c28db7f995071acc4851307354eede4cc68c70c2b2066e247d4"},"schema_version":"1.0","source":{"id":"1805.10573","kind":"arxiv","version":1}},"canonical_sha256":"147986336cdd656e8b9bb6124da92f27f4a03d6e9c4ccaaebb277ff4fd7d245a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"147986336cdd656e8b9bb6124da92f27f4a03d6e9c4ccaaebb277ff4fd7d245a","first_computed_at":"2026-05-18T00:14:52.034328Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:52.034328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BavlhNXN4t+YRKFbnruLrj0ug8xgTnUIKjPjaYxgJrAeR3EKvKuL01t8t++AHsiw6J1YiZ4/SdzOzAHFpLo8AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:52.035046Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.10573","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59065080e1d93dc47426b8cd47a2824698faa1d538b267186c79fba3b69c23df","sha256:22e3cdf11e565ff7367581c6ca7cca89dca22f8fb78249e3d9b0bbcf3de3ef0a"],"state_sha256":"dc2357b5f52e6fbe41b48d9d3cd483947bd5f60ec4f2932c8ba89e3eb0140aaa"}