{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:CR4YMM3M3VSW5C43WYJE3KJPE7","short_pith_number":"pith:CR4YMM3M","schema_version":"1.0","canonical_sha256":"147986336cdd656e8b9bb6124da92f27f4a03d6e9c4ccaaebb277ff4fd7d245a","source":{"kind":"arxiv","id":"1805.10573","version":1},"attestation_state":"computed","paper":{"title":"On the deformation of ball packings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"Huabin Ge, Liangming Shen, Wenshuai Jiang","submitted_at":"2018-05-27T03:01:54Z","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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1805.10573","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-05-27T03:01:54Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"fbf7fbb7516a3c28db7f995071acc4851307354eede4cc68c70c2b2066e247d4","abstract_canon_sha256":"f39d0bf98c497f0fda16cfb5925652731332156e457c10919a1cf557557ad4b2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:52.035046Z","signature_b64":"BavlhNXN4t+YRKFbnruLrj0ug8xgTnUIKjPjaYxgJrAeR3EKvKuL01t8t++AHsiw6J1YiZ4/SdzOzAHFpLo8AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"147986336cdd656e8b9bb6124da92f27f4a03d6e9c4ccaaebb277ff4fd7d245a","last_reissued_at":"2026-05-18T00:14:52.034328Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:52.034328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the deformation of ball packings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"Huabin Ge, Liangming Shen, Wenshuai Jiang","submitted_at":"2018-05-27T03:01:54Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10573","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1805.10573","created_at":"2026-05-18T00:14:52.034420+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.10573v1","created_at":"2026-05-18T00:14:52.034420+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10573","created_at":"2026-05-18T00:14:52.034420+00:00"},{"alias_kind":"pith_short_12","alias_value":"CR4YMM3M3VSW","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_16","alias_value":"CR4YMM3M3VSW5C43","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_8","alias_value":"CR4YMM3M","created_at":"2026-05-18T12:32:16.446611+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CR4YMM3M3VSW5C43WYJE3KJPE7","json":"https://pith.science/pith/CR4YMM3M3VSW5C43WYJE3KJPE7.json","graph_json":"https://pith.science/api/pith-number/CR4YMM3M3VSW5C43WYJE3KJPE7/graph.json","events_json":"https://pith.science/api/pith-number/CR4YMM3M3VSW5C43WYJE3KJPE7/events.json","paper":"https://pith.science/paper/CR4YMM3M"},"agent_actions":{"view_html":"https://pith.science/pith/CR4YMM3M3VSW5C43WYJE3KJPE7","download_json":"https://pith.science/pith/CR4YMM3M3VSW5C43WYJE3KJPE7.json","view_paper":"https://pith.science/paper/CR4YMM3M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.10573&json=true","fetch_graph":"https://pith.science/api/pith-number/CR4YMM3M3VSW5C43WYJE3KJPE7/graph.json","fetch_events":"https://pith.science/api/pith-number/CR4YMM3M3VSW5C43WYJE3KJPE7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CR4YMM3M3VSW5C43WYJE3KJPE7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CR4YMM3M3VSW5C43WYJE3KJPE7/action/storage_attestation","attest_author":"https://pith.science/pith/CR4YMM3M3VSW5C43WYJE3KJPE7/action/author_attestation","sign_citation":"https://pith.science/pith/CR4YMM3M3VSW5C43WYJE3KJPE7/action/citation_signature","submit_replication":"https://pith.science/pith/CR4YMM3M3VSW5C43WYJE3KJPE7/action/replication_record"}},"created_at":"2026-05-18T00:14:52.034420+00:00","updated_at":"2026-05-18T00:14:52.034420+00:00"}