{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:KG26DYAWO6ZVWNV7SDADLPNSWV","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":"c3aaa9522d6be409ff2958e4790a9add3f6523aba1533053efce518b90d98d9e","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2025-02-26T20:48:57Z","title_canon_sha256":"05374b69f3930764332edc428047c05a5470195f1526f52da9632b8f61a3a9f3"},"schema_version":"1.0","source":{"id":"2502.19554","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.19554","created_at":"2026-07-05T10:20:48Z"},{"alias_kind":"arxiv_version","alias_value":"2502.19554v1","created_at":"2026-07-05T10:20:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.19554","created_at":"2026-07-05T10:20:48Z"},{"alias_kind":"pith_short_12","alias_value":"KG26DYAWO6ZV","created_at":"2026-07-05T10:20:48Z"},{"alias_kind":"pith_short_16","alias_value":"KG26DYAWO6ZVWNV7","created_at":"2026-07-05T10:20:48Z"},{"alias_kind":"pith_short_8","alias_value":"KG26DYAW","created_at":"2026-07-05T10:20:48Z"}],"graph_snapshots":[{"event_id":"sha256:1b5f6efc0d699cbb419eb743cd9bcb9d4ed61fc8b30b25902a3b5789ecefe032","target":"graph","created_at":"2026-07-05T10:20:48Z","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/2502.19554/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It is shown that the smallest possible distance between two disjoint lattice polytopes contained in the cube $[0,k]^3$ is exactly $$ \\frac{1}{\\sqrt{2(2k^2-4k+5)(2k^2-2k+1)}} $$ for every integer $k$ at least $4$. The proof relies on modeling this as a minimization problem over a subset of the lattice points in the hypercube $[-k,k]^9$. A precise characterization of this subset allows to reduce the problem to computing the roots of a finite number of degree at most $4$ polynomials, which is done using symbolic computation.","authors_text":"Antoine Deza, Lionel Pournin, Zhongyuan Liu","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2025-02-26T20:48:57Z","title":"Kissing polytopes in dimension 3"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.19554","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:ea47d170c7070fb1064a1c6c224c9d7bcdc2f5ee72aa86337012e865402718ea","target":"record","created_at":"2026-07-05T10:20:48Z","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":"c3aaa9522d6be409ff2958e4790a9add3f6523aba1533053efce518b90d98d9e","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2025-02-26T20:48:57Z","title_canon_sha256":"05374b69f3930764332edc428047c05a5470195f1526f52da9632b8f61a3a9f3"},"schema_version":"1.0","source":{"id":"2502.19554","kind":"arxiv","version":1}},"canonical_sha256":"51b5e1e01677b35b36bf90c035bdb2b55dc30dc7d387328e952a49b75c4549dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51b5e1e01677b35b36bf90c035bdb2b55dc30dc7d387328e952a49b75c4549dd","first_computed_at":"2026-07-05T10:20:48.571636Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:20:48.571636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uAoufFGRLZNHuiVd6l6oslv+pCcYYC/CqGu+gkzRpKZG6Tu+yjdYVh3nYEjFQbxJemBrbyD+8BaNp5k5QBEkDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:20:48.572132Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.19554","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea47d170c7070fb1064a1c6c224c9d7bcdc2f5ee72aa86337012e865402718ea","sha256:1b5f6efc0d699cbb419eb743cd9bcb9d4ed61fc8b30b25902a3b5789ecefe032"],"state_sha256":"abe7784d5b439dc5625904d854a81eb4ef68d7e08f42b0fdbb4753ab903ad50e"}