{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IWB56IA2K362F7AQXTPOIGXC2R","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":"732125b8a0662ddd330a1f104898715fa97ae7aa7b262776b5f81353ffc3f542","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-02-21T13:27:48Z","title_canon_sha256":"aaa02a0d0b2e79c184f633968312ade9c1c2e6dff40c965d7de820a0a8bbfe47"},"schema_version":"1.0","source":{"id":"1802.07561","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.07561","created_at":"2026-05-18T00:22:49Z"},{"alias_kind":"arxiv_version","alias_value":"1802.07561v1","created_at":"2026-05-18T00:22:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.07561","created_at":"2026-05-18T00:22:49Z"},{"alias_kind":"pith_short_12","alias_value":"IWB56IA2K362","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"IWB56IA2K362F7AQ","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"IWB56IA2","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:4efda8e216b7e6b5ab5cde0222e5f1621a2833b434eb72c9b890351675fec26c","target":"graph","created_at":"2026-05-18T00:22:49Z","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":"For $1 \\leq p < \\infty$, Ludwig, Haberl and Parapatits classified $L_p$ Minkowski valuations intertwining the special linear group with additional conditions such as homogeneity and continuity. In this paper,a complete classification of $L_p$ Minkowski valuations intertwining the special linear group on polytopes without any additional conditions is established for $p \\geq 1$ including $p = \\infty$. For $n=3$ and $p=1$, there exist valuations not mentioned before.","authors_text":"Gangsong Leng, Jin Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-02-21T13:27:48Z","title":"$L_p$ Minkowski Valuations on polytopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07561","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":"sha256:268f0815919567ee470d14a0268f564ad6bea50154fc7e7427b63c315c95130c","target":"record","created_at":"2026-05-18T00:22:49Z","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":"732125b8a0662ddd330a1f104898715fa97ae7aa7b262776b5f81353ffc3f542","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-02-21T13:27:48Z","title_canon_sha256":"aaa02a0d0b2e79c184f633968312ade9c1c2e6dff40c965d7de820a0a8bbfe47"},"schema_version":"1.0","source":{"id":"1802.07561","kind":"arxiv","version":1}},"canonical_sha256":"4583df201a56fda2fc10bcdee41ae2d466a9685fe8b13e479d9933c3de8dea11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4583df201a56fda2fc10bcdee41ae2d466a9685fe8b13e479d9933c3de8dea11","first_computed_at":"2026-05-18T00:22:49.908845Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:49.908845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r055ulx3WRGRgt3+dmNyWx+05+5/sbuJKYkVtalO3cltUnYWNPTz+nDHrxRau22zXWwL8jv/m1I+oUh2q491DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:49.909328Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.07561","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:268f0815919567ee470d14a0268f564ad6bea50154fc7e7427b63c315c95130c","sha256:4efda8e216b7e6b5ab5cde0222e5f1621a2833b434eb72c9b890351675fec26c"],"state_sha256":"ef271463d383675d0f9260e256521f14e84443e9b4d424bf7ac05169c102cb42"}