{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:QITSBDEWBPBV6SK7XRYRMLJMU6","short_pith_number":"pith:QITSBDEW","canonical_record":{"source":{"id":"1902.01732","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-02-05T15:12:57Z","cross_cats_sorted":[],"title_canon_sha256":"119bc7735e4f2bbac98b847f2e04a5c03d9dfbb033d3a11ac93edc02f4aa4090","abstract_canon_sha256":"3527265fd20c9c32f9f28d9ee74ddc521a4be9bcdfd02e4783a9073c810958a2"},"schema_version":"1.0"},"canonical_sha256":"8227208c960bc35f495fbc71162d2ca7a9fefc5b49fa6443760ace6fd4d446ac","source":{"kind":"arxiv","id":"1902.01732","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.01732","created_at":"2026-05-17T23:54:46Z"},{"alias_kind":"arxiv_version","alias_value":"1902.01732v1","created_at":"2026-05-17T23:54:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.01732","created_at":"2026-05-17T23:54:46Z"},{"alias_kind":"pith_short_12","alias_value":"QITSBDEWBPBV","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QITSBDEWBPBV6SK7","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QITSBDEW","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:QITSBDEWBPBV6SK7XRYRMLJMU6","target":"record","payload":{"canonical_record":{"source":{"id":"1902.01732","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-02-05T15:12:57Z","cross_cats_sorted":[],"title_canon_sha256":"119bc7735e4f2bbac98b847f2e04a5c03d9dfbb033d3a11ac93edc02f4aa4090","abstract_canon_sha256":"3527265fd20c9c32f9f28d9ee74ddc521a4be9bcdfd02e4783a9073c810958a2"},"schema_version":"1.0"},"canonical_sha256":"8227208c960bc35f495fbc71162d2ca7a9fefc5b49fa6443760ace6fd4d446ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:46.907664Z","signature_b64":"LIL7sipro79WgKkmRep97Uzo6frQM0K+Ubr+EunNhNW+8ovozI9IRqd/dAOLGpDaaWOOP5RS56YRxSiQkigJDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8227208c960bc35f495fbc71162d2ca7a9fefc5b49fa6443760ace6fd4d446ac","last_reissued_at":"2026-05-17T23:54:46.907002Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:46.907002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.01732","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:54:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yUyvDNOQnBg+3t6T5qi0GRiKERzARmDUk+U3UVQJN9cyRYZFOpUJWRsFlO7M6OJl+9uomKKHqk5C/PhIkNaCDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:55:52.830363Z"},"content_sha256":"8798641ea75d72a8d0342f1769ba4159aa62fa5d3f1cc7e757d811285a14c218","schema_version":"1.0","event_id":"sha256:8798641ea75d72a8d0342f1769ba4159aa62fa5d3f1cc7e757d811285a14c218"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:QITSBDEWBPBV6SK7XRYRMLJMU6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classifying Convex Bodies by their Contact and Intersection Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Anders Aamand, Jakob B{\\ae}k Tejs Knudsen, Mikkel Abrahamsen, Peter Michael Reichstein Rasmussen","submitted_at":"2019-02-05T15:12:57Z","abstract_excerpt":"Suppose that $A$ is a convex body in the plane and that $A_1,\\dots,A_n$ are translates of $A$. Such translates give rise to an intersection graph of $A$, $G=(V,E)$, with vertices $V=\\{1,\\dots,n\\}$ and edges $E=\\{uv\\mid A_u\\cap A_v\\neq \\emptyset\\}$. The subgraph $G'=(V, E')$ satisfying that $E'\\subset E$ is the set of edges $uv$ for which the interiors of $A_u$ and $A_v$ are disjoint is a unit distance graph of $A$. If furthermore $G'=G$, i.e., if the interiors of $A_u$ and $A_v$ are disjoint whenever $u\\neq v$, then $G$ is a contact graph of $A$.\n  In this paper we study which pairs of convex "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01732","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:54:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I3Dtu5fSJpTA2A0cgFtPAHXwhH3As7zpTfADf0XHX+cXnkIG1m62UPLsAmNUMpiUrwrl/o7qedKYpdyDkGyeAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:55:52.831000Z"},"content_sha256":"4d244f41dadd160d3d883d005fe7d7f54fc8e61d48b7f7529991717f80427d12","schema_version":"1.0","event_id":"sha256:4d244f41dadd160d3d883d005fe7d7f54fc8e61d48b7f7529991717f80427d12"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QITSBDEWBPBV6SK7XRYRMLJMU6/bundle.json","state_url":"https://pith.science/pith/QITSBDEWBPBV6SK7XRYRMLJMU6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QITSBDEWBPBV6SK7XRYRMLJMU6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T15:55:52Z","links":{"resolver":"https://pith.science/pith/QITSBDEWBPBV6SK7XRYRMLJMU6","bundle":"https://pith.science/pith/QITSBDEWBPBV6SK7XRYRMLJMU6/bundle.json","state":"https://pith.science/pith/QITSBDEWBPBV6SK7XRYRMLJMU6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QITSBDEWBPBV6SK7XRYRMLJMU6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QITSBDEWBPBV6SK7XRYRMLJMU6","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":"3527265fd20c9c32f9f28d9ee74ddc521a4be9bcdfd02e4783a9073c810958a2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-02-05T15:12:57Z","title_canon_sha256":"119bc7735e4f2bbac98b847f2e04a5c03d9dfbb033d3a11ac93edc02f4aa4090"},"schema_version":"1.0","source":{"id":"1902.01732","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.01732","created_at":"2026-05-17T23:54:46Z"},{"alias_kind":"arxiv_version","alias_value":"1902.01732v1","created_at":"2026-05-17T23:54:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.01732","created_at":"2026-05-17T23:54:46Z"},{"alias_kind":"pith_short_12","alias_value":"QITSBDEWBPBV","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QITSBDEWBPBV6SK7","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QITSBDEW","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:4d244f41dadd160d3d883d005fe7d7f54fc8e61d48b7f7529991717f80427d12","target":"graph","created_at":"2026-05-17T23:54:46Z","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":"Suppose that $A$ is a convex body in the plane and that $A_1,\\dots,A_n$ are translates of $A$. Such translates give rise to an intersection graph of $A$, $G=(V,E)$, with vertices $V=\\{1,\\dots,n\\}$ and edges $E=\\{uv\\mid A_u\\cap A_v\\neq \\emptyset\\}$. The subgraph $G'=(V, E')$ satisfying that $E'\\subset E$ is the set of edges $uv$ for which the interiors of $A_u$ and $A_v$ are disjoint is a unit distance graph of $A$. If furthermore $G'=G$, i.e., if the interiors of $A_u$ and $A_v$ are disjoint whenever $u\\neq v$, then $G$ is a contact graph of $A$.\n  In this paper we study which pairs of convex ","authors_text":"Anders Aamand, Jakob B{\\ae}k Tejs Knudsen, Mikkel Abrahamsen, Peter Michael Reichstein Rasmussen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-02-05T15:12:57Z","title":"Classifying Convex Bodies by their Contact and Intersection Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01732","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":"sha256:8798641ea75d72a8d0342f1769ba4159aa62fa5d3f1cc7e757d811285a14c218","target":"record","created_at":"2026-05-17T23:54:46Z","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":"3527265fd20c9c32f9f28d9ee74ddc521a4be9bcdfd02e4783a9073c810958a2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-02-05T15:12:57Z","title_canon_sha256":"119bc7735e4f2bbac98b847f2e04a5c03d9dfbb033d3a11ac93edc02f4aa4090"},"schema_version":"1.0","source":{"id":"1902.01732","kind":"arxiv","version":1}},"canonical_sha256":"8227208c960bc35f495fbc71162d2ca7a9fefc5b49fa6443760ace6fd4d446ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8227208c960bc35f495fbc71162d2ca7a9fefc5b49fa6443760ace6fd4d446ac","first_computed_at":"2026-05-17T23:54:46.907002Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:46.907002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LIL7sipro79WgKkmRep97Uzo6frQM0K+Ubr+EunNhNW+8ovozI9IRqd/dAOLGpDaaWOOP5RS56YRxSiQkigJDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:46.907664Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.01732","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8798641ea75d72a8d0342f1769ba4159aa62fa5d3f1cc7e757d811285a14c218","sha256:4d244f41dadd160d3d883d005fe7d7f54fc8e61d48b7f7529991717f80427d12"],"state_sha256":"f2acf7ad2799a121433e23cb63e8a2b91c762db82302270a20b095e3fcec120f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZiwuBt30v1GNo+AiDg0N3exX8BgAEupmkKoa135eFJQkl3exLkJpJf3zUJNT8R0gJXTuJRWHjRJu+7D7tjJABQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T15:55:52.834372Z","bundle_sha256":"adaff37e8b781ef2991803a17b72a2b4e8ca173c52747108c30d0dfa3a1c70b0"}}