{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:C4VE4SYNCINFEHPGR2JRCUXXU4","short_pith_number":"pith:C4VE4SYN","canonical_record":{"source":{"id":"1002.3294","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-02-17T16:07:22Z","cross_cats_sorted":[],"title_canon_sha256":"2f5fc55844361087fb0843334b4534c10cf4c318ec2c83e6a05db42f4522f163","abstract_canon_sha256":"3058d3ed0e40d5f23c1e16f921c3c62cbdfa27a784a1c1b09e07e9fb23d09073"},"schema_version":"1.0"},"canonical_sha256":"172a4e4b0d121a521de68e931152f7a73c92cb3581eae172d6d82e7d565fba51","source":{"kind":"arxiv","id":"1002.3294","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.3294","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"arxiv_version","alias_value":"1002.3294v1","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.3294","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"pith_short_12","alias_value":"C4VE4SYNCINF","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"C4VE4SYNCINFEHPG","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"C4VE4SYN","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:C4VE4SYNCINFEHPGR2JRCUXXU4","target":"record","payload":{"canonical_record":{"source":{"id":"1002.3294","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-02-17T16:07:22Z","cross_cats_sorted":[],"title_canon_sha256":"2f5fc55844361087fb0843334b4534c10cf4c318ec2c83e6a05db42f4522f163","abstract_canon_sha256":"3058d3ed0e40d5f23c1e16f921c3c62cbdfa27a784a1c1b09e07e9fb23d09073"},"schema_version":"1.0"},"canonical_sha256":"172a4e4b0d121a521de68e931152f7a73c92cb3581eae172d6d82e7d565fba51","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:59.279936Z","signature_b64":"iZOQwbbvirij8B7PWwxopWvc/3McXdlrQIqdSJVFD2onGXL+x5OUpA0vMWBuNL6vItPULIqv78BArFkuTEdxDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"172a4e4b0d121a521de68e931152f7a73c92cb3581eae172d6d82e7d565fba51","last_reissued_at":"2026-05-18T02:26:59.279578Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:59.279578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.3294","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":"2026-05-18T02:26:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tu425yVIdIxWUm2EiSH6E7LnnW/isUD+Uyx6/QI5QNCeoqd6tjsiu2Z3Wu4nJBJx5PH7hvks8POYU0PXlHdaBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:39:25.209997Z"},"content_sha256":"1d96f39323c2c8872c03467368a8ffb6d017aac14e73483a946b083ca2e63432","schema_version":"1.0","event_id":"sha256:1d96f39323c2c8872c03467368a8ffb6d017aac14e73483a946b083ca2e63432"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:C4VE4SYNCINFEHPGR2JRCUXXU4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lines pinning lines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Boris Aronov, G\\\"unter Rote, Otfried Cheong, Xavier Goaoc","submitted_at":"2010-02-17T16:07:22Z","abstract_excerpt":"A line g is a transversal to a family F of convex polytopes in 3-dimensional space if it intersects every member of F. If, in addition, g is an isolated point of the space of line transversals to F, we say that F is a pinning of g. We show that any minimal pinning of a line by convex polytopes such that no face of a polytope is coplanar with the line has size at most eight. If, in addition, the polytopes are disjoint, then it has size at most six. We completely characterize configurations of disjoint polytopes that form minimal pinnings of a line."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.3294","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":"2026-05-18T02:26:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Asbd70uws90T43t3rbPgrdMpAt9e3oLnxMx+pj/6TPh2Baxl70FTVwhaGeZGcvYLULRfVKRWcj7s/nz5kt9kBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:39:25.210448Z"},"content_sha256":"6d600b6b724c95c4b3dd27bdec2e1fa2d5ae5889727f9a05ba55090564e5cbdd","schema_version":"1.0","event_id":"sha256:6d600b6b724c95c4b3dd27bdec2e1fa2d5ae5889727f9a05ba55090564e5cbdd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C4VE4SYNCINFEHPGR2JRCUXXU4/bundle.json","state_url":"https://pith.science/pith/C4VE4SYNCINFEHPGR2JRCUXXU4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C4VE4SYNCINFEHPGR2JRCUXXU4/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":"2026-05-26T22:39:25Z","links":{"resolver":"https://pith.science/pith/C4VE4SYNCINFEHPGR2JRCUXXU4","bundle":"https://pith.science/pith/C4VE4SYNCINFEHPGR2JRCUXXU4/bundle.json","state":"https://pith.science/pith/C4VE4SYNCINFEHPGR2JRCUXXU4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C4VE4SYNCINFEHPGR2JRCUXXU4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:C4VE4SYNCINFEHPGR2JRCUXXU4","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":"3058d3ed0e40d5f23c1e16f921c3c62cbdfa27a784a1c1b09e07e9fb23d09073","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-02-17T16:07:22Z","title_canon_sha256":"2f5fc55844361087fb0843334b4534c10cf4c318ec2c83e6a05db42f4522f163"},"schema_version":"1.0","source":{"id":"1002.3294","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.3294","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"arxiv_version","alias_value":"1002.3294v1","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.3294","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"pith_short_12","alias_value":"C4VE4SYNCINF","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"C4VE4SYNCINFEHPG","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"C4VE4SYN","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:6d600b6b724c95c4b3dd27bdec2e1fa2d5ae5889727f9a05ba55090564e5cbdd","target":"graph","created_at":"2026-05-18T02:26:59Z","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":"A line g is a transversal to a family F of convex polytopes in 3-dimensional space if it intersects every member of F. If, in addition, g is an isolated point of the space of line transversals to F, we say that F is a pinning of g. We show that any minimal pinning of a line by convex polytopes such that no face of a polytope is coplanar with the line has size at most eight. If, in addition, the polytopes are disjoint, then it has size at most six. We completely characterize configurations of disjoint polytopes that form minimal pinnings of a line.","authors_text":"Boris Aronov, G\\\"unter Rote, Otfried Cheong, Xavier Goaoc","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-02-17T16:07:22Z","title":"Lines pinning lines"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.3294","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":"sha256:1d96f39323c2c8872c03467368a8ffb6d017aac14e73483a946b083ca2e63432","target":"record","created_at":"2026-05-18T02:26:59Z","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":"3058d3ed0e40d5f23c1e16f921c3c62cbdfa27a784a1c1b09e07e9fb23d09073","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-02-17T16:07:22Z","title_canon_sha256":"2f5fc55844361087fb0843334b4534c10cf4c318ec2c83e6a05db42f4522f163"},"schema_version":"1.0","source":{"id":"1002.3294","kind":"arxiv","version":1}},"canonical_sha256":"172a4e4b0d121a521de68e931152f7a73c92cb3581eae172d6d82e7d565fba51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"172a4e4b0d121a521de68e931152f7a73c92cb3581eae172d6d82e7d565fba51","first_computed_at":"2026-05-18T02:26:59.279578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:59.279578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iZOQwbbvirij8B7PWwxopWvc/3McXdlrQIqdSJVFD2onGXL+x5OUpA0vMWBuNL6vItPULIqv78BArFkuTEdxDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:59.279936Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.3294","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d96f39323c2c8872c03467368a8ffb6d017aac14e73483a946b083ca2e63432","sha256:6d600b6b724c95c4b3dd27bdec2e1fa2d5ae5889727f9a05ba55090564e5cbdd"],"state_sha256":"c0aa63f6682e58482df3aa1e5ba0c6ae31dce314e1eb01a8e71fcdd47352046a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qYrqVNdIh/zKwd0UEq7dzRQiqKAPzOqIupl4gR/yBnEHifZ9ZEM2v7be6gHxJpG39SKna3Lplw1taV3xf8QhDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T22:39:25.213408Z","bundle_sha256":"66189b68c4ae73ca40c20704573ceed39828d9998f020f860c1a90e7490b0317"}}