{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:MWMFKNJLJLE2DJDYFLXCF4BUKY","short_pith_number":"pith:MWMFKNJL","canonical_record":{"source":{"id":"1201.2580","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-01-09T00:58:55Z","cross_cats_sorted":[],"title_canon_sha256":"cdb9a9400db127f2a634f743522a682c55d65e0dde35245a56c85af9480f05da","abstract_canon_sha256":"3928e2e0e5e7535e35fcb804026ba63fad0e40fd91e2bad5d9e84adf2b04b0ea"},"schema_version":"1.0"},"canonical_sha256":"659855352b4ac9a1a4782aee22f03456012df150579b3315f2fdefd6b194d1ef","source":{"kind":"arxiv","id":"1201.2580","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.2580","created_at":"2026-05-18T02:21:18Z"},{"alias_kind":"arxiv_version","alias_value":"1201.2580v1","created_at":"2026-05-18T02:21:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.2580","created_at":"2026-05-18T02:21:18Z"},{"alias_kind":"pith_short_12","alias_value":"MWMFKNJLJLE2","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MWMFKNJLJLE2DJDY","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MWMFKNJL","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:MWMFKNJLJLE2DJDYFLXCF4BUKY","target":"record","payload":{"canonical_record":{"source":{"id":"1201.2580","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-01-09T00:58:55Z","cross_cats_sorted":[],"title_canon_sha256":"cdb9a9400db127f2a634f743522a682c55d65e0dde35245a56c85af9480f05da","abstract_canon_sha256":"3928e2e0e5e7535e35fcb804026ba63fad0e40fd91e2bad5d9e84adf2b04b0ea"},"schema_version":"1.0"},"canonical_sha256":"659855352b4ac9a1a4782aee22f03456012df150579b3315f2fdefd6b194d1ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:18.540612Z","signature_b64":"Lq2IhM439DyumuFYD7auy1QMAk8CipCQ08nA3sy07T+/Ys6VVZKoQmM5H5Ipp/llSpU1epPyg5V5bK8VJ9XsDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"659855352b4ac9a1a4782aee22f03456012df150579b3315f2fdefd6b194d1ef","last_reissued_at":"2026-05-18T02:21:18.539902Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:18.539902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.2580","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":"2026-05-18T02:21:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RERJ5PoPn2qOVZ/FJHb33ILxWjvMBZxZDMHaa/TKsqUl5gFD3EBJO8/Ea3jJgk0C+e0SvTlLQnkJD8mxjQDxCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T05:29:27.468575Z"},"content_sha256":"f94b1d6c66208029cd106760e9a7de673a81e7aa68ff6088909a03baa2ddde9b","schema_version":"1.0","event_id":"sha256:f94b1d6c66208029cd106760e9a7de673a81e7aa68ff6088909a03baa2ddde9b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:MWMFKNJLJLE2DJDYFLXCF4BUKY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximizing Volume Ratios for Shadow Covering by Tetrahedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Christina Chen","submitted_at":"2012-01-09T00:58:55Z","abstract_excerpt":"Define a body A to be able to hide behind a body B if the orthogonal projection of B contains a translation of the corresponding orthogonal projection of A in every direction. In two dimensions, it is easy to observe that there exist two objects such that one can hide behind another and have a larger area than the other. It was recently shown that similar examples exist in higher dimensions as well. However, the highest possible volume ratio for such bodies is still undetermined. We investigated two three-dimensional examples, one involving a tetrahedron and a ball and the other involving a te"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2580","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":"2026-05-18T02:21:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kSKRtWuqFma+FVlU7y6hHSNiD0PSrpnKou8UPzKTITHz7pbbLUygBkSNuivxKVDAvDySDjeWgau0L8ZCB04qBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T05:29:27.469168Z"},"content_sha256":"160c52a62448fe32bceb4d413245cc1a0d2f848b3d582ae97db03b8f426da1ae","schema_version":"1.0","event_id":"sha256:160c52a62448fe32bceb4d413245cc1a0d2f848b3d582ae97db03b8f426da1ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MWMFKNJLJLE2DJDYFLXCF4BUKY/bundle.json","state_url":"https://pith.science/pith/MWMFKNJLJLE2DJDYFLXCF4BUKY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MWMFKNJLJLE2DJDYFLXCF4BUKY/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":"2026-07-07T05:29:27Z","links":{"resolver":"https://pith.science/pith/MWMFKNJLJLE2DJDYFLXCF4BUKY","bundle":"https://pith.science/pith/MWMFKNJLJLE2DJDYFLXCF4BUKY/bundle.json","state":"https://pith.science/pith/MWMFKNJLJLE2DJDYFLXCF4BUKY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MWMFKNJLJLE2DJDYFLXCF4BUKY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MWMFKNJLJLE2DJDYFLXCF4BUKY","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":"3928e2e0e5e7535e35fcb804026ba63fad0e40fd91e2bad5d9e84adf2b04b0ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-01-09T00:58:55Z","title_canon_sha256":"cdb9a9400db127f2a634f743522a682c55d65e0dde35245a56c85af9480f05da"},"schema_version":"1.0","source":{"id":"1201.2580","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.2580","created_at":"2026-05-18T02:21:18Z"},{"alias_kind":"arxiv_version","alias_value":"1201.2580v1","created_at":"2026-05-18T02:21:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.2580","created_at":"2026-05-18T02:21:18Z"},{"alias_kind":"pith_short_12","alias_value":"MWMFKNJLJLE2","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MWMFKNJLJLE2DJDY","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MWMFKNJL","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:160c52a62448fe32bceb4d413245cc1a0d2f848b3d582ae97db03b8f426da1ae","target":"graph","created_at":"2026-05-18T02:21:18Z","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":"Define a body A to be able to hide behind a body B if the orthogonal projection of B contains a translation of the corresponding orthogonal projection of A in every direction. In two dimensions, it is easy to observe that there exist two objects such that one can hide behind another and have a larger area than the other. It was recently shown that similar examples exist in higher dimensions as well. However, the highest possible volume ratio for such bodies is still undetermined. We investigated two three-dimensional examples, one involving a tetrahedron and a ball and the other involving a te","authors_text":"Christina Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-01-09T00:58:55Z","title":"Maximizing Volume Ratios for Shadow Covering by Tetrahedra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2580","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:f94b1d6c66208029cd106760e9a7de673a81e7aa68ff6088909a03baa2ddde9b","target":"record","created_at":"2026-05-18T02:21:18Z","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":"3928e2e0e5e7535e35fcb804026ba63fad0e40fd91e2bad5d9e84adf2b04b0ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-01-09T00:58:55Z","title_canon_sha256":"cdb9a9400db127f2a634f743522a682c55d65e0dde35245a56c85af9480f05da"},"schema_version":"1.0","source":{"id":"1201.2580","kind":"arxiv","version":1}},"canonical_sha256":"659855352b4ac9a1a4782aee22f03456012df150579b3315f2fdefd6b194d1ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"659855352b4ac9a1a4782aee22f03456012df150579b3315f2fdefd6b194d1ef","first_computed_at":"2026-05-18T02:21:18.539902Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:18.539902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lq2IhM439DyumuFYD7auy1QMAk8CipCQ08nA3sy07T+/Ys6VVZKoQmM5H5Ipp/llSpU1epPyg5V5bK8VJ9XsDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:18.540612Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.2580","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f94b1d6c66208029cd106760e9a7de673a81e7aa68ff6088909a03baa2ddde9b","sha256:160c52a62448fe32bceb4d413245cc1a0d2f848b3d582ae97db03b8f426da1ae"],"state_sha256":"2e15169fd2ef3d7a270803250032937b8718340793b36336198ea2ae4e912676"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wFYVjbm9HTUhXaqEX1DxiCU0CQsYmpf1zTy0nOR/8QkvHbo1CQQta3BVK+atL5+C/sI8MtgZKaeR/L/tX7GWBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T05:29:27.472466Z","bundle_sha256":"0a6684db645e10c47ca8f87b352232e03368e7e031cf0408d5508b24bf374bf7"}}