{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:Y6CBFJGQAMDVRTYMTL2EBCANBM","short_pith_number":"pith:Y6CBFJGQ","canonical_record":{"source":{"id":"1801.08987","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-01-26T21:51:19Z","cross_cats_sorted":[],"title_canon_sha256":"222085f69bd6a7643cc994aa1d4378cb53000baea6a0419470bb5271f8b6bf2a","abstract_canon_sha256":"ae56a2200874751661040e96e5591bf6099c39319c5315b2f14e4fdf413c2fa6"},"schema_version":"1.0"},"canonical_sha256":"c78412a4d0030758cf0c9af440880d0b1ae15aae88ff2f1b01f8191c576965b9","source":{"kind":"arxiv","id":"1801.08987","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.08987","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"arxiv_version","alias_value":"1801.08987v1","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.08987","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"pith_short_12","alias_value":"Y6CBFJGQAMDV","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"Y6CBFJGQAMDVRTYM","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"Y6CBFJGQ","created_at":"2026-05-18T12:33:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:Y6CBFJGQAMDVRTYMTL2EBCANBM","target":"record","payload":{"canonical_record":{"source":{"id":"1801.08987","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-01-26T21:51:19Z","cross_cats_sorted":[],"title_canon_sha256":"222085f69bd6a7643cc994aa1d4378cb53000baea6a0419470bb5271f8b6bf2a","abstract_canon_sha256":"ae56a2200874751661040e96e5591bf6099c39319c5315b2f14e4fdf413c2fa6"},"schema_version":"1.0"},"canonical_sha256":"c78412a4d0030758cf0c9af440880d0b1ae15aae88ff2f1b01f8191c576965b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:58.940895Z","signature_b64":"BVrRiFq5Oz8i9Or6B7av5dwbl3CyOzEafv2hK75Lo1pzZqx456V3JAvpj891dn2rgClx0RFeaxGpgvQgOreoCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c78412a4d0030758cf0c9af440880d0b1ae15aae88ff2f1b01f8191c576965b9","last_reissued_at":"2026-05-18T00:24:58.940232Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:58.940232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.08987","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":"2026-05-18T00:24:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qdmVv5So748glmvLGj2dsvlTjXtO6+98dVlLDUO36V7LFTism2TX1slz+H+qsJbAOGo6WXzylLR+uPdACaJZBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:18:53.894288Z"},"content_sha256":"e8fa5a121808a195692125e592efe13b88c1894cd464b2f4813e542734ff2fa9","schema_version":"1.0","event_id":"sha256:e8fa5a121808a195692125e592efe13b88c1894cd464b2f4813e542734ff2fa9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:Y6CBFJGQAMDVRTYMTL2EBCANBM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On bodies in $\\mathbb{R}^5$ with directly congruent projections or sections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Dmitry Ryabogin, M.Angeles Alfonseca, Michelle Cordier","submitted_at":"2018-01-26T21:51:19Z","abstract_excerpt":"Let $K$ and $L$ be two convex bodies in ${\\mathbb R^5}$ with countably many diameters, such that their projections onto all $4$ dimensional subspaces containing one fixed diameter are directly congruent. We show that if these projections have no rotational symmetries, and the projections of $K,L$ on certain 3 dimensional subspaces have no symmetries, then $K=\\pm L$ up to a translation. We also prove the corresponding result for sections of star bodies."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08987","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":"2026-05-18T00:24:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dXT9grzcQP4umDPiSGwjKjg8dVcCZwJAAfFPau9yD/yxNU9Ma6+jgVhg+3+wCKU1oyGkUIjkRtyTfKj84q7ZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:18:53.894654Z"},"content_sha256":"ae2a8d1e011e0cd6ae85869e0dfea7d62ee02d06d1d2e4fb221cc3c8bf42a7b4","schema_version":"1.0","event_id":"sha256:ae2a8d1e011e0cd6ae85869e0dfea7d62ee02d06d1d2e4fb221cc3c8bf42a7b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y6CBFJGQAMDVRTYMTL2EBCANBM/bundle.json","state_url":"https://pith.science/pith/Y6CBFJGQAMDVRTYMTL2EBCANBM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y6CBFJGQAMDVRTYMTL2EBCANBM/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":"2026-06-23T16:18:53Z","links":{"resolver":"https://pith.science/pith/Y6CBFJGQAMDVRTYMTL2EBCANBM","bundle":"https://pith.science/pith/Y6CBFJGQAMDVRTYMTL2EBCANBM/bundle.json","state":"https://pith.science/pith/Y6CBFJGQAMDVRTYMTL2EBCANBM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y6CBFJGQAMDVRTYMTL2EBCANBM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:Y6CBFJGQAMDVRTYMTL2EBCANBM","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":"ae56a2200874751661040e96e5591bf6099c39319c5315b2f14e4fdf413c2fa6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-01-26T21:51:19Z","title_canon_sha256":"222085f69bd6a7643cc994aa1d4378cb53000baea6a0419470bb5271f8b6bf2a"},"schema_version":"1.0","source":{"id":"1801.08987","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.08987","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"arxiv_version","alias_value":"1801.08987v1","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.08987","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"pith_short_12","alias_value":"Y6CBFJGQAMDV","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"Y6CBFJGQAMDVRTYM","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"Y6CBFJGQ","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:ae2a8d1e011e0cd6ae85869e0dfea7d62ee02d06d1d2e4fb221cc3c8bf42a7b4","target":"graph","created_at":"2026-05-18T00:24:58Z","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":"Let $K$ and $L$ be two convex bodies in ${\\mathbb R^5}$ with countably many diameters, such that their projections onto all $4$ dimensional subspaces containing one fixed diameter are directly congruent. We show that if these projections have no rotational symmetries, and the projections of $K,L$ on certain 3 dimensional subspaces have no symmetries, then $K=\\pm L$ up to a translation. We also prove the corresponding result for sections of star bodies.","authors_text":"Dmitry Ryabogin, M.Angeles Alfonseca, Michelle Cordier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-01-26T21:51:19Z","title":"On bodies in $\\mathbb{R}^5$ with directly congruent projections or sections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08987","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:e8fa5a121808a195692125e592efe13b88c1894cd464b2f4813e542734ff2fa9","target":"record","created_at":"2026-05-18T00:24:58Z","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":"ae56a2200874751661040e96e5591bf6099c39319c5315b2f14e4fdf413c2fa6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-01-26T21:51:19Z","title_canon_sha256":"222085f69bd6a7643cc994aa1d4378cb53000baea6a0419470bb5271f8b6bf2a"},"schema_version":"1.0","source":{"id":"1801.08987","kind":"arxiv","version":1}},"canonical_sha256":"c78412a4d0030758cf0c9af440880d0b1ae15aae88ff2f1b01f8191c576965b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c78412a4d0030758cf0c9af440880d0b1ae15aae88ff2f1b01f8191c576965b9","first_computed_at":"2026-05-18T00:24:58.940232Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:58.940232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BVrRiFq5Oz8i9Or6B7av5dwbl3CyOzEafv2hK75Lo1pzZqx456V3JAvpj891dn2rgClx0RFeaxGpgvQgOreoCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:58.940895Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.08987","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8fa5a121808a195692125e592efe13b88c1894cd464b2f4813e542734ff2fa9","sha256:ae2a8d1e011e0cd6ae85869e0dfea7d62ee02d06d1d2e4fb221cc3c8bf42a7b4"],"state_sha256":"2d26c4f51fda0e66072c7c835a07dc6e85fb818501bf6480be59a5793753b0e1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZAj/0KlRnhVWzDWPDlWAZkkf9t3isIHKzZ65MJiZkLsivwyjB/ZXagc6uEFluQyfDNCmNB6R/2ANnIsTUpvgAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T16:18:53.896551Z","bundle_sha256":"4c729867bd8931883a89e426a444b778ae3e618c754177937fca1a2a109ff7ba"}}