{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:KDWZLREOAX6PSWIZQWMQPDJO2Y","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":"94bfd197c47e309d8d9504765dd9ff5fb780955ed9c32b899ff8bd4aca3b2ae7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2025-01-10T20:45:11Z","title_canon_sha256":"239a9eb064b4c75c587f792373dea0e1f01e170b2cd4997ab3d86a0de95f35b2"},"schema_version":"1.0","source":{"id":"2501.06337","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.06337","created_at":"2026-05-18T03:09:46Z"},{"alias_kind":"arxiv_version","alias_value":"2501.06337v2","created_at":"2026-05-18T03:09:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.06337","created_at":"2026-05-18T03:09:46Z"},{"alias_kind":"pith_short_12","alias_value":"KDWZLREOAX6P","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"KDWZLREOAX6PSWIZ","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"KDWZLREO","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:21b9069352235f38bdd318ff23ad0f4f44d5612831f4944f8f776c05abdab85f","target":"graph","created_at":"2026-05-18T03:09:46Z","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":"In 1999, K. Bezdek posed a conjecture stating that among all convex bodies in $\\mathbb R^3$, ellipsoids and bodies of revolution are characterized by the fact that all their planar sections have an axis of reflection. We prove Bezdek's conjecture in arbitrary dimension $n\\geq 3$, assuming only that sections passing through a fixed point have an axis of reflection, provided that the complementary invariant subspaces are all parallel to a fixed hyperplane. The result is proven in both orthogonal and affine settings.","authors_text":"B. Zawalski, M. Angeles Alfonseca","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2025-01-10T20:45:11Z","title":"On Bezdek's conjecture for high-dimensional convex bodies with an aligned center of symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.06337","kind":"arxiv","version":2},"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":"sha256:2e06d16dc5b7430df4b22154cf441cb4d1ef8b35c9c554179c1823938ba8bd8f","target":"record","created_at":"2026-05-18T03:09:46Z","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":"94bfd197c47e309d8d9504765dd9ff5fb780955ed9c32b899ff8bd4aca3b2ae7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2025-01-10T20:45:11Z","title_canon_sha256":"239a9eb064b4c75c587f792373dea0e1f01e170b2cd4997ab3d86a0de95f35b2"},"schema_version":"1.0","source":{"id":"2501.06337","kind":"arxiv","version":2}},"canonical_sha256":"50ed95c48e05fcf959198599078d2ed62822e7cb3b506e6b6a64d2e3fe5dc0cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50ed95c48e05fcf959198599078d2ed62822e7cb3b506e6b6a64d2e3fe5dc0cf","first_computed_at":"2026-05-18T03:09:46.219350Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:46.219350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7YVFTQj65EF5IlV9GP36ClZDxdYh5ViufMflgkoV75fiI78EKvZbdPfY4CApJsvLNI0thgDl9hD5tXBNKCUPAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:46.220265Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.06337","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e06d16dc5b7430df4b22154cf441cb4d1ef8b35c9c554179c1823938ba8bd8f","sha256:21b9069352235f38bdd318ff23ad0f4f44d5612831f4944f8f776c05abdab85f"],"state_sha256":"05d51ba8ed72c420e8220eacd7461602f60d54d42d04f4eb954581b7099fac31"}