{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:27SNQSPXCS6GUIR6GTQSQW34VZ","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":"22c753fb588be34d38d2adfa42fc6fece6f1a934fbdb1f189faa7d324f221ba3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-07-22T09:08:26Z","title_canon_sha256":"d80be6659d8a8038b30bce45071540bbcee90be6e3c2bbdbd9c7fb1c3d9b4977"},"schema_version":"1.0","source":{"id":"1607.06604","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.06604","created_at":"2026-05-18T00:38:32Z"},{"alias_kind":"arxiv_version","alias_value":"1607.06604v2","created_at":"2026-05-18T00:38:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06604","created_at":"2026-05-18T00:38:32Z"},{"alias_kind":"pith_short_12","alias_value":"27SNQSPXCS6G","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"27SNQSPXCS6GUIR6","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"27SNQSPX","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:0fd2acfbfabbb76ef5f252339ffead5ee62befcb5ead5c7fcb2c5020994706bd","target":"graph","created_at":"2026-05-18T00:38:32Z","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":"We prove that the answer to the question of the title is `as many times as you want.' More precisely, given any constant $c>0$, we construct two oblique triangular bipyramids, $P$ and $Q$, such that $P$ is convex, $Q$ is nonconvex and intrinsically isometric to $P$, and $\\textrm{vol} Q>c\\cdot \\textrm{vol} P>0$.","authors_text":"Victor Alexandrov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-07-22T09:08:26Z","title":"How many times can the volume of a convex polyhedron be increased by isometric deformations?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06604","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":"sha256:1011852c1c4e0bb223c6e361e9a6058b06dce5f5eb354036634d54fe9049da41","target":"record","created_at":"2026-05-18T00:38:32Z","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":"22c753fb588be34d38d2adfa42fc6fece6f1a934fbdb1f189faa7d324f221ba3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-07-22T09:08:26Z","title_canon_sha256":"d80be6659d8a8038b30bce45071540bbcee90be6e3c2bbdbd9c7fb1c3d9b4977"},"schema_version":"1.0","source":{"id":"1607.06604","kind":"arxiv","version":2}},"canonical_sha256":"d7e4d849f714bc6a223e34e1285b7cae5a361f3f64006ba8ecb10f565073b811","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7e4d849f714bc6a223e34e1285b7cae5a361f3f64006ba8ecb10f565073b811","first_computed_at":"2026-05-18T00:38:32.135701Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:32.135701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WafCt/VGcUWVbQ5hFjoOd78azvZkJJIUVs2B/EOHy+W3dRhtETIHboecUIwddJ8gUB8pdhTz4ilzTk4+prm9DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:32.136177Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.06604","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1011852c1c4e0bb223c6e361e9a6058b06dce5f5eb354036634d54fe9049da41","sha256:0fd2acfbfabbb76ef5f252339ffead5ee62befcb5ead5c7fcb2c5020994706bd"],"state_sha256":"3140f9cc4a5f370b81f19d70339c5fbc114a9a2bce2f32aa831962029885a2b3"}