{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:LKZUS3RSCB2K47RHNJ6J5MTAXZ","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":"e16149a38263608f012ebdecae0278a5eaa4f8a3e83cec35fb48bde63a023953","cross_cats_sorted":["math.AC"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2025-03-03T15:24:06Z","title_canon_sha256":"7b22adc824c75d7d0213d684d4d6f27561b56cb9dfb067c29cae2c4234ffb7b0"},"schema_version":"1.0","source":{"id":"2503.01647","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.01647","created_at":"2026-06-19T16:12:13Z"},{"alias_kind":"arxiv_version","alias_value":"2503.01647v2","created_at":"2026-06-19T16:12:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.01647","created_at":"2026-06-19T16:12:13Z"},{"alias_kind":"pith_short_12","alias_value":"LKZUS3RSCB2K","created_at":"2026-06-19T16:12:13Z"},{"alias_kind":"pith_short_16","alias_value":"LKZUS3RSCB2K47RH","created_at":"2026-06-19T16:12:13Z"},{"alias_kind":"pith_short_8","alias_value":"LKZUS3RS","created_at":"2026-06-19T16:12:13Z"}],"graph_snapshots":[{"event_id":"sha256:edb8ada1db16c736a6f7c41d4830cd04e9234bf4483364466a3a5e30e451520f","target":"graph","created_at":"2026-06-19T16:12:13Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2503.01647/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Classical results of Cauchy and Dehn imply that the 1-skeleton of a convex simplicial polyhedron $P$ is rigid i.e. every continuous motion of the vertices of $P$ in $\\mathbb R^3$ which preserves its edge lengths results in a polyhedron which is congruent to $P$. This result was extended to convex smplicial polytopes in $\\mathbb R^d$ for all $d\\geq 3$ by Whiteley, and to generic realisations of 1-skeletons of simplicial $(d-1)$-manifolds in $\\mathbb R^{d}$ by Kalai for $d\\geq 4$ and Fogelsanger for $d\\geq 3$. We will generalise Kalai's result by showing that, for all $d\\geq 4$ and any fixed $1\\","authors_text":"Bill Jackson, James Cruickshank, Shin-ichi Tanigawa","cross_cats":["math.AC"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2025-03-03T15:24:06Z","title":"Volume Rigidity of Simplicial Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.01647","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":"sha256:01be13c683e898f182e60b8081efe65134176929e29d8b0892d571a83ee11abc","target":"record","created_at":"2026-06-19T16:12:13Z","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":"e16149a38263608f012ebdecae0278a5eaa4f8a3e83cec35fb48bde63a023953","cross_cats_sorted":["math.AC"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2025-03-03T15:24:06Z","title_canon_sha256":"7b22adc824c75d7d0213d684d4d6f27561b56cb9dfb067c29cae2c4234ffb7b0"},"schema_version":"1.0","source":{"id":"2503.01647","kind":"arxiv","version":2}},"canonical_sha256":"5ab3496e321074ae7e276a7c9eb260be7859d35b18ac8dca420d751c27f6c3a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ab3496e321074ae7e276a7c9eb260be7859d35b18ac8dca420d751c27f6c3a3","first_computed_at":"2026-06-19T16:12:13.377592Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:12:13.377592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tO6/1NMl3G6GlU7Lqk1UdWt/zw4DWH/nP5Tmnk77ryY9wChTbDEZm/u5QVc/RCJds51K1K7fljBJgai5+F3HBw==","signature_status":"signed_v1","signed_at":"2026-06-19T16:12:13.378000Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.01647","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01be13c683e898f182e60b8081efe65134176929e29d8b0892d571a83ee11abc","sha256:edb8ada1db16c736a6f7c41d4830cd04e9234bf4483364466a3a5e30e451520f"],"state_sha256":"55c311246682be6aa3fe14cc471edefe4e893e110e2b3a0735b36bceb00045b2"}