{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:SWXIN7HYT3YY5LSSE4SLGHXDFJ","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":"224782dac080e141e4d91eb1b417be7299d135ac41916c88a504ca43eee59e03","cross_cats_sorted":["cond-mat.soft","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2024-10-01T01:32:55Z","title_canon_sha256":"f7fff6a5967e72abd5e4fbdc5e819eaafbc0b37401b0b70109ee4a2ce4bdd907"},"schema_version":"1.0","source":{"id":"2410.00317","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.00317","created_at":"2026-07-05T09:14:03Z"},{"alias_kind":"arxiv_version","alias_value":"2410.00317v1","created_at":"2026-07-05T09:14:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.00317","created_at":"2026-07-05T09:14:03Z"},{"alias_kind":"pith_short_12","alias_value":"SWXIN7HYT3YY","created_at":"2026-07-05T09:14:03Z"},{"alias_kind":"pith_short_16","alias_value":"SWXIN7HYT3YY5LSS","created_at":"2026-07-05T09:14:03Z"},{"alias_kind":"pith_short_8","alias_value":"SWXIN7HY","created_at":"2026-07-05T09:14:03Z"}],"graph_snapshots":[{"event_id":"sha256:5e7be3ea24c58441d08d6a8aedf4fc23a35b7d912012a90fecda76f41aaf7e2c","target":"graph","created_at":"2026-07-05T09:14:03Z","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/2410.00317/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"How does one determine if a collection of bars joined by freely rotating hinges cannot be deformed without changing the length of any of the bars? In other words, how does one determine if a bar-joint graph is rigid? This question has been definitively answered using combinatorial rigidity theory in two dimensions via the Geiringer-Laman Theorem. However, it has not yet been answered using combinatorial rigidity theory in higher dimensions, given known counterexamples to the trivial dimensional extension of the Geiringer-Laman Theorem. To work towards a combinatorial approach in dimensions bey","authors_text":"J. M. Schwarz, Kyungeun Kim","cross_cats":["cond-mat.soft","math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2024-10-01T01:32:55Z","title":"Rigidity condition for gluing two bar-joint rigid graphs embedded in $\\mathbb{R}^d$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.00317","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":"sha256:3040457d981746e8a4ca1072224ca7d33518d4f765930aff6516f8c98a6ce5a8","target":"record","created_at":"2026-07-05T09:14:03Z","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":"224782dac080e141e4d91eb1b417be7299d135ac41916c88a504ca43eee59e03","cross_cats_sorted":["cond-mat.soft","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2024-10-01T01:32:55Z","title_canon_sha256":"f7fff6a5967e72abd5e4fbdc5e819eaafbc0b37401b0b70109ee4a2ce4bdd907"},"schema_version":"1.0","source":{"id":"2410.00317","kind":"arxiv","version":1}},"canonical_sha256":"95ae86fcf89ef18eae522724b31ee32a7bb331d1be706d36427931c5aa63b997","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95ae86fcf89ef18eae522724b31ee32a7bb331d1be706d36427931c5aa63b997","first_computed_at":"2026-07-05T09:14:03.068499Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:14:03.068499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1Ey5PT8aGqybayiujqOVSbUg3yLAm0wsy47vCLyXnOJNGrPp46BeeA/8YTXZfZKROm32WB25KwRM+0zZRg1TCg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:14:03.068921Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.00317","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3040457d981746e8a4ca1072224ca7d33518d4f765930aff6516f8c98a6ce5a8","sha256:5e7be3ea24c58441d08d6a8aedf4fc23a35b7d912012a90fecda76f41aaf7e2c"],"state_sha256":"6b12467da91335b4022bf2933247f7aea083fa8719fc96d311e787c4a4f3579c"}