{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:WDPPRRQI5KZT7ZOLBKCASKWT4Z","short_pith_number":"pith:WDPPRRQI","canonical_record":{"source":{"id":"2312.09891","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2023-12-15T15:41:54Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"1c2c8932db281e8e1948c652c1a4e21d5c84dac0a535517751f85bda67a06101","abstract_canon_sha256":"d5b1d273a9e958c73122645f432fb9fbe75c4bb4136a933124e37757bae5678c"},"schema_version":"1.0"},"canonical_sha256":"b0def8c608eab33fe5cb0a84092ad3e660c70b88573c67d0c1201612f8a9098b","source":{"kind":"arxiv","id":"2312.09891","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.09891","created_at":"2026-07-05T07:24:41Z"},{"alias_kind":"arxiv_version","alias_value":"2312.09891v1","created_at":"2026-07-05T07:24:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.09891","created_at":"2026-07-05T07:24:41Z"},{"alias_kind":"pith_short_12","alias_value":"WDPPRRQI5KZT","created_at":"2026-07-05T07:24:41Z"},{"alias_kind":"pith_short_16","alias_value":"WDPPRRQI5KZT7ZOL","created_at":"2026-07-05T07:24:41Z"},{"alias_kind":"pith_short_8","alias_value":"WDPPRRQI","created_at":"2026-07-05T07:24:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:WDPPRRQI5KZT7ZOLBKCASKWT4Z","target":"record","payload":{"canonical_record":{"source":{"id":"2312.09891","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2023-12-15T15:41:54Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"1c2c8932db281e8e1948c652c1a4e21d5c84dac0a535517751f85bda67a06101","abstract_canon_sha256":"d5b1d273a9e958c73122645f432fb9fbe75c4bb4136a933124e37757bae5678c"},"schema_version":"1.0"},"canonical_sha256":"b0def8c608eab33fe5cb0a84092ad3e660c70b88573c67d0c1201612f8a9098b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:24:41.746874Z","signature_b64":"3dBLxO+dL6BedRWfFJoh0hNTcZQFe4WoQD/jGFjzLSjNRpyUfJZOUHBx3gPJ9iZOXLSVZA5XBRMte6lIa+ghCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0def8c608eab33fe5cb0a84092ad3e660c70b88573c67d0c1201612f8a9098b","last_reissued_at":"2026-07-05T07:24:41.746387Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:24:41.746387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.09891","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":"2026-07-05T07:24:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Emx3wdFII3eryJ14eqpCufS4gM8Ztqbivmr+4YJBC+Y4lnLOf0a9SDKrqXM1kW0ryJI0ex9Ztsw5fNi2KG7ZDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:08:28.461237Z"},"content_sha256":"6e699b07b66068f347555565c5d63097a9abf4c60fc36b750cfcbf8dfbba20a5","schema_version":"1.0","event_id":"sha256:6e699b07b66068f347555565c5d63097a9abf4c60fc36b750cfcbf8dfbba20a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:WDPPRRQI5KZT7ZOLBKCASKWT4Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A differential approach to Maxwell-Cremona liftings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Bernd Schulze, Christian M\\\"uller, Fatemeh Mohammadi, Oleg Karpenkov","submitted_at":"2023-12-15T15:41:54Z","abstract_excerpt":"In 1864, J. C. Maxwell introduced a link between self-stressed frameworks in the plane and piecewise linear liftings to 3-space. This connection has found numerous applications in areas such as discrete geometry, control theory and structural engineering. While there are some generalisations of this theory to liftings of $d$-complexes in $d$-space, extensions for liftings of frameworks in $d$-space for $d\\geq 3$ have been missing. In this paper, we introduce and study differential liftings on general graphs using differential forms associated with the elements of the homotopy groups of the com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.09891","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.09891/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T07:24:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cCVZQQSq+tm8WJ0EXzupfhUwcS+Pi4Bznf4W+QYPF13NC7ctx2FY10q9zzEw+cEWuSnMLS2agYKqIbQ+qbK0BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:08:28.461961Z"},"content_sha256":"5fb755844b3b47652a63c0e9f430c088a67c2fc0e0d27f1ce775fc63a9bb1694","schema_version":"1.0","event_id":"sha256:5fb755844b3b47652a63c0e9f430c088a67c2fc0e0d27f1ce775fc63a9bb1694"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WDPPRRQI5KZT7ZOLBKCASKWT4Z/bundle.json","state_url":"https://pith.science/pith/WDPPRRQI5KZT7ZOLBKCASKWT4Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WDPPRRQI5KZT7ZOLBKCASKWT4Z/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":"2026-08-09T07:08:28Z","links":{"resolver":"https://pith.science/pith/WDPPRRQI5KZT7ZOLBKCASKWT4Z","bundle":"https://pith.science/pith/WDPPRRQI5KZT7ZOLBKCASKWT4Z/bundle.json","state":"https://pith.science/pith/WDPPRRQI5KZT7ZOLBKCASKWT4Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WDPPRRQI5KZT7ZOLBKCASKWT4Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:WDPPRRQI5KZT7ZOLBKCASKWT4Z","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":"d5b1d273a9e958c73122645f432fb9fbe75c4bb4136a933124e37757bae5678c","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2023-12-15T15:41:54Z","title_canon_sha256":"1c2c8932db281e8e1948c652c1a4e21d5c84dac0a535517751f85bda67a06101"},"schema_version":"1.0","source":{"id":"2312.09891","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.09891","created_at":"2026-07-05T07:24:41Z"},{"alias_kind":"arxiv_version","alias_value":"2312.09891v1","created_at":"2026-07-05T07:24:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.09891","created_at":"2026-07-05T07:24:41Z"},{"alias_kind":"pith_short_12","alias_value":"WDPPRRQI5KZT","created_at":"2026-07-05T07:24:41Z"},{"alias_kind":"pith_short_16","alias_value":"WDPPRRQI5KZT7ZOL","created_at":"2026-07-05T07:24:41Z"},{"alias_kind":"pith_short_8","alias_value":"WDPPRRQI","created_at":"2026-07-05T07:24:41Z"}],"graph_snapshots":[{"event_id":"sha256:5fb755844b3b47652a63c0e9f430c088a67c2fc0e0d27f1ce775fc63a9bb1694","target":"graph","created_at":"2026-07-05T07:24:41Z","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/2312.09891/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In 1864, J. C. Maxwell introduced a link between self-stressed frameworks in the plane and piecewise linear liftings to 3-space. This connection has found numerous applications in areas such as discrete geometry, control theory and structural engineering. While there are some generalisations of this theory to liftings of $d$-complexes in $d$-space, extensions for liftings of frameworks in $d$-space for $d\\geq 3$ have been missing. In this paper, we introduce and study differential liftings on general graphs using differential forms associated with the elements of the homotopy groups of the com","authors_text":"Bernd Schulze, Christian M\\\"uller, Fatemeh Mohammadi, Oleg Karpenkov","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2023-12-15T15:41:54Z","title":"A differential approach to Maxwell-Cremona liftings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.09891","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":"sha256:6e699b07b66068f347555565c5d63097a9abf4c60fc36b750cfcbf8dfbba20a5","target":"record","created_at":"2026-07-05T07:24:41Z","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":"d5b1d273a9e958c73122645f432fb9fbe75c4bb4136a933124e37757bae5678c","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2023-12-15T15:41:54Z","title_canon_sha256":"1c2c8932db281e8e1948c652c1a4e21d5c84dac0a535517751f85bda67a06101"},"schema_version":"1.0","source":{"id":"2312.09891","kind":"arxiv","version":1}},"canonical_sha256":"b0def8c608eab33fe5cb0a84092ad3e660c70b88573c67d0c1201612f8a9098b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0def8c608eab33fe5cb0a84092ad3e660c70b88573c67d0c1201612f8a9098b","first_computed_at":"2026-07-05T07:24:41.746387Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:24:41.746387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3dBLxO+dL6BedRWfFJoh0hNTcZQFe4WoQD/jGFjzLSjNRpyUfJZOUHBx3gPJ9iZOXLSVZA5XBRMte6lIa+ghCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:24:41.746874Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.09891","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e699b07b66068f347555565c5d63097a9abf4c60fc36b750cfcbf8dfbba20a5","sha256:5fb755844b3b47652a63c0e9f430c088a67c2fc0e0d27f1ce775fc63a9bb1694"],"state_sha256":"b5a072b4e03a2fd331e0c08d212627277f03af8d5fdee51d096cd0d31cb7485a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kos6EbM/PSWFtOW+2WdslUGaZrXNOzMg/RO5JKQauIfW8gMj64b8u36YcS/AEOQEqOxxW+38rwmM30auw/j9CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T07:08:28.468672Z","bundle_sha256":"0ae9304760a4f203a1f90569791dd9fe84fffca755c053ea91c8b6abbdef1140"}}