{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:XUUD2CI2IZ4NDQB5XXZCBNK5QO","short_pith_number":"pith:XUUD2CI2","canonical_record":{"source":{"id":"2111.02607","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2021-11-04T03:27:17Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"50a60395582c537696346b8dbb389cba9f53aef0057be89143e1db94766c4c48","abstract_canon_sha256":"d9049eb08b47b67b7bed9c4d6435ab5cef9946f7769dac3a50e3f43c80286158"},"schema_version":"1.0"},"canonical_sha256":"bd283d091a4678d1c03dbdf220b55d83a67cbeefe417eb9989dc040300f1699a","source":{"kind":"arxiv","id":"2111.02607","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.02607","created_at":"2026-07-05T04:55:37Z"},{"alias_kind":"arxiv_version","alias_value":"2111.02607v2","created_at":"2026-07-05T04:55:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.02607","created_at":"2026-07-05T04:55:37Z"},{"alias_kind":"pith_short_12","alias_value":"XUUD2CI2IZ4N","created_at":"2026-07-05T04:55:37Z"},{"alias_kind":"pith_short_16","alias_value":"XUUD2CI2IZ4NDQB5","created_at":"2026-07-05T04:55:37Z"},{"alias_kind":"pith_short_8","alias_value":"XUUD2CI2","created_at":"2026-07-05T04:55:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:XUUD2CI2IZ4NDQB5XXZCBNK5QO","target":"record","payload":{"canonical_record":{"source":{"id":"2111.02607","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2021-11-04T03:27:17Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"50a60395582c537696346b8dbb389cba9f53aef0057be89143e1db94766c4c48","abstract_canon_sha256":"d9049eb08b47b67b7bed9c4d6435ab5cef9946f7769dac3a50e3f43c80286158"},"schema_version":"1.0"},"canonical_sha256":"bd283d091a4678d1c03dbdf220b55d83a67cbeefe417eb9989dc040300f1699a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:55:37.044706Z","signature_b64":"4U6awWSFxKFY1L3t9tU3MI8e9MdgxVtQ+ZZx6dyyiQmkkZWIyNxuGMNjosrdlVNhUywQx4bXDU5BcMUGdHW1BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd283d091a4678d1c03dbdf220b55d83a67cbeefe417eb9989dc040300f1699a","last_reissued_at":"2026-07-05T04:55:37.044228Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:55:37.044228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2111.02607","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:55:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CKZVTXVZ/ggtwWCA4s6xDE0m9UYicwsjZlnzdnfCuDVNomBddBf9ycaSt1KTm11aDpqI32mSiEnMq4n6L7kqDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T00:01:45.447415Z"},"content_sha256":"23a5876c9eaf49fd4f924eba30d662c2d49eedd3523f87b352809257684cbaf2","schema_version":"1.0","event_id":"sha256:23a5876c9eaf49fd4f924eba30d662c2d49eedd3523f87b352809257684cbaf2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:XUUD2CI2IZ4NDQB5XXZCBNK5QO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constrained Form-Finding of Tension-Compression Structures using Automatic Differentiation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.CE","authors_text":"Patrick Ole Ohlbrock, Pierluigi D'Acunto, Rafael Pastrana, Stefana Parascho, Thomas Oberbichler","submitted_at":"2021-11-04T03:27:17Z","abstract_excerpt":"This paper proposes a computational approach to form-find pin-jointed, bar structures subjected to combinations of tension and compression forces. The generated equilibrium states can meet force and geometric constraints via gradient-based optimization. We achieve this by extending the combinatorial equilibrium modeling (CEM) framework in three important ways. First, we introduce a new topological object, the auxiliary trail, to expand the range of structures that can be form-found with the framework. Then, we leverage automatic differentiation (AD) to obtain an exact value of the gradient of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.02607","kind":"arxiv","version":2},"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/2111.02607/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":"2026-07-05T04:55:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h/b0N0bNbh+HqWFbagfzMTWP2hrUAukqT1kUT3pS9B1b7vk448wLMPsY2d36JFT/xndV5Yga8QNcqtDv4xRQCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T00:01:45.448336Z"},"content_sha256":"63fd40d8afba280fda50cf38b9f45150242e80fbef07d7644c09248a172ec575","schema_version":"1.0","event_id":"sha256:63fd40d8afba280fda50cf38b9f45150242e80fbef07d7644c09248a172ec575"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XUUD2CI2IZ4NDQB5XXZCBNK5QO/bundle.json","state_url":"https://pith.science/pith/XUUD2CI2IZ4NDQB5XXZCBNK5QO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XUUD2CI2IZ4NDQB5XXZCBNK5QO/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":"2026-08-17T00:01:45Z","links":{"resolver":"https://pith.science/pith/XUUD2CI2IZ4NDQB5XXZCBNK5QO","bundle":"https://pith.science/pith/XUUD2CI2IZ4NDQB5XXZCBNK5QO/bundle.json","state":"https://pith.science/pith/XUUD2CI2IZ4NDQB5XXZCBNK5QO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XUUD2CI2IZ4NDQB5XXZCBNK5QO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:XUUD2CI2IZ4NDQB5XXZCBNK5QO","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":"d9049eb08b47b67b7bed9c4d6435ab5cef9946f7769dac3a50e3f43c80286158","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2021-11-04T03:27:17Z","title_canon_sha256":"50a60395582c537696346b8dbb389cba9f53aef0057be89143e1db94766c4c48"},"schema_version":"1.0","source":{"id":"2111.02607","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.02607","created_at":"2026-07-05T04:55:37Z"},{"alias_kind":"arxiv_version","alias_value":"2111.02607v2","created_at":"2026-07-05T04:55:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.02607","created_at":"2026-07-05T04:55:37Z"},{"alias_kind":"pith_short_12","alias_value":"XUUD2CI2IZ4N","created_at":"2026-07-05T04:55:37Z"},{"alias_kind":"pith_short_16","alias_value":"XUUD2CI2IZ4NDQB5","created_at":"2026-07-05T04:55:37Z"},{"alias_kind":"pith_short_8","alias_value":"XUUD2CI2","created_at":"2026-07-05T04:55:37Z"}],"graph_snapshots":[{"event_id":"sha256:63fd40d8afba280fda50cf38b9f45150242e80fbef07d7644c09248a172ec575","target":"graph","created_at":"2026-07-05T04:55:37Z","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/2111.02607/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper proposes a computational approach to form-find pin-jointed, bar structures subjected to combinations of tension and compression forces. The generated equilibrium states can meet force and geometric constraints via gradient-based optimization. We achieve this by extending the combinatorial equilibrium modeling (CEM) framework in three important ways. First, we introduce a new topological object, the auxiliary trail, to expand the range of structures that can be form-found with the framework. Then, we leverage automatic differentiation (AD) to obtain an exact value of the gradient of ","authors_text":"Patrick Ole Ohlbrock, Pierluigi D'Acunto, Rafael Pastrana, Stefana Parascho, Thomas Oberbichler","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2021-11-04T03:27:17Z","title":"Constrained Form-Finding of Tension-Compression Structures using Automatic Differentiation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.02607","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":"sha256:23a5876c9eaf49fd4f924eba30d662c2d49eedd3523f87b352809257684cbaf2","target":"record","created_at":"2026-07-05T04:55:37Z","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":"d9049eb08b47b67b7bed9c4d6435ab5cef9946f7769dac3a50e3f43c80286158","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2021-11-04T03:27:17Z","title_canon_sha256":"50a60395582c537696346b8dbb389cba9f53aef0057be89143e1db94766c4c48"},"schema_version":"1.0","source":{"id":"2111.02607","kind":"arxiv","version":2}},"canonical_sha256":"bd283d091a4678d1c03dbdf220b55d83a67cbeefe417eb9989dc040300f1699a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd283d091a4678d1c03dbdf220b55d83a67cbeefe417eb9989dc040300f1699a","first_computed_at":"2026-07-05T04:55:37.044228Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:55:37.044228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4U6awWSFxKFY1L3t9tU3MI8e9MdgxVtQ+ZZx6dyyiQmkkZWIyNxuGMNjosrdlVNhUywQx4bXDU5BcMUGdHW1BA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:55:37.044706Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.02607","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23a5876c9eaf49fd4f924eba30d662c2d49eedd3523f87b352809257684cbaf2","sha256:63fd40d8afba280fda50cf38b9f45150242e80fbef07d7644c09248a172ec575"],"state_sha256":"c5b0339f46f4a8623f3ecd128341f504c7a974fb5dc9d9775668fa61167cbbb5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3wwDmmucv88SmxgUoPFeyxpq0bpX9/dsESR64DUiShmXW/OXvcpS8TmgjKZuvz3ocotkfyr2kcHmubYXrt/iDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T00:01:45.453012Z","bundle_sha256":"dd8ca43ff7d23f9dfae926691a4a91e5b71dfaf31d8493bff508db60dd480d70"}}