{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:IEDENQGAIJORNUGKTIXQ2GKZVO","short_pith_number":"pith:IEDENQGA","canonical_record":{"source":{"id":"1812.09354","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-12-21T19:47:08Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"b7c4062f16bb2f71e4c62b2d71331d8912fdd6c93c084b5f42a75451dcb69a27","abstract_canon_sha256":"6a1507a1a28f2c6789c105840db722139839cdddae3802ec440260316ada3aaf"},"schema_version":"1.0"},"canonical_sha256":"410646c0c0425d16d0ca9a2f0d1959ab86396f821280cc606bcfdaccd1a527ee","source":{"kind":"arxiv","id":"1812.09354","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.09354","created_at":"2026-05-17T23:57:30Z"},{"alias_kind":"arxiv_version","alias_value":"1812.09354v1","created_at":"2026-05-17T23:57:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09354","created_at":"2026-05-17T23:57:30Z"},{"alias_kind":"pith_short_12","alias_value":"IEDENQGAIJOR","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"IEDENQGAIJORNUGK","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"IEDENQGA","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:IEDENQGAIJORNUGKTIXQ2GKZVO","target":"record","payload":{"canonical_record":{"source":{"id":"1812.09354","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-12-21T19:47:08Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"b7c4062f16bb2f71e4c62b2d71331d8912fdd6c93c084b5f42a75451dcb69a27","abstract_canon_sha256":"6a1507a1a28f2c6789c105840db722139839cdddae3802ec440260316ada3aaf"},"schema_version":"1.0"},"canonical_sha256":"410646c0c0425d16d0ca9a2f0d1959ab86396f821280cc606bcfdaccd1a527ee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:30.319303Z","signature_b64":"Gx/iOIrqqS7K6HqEXXhfkEGBdgmoIDwJr5+2WH0gKxGCvVEsWkDRG8yKMVCBu4ljs3PZ1CgtSSXxujc2pqm9Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"410646c0c0425d16d0ca9a2f0d1959ab86396f821280cc606bcfdaccd1a527ee","last_reissued_at":"2026-05-17T23:57:30.318681Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:30.318681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.09354","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":"2026-05-17T23:57:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tZE3l/4FTWpf6eV55VRuzZdDgtiuhdwAUipdDzhWeV9gNi6kxPZXo+rU+Ry5ThgY3Pe5HmOoSu9U8hwP5H8WBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T13:31:46.698697Z"},"content_sha256":"7e3b02eb9a63d585ad073dbd89e953ae997cc526a2964ca603ae5d2292a2eef4","schema_version":"1.0","event_id":"sha256:7e3b02eb9a63d585ad073dbd89e953ae997cc526a2964ca603ae5d2292a2eef4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:IEDENQGAIJORNUGKTIXQ2GKZVO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Compatibility Conditions for Discrete Planar Structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Andrej Cherkaev, Andrejs Treibergs, Predrag Krtolica","submitted_at":"2018-12-21T19:47:08Z","abstract_excerpt":"Compatibility conditions are investigated for planar network structures consisting of nodes and connecting bars; these conditions restrict the elongations of bars and are analogous to the compatibility conditions of deformation in continuum mechanics. The requirement that the deformations remain planar imposes compatibility. Compatibility for structures with prescribed lengths and its linearization is considered. For triangulated structures, compatibility is expressed as a polynomial equation in the lengths of edges of the star domain surrounding each interior node. The continuum limits of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09354","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":""},"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":"2026-05-17T23:57:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nf3aVvKv/b69zpiVTzZmY17G2wgx/AMfE/w6aZJIwNKqRZ8uHyLoP9xKES4kfX7uFTf+g1ccqUh/KCUlP2HoCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T13:31:46.699054Z"},"content_sha256":"6b038aff66c7eb3ecf62b3eef956d58c960ec6e0f179306eb5cf45fc0db33d05","schema_version":"1.0","event_id":"sha256:6b038aff66c7eb3ecf62b3eef956d58c960ec6e0f179306eb5cf45fc0db33d05"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IEDENQGAIJORNUGKTIXQ2GKZVO/bundle.json","state_url":"https://pith.science/pith/IEDENQGAIJORNUGKTIXQ2GKZVO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IEDENQGAIJORNUGKTIXQ2GKZVO/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":"2026-07-04T13:31:46Z","links":{"resolver":"https://pith.science/pith/IEDENQGAIJORNUGKTIXQ2GKZVO","bundle":"https://pith.science/pith/IEDENQGAIJORNUGKTIXQ2GKZVO/bundle.json","state":"https://pith.science/pith/IEDENQGAIJORNUGKTIXQ2GKZVO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IEDENQGAIJORNUGKTIXQ2GKZVO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IEDENQGAIJORNUGKTIXQ2GKZVO","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":"6a1507a1a28f2c6789c105840db722139839cdddae3802ec440260316ada3aaf","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-12-21T19:47:08Z","title_canon_sha256":"b7c4062f16bb2f71e4c62b2d71331d8912fdd6c93c084b5f42a75451dcb69a27"},"schema_version":"1.0","source":{"id":"1812.09354","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.09354","created_at":"2026-05-17T23:57:30Z"},{"alias_kind":"arxiv_version","alias_value":"1812.09354v1","created_at":"2026-05-17T23:57:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09354","created_at":"2026-05-17T23:57:30Z"},{"alias_kind":"pith_short_12","alias_value":"IEDENQGAIJOR","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"IEDENQGAIJORNUGK","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"IEDENQGA","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:6b038aff66c7eb3ecf62b3eef956d58c960ec6e0f179306eb5cf45fc0db33d05","target":"graph","created_at":"2026-05-17T23:57:30Z","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":"Compatibility conditions are investigated for planar network structures consisting of nodes and connecting bars; these conditions restrict the elongations of bars and are analogous to the compatibility conditions of deformation in continuum mechanics. The requirement that the deformations remain planar imposes compatibility. Compatibility for structures with prescribed lengths and its linearization is considered. For triangulated structures, compatibility is expressed as a polynomial equation in the lengths of edges of the star domain surrounding each interior node. The continuum limits of the","authors_text":"Andrej Cherkaev, Andrejs Treibergs, Predrag Krtolica","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-12-21T19:47:08Z","title":"Compatibility Conditions for Discrete Planar Structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09354","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":"sha256:7e3b02eb9a63d585ad073dbd89e953ae997cc526a2964ca603ae5d2292a2eef4","target":"record","created_at":"2026-05-17T23:57:30Z","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":"6a1507a1a28f2c6789c105840db722139839cdddae3802ec440260316ada3aaf","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-12-21T19:47:08Z","title_canon_sha256":"b7c4062f16bb2f71e4c62b2d71331d8912fdd6c93c084b5f42a75451dcb69a27"},"schema_version":"1.0","source":{"id":"1812.09354","kind":"arxiv","version":1}},"canonical_sha256":"410646c0c0425d16d0ca9a2f0d1959ab86396f821280cc606bcfdaccd1a527ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"410646c0c0425d16d0ca9a2f0d1959ab86396f821280cc606bcfdaccd1a527ee","first_computed_at":"2026-05-17T23:57:30.318681Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:30.318681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gx/iOIrqqS7K6HqEXXhfkEGBdgmoIDwJr5+2WH0gKxGCvVEsWkDRG8yKMVCBu4ljs3PZ1CgtSSXxujc2pqm9Bg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:30.319303Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.09354","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e3b02eb9a63d585ad073dbd89e953ae997cc526a2964ca603ae5d2292a2eef4","sha256:6b038aff66c7eb3ecf62b3eef956d58c960ec6e0f179306eb5cf45fc0db33d05"],"state_sha256":"d9c73a407098c5125cd717539eb3ff4c515dbd51a607f57515316f20903a01da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MN/v+39WXElw/X/pj8RqithG8KuYrfmo8sgv0oeC7tq9NqJsDwFIzff9YCslM7Yy8f2xNO0SvLoinblj1PHJAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T13:31:46.701751Z","bundle_sha256":"cbc44cc39967b5a0f26d976c7e6e4019e08bfdd316b8593439d8ba48c73544a2"}}