{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:AFMT2AKL7TRKN7SIVLCPZB4MTJ","short_pith_number":"pith:AFMT2AKL","canonical_record":{"source":{"id":"1306.0240","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-06-02T18:54:03Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"122b9eeb7e325e061ab377443ba918a390c90e97e23a40128f50f9532887ae2d","abstract_canon_sha256":"13352ce96716a1272bbe09dd30995f93a9aafc0c9c97a9eba559fa28c0faaf39"},"schema_version":"1.0"},"canonical_sha256":"01593d014bfce2a6fe48aac4fc878c9a41c46f82248858c5525b7b00e353b0b5","source":{"kind":"arxiv","id":"1306.0240","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.0240","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"arxiv_version","alias_value":"1306.0240v1","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.0240","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"pith_short_12","alias_value":"AFMT2AKL7TRK","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AFMT2AKL7TRKN7SI","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AFMT2AKL","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:AFMT2AKL7TRKN7SIVLCPZB4MTJ","target":"record","payload":{"canonical_record":{"source":{"id":"1306.0240","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-06-02T18:54:03Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"122b9eeb7e325e061ab377443ba918a390c90e97e23a40128f50f9532887ae2d","abstract_canon_sha256":"13352ce96716a1272bbe09dd30995f93a9aafc0c9c97a9eba559fa28c0faaf39"},"schema_version":"1.0"},"canonical_sha256":"01593d014bfce2a6fe48aac4fc878c9a41c46f82248858c5525b7b00e353b0b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:42.327368Z","signature_b64":"CXaPoktEn/bEIxB+SDCUl+JbZCxXhqYGnn2GAT8WusBHsOtHq2VcqLSXSDk/YtllYhdEZIfRA9Ffg1UjpAujAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01593d014bfce2a6fe48aac4fc878c9a41c46f82248858c5525b7b00e353b0b5","last_reissued_at":"2026-05-18T02:51:42.326919Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:42.326919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.0240","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":"2026-05-18T02:51:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uFfY+bH589K86oPso4BCljL2mLJKyxxezHZTO0+zRP/lR0JUslI3eO+UkB6aI6QvZVCXophpjfGr4Ufn8rihAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:44:33.369354Z"},"content_sha256":"65216b600ef29de84b60600c8c9b7d9354926e61e92fd6e65bfa859cb56bc6bf","schema_version":"1.0","event_id":"sha256:65216b600ef29de84b60600c8c9b7d9354926e61e92fd6e65bfa859cb56bc6bf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:AFMT2AKL7TRKN7SIVLCPZB4MTJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Deformations of period lattices of flexible polyhedral surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.MG","authors_text":"Alexander A. Gaifullin, Sergey A. Gaifullin","submitted_at":"2013-06-02T18:54:03Z","abstract_excerpt":"In the end of the 19th century Bricard discovered a phenomenon of flexible polyhedra, that is, polyhedra with rigid faces and hinges at edges that admit non-trivial flexes. One of the most important results in this field is a theorem of Sabitov asserting that the volume of a flexible polyhedron is constant during the flexion. In this paper we study flexible polyhedral surfaces in the 3-space two-periodic with respect to translations by two non-colinear vectors that can vary continuously during the flexion. The main result is that the period lattice of a flexible two-periodic surface homeomorph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0240","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":"2026-05-18T02:51:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IkUxK68H8p29td2V138G+qNvPKF8/FcGZEi48ax/5iJDjVFEnFXQjiZrWFyV7Hmw8nj9GlW+qiv40nE039CFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:44:33.369704Z"},"content_sha256":"c9c3bce4689f7ed2cc2d34fe5b34105c0f49f2f6249d248052be8be805da1799","schema_version":"1.0","event_id":"sha256:c9c3bce4689f7ed2cc2d34fe5b34105c0f49f2f6249d248052be8be805da1799"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AFMT2AKL7TRKN7SIVLCPZB4MTJ/bundle.json","state_url":"https://pith.science/pith/AFMT2AKL7TRKN7SIVLCPZB4MTJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AFMT2AKL7TRKN7SIVLCPZB4MTJ/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":"2026-06-10T22:44:33Z","links":{"resolver":"https://pith.science/pith/AFMT2AKL7TRKN7SIVLCPZB4MTJ","bundle":"https://pith.science/pith/AFMT2AKL7TRKN7SIVLCPZB4MTJ/bundle.json","state":"https://pith.science/pith/AFMT2AKL7TRKN7SIVLCPZB4MTJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AFMT2AKL7TRKN7SIVLCPZB4MTJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:AFMT2AKL7TRKN7SIVLCPZB4MTJ","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":"13352ce96716a1272bbe09dd30995f93a9aafc0c9c97a9eba559fa28c0faaf39","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-06-02T18:54:03Z","title_canon_sha256":"122b9eeb7e325e061ab377443ba918a390c90e97e23a40128f50f9532887ae2d"},"schema_version":"1.0","source":{"id":"1306.0240","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.0240","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"arxiv_version","alias_value":"1306.0240v1","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.0240","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"pith_short_12","alias_value":"AFMT2AKL7TRK","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AFMT2AKL7TRKN7SI","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AFMT2AKL","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:c9c3bce4689f7ed2cc2d34fe5b34105c0f49f2f6249d248052be8be805da1799","target":"graph","created_at":"2026-05-18T02:51:42Z","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":"In the end of the 19th century Bricard discovered a phenomenon of flexible polyhedra, that is, polyhedra with rigid faces and hinges at edges that admit non-trivial flexes. One of the most important results in this field is a theorem of Sabitov asserting that the volume of a flexible polyhedron is constant during the flexion. In this paper we study flexible polyhedral surfaces in the 3-space two-periodic with respect to translations by two non-colinear vectors that can vary continuously during the flexion. The main result is that the period lattice of a flexible two-periodic surface homeomorph","authors_text":"Alexander A. Gaifullin, Sergey A. Gaifullin","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-06-02T18:54:03Z","title":"Deformations of period lattices of flexible polyhedral surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0240","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":"sha256:65216b600ef29de84b60600c8c9b7d9354926e61e92fd6e65bfa859cb56bc6bf","target":"record","created_at":"2026-05-18T02:51:42Z","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":"13352ce96716a1272bbe09dd30995f93a9aafc0c9c97a9eba559fa28c0faaf39","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-06-02T18:54:03Z","title_canon_sha256":"122b9eeb7e325e061ab377443ba918a390c90e97e23a40128f50f9532887ae2d"},"schema_version":"1.0","source":{"id":"1306.0240","kind":"arxiv","version":1}},"canonical_sha256":"01593d014bfce2a6fe48aac4fc878c9a41c46f82248858c5525b7b00e353b0b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01593d014bfce2a6fe48aac4fc878c9a41c46f82248858c5525b7b00e353b0b5","first_computed_at":"2026-05-18T02:51:42.326919Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:42.326919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CXaPoktEn/bEIxB+SDCUl+JbZCxXhqYGnn2GAT8WusBHsOtHq2VcqLSXSDk/YtllYhdEZIfRA9Ffg1UjpAujAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:42.327368Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.0240","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65216b600ef29de84b60600c8c9b7d9354926e61e92fd6e65bfa859cb56bc6bf","sha256:c9c3bce4689f7ed2cc2d34fe5b34105c0f49f2f6249d248052be8be805da1799"],"state_sha256":"b68f4e67b6a1745773d00299fccce88d5505159f4895ef5e3657d7c84f01777c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WtTF7ZeHcwT3w53BcGX86KFmMD1wDM+5qoEEsm3MVuXvvMWIwlm0damnKhTHXEKZmfpvjUGxqM2N80BRG2bODw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T22:44:33.371556Z","bundle_sha256":"3f4fb463481d15056d364cc3fe5dbeef70640874ff1e18e52c842e088ac2628b"}}