{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:U2TU2QSBVNBZ6R7ZAZO3QA6RRY","short_pith_number":"pith:U2TU2QSB","canonical_record":{"source":{"id":"1203.6611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-03-29T18:03:53Z","cross_cats_sorted":[],"title_canon_sha256":"7c0e73d842a1845e7060933bf3457dc6418320b7b0055d3fcd5e8e2998fc592e","abstract_canon_sha256":"a8b27636f87999246334fe63ad9a88c2a2d7b5e6b96a64ca7646aceebee2cde9"},"schema_version":"1.0"},"canonical_sha256":"a6a74d4241ab439f47f9065db803d18e1705136aa778c29af28abf36a2bd33c1","source":{"kind":"arxiv","id":"1203.6611","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.6611","created_at":"2026-05-18T02:57:15Z"},{"alias_kind":"arxiv_version","alias_value":"1203.6611v1","created_at":"2026-05-18T02:57:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6611","created_at":"2026-05-18T02:57:15Z"},{"alias_kind":"pith_short_12","alias_value":"U2TU2QSBVNBZ","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"U2TU2QSBVNBZ6R7Z","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"U2TU2QSB","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:U2TU2QSBVNBZ6R7ZAZO3QA6RRY","target":"record","payload":{"canonical_record":{"source":{"id":"1203.6611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-03-29T18:03:53Z","cross_cats_sorted":[],"title_canon_sha256":"7c0e73d842a1845e7060933bf3457dc6418320b7b0055d3fcd5e8e2998fc592e","abstract_canon_sha256":"a8b27636f87999246334fe63ad9a88c2a2d7b5e6b96a64ca7646aceebee2cde9"},"schema_version":"1.0"},"canonical_sha256":"a6a74d4241ab439f47f9065db803d18e1705136aa778c29af28abf36a2bd33c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:15.165163Z","signature_b64":"xGS+Nm4r9VigmHD8GGCifpZBz1vj5MTZg+GRRGOf5Qms1+UST+EXnqbbfHLo9s9/ig8n2hUwumfFyTWGSLvvAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6a74d4241ab439f47f9065db803d18e1705136aa778c29af28abf36a2bd33c1","last_reissued_at":"2026-05-18T02:57:15.164699Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:15.164699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.6611","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":"2026-05-18T02:57:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6KdjxGkHyXVLClOiQlCybeDkwULBmZ3tmwdrLkOlNBXw/w9g02/yDwPLSSiSLUkFNSZScuLOjKEH1OkjL/zFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T14:01:08.479930Z"},"content_sha256":"f5dbb0b8ff08cd2b724d67efc6a4170ab3d9c28957ac46b092e2aed85a61c14d","schema_version":"1.0","event_id":"sha256:f5dbb0b8ff08cd2b724d67efc6a4170ab3d9c28957ac46b092e2aed85a61c14d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:U2TU2QSBVNBZ6R7ZAZO3QA6RRY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The rigidity of periodic body-bar frameworks on the three-dimensional fixed torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Elissa Ross","submitted_at":"2012-03-29T18:03:53Z","abstract_excerpt":"We present necessary and sufficient conditions for the generic rigidity of body-bar frameworks on the three-dimensional fixed torus. These frameworks correspond to infinite periodic body-bar frameworks in $\\mathbb{R}^3$ with a fixed periodic lattice."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6611","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":"2026-05-18T02:57:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5MdnQgoFcgHH/fCSDzGPoBa3JJ43baKv7OFeoSzWQDeBI48NUHQn3HZ9UgjnrcP/gIBS0kYiwvqAfLW4A4ewDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T14:01:08.480274Z"},"content_sha256":"c58ed8cc11130ffa64b31576447ca82c018f0c743a157a5da9abda276141af76","schema_version":"1.0","event_id":"sha256:c58ed8cc11130ffa64b31576447ca82c018f0c743a157a5da9abda276141af76"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U2TU2QSBVNBZ6R7ZAZO3QA6RRY/bundle.json","state_url":"https://pith.science/pith/U2TU2QSBVNBZ6R7ZAZO3QA6RRY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U2TU2QSBVNBZ6R7ZAZO3QA6RRY/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":"2026-06-21T14:01:08Z","links":{"resolver":"https://pith.science/pith/U2TU2QSBVNBZ6R7ZAZO3QA6RRY","bundle":"https://pith.science/pith/U2TU2QSBVNBZ6R7ZAZO3QA6RRY/bundle.json","state":"https://pith.science/pith/U2TU2QSBVNBZ6R7ZAZO3QA6RRY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U2TU2QSBVNBZ6R7ZAZO3QA6RRY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:U2TU2QSBVNBZ6R7ZAZO3QA6RRY","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":"a8b27636f87999246334fe63ad9a88c2a2d7b5e6b96a64ca7646aceebee2cde9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-03-29T18:03:53Z","title_canon_sha256":"7c0e73d842a1845e7060933bf3457dc6418320b7b0055d3fcd5e8e2998fc592e"},"schema_version":"1.0","source":{"id":"1203.6611","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.6611","created_at":"2026-05-18T02:57:15Z"},{"alias_kind":"arxiv_version","alias_value":"1203.6611v1","created_at":"2026-05-18T02:57:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6611","created_at":"2026-05-18T02:57:15Z"},{"alias_kind":"pith_short_12","alias_value":"U2TU2QSBVNBZ","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"U2TU2QSBVNBZ6R7Z","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"U2TU2QSB","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:c58ed8cc11130ffa64b31576447ca82c018f0c743a157a5da9abda276141af76","target":"graph","created_at":"2026-05-18T02:57:15Z","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":"We present necessary and sufficient conditions for the generic rigidity of body-bar frameworks on the three-dimensional fixed torus. These frameworks correspond to infinite periodic body-bar frameworks in $\\mathbb{R}^3$ with a fixed periodic lattice.","authors_text":"Elissa Ross","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-03-29T18:03:53Z","title":"The rigidity of periodic body-bar frameworks on the three-dimensional fixed torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6611","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:f5dbb0b8ff08cd2b724d67efc6a4170ab3d9c28957ac46b092e2aed85a61c14d","target":"record","created_at":"2026-05-18T02:57:15Z","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":"a8b27636f87999246334fe63ad9a88c2a2d7b5e6b96a64ca7646aceebee2cde9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-03-29T18:03:53Z","title_canon_sha256":"7c0e73d842a1845e7060933bf3457dc6418320b7b0055d3fcd5e8e2998fc592e"},"schema_version":"1.0","source":{"id":"1203.6611","kind":"arxiv","version":1}},"canonical_sha256":"a6a74d4241ab439f47f9065db803d18e1705136aa778c29af28abf36a2bd33c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6a74d4241ab439f47f9065db803d18e1705136aa778c29af28abf36a2bd33c1","first_computed_at":"2026-05-18T02:57:15.164699Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:15.164699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xGS+Nm4r9VigmHD8GGCifpZBz1vj5MTZg+GRRGOf5Qms1+UST+EXnqbbfHLo9s9/ig8n2hUwumfFyTWGSLvvAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:15.165163Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.6611","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5dbb0b8ff08cd2b724d67efc6a4170ab3d9c28957ac46b092e2aed85a61c14d","sha256:c58ed8cc11130ffa64b31576447ca82c018f0c743a157a5da9abda276141af76"],"state_sha256":"79b1472a5ba7f6f23dff39cbd0a64f1cc901513c856eca138e10d76704c21706"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oMwQnezEKDVCiWC7GoF9rQeStk1Zn8qNEhSLEjKBpvUAjV8jSK7arfWTNQ5UuWS+iVbHMEV/NlkxmJZxMCIpBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T14:01:08.482916Z","bundle_sha256":"86dfea941fb5c61b696b7d62a1a25836fcc19d3765803cb0347749c8cf35ca9c"}}