{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:DBOA5QFB4FUTKFCCYESSNLTLSK","short_pith_number":"pith:DBOA5QFB","canonical_record":{"source":{"id":"1403.2908","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-11T09:20:54Z","cross_cats_sorted":["q-bio.BM"],"title_canon_sha256":"4f287f1fe489cc1563c43dc3c4b127148e9df20ea92a344a367bc60cb64aa325","abstract_canon_sha256":"5fdfcb017693bc89cb7f74688dc78d0407a65ef9f74db69e5c777c4d32cddc8b"},"schema_version":"1.0"},"canonical_sha256":"185c0ec0a1e169351442c12526ae6b92a2545a461efc7fd622d3a311c8f07046","source":{"kind":"arxiv","id":"1403.2908","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.2908","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"arxiv_version","alias_value":"1403.2908v1","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2908","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"pith_short_12","alias_value":"DBOA5QFB4FUT","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DBOA5QFB4FUTKFCC","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DBOA5QFB","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:DBOA5QFB4FUTKFCCYESSNLTLSK","target":"record","payload":{"canonical_record":{"source":{"id":"1403.2908","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-11T09:20:54Z","cross_cats_sorted":["q-bio.BM"],"title_canon_sha256":"4f287f1fe489cc1563c43dc3c4b127148e9df20ea92a344a367bc60cb64aa325","abstract_canon_sha256":"5fdfcb017693bc89cb7f74688dc78d0407a65ef9f74db69e5c777c4d32cddc8b"},"schema_version":"1.0"},"canonical_sha256":"185c0ec0a1e169351442c12526ae6b92a2545a461efc7fd622d3a311c8f07046","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:33.619583Z","signature_b64":"Xtgy3epU84d9r9QXnRZzlXIDYTBgo3znxUt7nBloMEKVNWfinNqNpDmKFQx0Ex8KseZ4rMVaZtAPd22a5eCiCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"185c0ec0a1e169351442c12526ae6b92a2545a461efc7fd622d3a311c8f07046","last_reissued_at":"2026-05-18T02:56:33.618842Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:33.618842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.2908","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":"2026-05-18T02:56:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IP+w8t+H8AoGfbeymA2PyL+DC/lD8Y7jHcKlhvJjmPZNR4S5oWitAN6WiKcujW7q5lzbVTowFSfg30gc+2hRCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:22:15.058032Z"},"content_sha256":"742c585ba20d4c173fb961f35094c1e058e2dc7bde17a4f894c8f978b90affda","schema_version":"1.0","event_id":"sha256:742c585ba20d4c173fb961f35094c1e058e2dc7bde17a4f894c8f978b90affda"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:DBOA5QFB4FUTKFCCYESSNLTLSK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Shapes of topological RNA structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.BM"],"primary_cat":"math.CO","authors_text":"Christian M. Reidys, Fenix W.D. Huang","submitted_at":"2014-03-11T09:20:54Z","abstract_excerpt":"A topological RNA structure is derived from a diagram and its shape is obtained by collapsing the stacks of the structure into single arcs and by removing any arcs of length one. Shapes contain key topological, information and for fixed topological genus there exist only finitely many such shapes. We shall express topological RNA structures as unicellular maps, i.e. graphs together with a cyclic ordering of their half-edges. In this paper we prove a bijection of shapes of topological RNA structures. We furthermore derive a linear time algorithm generating shapes of fixed topological genus. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2908","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":"2026-05-18T02:56:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"keSXtKVUNSjNOgz7P25kEzJs9jkCPgNohtcBlI/tX3uU+xMg0VzCz3oeC6cwpqMNDfhomVLjowomLlDsjOySBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:22:15.058652Z"},"content_sha256":"1679dce52a423636acbf79765bf252a9b52625abab22c91ddabb257a5cb15b50","schema_version":"1.0","event_id":"sha256:1679dce52a423636acbf79765bf252a9b52625abab22c91ddabb257a5cb15b50"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DBOA5QFB4FUTKFCCYESSNLTLSK/bundle.json","state_url":"https://pith.science/pith/DBOA5QFB4FUTKFCCYESSNLTLSK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DBOA5QFB4FUTKFCCYESSNLTLSK/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":"2026-06-02T19:22:15Z","links":{"resolver":"https://pith.science/pith/DBOA5QFB4FUTKFCCYESSNLTLSK","bundle":"https://pith.science/pith/DBOA5QFB4FUTKFCCYESSNLTLSK/bundle.json","state":"https://pith.science/pith/DBOA5QFB4FUTKFCCYESSNLTLSK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DBOA5QFB4FUTKFCCYESSNLTLSK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DBOA5QFB4FUTKFCCYESSNLTLSK","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":"5fdfcb017693bc89cb7f74688dc78d0407a65ef9f74db69e5c777c4d32cddc8b","cross_cats_sorted":["q-bio.BM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-11T09:20:54Z","title_canon_sha256":"4f287f1fe489cc1563c43dc3c4b127148e9df20ea92a344a367bc60cb64aa325"},"schema_version":"1.0","source":{"id":"1403.2908","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.2908","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"arxiv_version","alias_value":"1403.2908v1","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2908","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"pith_short_12","alias_value":"DBOA5QFB4FUT","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DBOA5QFB4FUTKFCC","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DBOA5QFB","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:1679dce52a423636acbf79765bf252a9b52625abab22c91ddabb257a5cb15b50","target":"graph","created_at":"2026-05-18T02:56:33Z","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":"A topological RNA structure is derived from a diagram and its shape is obtained by collapsing the stacks of the structure into single arcs and by removing any arcs of length one. Shapes contain key topological, information and for fixed topological genus there exist only finitely many such shapes. We shall express topological RNA structures as unicellular maps, i.e. graphs together with a cyclic ordering of their half-edges. In this paper we prove a bijection of shapes of topological RNA structures. We furthermore derive a linear time algorithm generating shapes of fixed topological genus. We ","authors_text":"Christian M. Reidys, Fenix W.D. Huang","cross_cats":["q-bio.BM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-11T09:20:54Z","title":"Shapes of topological RNA structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2908","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":"sha256:742c585ba20d4c173fb961f35094c1e058e2dc7bde17a4f894c8f978b90affda","target":"record","created_at":"2026-05-18T02:56:33Z","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":"5fdfcb017693bc89cb7f74688dc78d0407a65ef9f74db69e5c777c4d32cddc8b","cross_cats_sorted":["q-bio.BM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-11T09:20:54Z","title_canon_sha256":"4f287f1fe489cc1563c43dc3c4b127148e9df20ea92a344a367bc60cb64aa325"},"schema_version":"1.0","source":{"id":"1403.2908","kind":"arxiv","version":1}},"canonical_sha256":"185c0ec0a1e169351442c12526ae6b92a2545a461efc7fd622d3a311c8f07046","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"185c0ec0a1e169351442c12526ae6b92a2545a461efc7fd622d3a311c8f07046","first_computed_at":"2026-05-18T02:56:33.618842Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:33.618842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xtgy3epU84d9r9QXnRZzlXIDYTBgo3znxUt7nBloMEKVNWfinNqNpDmKFQx0Ex8KseZ4rMVaZtAPd22a5eCiCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:33.619583Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.2908","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:742c585ba20d4c173fb961f35094c1e058e2dc7bde17a4f894c8f978b90affda","sha256:1679dce52a423636acbf79765bf252a9b52625abab22c91ddabb257a5cb15b50"],"state_sha256":"39a64288149a39e94ea8d001837cefc1a2c0a6537ae9aa2e093d089ba26a1721"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Te7RyzbhlTgR+RnrvSuFm504hChqWJ5A8QilB2lG3YqozXDPPK9pXMU7jmeHPUIR8XqHh6TpXiyd9nhODm6wBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T19:22:15.061586Z","bundle_sha256":"b9a8d44de8786f33d9478c7e60fa999b3f86e587287d63df0b616d735fb48189"}}