{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:EHBAFOIUYMVGIHPPNGMMOOE4BP","short_pith_number":"pith:EHBAFOIU","canonical_record":{"source":{"id":"0908.4003","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2009-08-27T12:58:40Z","cross_cats_sorted":["q-bio.BM"],"title_canon_sha256":"63a6c12a2e2b1af1c8ce521518df0a90ee09f96eff5506454b0af5bfc13fb019","abstract_canon_sha256":"b453f227f394ca38b0f8d0b53cbd5b843b24d9f650b5a38186d1b6ae808a8f71"},"schema_version":"1.0"},"canonical_sha256":"21c202b914c32a641def6998c7389c0bc81036ab08c6547517f6798e4b6283d8","source":{"kind":"arxiv","id":"0908.4003","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.4003","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"arxiv_version","alias_value":"0908.4003v1","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.4003","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"pith_short_12","alias_value":"EHBAFOIUYMVG","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"EHBAFOIUYMVGIHPP","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"EHBAFOIU","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:EHBAFOIUYMVGIHPPNGMMOOE4BP","target":"record","payload":{"canonical_record":{"source":{"id":"0908.4003","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2009-08-27T12:58:40Z","cross_cats_sorted":["q-bio.BM"],"title_canon_sha256":"63a6c12a2e2b1af1c8ce521518df0a90ee09f96eff5506454b0af5bfc13fb019","abstract_canon_sha256":"b453f227f394ca38b0f8d0b53cbd5b843b24d9f650b5a38186d1b6ae808a8f71"},"schema_version":"1.0"},"canonical_sha256":"21c202b914c32a641def6998c7389c0bc81036ab08c6547517f6798e4b6283d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:45.764657Z","signature_b64":"j13rvYupjW3g/g4GPjqT4BG9yS8d7kP99zbrce+t6lDAoDw1ejOBSJA7FlFgazanxCS/DS/wzqqsW3+yjQ/JAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21c202b914c32a641def6998c7389c0bc81036ab08c6547517f6798e4b6283d8","last_reissued_at":"2026-05-18T03:20:45.764143Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:45.764143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0908.4003","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":"2026-05-18T03:20:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VOgjfCvfMdag4sMIatA7g3xUgiDu8PcwBArl/fIfzhHqihQa2Npp1EPVkDaVhGIBRMc6cr7gUpBzVd/esD9YDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T21:11:17.388755Z"},"content_sha256":"fc30ea210febf06343915b463c5a20b8a86ff6899911cfd2496cde4af01c2627","schema_version":"1.0","event_id":"sha256:fc30ea210febf06343915b463c5a20b8a86ff6899911cfd2496cde4af01c2627"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:EHBAFOIUYMVGIHPPNGMMOOE4BP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotics of Canonical and Saturated RNA Secondary Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.BM"],"primary_cat":"q-bio.QM","authors_text":"Bruno Salvy (INRIA Rocquencourt), Danny Krizanc, Evangelos Kranakis, Peter Clote","submitted_at":"2009-08-27T12:58:40Z","abstract_excerpt":"It is a classical result of Stein and Waterman that the asymptotic number of RNA secondary structures is $1.104366 n^{-3/2} 2.618034^n$. In this paper, we study combinatorial asymptotics for two special subclasses of RNA secondary structures - canonical and saturated structures. Canonical secondary structures were introduced by Bompf\\\"unewerer et al., who noted that the run time of Vienna RNA Package is substantially reduced when restricting computations to canonical structures. Here we provide an explanation for the speed-up. Saturated secondary structures have the property that no base pairs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.4003","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":"2026-05-18T03:20:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OBXKzmK6u5VUWOPlNEBDG8NSR2U4uaQ7b0vdLZS+h+QzWvqzPB3Q+zaG3eTZldCqRVjTm660P8SRIb8ShmrZBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T21:11:17.389107Z"},"content_sha256":"2648c06600351d924acb0e470cd7ce13faeb9f5810fcf7e85b44ddccc0577180","schema_version":"1.0","event_id":"sha256:2648c06600351d924acb0e470cd7ce13faeb9f5810fcf7e85b44ddccc0577180"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EHBAFOIUYMVGIHPPNGMMOOE4BP/bundle.json","state_url":"https://pith.science/pith/EHBAFOIUYMVGIHPPNGMMOOE4BP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EHBAFOIUYMVGIHPPNGMMOOE4BP/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":"2026-05-19T21:11:17Z","links":{"resolver":"https://pith.science/pith/EHBAFOIUYMVGIHPPNGMMOOE4BP","bundle":"https://pith.science/pith/EHBAFOIUYMVGIHPPNGMMOOE4BP/bundle.json","state":"https://pith.science/pith/EHBAFOIUYMVGIHPPNGMMOOE4BP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EHBAFOIUYMVGIHPPNGMMOOE4BP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:EHBAFOIUYMVGIHPPNGMMOOE4BP","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":"b453f227f394ca38b0f8d0b53cbd5b843b24d9f650b5a38186d1b6ae808a8f71","cross_cats_sorted":["q-bio.BM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2009-08-27T12:58:40Z","title_canon_sha256":"63a6c12a2e2b1af1c8ce521518df0a90ee09f96eff5506454b0af5bfc13fb019"},"schema_version":"1.0","source":{"id":"0908.4003","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.4003","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"arxiv_version","alias_value":"0908.4003v1","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.4003","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"pith_short_12","alias_value":"EHBAFOIUYMVG","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"EHBAFOIUYMVGIHPP","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"EHBAFOIU","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:2648c06600351d924acb0e470cd7ce13faeb9f5810fcf7e85b44ddccc0577180","target":"graph","created_at":"2026-05-18T03:20:45Z","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":"It is a classical result of Stein and Waterman that the asymptotic number of RNA secondary structures is $1.104366 n^{-3/2} 2.618034^n$. In this paper, we study combinatorial asymptotics for two special subclasses of RNA secondary structures - canonical and saturated structures. Canonical secondary structures were introduced by Bompf\\\"unewerer et al., who noted that the run time of Vienna RNA Package is substantially reduced when restricting computations to canonical structures. Here we provide an explanation for the speed-up. Saturated secondary structures have the property that no base pairs","authors_text":"Bruno Salvy (INRIA Rocquencourt), Danny Krizanc, Evangelos Kranakis, Peter Clote","cross_cats":["q-bio.BM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2009-08-27T12:58:40Z","title":"Asymptotics of Canonical and Saturated RNA Secondary Structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.4003","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:fc30ea210febf06343915b463c5a20b8a86ff6899911cfd2496cde4af01c2627","target":"record","created_at":"2026-05-18T03:20:45Z","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":"b453f227f394ca38b0f8d0b53cbd5b843b24d9f650b5a38186d1b6ae808a8f71","cross_cats_sorted":["q-bio.BM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2009-08-27T12:58:40Z","title_canon_sha256":"63a6c12a2e2b1af1c8ce521518df0a90ee09f96eff5506454b0af5bfc13fb019"},"schema_version":"1.0","source":{"id":"0908.4003","kind":"arxiv","version":1}},"canonical_sha256":"21c202b914c32a641def6998c7389c0bc81036ab08c6547517f6798e4b6283d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21c202b914c32a641def6998c7389c0bc81036ab08c6547517f6798e4b6283d8","first_computed_at":"2026-05-18T03:20:45.764143Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:45.764143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j13rvYupjW3g/g4GPjqT4BG9yS8d7kP99zbrce+t6lDAoDw1ejOBSJA7FlFgazanxCS/DS/wzqqsW3+yjQ/JAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:45.764657Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.4003","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc30ea210febf06343915b463c5a20b8a86ff6899911cfd2496cde4af01c2627","sha256:2648c06600351d924acb0e470cd7ce13faeb9f5810fcf7e85b44ddccc0577180"],"state_sha256":"48eade02306f51650ccbcecaf3bfa2b86f8c3e6d0d657fa39fde6c40003c49a6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Aw8RQcWKl4QCLQ6qj2hmuCGWSu4e8yynEvJd0Wys/ftRMlUA6KZidI6+MlyYNDh17nqLXSVR62RlCv1kxgdqBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T21:11:17.391329Z","bundle_sha256":"43a7dd8b000734ec16e75f65ea6071620e1714405c0aea042f0a8c87e267b89e"}}