{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:A4VXSF33TH5WB45YNLFFJFBO6B","short_pith_number":"pith:A4VXSF33","canonical_record":{"source":{"id":"1806.03333","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-08T19:40:27Z","cross_cats_sorted":["math.PR","q-bio.BM"],"title_canon_sha256":"74ec2c0d9ef9085991550ccff1dd1e4cee07002e235d54e73e724113a39750ac","abstract_canon_sha256":"415c64d7d8f91adee8e4a6311150e4a64445d6e82ec0379224c43957a479bd9c"},"schema_version":"1.0"},"canonical_sha256":"072b79177b99fb60f3b86aca54942ef07a767469e92a706c8ed77344f56c185c","source":{"kind":"arxiv","id":"1806.03333","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.03333","created_at":"2026-05-18T00:13:43Z"},{"alias_kind":"arxiv_version","alias_value":"1806.03333v1","created_at":"2026-05-18T00:13:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03333","created_at":"2026-05-18T00:13:43Z"},{"alias_kind":"pith_short_12","alias_value":"A4VXSF33TH5W","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"A4VXSF33TH5WB45Y","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"A4VXSF33","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:A4VXSF33TH5WB45YNLFFJFBO6B","target":"record","payload":{"canonical_record":{"source":{"id":"1806.03333","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-08T19:40:27Z","cross_cats_sorted":["math.PR","q-bio.BM"],"title_canon_sha256":"74ec2c0d9ef9085991550ccff1dd1e4cee07002e235d54e73e724113a39750ac","abstract_canon_sha256":"415c64d7d8f91adee8e4a6311150e4a64445d6e82ec0379224c43957a479bd9c"},"schema_version":"1.0"},"canonical_sha256":"072b79177b99fb60f3b86aca54942ef07a767469e92a706c8ed77344f56c185c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:43.740374Z","signature_b64":"aQ54pfDPPiZJOyk/Q/QEs0erEDQG0MoyYlnxYyrQO5HARgoyNvXi4yt1o+kDY+Q1z6IG2Ve+HhUUu8HrRB6sCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"072b79177b99fb60f3b86aca54942ef07a767469e92a706c8ed77344f56c185c","last_reissued_at":"2026-05-18T00:13:43.739677Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:43.739677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.03333","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":"2026-05-18T00:13:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GFFJ0Lphkd9/WfHGXyZrNVDEVnoct2qorDTTPnYQggPZnuqnCiezHPb/bb86rzWK8nEDszvd5rrM1w1iMqU0Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T16:01:15.698939Z"},"content_sha256":"e85cff72993bea4bbc378cbe28f806c1198f9ac7b6d3a7ceae46931d0939f59d","schema_version":"1.0","event_id":"sha256:e85cff72993bea4bbc378cbe28f806c1198f9ac7b6d3a7ceae46931d0939f59d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:A4VXSF33TH5WB45YNLFFJFBO6B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The rainbow-spectrum of RNA secondary structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","q-bio.BM"],"primary_cat":"math.CO","authors_text":"Christian M. Reidys, Thomas J. X. Li","submitted_at":"2018-06-08T19:40:27Z","abstract_excerpt":"In this paper we analyze the length-spectrum of rainbows in RNA secondary structures. A rainbow in a secondary structure is a maximal arc with respect to the partial order induced by nesting. We show that there is a significant gap in this length-spectrum. We shall prove that there asymptotically almost surely exists a unique longest rainbow of length at least $n-O(n^{1/2})$ and that with high probability any other rainbow has finite length. We show that the distribution of the length of the longest rainbow converges to a discrete limit law and that, for finite $k$, the distribution of rainbow"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03333","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":"2026-05-18T00:13:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q9FrvkHH+dNXzyvRY39KG2A4b1eXSnK7sY+MY9VuME+Wbv3Yn0YKvEvW7cNVe4fzQmxKV4GjoFpRyy2JcH5FDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T16:01:15.699283Z"},"content_sha256":"cd4b83367baf87842cb3feff02faba1f72c73de2bf1e807dd8e1ac9db831a4c0","schema_version":"1.0","event_id":"sha256:cd4b83367baf87842cb3feff02faba1f72c73de2bf1e807dd8e1ac9db831a4c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A4VXSF33TH5WB45YNLFFJFBO6B/bundle.json","state_url":"https://pith.science/pith/A4VXSF33TH5WB45YNLFFJFBO6B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A4VXSF33TH5WB45YNLFFJFBO6B/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":"2026-06-05T16:01:15Z","links":{"resolver":"https://pith.science/pith/A4VXSF33TH5WB45YNLFFJFBO6B","bundle":"https://pith.science/pith/A4VXSF33TH5WB45YNLFFJFBO6B/bundle.json","state":"https://pith.science/pith/A4VXSF33TH5WB45YNLFFJFBO6B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A4VXSF33TH5WB45YNLFFJFBO6B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:A4VXSF33TH5WB45YNLFFJFBO6B","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":"415c64d7d8f91adee8e4a6311150e4a64445d6e82ec0379224c43957a479bd9c","cross_cats_sorted":["math.PR","q-bio.BM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-08T19:40:27Z","title_canon_sha256":"74ec2c0d9ef9085991550ccff1dd1e4cee07002e235d54e73e724113a39750ac"},"schema_version":"1.0","source":{"id":"1806.03333","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.03333","created_at":"2026-05-18T00:13:43Z"},{"alias_kind":"arxiv_version","alias_value":"1806.03333v1","created_at":"2026-05-18T00:13:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03333","created_at":"2026-05-18T00:13:43Z"},{"alias_kind":"pith_short_12","alias_value":"A4VXSF33TH5W","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"A4VXSF33TH5WB45Y","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"A4VXSF33","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:cd4b83367baf87842cb3feff02faba1f72c73de2bf1e807dd8e1ac9db831a4c0","target":"graph","created_at":"2026-05-18T00:13:43Z","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 this paper we analyze the length-spectrum of rainbows in RNA secondary structures. A rainbow in a secondary structure is a maximal arc with respect to the partial order induced by nesting. We show that there is a significant gap in this length-spectrum. We shall prove that there asymptotically almost surely exists a unique longest rainbow of length at least $n-O(n^{1/2})$ and that with high probability any other rainbow has finite length. We show that the distribution of the length of the longest rainbow converges to a discrete limit law and that, for finite $k$, the distribution of rainbow","authors_text":"Christian M. Reidys, Thomas J. X. Li","cross_cats":["math.PR","q-bio.BM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-08T19:40:27Z","title":"The rainbow-spectrum of RNA secondary structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03333","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:e85cff72993bea4bbc378cbe28f806c1198f9ac7b6d3a7ceae46931d0939f59d","target":"record","created_at":"2026-05-18T00:13:43Z","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":"415c64d7d8f91adee8e4a6311150e4a64445d6e82ec0379224c43957a479bd9c","cross_cats_sorted":["math.PR","q-bio.BM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-08T19:40:27Z","title_canon_sha256":"74ec2c0d9ef9085991550ccff1dd1e4cee07002e235d54e73e724113a39750ac"},"schema_version":"1.0","source":{"id":"1806.03333","kind":"arxiv","version":1}},"canonical_sha256":"072b79177b99fb60f3b86aca54942ef07a767469e92a706c8ed77344f56c185c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"072b79177b99fb60f3b86aca54942ef07a767469e92a706c8ed77344f56c185c","first_computed_at":"2026-05-18T00:13:43.739677Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:43.739677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aQ54pfDPPiZJOyk/Q/QEs0erEDQG0MoyYlnxYyrQO5HARgoyNvXi4yt1o+kDY+Q1z6IG2Ve+HhUUu8HrRB6sCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:43.740374Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.03333","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e85cff72993bea4bbc378cbe28f806c1198f9ac7b6d3a7ceae46931d0939f59d","sha256:cd4b83367baf87842cb3feff02faba1f72c73de2bf1e807dd8e1ac9db831a4c0"],"state_sha256":"27c366be09cc7d76095fa38e0451021f60108bde3b0fd88af798466d9dcbc52a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dO/RmgmjVR8/W2SdV2teZk0b9LC4ASqphU4dNPn1IvVTyduWMt4/In6Ktnh7rrXN83aWOfwyfG0hyuoXFl7FDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T16:01:15.701328Z","bundle_sha256":"179a7f772aabb8a3a349d87a0bb7c653f6f694dc440590cd66d9e6afb262b5da"}}