{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:DNGWFHMHUTA6KBPF2JQKMXBOGT","short_pith_number":"pith:DNGWFHMH","canonical_record":{"source":{"id":"0807.0051","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.GN","submitted_at":"2008-07-01T01:29:06Z","cross_cats_sorted":["q-bio.QM"],"title_canon_sha256":"f53cf4bdaf4b41cfb61a7bf3345c96d57d5e477d64d7d416c2a8749638d27cc3","abstract_canon_sha256":"e27f7accbaf14fda3b35bee02126c3d6ebb2cfb5ecbf8ad81ab59b26a9a34b22"},"schema_version":"1.0"},"canonical_sha256":"1b4d629d87a4c1e505e5d260a65c2e34cb53ca2acc33bfd83267659037ee2d56","source":{"kind":"arxiv","id":"0807.0051","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.0051","created_at":"2026-05-18T04:31:30Z"},{"alias_kind":"arxiv_version","alias_value":"0807.0051v2","created_at":"2026-05-18T04:31:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.0051","created_at":"2026-05-18T04:31:30Z"},{"alias_kind":"pith_short_12","alias_value":"DNGWFHMHUTA6","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"DNGWFHMHUTA6KBPF","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"DNGWFHMH","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:DNGWFHMHUTA6KBPF2JQKMXBOGT","target":"record","payload":{"canonical_record":{"source":{"id":"0807.0051","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.GN","submitted_at":"2008-07-01T01:29:06Z","cross_cats_sorted":["q-bio.QM"],"title_canon_sha256":"f53cf4bdaf4b41cfb61a7bf3345c96d57d5e477d64d7d416c2a8749638d27cc3","abstract_canon_sha256":"e27f7accbaf14fda3b35bee02126c3d6ebb2cfb5ecbf8ad81ab59b26a9a34b22"},"schema_version":"1.0"},"canonical_sha256":"1b4d629d87a4c1e505e5d260a65c2e34cb53ca2acc33bfd83267659037ee2d56","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:30.045137Z","signature_b64":"NPW0qjWXhvemuanlbe53NTHEohEyTpJ0kLYoJgs/IYl/S8r8TBc+9JQAXJhKaryQpeHPUDaHXncy1u1BzOn+Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b4d629d87a4c1e505e5d260a65c2e34cb53ca2acc33bfd83267659037ee2d56","last_reissued_at":"2026-05-18T04:31:30.044650Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:30.044650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0807.0051","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:31:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AnxLJXqWiaMwGAP0yrFwiRcm8G/5w68cTHAnzBPY0XT7EnHHN8BwjSQlAzf5JP4NKLX4loDqN/xi6vnE4bs6AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T10:34:03.419746Z"},"content_sha256":"2e84c3b84e5fdea33684f96ef550d54b60a507949f283dfa97adb7a32b83e81c","schema_version":"1.0","event_id":"sha256:2e84c3b84e5fdea33684f96ef550d54b60a507949f283dfa97adb7a32b83e81c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:DNGWFHMHUTA6KBPF2JQKMXBOGT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lower Bounds for Optimal Alignments of Binary Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.QM"],"primary_cat":"q-bio.GN","authors_text":"Cynthia Vinzant","submitted_at":"2008-07-01T01:29:06Z","abstract_excerpt":"In parametric sequence alignment, optimal alignments of two sequences are computed as a function of the penalties for mismatches and spaces, producing many different optimal alignments. Here we give a 3/(2^{7/3}\\pi^{2/3})n^{2/3} +O(n^{1/3} \\log n) lower bound on the maximum number of distinct optimal alignment summaries of length-n binary sequences. This shows that the upper bound given by Gusfield et. al. is tight over all alphabets, thereby disproving the \"square root of n conjecture\". Thus the maximum number of distinct optimal alignment summaries (i.e. vertices of the alignment polytope) o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.0051","kind":"arxiv","version":2},"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":"2026-05-18T04:31:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oUWL+VV8v3/Mh12sMUNs72x0VwEX52SsA4OkfMAUOArpXnR9YVpt8CWyHrS7/6j6CcT6Kmvu++yQmMcdYcyRBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T10:34:03.420092Z"},"content_sha256":"c6796d1066bf1b5f3be43ac1a77e2db8975095362a9060224af20cd3fb3f8243","schema_version":"1.0","event_id":"sha256:c6796d1066bf1b5f3be43ac1a77e2db8975095362a9060224af20cd3fb3f8243"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DNGWFHMHUTA6KBPF2JQKMXBOGT/bundle.json","state_url":"https://pith.science/pith/DNGWFHMHUTA6KBPF2JQKMXBOGT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DNGWFHMHUTA6KBPF2JQKMXBOGT/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":"2026-06-22T10:34:03Z","links":{"resolver":"https://pith.science/pith/DNGWFHMHUTA6KBPF2JQKMXBOGT","bundle":"https://pith.science/pith/DNGWFHMHUTA6KBPF2JQKMXBOGT/bundle.json","state":"https://pith.science/pith/DNGWFHMHUTA6KBPF2JQKMXBOGT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DNGWFHMHUTA6KBPF2JQKMXBOGT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:DNGWFHMHUTA6KBPF2JQKMXBOGT","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":"e27f7accbaf14fda3b35bee02126c3d6ebb2cfb5ecbf8ad81ab59b26a9a34b22","cross_cats_sorted":["q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.GN","submitted_at":"2008-07-01T01:29:06Z","title_canon_sha256":"f53cf4bdaf4b41cfb61a7bf3345c96d57d5e477d64d7d416c2a8749638d27cc3"},"schema_version":"1.0","source":{"id":"0807.0051","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.0051","created_at":"2026-05-18T04:31:30Z"},{"alias_kind":"arxiv_version","alias_value":"0807.0051v2","created_at":"2026-05-18T04:31:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.0051","created_at":"2026-05-18T04:31:30Z"},{"alias_kind":"pith_short_12","alias_value":"DNGWFHMHUTA6","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"DNGWFHMHUTA6KBPF","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"DNGWFHMH","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:c6796d1066bf1b5f3be43ac1a77e2db8975095362a9060224af20cd3fb3f8243","target":"graph","created_at":"2026-05-18T04:31:30Z","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 parametric sequence alignment, optimal alignments of two sequences are computed as a function of the penalties for mismatches and spaces, producing many different optimal alignments. Here we give a 3/(2^{7/3}\\pi^{2/3})n^{2/3} +O(n^{1/3} \\log n) lower bound on the maximum number of distinct optimal alignment summaries of length-n binary sequences. This shows that the upper bound given by Gusfield et. al. is tight over all alphabets, thereby disproving the \"square root of n conjecture\". Thus the maximum number of distinct optimal alignment summaries (i.e. vertices of the alignment polytope) o","authors_text":"Cynthia Vinzant","cross_cats":["q-bio.QM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.GN","submitted_at":"2008-07-01T01:29:06Z","title":"Lower Bounds for Optimal Alignments of Binary Sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.0051","kind":"arxiv","version":2},"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":"sha256:2e84c3b84e5fdea33684f96ef550d54b60a507949f283dfa97adb7a32b83e81c","target":"record","created_at":"2026-05-18T04:31:30Z","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":"e27f7accbaf14fda3b35bee02126c3d6ebb2cfb5ecbf8ad81ab59b26a9a34b22","cross_cats_sorted":["q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.GN","submitted_at":"2008-07-01T01:29:06Z","title_canon_sha256":"f53cf4bdaf4b41cfb61a7bf3345c96d57d5e477d64d7d416c2a8749638d27cc3"},"schema_version":"1.0","source":{"id":"0807.0051","kind":"arxiv","version":2}},"canonical_sha256":"1b4d629d87a4c1e505e5d260a65c2e34cb53ca2acc33bfd83267659037ee2d56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b4d629d87a4c1e505e5d260a65c2e34cb53ca2acc33bfd83267659037ee2d56","first_computed_at":"2026-05-18T04:31:30.044650Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:30.044650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NPW0qjWXhvemuanlbe53NTHEohEyTpJ0kLYoJgs/IYl/S8r8TBc+9JQAXJhKaryQpeHPUDaHXncy1u1BzOn+Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:30.045137Z","signed_message":"canonical_sha256_bytes"},"source_id":"0807.0051","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e84c3b84e5fdea33684f96ef550d54b60a507949f283dfa97adb7a32b83e81c","sha256:c6796d1066bf1b5f3be43ac1a77e2db8975095362a9060224af20cd3fb3f8243"],"state_sha256":"0bfef13f59dbdb16af2ae4fb0299107a95ffff6ca1f218c4ac3e11bd15122c2f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MpACWBx8N4UIhYJlfVH5my+OHBEqMCuU1F9IKjTX1tCMyA2dqg+Gq22bHx2eWLNrOGMgtTjsV0YfizBkhqiPAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T10:34:03.422113Z","bundle_sha256":"8a6091a9fcf82299d51fd26980e769e4266040c4182527bf9e6e6289a0d7eb3b"}}