{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:BLNK6ZUFVAM5NUBPZVIJ4ZR7VU","short_pith_number":"pith:BLNK6ZUF","canonical_record":{"source":{"id":"0801.2524","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2008-01-16T16:03:05Z","cross_cats_sorted":["q-bio.GN"],"title_canon_sha256":"ad02a1cf71f240597411f544e117e2a5bbab14cb28fde56a257138f2d94c7c78","abstract_canon_sha256":"1a04b132dbf9a1a4a4a8bc26ff5f9293073d21dda1801eed4b56224bf5ca8c82"},"schema_version":"1.0"},"canonical_sha256":"0adaaf6685a819d6d02fcd509e663fad0ae222e3dcae1968c082bc702e356206","source":{"kind":"arxiv","id":"0801.2524","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.2524","created_at":"2026-05-18T04:07:05Z"},{"alias_kind":"arxiv_version","alias_value":"0801.2524v1","created_at":"2026-05-18T04:07:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.2524","created_at":"2026-05-18T04:07:05Z"},{"alias_kind":"pith_short_12","alias_value":"BLNK6ZUFVAM5","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"BLNK6ZUFVAM5NUBP","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"BLNK6ZUF","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:BLNK6ZUFVAM5NUBPZVIJ4ZR7VU","target":"record","payload":{"canonical_record":{"source":{"id":"0801.2524","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2008-01-16T16:03:05Z","cross_cats_sorted":["q-bio.GN"],"title_canon_sha256":"ad02a1cf71f240597411f544e117e2a5bbab14cb28fde56a257138f2d94c7c78","abstract_canon_sha256":"1a04b132dbf9a1a4a4a8bc26ff5f9293073d21dda1801eed4b56224bf5ca8c82"},"schema_version":"1.0"},"canonical_sha256":"0adaaf6685a819d6d02fcd509e663fad0ae222e3dcae1968c082bc702e356206","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:05.533810Z","signature_b64":"ZVKde1sykcHBOxIdW83l2bcmbl4+bwmGQCGZWzMdtFiWNGBeWDBNQHfZDKI7HTLVwCkUH6u5qPiOQUTvq2kvBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0adaaf6685a819d6d02fcd509e663fad0ae222e3dcae1968c082bc702e356206","last_reissued_at":"2026-05-18T04:07:05.533101Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:05.533101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0801.2524","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":"2026-05-18T04:07:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jPamg1m+sX6bXfYAP1pcXz5ChGonRzN0XHQOfwLna7Bg4fW4ch7qDeSxayU3eOs+UAHHUExbpijZTXpXMVhoAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:55:42.154082Z"},"content_sha256":"82bce21b7362e5062c5008b6b39fb9062536094a0154dd0551309b0d41b50603","schema_version":"1.0","event_id":"sha256:82bce21b7362e5062c5008b6b39fb9062536094a0154dd0551309b0d41b50603"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:BLNK6ZUFVAM5NUBPZVIJ4ZR7VU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A variant of the tandem duplication - random loss model of genome rearrangement","license":"","headline":"","cross_cats":["q-bio.GN"],"primary_cat":"math.CO","authors_text":"Dominique Rossin (LIAFA), Mathilde Bouvel (LIAFA)","submitted_at":"2008-01-16T16:03:05Z","abstract_excerpt":"In Soda'06, Chaudhuri, Chen, Mihaescu and Rao study algorithmic properties of the tandem duplication - random loss model of genome rearrangement, well-known in evolutionary biology. In their model, the cost of one step of duplication-loss of width k is $\\alpha^k$ for $\\alpha =1$ or $\\alpha >=2 $. In this paper, we study a variant of this model, where the cost of one step of width $k$ is 1 if $k <= K$ and $\\infty$ if $k > K$, for any value of the parameter $K in N$. We first show that permutations obtained after $p$ steps of width $K$ define classes of pattern-avoiding permutations. We also com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.2524","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":"2026-05-18T04:07:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+6z9Pj6yF60DJm9GdfmichDUVk09bzkLeu2bvJrVMKEW01vbwFJStpSO2YKB5O24tHBnK8+nIsKZUIV/cr6EBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:55:42.154818Z"},"content_sha256":"e15b4645b2d2758d41bbd396c990e0d2ed817b15b5eb842bcb328476c693c012","schema_version":"1.0","event_id":"sha256:e15b4645b2d2758d41bbd396c990e0d2ed817b15b5eb842bcb328476c693c012"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BLNK6ZUFVAM5NUBPZVIJ4ZR7VU/bundle.json","state_url":"https://pith.science/pith/BLNK6ZUFVAM5NUBPZVIJ4ZR7VU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BLNK6ZUFVAM5NUBPZVIJ4ZR7VU/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":"2026-06-09T03:55:42Z","links":{"resolver":"https://pith.science/pith/BLNK6ZUFVAM5NUBPZVIJ4ZR7VU","bundle":"https://pith.science/pith/BLNK6ZUFVAM5NUBPZVIJ4ZR7VU/bundle.json","state":"https://pith.science/pith/BLNK6ZUFVAM5NUBPZVIJ4ZR7VU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BLNK6ZUFVAM5NUBPZVIJ4ZR7VU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:BLNK6ZUFVAM5NUBPZVIJ4ZR7VU","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":"1a04b132dbf9a1a4a4a8bc26ff5f9293073d21dda1801eed4b56224bf5ca8c82","cross_cats_sorted":["q-bio.GN"],"license":"","primary_cat":"math.CO","submitted_at":"2008-01-16T16:03:05Z","title_canon_sha256":"ad02a1cf71f240597411f544e117e2a5bbab14cb28fde56a257138f2d94c7c78"},"schema_version":"1.0","source":{"id":"0801.2524","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.2524","created_at":"2026-05-18T04:07:05Z"},{"alias_kind":"arxiv_version","alias_value":"0801.2524v1","created_at":"2026-05-18T04:07:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.2524","created_at":"2026-05-18T04:07:05Z"},{"alias_kind":"pith_short_12","alias_value":"BLNK6ZUFVAM5","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"BLNK6ZUFVAM5NUBP","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"BLNK6ZUF","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:e15b4645b2d2758d41bbd396c990e0d2ed817b15b5eb842bcb328476c693c012","target":"graph","created_at":"2026-05-18T04:07:05Z","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 Soda'06, Chaudhuri, Chen, Mihaescu and Rao study algorithmic properties of the tandem duplication - random loss model of genome rearrangement, well-known in evolutionary biology. In their model, the cost of one step of duplication-loss of width k is $\\alpha^k$ for $\\alpha =1$ or $\\alpha >=2 $. In this paper, we study a variant of this model, where the cost of one step of width $k$ is 1 if $k <= K$ and $\\infty$ if $k > K$, for any value of the parameter $K in N$. We first show that permutations obtained after $p$ steps of width $K$ define classes of pattern-avoiding permutations. We also com","authors_text":"Dominique Rossin (LIAFA), Mathilde Bouvel (LIAFA)","cross_cats":["q-bio.GN"],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"2008-01-16T16:03:05Z","title":"A variant of the tandem duplication - random loss model of genome rearrangement"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.2524","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":"sha256:82bce21b7362e5062c5008b6b39fb9062536094a0154dd0551309b0d41b50603","target":"record","created_at":"2026-05-18T04:07:05Z","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":"1a04b132dbf9a1a4a4a8bc26ff5f9293073d21dda1801eed4b56224bf5ca8c82","cross_cats_sorted":["q-bio.GN"],"license":"","primary_cat":"math.CO","submitted_at":"2008-01-16T16:03:05Z","title_canon_sha256":"ad02a1cf71f240597411f544e117e2a5bbab14cb28fde56a257138f2d94c7c78"},"schema_version":"1.0","source":{"id":"0801.2524","kind":"arxiv","version":1}},"canonical_sha256":"0adaaf6685a819d6d02fcd509e663fad0ae222e3dcae1968c082bc702e356206","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0adaaf6685a819d6d02fcd509e663fad0ae222e3dcae1968c082bc702e356206","first_computed_at":"2026-05-18T04:07:05.533101Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:05.533101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZVKde1sykcHBOxIdW83l2bcmbl4+bwmGQCGZWzMdtFiWNGBeWDBNQHfZDKI7HTLVwCkUH6u5qPiOQUTvq2kvBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:05.533810Z","signed_message":"canonical_sha256_bytes"},"source_id":"0801.2524","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82bce21b7362e5062c5008b6b39fb9062536094a0154dd0551309b0d41b50603","sha256:e15b4645b2d2758d41bbd396c990e0d2ed817b15b5eb842bcb328476c693c012"],"state_sha256":"c71848cbc1e19fe4f0983a56d5aad677a9a929491b0739ee63800066a88c204b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4kSYZNJRh/KMuzSJuJ2yVXB33U/30bwLLkamOTAKxET2ZZN3m2eRH4N2cRb5nJasUieV5+oekQ+7efLcXHVHCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T03:55:42.158970Z","bundle_sha256":"cf218cb319cf3df541d37d4f2eb86a9a64fbd1bd0473a307f7a0d8cb12a0410c"}}