{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:36KVBMYKZUHMD46GTD3VZWZSGI","short_pith_number":"pith:36KVBMYK","canonical_record":{"source":{"id":"1607.02279","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-07-08T09:09:08Z","cross_cats_sorted":["math.CO","math.IT"],"title_canon_sha256":"72d0c0c4b418277024897f42aa1a095d3d8b75022f3a10d2ff994cf1b3b47305","abstract_canon_sha256":"da4f008cc835f36d5f68474bceb2c4799606c5e60e4026ef285d48eca7dbb267"},"schema_version":"1.0"},"canonical_sha256":"df9550b30acd0ec1f3c698f75cdb32323a7b4e1c8b679f075c1d21c0d7eaa661","source":{"kind":"arxiv","id":"1607.02279","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.02279","created_at":"2026-05-18T01:11:20Z"},{"alias_kind":"arxiv_version","alias_value":"1607.02279v1","created_at":"2026-05-18T01:11:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.02279","created_at":"2026-05-18T01:11:20Z"},{"alias_kind":"pith_short_12","alias_value":"36KVBMYKZUHM","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"36KVBMYKZUHMD46G","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"36KVBMYK","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:36KVBMYKZUHMD46GTD3VZWZSGI","target":"record","payload":{"canonical_record":{"source":{"id":"1607.02279","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-07-08T09:09:08Z","cross_cats_sorted":["math.CO","math.IT"],"title_canon_sha256":"72d0c0c4b418277024897f42aa1a095d3d8b75022f3a10d2ff994cf1b3b47305","abstract_canon_sha256":"da4f008cc835f36d5f68474bceb2c4799606c5e60e4026ef285d48eca7dbb267"},"schema_version":"1.0"},"canonical_sha256":"df9550b30acd0ec1f3c698f75cdb32323a7b4e1c8b679f075c1d21c0d7eaa661","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:20.770006Z","signature_b64":"URRfJ4OYPiBm6hOw3oFbBaOnZbcMhEIPxwRvN5oLyAwZBfRkbiVfk/UJvH7xlag+/RO77yxYrnFhsPLsE4j4Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df9550b30acd0ec1f3c698f75cdb32323a7b4e1c8b679f075c1d21c0d7eaa661","last_reissued_at":"2026-05-18T01:11:20.769307Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:20.769307Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.02279","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":"2026-05-18T01:11:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cv88el4p6HSDDRXsvZNef3D1bDjdbeJQPL9z0DUk8N44c8Dmts1aBmrsb4RmZMPXizrDO8wgV22EoTG6MFqsBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:44:45.366174Z"},"content_sha256":"b99a435df2fc3ef8a4031f575d04c07d4f1978a91c29a79ab5bb3a5edff05e57","schema_version":"1.0","event_id":"sha256:b99a435df2fc3ef8a4031f575d04c07d4f1978a91c29a79ab5bb3a5edff05e57"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:36KVBMYKZUHMD46GTD3VZWZSGI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rates of DNA Sequence Profiles for Practical Values of Read Lengths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Han Mao Kiah, Johan Chrisnata, Martianus Frederic Ezerman, Zuling Chang","submitted_at":"2016-07-08T09:09:08Z","abstract_excerpt":"A recent study by one of the authors has demonstrated the importance of profile vectors in DNA-based data storage. We provide exact values and lower bounds on the number of profile vectors for finite values of alphabet size $q$, read length $\\ell$, and word length $n$.Consequently, we demonstrate that for $q\\ge 2$ and $n\\le q^{\\ell/2-1}$, the number of profile vectors is at least $q^{\\kappa n}$ with $\\kappa$ very close to one.In addition to enumeration results, we provide a set of efficient encoding and decoding algorithms for each of two particular families of profile vectors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02279","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":"2026-05-18T01:11:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E+2KunyxI+wkOWsH3nE/+EPaxBylH2FhijMscgi6k6cWlucuHhWt/aiUF+aiDm54NbThaatNtfaF6oPvJaMsCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:44:45.366542Z"},"content_sha256":"7defdb871126c4a7827cc7467f850b2b77c6c3f2ad7984d35635654095fc7cea","schema_version":"1.0","event_id":"sha256:7defdb871126c4a7827cc7467f850b2b77c6c3f2ad7984d35635654095fc7cea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/36KVBMYKZUHMD46GTD3VZWZSGI/bundle.json","state_url":"https://pith.science/pith/36KVBMYKZUHMD46GTD3VZWZSGI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/36KVBMYKZUHMD46GTD3VZWZSGI/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":"2026-06-03T05:44:45Z","links":{"resolver":"https://pith.science/pith/36KVBMYKZUHMD46GTD3VZWZSGI","bundle":"https://pith.science/pith/36KVBMYKZUHMD46GTD3VZWZSGI/bundle.json","state":"https://pith.science/pith/36KVBMYKZUHMD46GTD3VZWZSGI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/36KVBMYKZUHMD46GTD3VZWZSGI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:36KVBMYKZUHMD46GTD3VZWZSGI","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":"da4f008cc835f36d5f68474bceb2c4799606c5e60e4026ef285d48eca7dbb267","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-07-08T09:09:08Z","title_canon_sha256":"72d0c0c4b418277024897f42aa1a095d3d8b75022f3a10d2ff994cf1b3b47305"},"schema_version":"1.0","source":{"id":"1607.02279","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.02279","created_at":"2026-05-18T01:11:20Z"},{"alias_kind":"arxiv_version","alias_value":"1607.02279v1","created_at":"2026-05-18T01:11:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.02279","created_at":"2026-05-18T01:11:20Z"},{"alias_kind":"pith_short_12","alias_value":"36KVBMYKZUHM","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"36KVBMYKZUHMD46G","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"36KVBMYK","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:7defdb871126c4a7827cc7467f850b2b77c6c3f2ad7984d35635654095fc7cea","target":"graph","created_at":"2026-05-18T01:11:20Z","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 recent study by one of the authors has demonstrated the importance of profile vectors in DNA-based data storage. We provide exact values and lower bounds on the number of profile vectors for finite values of alphabet size $q$, read length $\\ell$, and word length $n$.Consequently, we demonstrate that for $q\\ge 2$ and $n\\le q^{\\ell/2-1}$, the number of profile vectors is at least $q^{\\kappa n}$ with $\\kappa$ very close to one.In addition to enumeration results, we provide a set of efficient encoding and decoding algorithms for each of two particular families of profile vectors.","authors_text":"Han Mao Kiah, Johan Chrisnata, Martianus Frederic Ezerman, Zuling Chang","cross_cats":["math.CO","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-07-08T09:09:08Z","title":"Rates of DNA Sequence Profiles for Practical Values of Read Lengths"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02279","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:b99a435df2fc3ef8a4031f575d04c07d4f1978a91c29a79ab5bb3a5edff05e57","target":"record","created_at":"2026-05-18T01:11:20Z","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":"da4f008cc835f36d5f68474bceb2c4799606c5e60e4026ef285d48eca7dbb267","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-07-08T09:09:08Z","title_canon_sha256":"72d0c0c4b418277024897f42aa1a095d3d8b75022f3a10d2ff994cf1b3b47305"},"schema_version":"1.0","source":{"id":"1607.02279","kind":"arxiv","version":1}},"canonical_sha256":"df9550b30acd0ec1f3c698f75cdb32323a7b4e1c8b679f075c1d21c0d7eaa661","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df9550b30acd0ec1f3c698f75cdb32323a7b4e1c8b679f075c1d21c0d7eaa661","first_computed_at":"2026-05-18T01:11:20.769307Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:20.769307Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"URRfJ4OYPiBm6hOw3oFbBaOnZbcMhEIPxwRvN5oLyAwZBfRkbiVfk/UJvH7xlag+/RO77yxYrnFhsPLsE4j4Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:20.770006Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.02279","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b99a435df2fc3ef8a4031f575d04c07d4f1978a91c29a79ab5bb3a5edff05e57","sha256:7defdb871126c4a7827cc7467f850b2b77c6c3f2ad7984d35635654095fc7cea"],"state_sha256":"2325dcfb8ba91f28425660b039c3cd0945a2d64979beb10c66236beb5e153e26"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rdIqSSUfAdayy3K04SCS/DVllsYELmL6A0u1RYE4cWmUK1XY6DUd7hFguABe4NhT+U5ZM6JiaICqHHj/B4OjDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T05:44:45.368522Z","bundle_sha256":"025a5236513611f09fb4d17bcb10453a616e8cb46b3dc10f863ddf78455adfae"}}