Pith Number

pith:NLJ4OXOR

pith:2026:NLJ4OXOROXTQPTGP7DAM4PVF2Y

not attested not anchored not stored refs resolved

More efficient PBWT prefix-array access via batching

Travis Gagie

Batching queries to the PBWT prefix array allows constant-time haplotype reporting using O(r log h) bits when batch sizes meet specified logarithmic thresholds.

arxiv:2605.15819 v1 · 2026-05-15 · cs.DS

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\usepackage{pith}
\pithnumber{NLJ4OXOROXTQPTGP7DAM4PVF2Y}

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4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

if we can batch queries until we have found r lg (h) / lg r such substrings and we report an average of at least lg (r) / lg h haplotypes in the panel per substring, for example, then for the second step we can easily use O (r log h) bits and constant time to report each haplotype.

C2weakest assumption

The premise that it is practical to batch queries until r lg(h)/lg(r) substrings have been identified and that the average number of haplotypes reported per substring will be at least lg(r)/lg(h); this workload-dependent condition is required for the constant-time claim to hold.

C3one line summary

Batching queries to accumulate r lg(h)/lg(r) substrings with average lg(r)/lg(h) haplotypes reported per substring enables O(r log h) bits and constant time per haplotype in PBWT prefix-array access.

References

12 extracted · 12 resolved · 2 Pith anchors

[1] Compressing Suffix Trees by Path Decompositions 2026 · arXiv:2506.14734

[2] Optimal-time mapping in run-length compressed PBWT.arXiv preprint 2602.13461, 2026 2026

[3] Faster Iterative $\phi$ Queries on the Positional BWT 2026 · arXiv:2605.04244

[4] Paola Bonnizoni and Younan Gao. Personal communication, 2026 2026

[5] RLBWT tricks.arXiv preprint arXiv:2112.04271v1, 2021 2021

Receipt and verification

First computed	2026-05-20T00:01:20.189492Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6ad3c75dd175e707cccff8c0ce3ea5d6059c71bed60554c0d4cb58bfca358159

Aliases

arxiv: 2605.15819 · arxiv_version: 2605.15819v1 · doi: 10.48550/arxiv.2605.15819 · pith_short_12: NLJ4OXOROXTQ · pith_short_16: NLJ4OXOROXTQPTGP · pith_short_8: NLJ4OXOR

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/NLJ4OXOROXTQPTGP7DAM4PVF2Y \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 6ad3c75dd175e707cccff8c0ce3ea5d6059c71bed60554c0d4cb58bfca358159

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e28a28d65babbffb79d93c0d21113a5d4759ee8f01077e73c5e18fea4e862aa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-05-15T10:18:25Z",
    "title_canon_sha256": "a7757e44fdf0b7ae8619919c42e629761e0d744a0c2c2782901b62b87bb95a6d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15819",
    "kind": "arxiv",
    "version": 1
  }
}