Pith Number

pith:J2NNRUXB

pith:2025:J2NNRUXBH5LIQPHUCB6IBSQH2V

not attested not anchored not stored refs pending

Smallest Suffixient Sets: Effectiveness, Resilience, and Calculation

Cristian Urbina, Giuseppe Romana, Gonzalo Navarro, Hiroto Fujimaru

The size of the smallest suffixient set is at most linear in the number of Burrows-Wheeler runs and strictly smaller than the smallest lexicographic parse on some string families.

arxiv:2506.05638 v6 · 2025-06-05 · cs.FL · cs.DS · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{J2NNRUXBH5LIQPHUCB6IBSQH2V}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

We show that χ = O(r) (where r is the number of runs in the Burrows-Wheeler Transform of the string), that there are string families where χ=o(v) (where v is the size of the smallest lexicographic parse of the string), and that χ ≤ σ+2 on episturmian words over alphabets of size σ.

C2weakest assumption

The definition and utility of a suffixient set rests on the assumption that, provided with a random access mechanism, it supports various forms of pattern matching on the underlying repetitive string.

C3one line summary

Smallest suffixient set size χ is O(r) for BWT runs r, o(v) for some lex parses, bounded by σ+2 on episturmian words, increases by at most 2 on append/prepend, and can increase by Ω(√n) under edits or rotations.

Formal links

2 machine-checked theorem links

Cited by

2 papers in Pith

Compressing Suffix Trees by Path Decompositions

Smallest suffixient set maintenance in near-real-time

Receipt and verification

First computed	2026-05-29T02:05:35.022367Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4e9ad8d2e13f56883cf4107c80ca07d54a3b1b34623366eaf89d2107380ed398

Aliases

arxiv: 2506.05638 · arxiv_version: 2506.05638v6 · doi: 10.48550/arxiv.2506.05638 · pith_short_12: J2NNRUXBH5LI · pith_short_16: J2NNRUXBH5LIQPHU · pith_short_8: J2NNRUXB

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/J2NNRUXBH5LIQPHUCB6IBSQH2V \
  | 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: 4e9ad8d2e13f56883cf4107c80ca07d54a3b1b34623366eaf89d2107380ed398

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "17c45dac4c9e6bf9c092a07cb530480ee282906c9f0b453ccfc106b6cbfbad8d",
    "cross_cats_sorted": [
      "cs.DS",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.FL",
    "submitted_at": "2025-06-05T23:58:03Z",
    "title_canon_sha256": "6faf0b39089c0898146278ffcc2c89366dc1c250eba093fe687c049e5382a108"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.05638",
    "kind": "arxiv",
    "version": 6
  }
}