Pith Number

pith:6GGET3YY

pith:2026:6GGET3YYEYQQJOM6R37VLZSU62

not attested not anchored not stored refs pending

Random Access Expectation in DNA Storage and Fountain Codes

Christoph Hofmeister, Eitan Yaakobi, Rawad Bitar

Fully symmetric fountain codes achieve a normalized random access expectation of approximately 0.7869.

arxiv:2605.10919 v2 · 2026-05-11 · cs.IT · math.IT

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\usepackage{pith}
\pithnumber{6GGET3YYEYQQJOM6R37VLZSU62}

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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

Under these assumptions, the random access expectation, normalized by the number of information symbols, is at least π/4 ≈ 0.7854, while a value of ≈ 0.7869 is achievable.

C2weakest assumption

The focus on generator matrices with a type of symmetry conjectured in prior work to be optimal (fully symmetric), the equivalence to LT codes, and the validity of the peeling decoder analysis in the large blocklength limit.

C3one line summary

Binary fully symmetric codes (equivalent to LT codes) have normalized random access expectation at least π/4 ≈0.7854 under peeling decoder in large blocklength limit, with ≈0.7869 achievable.

Formal links

3 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:17.099943Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f18c49ef18262104b99e8eff55e654f697b766dd65f4611aa08c1d3554414d03

Aliases

arxiv: 2605.10919 · arxiv_version: 2605.10919v2 · doi: 10.48550/arxiv.2605.10919 · pith_short_12: 6GGET3YYEYQQ · pith_short_16: 6GGET3YYEYQQJOM6 · pith_short_8: 6GGET3YY

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/6GGET3YYEYQQJOM6R37VLZSU62 \
  | 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: f18c49ef18262104b99e8eff55e654f697b766dd65f4611aa08c1d3554414d03

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "afe01e322a6f4df989583719d30db501a91fbe57f88a3d2fc8edc798b178f7a0",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-05-11T17:53:13Z",
    "title_canon_sha256": "51b7e53fc8bfa30a92160387b6d74aeaa1a747575755c3973fdea2e1fac1f146"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.10919",
    "kind": "arxiv",
    "version": 2
  }
}