Pith Number

pith:WNDIXE5Z

pith:2026:WNDIXE5ZMQCVL6A7GEW5VLMLNS

not attested not anchored not stored refs pending

A functional law of large numbers for a spatial model of Muller's ratchet

Jo\~ao Luiz de Oliveira Madeira, Marcel Ortgiese, Sarah Penington

arxiv:2603.06478 v2 · 2026-03-06 · math.PR · math.AP · q-bio.PE

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WNDIXE5ZMQCVL6A7GEW5VLMLNS}

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.

Receipt and verification

First computed	2026-07-17T01:21:47.027109Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3468b93b9640555f81f312ddaad8b6c9a9ea370f8a9c2cbba1d6bea1b324154

Aliases

arxiv: 2603.06478 · arxiv_version: 2603.06478v2 · doi: 10.48550/arxiv.2603.06478 · pith_short_12: WNDIXE5ZMQCV · pith_short_16: WNDIXE5ZMQCVL6A7 · pith_short_8: WNDIXE5Z

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/WNDIXE5ZMQCVL6A7GEW5VLMLNS \
  | 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: b3468b93b9640555f81f312ddaad8b6c9a9ea370f8a9c2cbba1d6bea1b324154

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e839187438ae4613f89274e3b04bfc7094c3ddbe5043b58dda4c746588fba406",
    "cross_cats_sorted": [
      "math.AP",
      "q-bio.PE"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-03-06T17:01:44Z",
    "title_canon_sha256": "7760c6a3694c5015dda689be3b15811d62bdfc384f0ccb8d12c0a4775ffd78e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.06478",
    "kind": "arxiv",
    "version": 2
  }
}