Pith Number

pith:VTSBWQFY

pith:2026:VTSBWQFY24EJN7TTIBHIXVV7XP

not attested not anchored not stored refs pending

Precise cover times for branching random walks on Hamming graphs: (iterated) logarithmic corrections

Zhenyuan Zhang

arxiv:2607.23791 v1 · 2026-07-26 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VTSBWQFY24EJN7TTIBHIXVV7XP}

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	2026-07-28T01:23:11.362302Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ace41b40b8d70896fe73404e8bd6bfbbc25c2ff15f1b60ed43a37308551a6be5

Aliases

arxiv: 2607.23791 · arxiv_version: 2607.23791v1 · doi: 10.48550/arxiv.2607.23791 · pith_short_12: VTSBWQFY24EJ · pith_short_16: VTSBWQFY24EJN7TT · pith_short_8: VTSBWQFY

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/VTSBWQFY24EJN7TTIBHIXVV7XP \
  | 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: ace41b40b8d70896fe73404e8bd6bfbbc25c2ff15f1b60ed43a37308551a6be5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "068db388a303390a6a5f0d2bc82268f8ae37ea7ed7500496c86c64b58cef46bd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-07-26T18:27:51Z",
    "title_canon_sha256": "ab6886264bc4e0919d841cc452e601f1be773264f911403c93725b17d7c75ca8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.23791",
    "kind": "arxiv",
    "version": 1
  }
}