Pith Number

pith:WI5WY3E2

pith:2011:WI5WY3E2453LY3CBFC3NJ5G4SI

not attested not anchored not stored refs pending

Random walks on Galton-Watson trees with random conductances

Marina Vachkovskaia, Nina Gantert, Sebastian M\"uller, Serguei Popov

arxiv:1101.2769 v2 · 2011-01-14 · 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{WI5WY3E2453LY3CBFC3NJ5G4SI}

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	2026-05-18T02:22:57.512739Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b23b6c6c9ae776bc6c4128b6d4f4dc922a214c36797f3b981a9d40e23a9c7389

Aliases

arxiv: 1101.2769 · arxiv_version: 1101.2769v2 · doi: 10.48550/arxiv.1101.2769 · pith_short_12: WI5WY3E2453L · pith_short_16: WI5WY3E2453LY3CB · pith_short_8: WI5WY3E2

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/WI5WY3E2453LY3CBFC3NJ5G4SI \
  | 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: b23b6c6c9ae776bc6c4128b6d4f4dc922a214c36797f3b981a9d40e23a9c7389

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0a37962e523b80693f73f5fb46c8f22418be18284aea33d372f8d788704e128",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-01-14T11:03:18Z",
    "title_canon_sha256": "7d978ca587adff503eeb657dfc97592d9f2e4d978a65e43573676783ed6a8c7e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.2769",
    "kind": "arxiv",
    "version": 2
  }
}