Pith Number

pith:VLFLJTAG

pith:2010:VLFLJTAGQYM4W7KQN3WABZXE4G

not attested not anchored not stored refs pending

Tightness for Maxima of Generalized Branching Random Walks

Ming Fang

arxiv:1012.0826 v1 · 2010-12-03 · 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{VLFLJTAGQYM4W7KQN3WABZXE4G}

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	2026-05-18T04:34:09.462348Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aacab4cc068619cb7d506eec00e6e4e1962a2c37a7f3ad3eba2ae1c20f21fcab

Aliases

arxiv: 1012.0826 · arxiv_version: 1012.0826v1 · doi: 10.48550/arxiv.1012.0826 · pith_short_12: VLFLJTAGQYM4 · pith_short_16: VLFLJTAGQYM4W7KQ · pith_short_8: VLFLJTAG

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/VLFLJTAGQYM4W7KQN3WABZXE4G \
  | 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: aacab4cc068619cb7d506eec00e6e4e1962a2c37a7f3ad3eba2ae1c20f21fcab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c772522ddc2c6156cc6d309463c16fc46a9284e2c866cef88cfbbab8e24c3f9c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-12-03T19:39:36Z",
    "title_canon_sha256": "0fccd6ce7643cd7e3baba6addd6a200fa16e48a1019389ae77e851b51d08d82f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.0826",
    "kind": "arxiv",
    "version": 1
  }
}