Pith Number

pith:DAPEQCKL

pith:2015:DAPEQCKLKMFCJBEBO6OWSTSVPY

not attested not anchored not stored refs pending

A central limit theorem and a law of the iterated logarithm for the Biggins martingale of the supercritical branching random walk

Alexander Iksanov, Zakhar Kabluchko

arxiv:1507.08458 v2 · 2015-07-30 · 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{DAPEQCKLKMFCJBEBO6OWSTSVPY}

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	2026-05-18T01:22:57.645866Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

181e48094b530a248481779d694e557e10a747689d835cf14e9493ca7ad9b02e

Aliases

arxiv: 1507.08458 · arxiv_version: 1507.08458v2 · doi: 10.48550/arxiv.1507.08458 · pith_short_12: DAPEQCKLKMFC · pith_short_16: DAPEQCKLKMFCJBEB · pith_short_8: DAPEQCKL

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/DAPEQCKLKMFCJBEBO6OWSTSVPY \
  | 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: 181e48094b530a248481779d694e557e10a747689d835cf14e9493ca7ad9b02e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6daebe8d438fdc792cf1ecde9d2c37ed2367aa2b7802f2e62a76efdb30d62edc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-07-30T11:21:44Z",
    "title_canon_sha256": "f270dcf1e57b7b9d1f4c0d7385f796d0ea5061e5089d05f26b081cc0c3d76e02"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.08458",
    "kind": "arxiv",
    "version": 2
  }
}