Pith Number

pith:DJ4BPK5R

pith:2015:DJ4BPK5R77C7JH4IKDIIBPGQMA

not attested not anchored not stored refs pending

Scaling limit of the recurrent biased random walk on a Galton-Watson tree

Elie A\"id\'ekon, Lo\"ic de Raph\'elis

arxiv:1509.07383 v1 · 2015-09-24 · 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{DJ4BPK5R77C7JH4IKDIIBPGQMA}

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	2026-05-18T01:32:09.140982Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1a7817abb1ffc5f49f8850d080bcd0603b71f8e404a1c4b41861b4c764b58853

Aliases

arxiv: 1509.07383 · arxiv_version: 1509.07383v1 · doi: 10.48550/arxiv.1509.07383 · pith_short_12: DJ4BPK5R77C7 · pith_short_16: DJ4BPK5R77C7JH4I · pith_short_8: DJ4BPK5R

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/DJ4BPK5R77C7JH4IKDIIBPGQMA \
  | 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: 1a7817abb1ffc5f49f8850d080bcd0603b71f8e404a1c4b41861b4c764b58853

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "259acda070ee1b9903d058f37c434ad5515d1173655991c916044421ed45c2b4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-09-24T14:17:50Z",
    "title_canon_sha256": "9d9e298e61ff7214eb6cb6e90f061dd05b70974eac44edf59dc58290148b3d78"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.07383",
    "kind": "arxiv",
    "version": 1
  }
}