Pith Number

pith:X2BHYZFH

pith:2010:X2BHYZFH7TCJVDDDPEQVCVF6XP

not attested not anchored not stored refs pending

Almost Sure Invariance Principle for Continuous-Space Random Walk in Dynamic Random Environment

Firas Rassoul-Agha, Mathew Joseph

arxiv:1004.0920 v2 · 2010-04-06 · 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{X2BHYZFH7TCJVDDDPEQVCVF6XP}

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	2026-05-18T04:33:29.331696Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be827c64a7fcc49a8c6379215154bebbc7600d7ecd1f396635598b637e152f80

Aliases

arxiv: 1004.0920 · arxiv_version: 1004.0920v2 · doi: 10.48550/arxiv.1004.0920 · pith_short_12: X2BHYZFH7TCJ · pith_short_16: X2BHYZFH7TCJVDDD · pith_short_8: X2BHYZFH

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/X2BHYZFH7TCJVDDDPEQVCVF6XP \
  | 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: be827c64a7fcc49a8c6379215154bebbc7600d7ecd1f396635598b637e152f80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8f1ce965655d0fd0ff47d152b53681d9f435d5f76e82e371a3fb2faa839139c3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-04-06T18:28:23Z",
    "title_canon_sha256": "088f0646cff7daad8826404dc91d222d55c62ef99df20567aeb5a654f3ea2a61"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.0920",
    "kind": "arxiv",
    "version": 2
  }
}