Pith Number

pith:XCPRAWQK

pith:2013:XCPRAWQK76JUATF3CTI3ES7EQZ

not attested not anchored not stored refs pending

Quenched invariance principles for random walks and elliptic diffusions in random media with boundary

David A. Croydon, Takashi Kumagai, Zhen-Qing Chen

arxiv:1306.0076 v2 · 2013-06-01 · 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{XCPRAWQK76JUATF3CTI3ES7EQZ}

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	2026-05-18T01:33:35.511366Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b89f105a0aff93404cbb14d1b24be4867b33a0ee41e9fc4d81bc07c98a439f09

Aliases

arxiv: 1306.0076 · arxiv_version: 1306.0076v2 · doi: 10.48550/arxiv.1306.0076 · pith_short_12: XCPRAWQK76JU · pith_short_16: XCPRAWQK76JUATF3 · pith_short_8: XCPRAWQK

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/XCPRAWQK76JUATF3CTI3ES7EQZ \
  | 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: b89f105a0aff93404cbb14d1b24be4867b33a0ee41e9fc4d81bc07c98a439f09

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "acabbbb14fe8f155468fe503947ff7eaac674d648c93a52fbbcfbe48a231120c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-06-01T04:32:25Z",
    "title_canon_sha256": "4df7bd00e99738138cbbc73f276c51776f922516179d030b61a38e30b7892806"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.0076",
    "kind": "arxiv",
    "version": 2
  }
}