Pith Number

pith:IKSAUHKJ

pith:2015:IKSAUHKJUT6GE2QDZ5NYSO2TY7

not attested not anchored not stored refs pending

Quenched invariance principle for random walk in time-dependent balanced random environment

Alejandro F. Ramirez, Jean-Dominique Deuschel, Xiaoqin Guo

arxiv:1503.01964 v2 · 2015-03-06 · 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{IKSAUHKJUT6GE2QDZ5NYSO2TY7}

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	2026-05-18T01:06:22.976622Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

42a40a1d49a4fc626a03cf5b893b53c7ec2982ad0ab99d4eafecbc6befd6d89a

Aliases

arxiv: 1503.01964 · arxiv_version: 1503.01964v2 · doi: 10.48550/arxiv.1503.01964 · pith_short_12: IKSAUHKJUT6G · pith_short_16: IKSAUHKJUT6GE2QD · pith_short_8: IKSAUHKJ

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/IKSAUHKJUT6GE2QDZ5NYSO2TY7 \
  | 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: 42a40a1d49a4fc626a03cf5b893b53c7ec2982ad0ab99d4eafecbc6befd6d89a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "941fd9f71ef4a986b5237abf88f25e0700c2f44dd43a51b2be79b89c1ab10cc2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-03-06T14:15:03Z",
    "title_canon_sha256": "5cb6c4605cd23af83bb9c1043bf3aa0e2434500ca46a6defb77bdfa3ab74fa35"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.01964",
    "kind": "arxiv",
    "version": 2
  }
}