Pith Number

pith:KV3RCFQ6

pith:2016:KV3RCFQ6PO5ZKKNIQYVQCYXO3P

not attested not anchored not stored refs pending

Conditions for ballisticity and invariance principle for random walk in non-elliptic random environment

Mark Holmes, Thomas S. Salisbury

arxiv:1612.04761 v1 · 2016-12-14 · 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{KV3RCFQ6PO5ZKKNIQYVQCYXO3P}

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	2026-05-18T00:00:02.644299Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

557711161e7bbb9529a8862b0162eedbd6ef4efdd6c6a7203d199ab28416df3d

Aliases

arxiv: 1612.04761 · arxiv_version: 1612.04761v1 · doi: 10.48550/arxiv.1612.04761 · pith_short_12: KV3RCFQ6PO5Z · pith_short_16: KV3RCFQ6PO5ZKKNI · pith_short_8: KV3RCFQ6

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/KV3RCFQ6PO5ZKKNIQYVQCYXO3P \
  | 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: 557711161e7bbb9529a8862b0162eedbd6ef4efdd6c6a7203d199ab28416df3d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "62e7df8da1cea90d442e9da2f3a7804f7835b0e59147a58977e174b8332099e8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-12-14T18:18:06Z",
    "title_canon_sha256": "60887dba7b5cccc951934c6d86e9b9bec3eadd7d7818f577ae6bff608e33a268"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.04761",
    "kind": "arxiv",
    "version": 1
  }
}