Pith Number

pith:V3H4IUKC

pith:2015:V3H4IUKCKJXH3OEJVEJV5FTTMC

not attested not anchored not stored refs pending

Asymptotic expansion of the invariant measure for ballistic random walk in the low disorder regime

Alejandro F. Ramirez, David Campos

arxiv:1511.02945 v1 · 2015-11-10 · 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{V3H4IUKCKJXH3OEJVEJV5FTTMC}

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	2026-05-18T01:27:17.397039Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aecfc45142526e7db889a9135e9673609f8821cbc7b835f1b9c2cb1d5e105914

Aliases

arxiv: 1511.02945 · arxiv_version: 1511.02945v1 · doi: 10.48550/arxiv.1511.02945 · pith_short_12: V3H4IUKCKJXH · pith_short_16: V3H4IUKCKJXH3OEJ · pith_short_8: V3H4IUKC

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/V3H4IUKCKJXH3OEJVEJV5FTTMC \
  | 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: aecfc45142526e7db889a9135e9673609f8821cbc7b835f1b9c2cb1d5e105914

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f2426aae9e68095b5ce1b07b5e462d7da22738feb9fab1d26af0cf4064f1be22",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-11-10T00:33:05Z",
    "title_canon_sha256": "a8cdde09eb4f93ffb732e7efcc080dd83ef14adbff99fb67f0b9e163da403e04"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.02945",
    "kind": "arxiv",
    "version": 1
  }
}