Pith Number

pith:SB3AGPJB

pith:2012:SB3AGPJBOXWLKA54KKKBZEYXZA

not attested not anchored not stored refs pending

Ellipticity criteria for ballistic behavior of random walks in random environment

Alejandro F. Ramirez, David Campos

arxiv:1212.4020 v3 · 2012-12-17 · 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{SB3AGPJBOXWLKA54KKKBZEYXZA}

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	2026-05-18T02:50:32.579240Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9076033d2175ecb503bc52941c9317c82709db67d3d329827ecd013af8f33f6d

Aliases

arxiv: 1212.4020 · arxiv_version: 1212.4020v3 · doi: 10.48550/arxiv.1212.4020 · pith_short_12: SB3AGPJBOXWL · pith_short_16: SB3AGPJBOXWLKA54 · pith_short_8: SB3AGPJB

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/SB3AGPJBOXWLKA54KKKBZEYXZA \
  | 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: 9076033d2175ecb503bc52941c9317c82709db67d3d329827ecd013af8f33f6d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c30966de40ea75060fb8aa6766a81596005f2c5685d8424a33dc8499d3318f80",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-12-17T15:21:01Z",
    "title_canon_sha256": "8a3490eb75c5e0dd16bb1cfe8a9194d40a73f34c449222142699acd7c2109b33"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.4020",
    "kind": "arxiv",
    "version": 3
  }
}