Pith Number

pith:P66QL6WP

pith:2013:P66QL6WPLEGO25A4ZLFP7UIAVF

not attested not anchored not stored refs pending

Sharp ellipticity conditions for ballistic behavior of random walks in random environment

Alejandro F. Ram\'irez, Christophe Sabot, \'Elodie Bouchet

arxiv:1310.6281 v3 · 2013-10-23 · 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{P66QL6WPLEGO25A4ZLFP7UIAVF}

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	2026-05-18T01:21:16.429787Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7fbd05facf590ced741ccacaffd100a9438ac419defd86830d20b3715eef869f

Aliases

arxiv: 1310.6281 · arxiv_version: 1310.6281v3 · doi: 10.48550/arxiv.1310.6281 · pith_short_12: P66QL6WPLEGO · pith_short_16: P66QL6WPLEGO25A4 · pith_short_8: P66QL6WP

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/P66QL6WPLEGO25A4ZLFP7UIAVF \
  | 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: 7fbd05facf590ced741ccacaffd100a9438ac419defd86830d20b3715eef869f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "69598b3ba230463a88f44d98b2b8bbf768205d092010084c7c68040fda156333",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-10-23T16:19:17Z",
    "title_canon_sha256": "5279370d6cbade0dce672e57b9de0608162e7b8517c68bcf77ee34549276ddd6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.6281",
    "kind": "arxiv",
    "version": 3
  }
}