Pith Number

pith:G2FD2DCX

pith:2012:G2FD2DCXH2TKDVY2Y67FOISLCY

not attested not anchored not stored refs pending

Sharp lower bounds for the asymptotic entropy of symmetric random walks

Fran\c{c}ois Maucourant (IRMAR), Fr\'ed\'eric Math\'eus (LMBA), S\'ebastien Gou\"ezel (IRMAR)

arxiv:1209.3378 v3 · 2012-09-15 · 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{G2FD2DCXH2TKDVY2Y67FOISLCY}

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	2026-05-18T02:59:45.048345Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

368a3d0c573ea6a1d71ac7be57224b1638f6938b220040a1eeecb54f36895349

Aliases

arxiv: 1209.3378 · arxiv_version: 1209.3378v3 · doi: 10.48550/arxiv.1209.3378 · pith_short_12: G2FD2DCXH2TK · pith_short_16: G2FD2DCXH2TKDVY2 · pith_short_8: G2FD2DCX

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/G2FD2DCXH2TKDVY2Y67FOISLCY \
  | 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: 368a3d0c573ea6a1d71ac7be57224b1638f6938b220040a1eeecb54f36895349

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b9f1c5a60e3cb4868fa28d62ea1eda29b5de8e5e4d583bac8fb68989270dd28",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-09-15T09:19:03Z",
    "title_canon_sha256": "014da75d4976bcdc67e3df1709e7dabc5399015a9da684e2478363ff60337b83"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.3378",
    "kind": "arxiv",
    "version": 3
  }
}