Pith Number

pith:VAXP6TG5

pith:2011:VAXP6TG5I6B5BBVK3UV45AA6IS

not attested not anchored not stored refs pending

Edge-reinforced random walk, Vertex-Reinforced Jump Process and the supersymmetric hyperbolic sigma model

Christophe Sabot, Pierre Tarres

arxiv:1111.3991 v4 · 2011-11-16 · math.PR · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VAXP6TG5I6B5BBVK3UV45AA6IS}

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	2026-05-18T03:10:12.347570Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a82eff4cdd4783d086aadd2bce801e449f1339e61b89a8c044afc7fedc3f4aa9

Aliases

arxiv: 1111.3991 · arxiv_version: 1111.3991v4 · doi: 10.48550/arxiv.1111.3991 · pith_short_12: VAXP6TG5I6B5 · pith_short_16: VAXP6TG5I6B5BBVK · pith_short_8: VAXP6TG5

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/VAXP6TG5I6B5BBVK3UV45AA6IS \
  | 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: a82eff4cdd4783d086aadd2bce801e449f1339e61b89a8c044afc7fedc3f4aa9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3ecbd248db856a909679141b3e209a3bbedc61c5fe6ff30159cc0fa3927091f6",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-11-16T23:28:21Z",
    "title_canon_sha256": "6231c28dad7bdff25446035988d589a3260048d026deef4229ed2e3852c7d934"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.3991",
    "kind": "arxiv",
    "version": 4
  }
}