Pith Number

pith:VDFSLXU3

pith:2003:VDFSLXU3RTSAGBJUEMCCBQRPH5

not attested not anchored not stored refs pending

Instability of set recurrence and Green's function on groups with the Liouville property

David Revelle, Itai Benjamini

arxiv:math/0310258 v1 · 2003-10-17 · math.PR · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VDFSLXU3RTSAGBJUEMCCBQRPH5}

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	2026-07-04T14:37:48.375471Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8cb25de9b8ce4030534230420c22f3f4ae8d277c2149ca2151fe3ffa00c58d6

Aliases

arxiv: math/0310258 · arxiv_version: math/0310258v1 · doi: 10.48550/arxiv.math/0310258 · pith_short_12: VDFSLXU3RTSA · pith_short_16: VDFSLXU3RTSAGBJU · pith_short_8: VDFSLXU3

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/VDFSLXU3RTSAGBJUEMCCBQRPH5 \
  | 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: a8cb25de9b8ce4030534230420c22f3f4ae8d277c2149ca2151fe3ffa00c58d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cff77ebc517ae5074a603d61828c7a3b44af889aa6e994bbf306d28ef2ba4fa2",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2003-10-17T07:22:06Z",
    "title_canon_sha256": "63039be825f9f208c2943940e80e4de698c7326f10df1a86d086554a99cbff1c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0310258",
    "kind": "arxiv",
    "version": 1
  }
}