Pith Number

pith:TDZNDFH6

pith:2010:TDZNDFH6BGRS46TMEBNKSDTGVO

not attested not anchored not stored refs pending

On the separation profile of infinite graphs

Adam Timar, Itai Benjamini, Oded Schramm

arxiv:1004.0921 v3 · 2010-04-06 · math.MG · 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{TDZNDFH6BGRS46TMEBNKSDTGVO}

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	2026-05-18T04:13:16.164768Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

98f2d194fe09a32e7a6c205aa90e66ab84658ea3704940e5fca32d6fc629427e

Aliases

arxiv: 1004.0921 · arxiv_version: 1004.0921v3 · doi: 10.48550/arxiv.1004.0921 · pith_short_12: TDZNDFH6BGRS · pith_short_16: TDZNDFH6BGRS46TM · pith_short_8: TDZNDFH6

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/TDZNDFH6BGRS46TMEBNKSDTGVO \
  | 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: 98f2d194fe09a32e7a6c205aa90e66ab84658ea3704940e5fca32d6fc629427e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4a7fe8151cc086d4a9aae34c4d5aa3167de591449536063ee0347604525c40c1",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2010-04-06T18:28:36Z",
    "title_canon_sha256": "9f3917e949bb24638010dd8f09d99a4d881523fd5fde2aa23b7b7776d293bd05"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.0921",
    "kind": "arxiv",
    "version": 3
  }
}