Pith Number

pith:DN7OYO2U

pith:2009:DN7OYO2U4NPNSTQM6CZBRZPJEO

not attested not anchored not stored refs pending

Lack of Sphere Packing of Graphs via Non-Linear Potential Theory

Itai Benjamini, Oded Schramm

arxiv:0910.3071 v2 · 2009-10-16 · math.MG · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DN7OYO2U4NPNSTQM6CZBRZPJEO}

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	2026-05-18T04:35:57.215578Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1b7eec3b54e35ed94e0cf0b218e5e923a3e53372f79079f085472a95b352247c

Aliases

arxiv: 0910.3071 · arxiv_version: 0910.3071v2 · doi: 10.48550/arxiv.0910.3071 · pith_short_12: DN7OYO2U4NPN · pith_short_16: DN7OYO2U4NPNSTQM · pith_short_8: DN7OYO2U

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/DN7OYO2U4NPNSTQM6CZBRZPJEO \
  | 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: 1b7eec3b54e35ed94e0cf0b218e5e923a3e53372f79079f085472a95b352247c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9bfe166f8415cae548e39af3b23f94022cbf1883f8a915d2716282c531794ae4",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2009-10-16T10:18:13Z",
    "title_canon_sha256": "f1baf286a843a969028f09e4c9252ab3d35e6d697693cff6ceb9f692c1863609"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.3071",
    "kind": "arxiv",
    "version": 2
  }
}