Pith Number

pith:6MQ3ZNC4

pith:2009:6MQ3ZNC4UCGCNFJENZZQZUZPWM

not attested not anchored not stored refs pending

On limits of Graphs Sphere Packed in Euclidean Space and Applications

Itai Benjamini, Nicolas Curien

arxiv:0907.2609 v4 · 2009-07-15 · math.PR · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6MQ3ZNC4UCGCNFJENZZQZUZPWM}

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	2026-05-18T04:39:27.833237Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f321bcb45ca08c2695246e730cd32fb339720bb95ff4aa2610f6d9986bdb83c8

Aliases

arxiv: 0907.2609 · arxiv_version: 0907.2609v4 · doi: 10.48550/arxiv.0907.2609 · pith_short_12: 6MQ3ZNC4UCGC · pith_short_16: 6MQ3ZNC4UCGCNFJE · pith_short_8: 6MQ3ZNC4

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/6MQ3ZNC4UCGCNFJENZZQZUZPWM \
  | 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: f321bcb45ca08c2695246e730cd32fb339720bb95ff4aa2610f6d9986bdb83c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "abae8bff7efc3f7e729e0cb80db7fae859a5a170bff7d8058ef824d258fa54ee",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-07-15T15:30:57Z",
    "title_canon_sha256": "d2e0497c747aabac3cbc33b7eae3c67c5d6b4d95ebdf2f75ab6b61d124f62a2c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.2609",
    "kind": "arxiv",
    "version": 4
  }
}