Pith Number

pith:U6K3B5U4

pith:2012:U6K3B5U4CKNCYQ4324JC7J2FXM

not attested not anchored not stored refs pending

Online Optimization of Product-Form Networks

Jaron Sanders, Johan S.H. van Leeuwaarden, Sem C. Borst

arxiv:1208.6167 v1 · 2012-08-30 · math.OC · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{U6K3B5U4CKNCYQ4324JC7J2FXM}

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	2026-05-18T03:46:46.316229Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a795b0f69c129a2c439bd7122fa745bb3fa3bb5c70f348495ff395188a017a89

Aliases

arxiv: 1208.6167 · arxiv_version: 1208.6167v1 · doi: 10.48550/arxiv.1208.6167 · pith_short_12: U6K3B5U4CKNC · pith_short_16: U6K3B5U4CKNCYQ43 · pith_short_8: U6K3B5U4

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/U6K3B5U4CKNCYQ4324JC7J2FXM \
  | 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: a795b0f69c129a2c439bd7122fa745bb3fa3bb5c70f348495ff395188a017a89

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6032841e6a95a19970b9e4c118bb75636ffbe16c757bd26859e165935d45d8d1",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2012-08-30T13:23:11Z",
    "title_canon_sha256": "238d4e770e5e46b68506d866225e3484211bd0e0afc147406ece30ff30d322be"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.6167",
    "kind": "arxiv",
    "version": 1
  }
}