Pith Number

pith:LPKFYK5W

pith:2010:LPKFYK5WRFV4YUNSLT3MYHZO76

not attested not anchored not stored refs pending

Polynomial Bottleneck Congestion Games with Optimal Price of Anarchy

Athanasios Vasilakos, Costas Busch, Rajgopal Kannan

arxiv:1010.4812 v1 · 2010-10-22 · cs.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LPKFYK5WRFV4YUNSLT3MYHZO76}

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	2026-05-18T04:38:50.108643Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5bd45c2bb6896bcc51b25cf6cc1f2eff89ce651e9d84cb5216b6940b012c36ce

Aliases

arxiv: 1010.4812 · arxiv_version: 1010.4812v1 · doi: 10.48550/arxiv.1010.4812 · pith_short_12: LPKFYK5WRFV4 · pith_short_16: LPKFYK5WRFV4YUNS · pith_short_8: LPKFYK5W

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/LPKFYK5WRFV4YUNSLT3MYHZO76 \
  | 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: 5bd45c2bb6896bcc51b25cf6cc1f2eff89ce651e9d84cb5216b6940b012c36ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "39043a83a75de6ec2b48a33ea04219caa40bf5e9ebe01f617768b0f8826856cd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2010-10-22T20:44:09Z",
    "title_canon_sha256": "99407ca1df52749ca9b1f9a9b7fe38a0409d585674b97cf20d5efeacefb0dfa4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.4812",
    "kind": "arxiv",
    "version": 1
  }
}