Pith Number

pith:H6OQWTVI

pith:2013:H6OQWTVILWGSAXIXG6U4GCCVPT

not attested not anchored not stored refs pending

A Necessary and Sufficient Condition for the Existence of Potential Functions for Heterogeneous Routing Games

Alexandre M. Bayen, Farhad Farokhi, Karl H. Johansson, Walid Krichene

arxiv:1312.1075 v2 · 2013-12-04 · cs.GT · cs.SY · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{H6OQWTVILWGSAXIXG6U4GCCVPT}

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	2026-05-18T03:00:25.455292Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3f9d0b4ea85d8d205d1737a9c308557ced018ec0fd83986047567ee454ff51f5

Aliases

arxiv: 1312.1075 · arxiv_version: 1312.1075v2 · doi: 10.48550/arxiv.1312.1075 · pith_short_12: H6OQWTVILWGS · pith_short_16: H6OQWTVILWGSAXIX · pith_short_8: H6OQWTVI

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/H6OQWTVILWGSAXIXG6U4GCCVPT \
  | 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: 3f9d0b4ea85d8d205d1737a9c308557ced018ec0fd83986047567ee454ff51f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "410aa177e943970ac7fa7e3d94cddde7451d5352a998637541332807613342a3",
    "cross_cats_sorted": [
      "cs.SY",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2013-12-04T09:28:51Z",
    "title_canon_sha256": "f0dccffff5cf73b8f2d89079c853486b440700450e34a64ba7db8a9291220601"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.1075",
    "kind": "arxiv",
    "version": 2
  }
}