Pith Number

pith:4TVI6VML

pith:2012:4TVI6VMLKSDNQIHZF6GFU7DN3P

not attested not anchored not stored refs pending

Congestion Games on Weighted Directed Graphs, with Applications to Spectrum Sharing

Biying Shou, Jianwei Huang, Richard Southwell

arxiv:1206.0430 v1 · 2012-06-03 · cs.NI · 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{4TVI6VMLKSDNQIHZF6GFU7DN3P}

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	2026-05-18T03:54:17.684536Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4ea8f558b5486d820f92f8c5a7c6ddbf4271867f3c9a0b8abc3d6f44583b3d1

Aliases

arxiv: 1206.0430 · arxiv_version: 1206.0430v1 · doi: 10.48550/arxiv.1206.0430 · pith_short_12: 4TVI6VMLKSDN · pith_short_16: 4TVI6VMLKSDNQIHZ · pith_short_8: 4TVI6VML

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/4TVI6VMLKSDNQIHZF6GFU7DN3P \
  | 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: e4ea8f558b5486d820f92f8c5a7c6ddbf4271867f3c9a0b8abc3d6f44583b3d1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7eb734a4c57987b545f979cc204677728c24551468771d1aeb1dc54f0a9e62e8",
    "cross_cats_sorted": [
      "cs.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.NI",
    "submitted_at": "2012-06-03T10:57:16Z",
    "title_canon_sha256": "ed25cf18ab95a15efd8d54e3ff2bbdf700a8a682567c1d5f7ce5295caeebc30f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.0430",
    "kind": "arxiv",
    "version": 1
  }
}