Pith Number

pith:PJJMMPKP

pith:2015:PJJMMPKPE3WKEG4XJ7YQXCBWX5

not attested not anchored not stored refs pending

Existence and uniqueness of solutions for Bertrand and Cournot mean field games

Alain Bensoussan, P. Jameson Graber

arxiv:1508.05408 v2 · 2015-08-21 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PJJMMPKPE3WKEG4XJ7YQXCBWX5}

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	2026-05-18T01:34:32.586987Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a52c63d4f26eca21b974ff10b8836bf61083c107413f8ea6610f27480c3b113

Aliases

arxiv: 1508.05408 · arxiv_version: 1508.05408v2 · doi: 10.48550/arxiv.1508.05408 · pith_short_12: PJJMMPKPE3WK · pith_short_16: PJJMMPKPE3WKEG4X · pith_short_8: PJJMMPKP

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/PJJMMPKPE3WKEG4XJ7YQXCBWX5 \
  | 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: 7a52c63d4f26eca21b974ff10b8836bf61083c107413f8ea6610f27480c3b113

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb5057e7bd0c918503e09bae77cb51175e694ea847be3390149f1d5492c57ecc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-08-21T20:55:46Z",
    "title_canon_sha256": "5bbf9d512e56ef2410c69536cb93e9aac2598a7cdf1a02b8890964498715f91d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.05408",
    "kind": "arxiv",
    "version": 2
  }
}