Pith Number

pith:ZPI4FFSG

pith:2011:ZPI4FFSGRXQHN7FDE5R4GYTGMT

not attested not anchored not stored refs pending

Existence and uniqueness result for mean field games with congestion effect on graphs

Olivier Gu\'eant

arxiv:1110.3442 v4 · 2011-10-15 · math.OC · 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{ZPI4FFSGRXQHN7FDE5R4GYTGMT}

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	2026-05-18T02:52:23.928472Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbd1c296468de076fca32763c3626664f1a57236d7b3fab5acaa35b591e9b48b

Aliases

arxiv: 1110.3442 · arxiv_version: 1110.3442v4 · doi: 10.48550/arxiv.1110.3442 · pith_short_12: ZPI4FFSGRXQH · pith_short_16: ZPI4FFSGRXQHN7FD · pith_short_8: ZPI4FFSG

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/ZPI4FFSGRXQHN7FDE5R4GYTGMT \
  | 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: cbd1c296468de076fca32763c3626664f1a57236d7b3fab5acaa35b591e9b48b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "127563e56e2037a61b25ec4890e8f3730c2c1933821c1a02c7a9dd53ae30c21b",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2011-10-15T22:20:05Z",
    "title_canon_sha256": "f3de87ace4226332401e7c5db8abfe69a7c7bd647eed0d84fe2ceb03aa1c502f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.3442",
    "kind": "arxiv",
    "version": 4
  }
}