Pith Number

pith:4RUKVIO2

pith:2016:4RUKVIO2Y6WPG7ALRHFRCWDHQB

not attested not anchored not stored refs pending

Mean Field Games with Singular Controls

Guanxing Fu, Ulrich Horst

arxiv:1612.05425 v3 · 2016-12-16 · 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{4RUKVIO2Y6WPG7ALRHFRCWDHQB}

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	2026-05-18T00:38:41.892855Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e468aaa1dac7acf37c0b89cb1158678074be94a62acddac73b5f4953f5f7cc97

Aliases

arxiv: 1612.05425 · arxiv_version: 1612.05425v3 · doi: 10.48550/arxiv.1612.05425 · pith_short_12: 4RUKVIO2Y6WP · pith_short_16: 4RUKVIO2Y6WPG7AL · pith_short_8: 4RUKVIO2

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/4RUKVIO2Y6WPG7ALRHFRCWDHQB \
  | 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: e468aaa1dac7acf37c0b89cb1158678074be94a62acddac73b5f4953f5f7cc97

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "52018b0b4d8e58efd41f33763366e057c7813d7cc32e537a99a3b2d61993330b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2016-12-16T10:54:43Z",
    "title_canon_sha256": "3b4257e096871014226bb54a7bfa674e3277c0c2ff6eae5f5ee871e0931b5ac9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.05425",
    "kind": "arxiv",
    "version": 3
  }
}