Pith Number

pith:VQM4OYHF

pith:2015:VQM4OYHFQXM3ZRWQKNEP2LVCLC

not attested not anchored not stored refs pending

Bifurcation and segregation in quadratic two-populations Mean Field Games systems

Gianmaria Verzini, Marco Cirant

arxiv:1511.09343 v1 · 2015-11-30 · 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{VQM4OYHFQXM3ZRWQKNEP2LVCLC}

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	2026-05-18T01:25:40.509444Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac19c760e585d9bcc6d05348fd2ea258a7f037764063e1d2cf84d9800449863a

Aliases

arxiv: 1511.09343 · arxiv_version: 1511.09343v1 · doi: 10.48550/arxiv.1511.09343 · pith_short_12: VQM4OYHFQXM3 · pith_short_16: VQM4OYHFQXM3ZRWQ · pith_short_8: VQM4OYHF

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/VQM4OYHFQXM3ZRWQKNEP2LVCLC \
  | 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: ac19c760e585d9bcc6d05348fd2ea258a7f037764063e1d2cf84d9800449863a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "858e67a8d5c0043f5fac4ce3b165365294f1e1e68e090da1f06209522246b5e0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-11-30T15:22:02Z",
    "title_canon_sha256": "34ae555619c3be0bb75038b6043557fdc171c46b5a28068d973fda80ddc4c43e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.09343",
    "kind": "arxiv",
    "version": 1
  }
}