Pith Number

pith:Y3YGIOME

pith:2014:Y3YGIOMEZPA5ZVAYCB2BJBW3IM

not attested not anchored not stored refs pending

On Gradient like Properties of Population games, Learning models and Self Reinforced Processes

Michel Benaim

arxiv:1409.4091 v3 · 2014-09-14 · math.DS · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y3YGIOMEZPA5ZVAYCB2BJBW3IM}

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	2026-05-18T01:17:33.360869Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c6f0643984cbc1dcd41810741486db4314966fcddd692c17736233323c1928bb

Aliases

arxiv: 1409.4091 · arxiv_version: 1409.4091v3 · doi: 10.48550/arxiv.1409.4091 · pith_short_12: Y3YGIOMEZPA5 · pith_short_16: Y3YGIOMEZPA5ZVAY · pith_short_8: Y3YGIOME

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/Y3YGIOMEZPA5ZVAYCB2BJBW3IM \
  | 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: c6f0643984cbc1dcd41810741486db4314966fcddd692c17736233323c1928bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a4bdf21058aebe84d54dd2b6fbb383bdb4ce91cf4493dc84546bd7cbf8ad0b47",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2014-09-14T19:05:06Z",
    "title_canon_sha256": "6f393233f0fddc1c2189f812bef9aad2223b2cd9d1d1dc74ba50e5a3f1cd372f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.4091",
    "kind": "arxiv",
    "version": 3
  }
}