Pith Number

pith:ZR4BB4IX

pith:2025:ZR4BB4IXZQAJRXJCGNTJEL647Q

not attested not anchored not stored refs pending

Dilution, Diffusion and Symbiosis in Spatial Prisoner's Dilemma with Reinforcement Learning

Gustavo C. Mangold, Heitor C. M. Fernandes, Mendeli H. Vainstein

arxiv:2507.02211 v2 · 2025-07-03 · cs.AI · cs.NE · physics.comp-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZR4BB4IXZQAJRXJCGNTJEL647Q}

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	2026-07-05T11:31:47.517984Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc7810f117cc0098dd223366922fdcfc2e5af9439b913525eba5a44b2e20ebf7

Aliases

arxiv: 2507.02211 · arxiv_version: 2507.02211v2 · doi: 10.48550/arxiv.2507.02211 · pith_short_12: ZR4BB4IXZQAJ · pith_short_16: ZR4BB4IXZQAJRXJC · pith_short_8: ZR4BB4IX

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/ZR4BB4IXZQAJRXJCGNTJEL647Q \
  | 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: cc7810f117cc0098dd223366922fdcfc2e5af9439b913525eba5a44b2e20ebf7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c34542bc881854a16812d17d6d702e9e6090bfdfa8cb847906c0e770073ed5f1",
    "cross_cats_sorted": [
      "cs.NE",
      "physics.comp-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.AI",
    "submitted_at": "2025-07-03T00:17:53Z",
    "title_canon_sha256": "46b0853d250194877731c30157e9a3efe50f50ee4bc955aa474edad4dbb612c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.02211",
    "kind": "arxiv",
    "version": 2
  }
}