Pith Number

pith:56BHYSQG

pith:2011:56BHYSQGLNGEYVIJJ65ESFHHYN

not attested not anchored not stored refs pending

Sharp benefit-to-cost rules for the evolution of cooperation on regular graphs

Yu-Ting Chen

arxiv:1107.1513 v3 · 2011-07-07 · 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{56BHYSQGLNGEYVIJJ65ESFHHYN}

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	2026-05-18T02:21:43.331835Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef827c4a065b4c4c55094fba4914e7c3461f2d15abd590d4a94f3820176dc456

Aliases

arxiv: 1107.1513 · arxiv_version: 1107.1513v3 · doi: 10.48550/arxiv.1107.1513 · pith_short_12: 56BHYSQGLNGE · pith_short_16: 56BHYSQGLNGEYVIJ · pith_short_8: 56BHYSQG

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/56BHYSQGLNGEYVIJJ65ESFHHYN \
  | 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: ef827c4a065b4c4c55094fba4914e7c3461f2d15abd590d4a94f3820176dc456

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cedbb803a6f40731714ae2ef02924a559d0521a9524b3502eb47bb5d690f9195",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-07-07T20:28:41Z",
    "title_canon_sha256": "4483babdfa644b446cf67a23d8be8e7a0a5b01a7a1931abca1513051f900aecf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.1513",
    "kind": "arxiv",
    "version": 3
  }
}