Pith Number

pith:3ML7HJ4V

pith:2017:3ML7HJ4VZSRXPUXGMYBZ532DIF

not attested not anchored not stored refs pending

On the expected number of internal equilibria in random evolutionary games with correlated payoff matrix

Hoang Minh Tran, Manh Hong Duong, The Anh Han

arxiv:1708.01672 v3 · 2017-08-04 · math.AP · math.DS · math.PR · q-bio.PE · q-bio.QM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3ML7HJ4VZSRXPUXGMYBZ532DIF}

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	2026-05-18T00:11:23.767899Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db17f3a795cca377d2e666039eef4341506772557505d42f066f3a8b11c57c33

Aliases

arxiv: 1708.01672 · arxiv_version: 1708.01672v3 · doi: 10.48550/arxiv.1708.01672 · pith_short_12: 3ML7HJ4VZSRX · pith_short_16: 3ML7HJ4VZSRXPUXG · pith_short_8: 3ML7HJ4V

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/3ML7HJ4VZSRXPUXGMYBZ532DIF \
  | 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: db17f3a795cca377d2e666039eef4341506772557505d42f066f3a8b11c57c33

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e183ee67de205acc6389f4bc56c7e228381389695f42245bd085dac3c1780d4e",
    "cross_cats_sorted": [
      "math.DS",
      "math.PR",
      "q-bio.PE",
      "q-bio.QM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-08-04T22:02:02Z",
    "title_canon_sha256": "4ca6fd405de53756491d0ae9067d018a9084cc8a288044fe127b902919b44554"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.01672",
    "kind": "arxiv",
    "version": 3
  }
}