Pith Number

pith:OFJZE2E7

pith:2026:OFJZE2E74QSCFEWQXNTGBNAYCY

not attested not anchored not stored refs pending

Formalizing Scarf, Brouwer, and Nash in Lean

Kai Li, Yuwei Lyu

arxiv:2607.05987 v1 · 2026-07-07 · cs.LO · cs.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OFJZE2E74QSCFEWQXNTGBNAYCY}

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	2026-07-08T01:18:52.491192Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

715392689fe4242292d0bb6660b418163d54ed91ec674a502c91ea3cad41faff

Aliases

arxiv: 2607.05987 · arxiv_version: 2607.05987v1 · doi: 10.48550/arxiv.2607.05987 · pith_short_12: OFJZE2E74QSC · pith_short_16: OFJZE2E74QSCFEWQ · pith_short_8: OFJZE2E7

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/OFJZE2E74QSCFEWQXNTGBNAYCY \
  | 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: 715392689fe4242292d0bb6660b418163d54ed91ec674a502c91ea3cad41faff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07bc93e39f8d1de6d3e1a975119409ef1c44140a580a45854759ef3bd1396357",
    "cross_cats_sorted": [
      "cs.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2026-07-07T08:18:43Z",
    "title_canon_sha256": "efa6cc9e9209574bb07bf8519bc1a76c68a1202dfff6c50dc6f8af3af765236c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.05987",
    "kind": "arxiv",
    "version": 1
  }
}