Pith Number

pith:TPZNMPYM

pith:2017:TPZNMPYMXM43PP2AWG6JD5F32V

not attested not anchored not stored refs pending

The Sprague-Grundy function for some nearly disjunctive sums of Nim and Silver Dollar games

Graham Farr, Nhan Bao Ho

arxiv:1702.07068 v1 · 2017-02-23 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TPZNMPYMXM43PP2AWG6JD5F32V}

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	2026-05-18T00:50:08.462816Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9bf2d63f0cbb39b7bf40b1bc91f4bbd5644d7d0c6378e3d8811da1fce030adec

Aliases

arxiv: 1702.07068 · arxiv_version: 1702.07068v1 · doi: 10.48550/arxiv.1702.07068 · pith_short_12: TPZNMPYMXM43 · pith_short_16: TPZNMPYMXM43PP2A · pith_short_8: TPZNMPYM

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/TPZNMPYMXM43PP2AWG6JD5F32V \
  | 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: 9bf2d63f0cbb39b7bf40b1bc91f4bbd5644d7d0c6378e3d8811da1fce030adec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c00c26f5c34f061e0961e9d436d2d9f72b1ac17d5911dcba3a0fb3ff75a24e58",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-02-23T02:19:02Z",
    "title_canon_sha256": "4c03589226c3ad7ac8143dd0762020f37a2342f151e5f5bfac06e38523f21622"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.07068",
    "kind": "arxiv",
    "version": 1
  }
}