Pith Number

pith:JVHXGLGX

pith:2015:JVHXGLGX7ZP52QGEA25Q66CQW6

not attested not anchored not stored refs pending

Invariance of the Sprague-Grundy Function for Variants of Wythoff's Game

Madeleine Weinstein

arxiv:1507.04665 v2 · 2015-07-16 · 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{JVHXGLGX7ZP52QGEA25Q66CQW6}

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	2026-05-18T01:33:51.357564Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4d4f732cd7fe5fdd40c406bb0f7850b79ef3252837f6f8e9b7b729cb750fc09d

Aliases

arxiv: 1507.04665 · arxiv_version: 1507.04665v2 · doi: 10.48550/arxiv.1507.04665 · pith_short_12: JVHXGLGX7ZP5 · pith_short_16: JVHXGLGX7ZP52QGE · pith_short_8: JVHXGLGX

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/JVHXGLGX7ZP52QGEA25Q66CQW6 \
  | 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: 4d4f732cd7fe5fdd40c406bb0f7850b79ef3252837f6f8e9b7b729cb750fc09d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c42ba8e0b097c8fad2308d3af3bcd2878c6826d0fce3693090ddc615c49e436b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-07-16T17:37:32Z",
    "title_canon_sha256": "1aa2eb0d7a5e86e8e286266c1bce9dd6f4764187c10e3b8f8e3da015f777dcbd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.04665",
    "kind": "arxiv",
    "version": 2
  }
}