Pith Number

pith:XYYCNQJQ

pith:2025:XYYCNQJQ7UJHHS2TKDNYZRNQ2P

not attested not anchored not stored refs pending

On sums of $\mathscr{P}$-free forms under mis\`ere play

Alfie Davies, Rebecca Milley, Sarah Miller

arxiv:2506.05257 v1 · 2025-06-05 · 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{XYYCNQJQ7UJHHS2TKDNYZRNQ2P}

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	2026-07-05T11:16:44.874033Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be3026c130fd1273cb5350db8cc5b0d3e2a02d9f465b79afbbb441949d48374f

Aliases

arxiv: 2506.05257 · arxiv_version: 2506.05257v1 · doi: 10.48550/arxiv.2506.05257 · pith_short_12: XYYCNQJQ7UJH · pith_short_16: XYYCNQJQ7UJHHS2T · pith_short_8: XYYCNQJQ

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/XYYCNQJQ7UJHHS2TKDNYZRNQ2P \
  | 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: be3026c130fd1273cb5350db8cc5b0d3e2a02d9f465b79afbbb441949d48374f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "536d24a2435415bc9bef91baed4d1f6e5ef395da1182d308e12d92293090f808",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-06-05T17:19:54Z",
    "title_canon_sha256": "82c3cb406dbe536198085e4b5fa3f8cbfd9c77155d6c3d3040f5660b0e5a826d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.05257",
    "kind": "arxiv",
    "version": 1
  }
}