Pith Number

pith:2QPDMLQQ

pith:2013:2QPDMLQQU2YOEOX626GTLADOFM

not attested not anchored not stored refs pending

Invariant games and non-homogeneous Beatty sequences

Eric Duch\^ene, Julien Cassaigne, Michel Rigo

arxiv:1312.2233 v1 · 2013-12-08 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2QPDMLQQU2YOEOX626GTLADOFM}

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	2026-05-18T03:05:10.906644Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d41e362e10a6b0e23afed78d35806e2b1e363d053c4c0aa08144382e62120e25

Aliases

arxiv: 1312.2233 · arxiv_version: 1312.2233v1 · doi: 10.48550/arxiv.1312.2233 · pith_short_12: 2QPDMLQQU2YO · pith_short_16: 2QPDMLQQU2YOEOX6 · pith_short_8: 2QPDMLQQ

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/2QPDMLQQU2YOEOX626GTLADOFM \
  | 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: d41e362e10a6b0e23afed78d35806e2b1e363d053c4c0aa08144382e62120e25

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6da6f37b0e5e17f9c5495f0f91c3832289b2067c21dbccfaa6c4af22664984cc",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-12-08T16:23:44Z",
    "title_canon_sha256": "4cacdc142095431e7dc415356eecaeda83fb9369db9af040239934b333bdd2b5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.2233",
    "kind": "arxiv",
    "version": 1
  }
}