Pith Number

pith:4GDKWNYC

pith:2017:4GDKWNYCDD63TDZH2WLSL6GSWM

not attested not anchored not stored refs pending

Characterizing the number of coloured $m$-ary partitions modulo $m$, with and without gaps

I. P. Goulden, Pavel Shuldiner

arxiv:1701.07077 v1 · 2017-01-24 · 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{4GDKWNYCDD63TDZH2WLSL6GSWM}

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	2026-05-18T00:52:07.576847Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e186ab370218fdb98f27d59725f8d2b325c03e7b85053e8d08c0cbc295fcf2a3

Aliases

arxiv: 1701.07077 · arxiv_version: 1701.07077v1 · doi: 10.48550/arxiv.1701.07077 · pith_short_12: 4GDKWNYCDD63 · pith_short_16: 4GDKWNYCDD63TDZH · pith_short_8: 4GDKWNYC

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/4GDKWNYCDD63TDZH2WLSL6GSWM \
  | 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: e186ab370218fdb98f27d59725f8d2b325c03e7b85053e8d08c0cbc295fcf2a3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b33087294cb692f65ef81bb5c0e3d67eb5e45a87ae1779330da9886246fcd545",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-01-24T20:39:36Z",
    "title_canon_sha256": "90e52827cae058475035c80a4218f786cf988fee1642039e973e386ca3aa660b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1701.07077",
    "kind": "arxiv",
    "version": 1
  }
}