Pith Number

pith:DPS4H7PV

pith:2016:DPS4H7PVRK7CVWJPQPZN67R4PU

not attested not anchored not stored refs pending

Congruences modulo powers of $2$ for the number of unique path partitions

Christian Krattenthaler (Universit\"at Wien)

arxiv:1604.05345 v1 · 2016-04-18 · math.CO · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DPS4H7PVRK7CVWJPQPZN67R4PU}

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	2026-05-18T00:24:31.822005Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1be5c3fdf58abe2ad92f83f2df7e3c7d3690673e8b8eb117026ceff261a404b6

Aliases

arxiv: 1604.05345 · arxiv_version: 1604.05345v1 · doi: 10.48550/arxiv.1604.05345 · pith_short_12: DPS4H7PVRK7C · pith_short_16: DPS4H7PVRK7CVWJP · pith_short_8: DPS4H7PV

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/DPS4H7PVRK7CVWJPQPZN67R4PU \
  | 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: 1be5c3fdf58abe2ad92f83f2df7e3c7d3690673e8b8eb117026ceff261a404b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d0b3b7046714db31e561ee9e0f59cdf6b620bd61deafcdf6edbd577034904406",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-04-18T20:29:43Z",
    "title_canon_sha256": "de0c87b82883882b6d89e6662ed743f0ede2b01ba34d1efa38657adcbd476f55"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.05345",
    "kind": "arxiv",
    "version": 1
  }
}