Pith Number

pith:Y3F6XN5O

pith:2013:Y3F6XN5OJBDA3JYGVFKBVB6K6R

not attested not anchored not stored refs pending

Asymptotic formulas for stacks and unimodal sequences

Karl Mahlburg, Kathrin Bringmann

arxiv:1308.6813 v1 · 2013-08-30 · math.NT · 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{Y3F6XN5OJBDA3JYGVFKBVB6K6R}

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	2026-05-18T03:14:30.828178Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c6cbebb7ae48460da706a9541a87caf47bd8f3003eba5eedf64aeded4908404e

Aliases

arxiv: 1308.6813 · arxiv_version: 1308.6813v1 · doi: 10.48550/arxiv.1308.6813 · pith_short_12: Y3F6XN5OJBDA · pith_short_16: Y3F6XN5OJBDA3JYG · pith_short_8: Y3F6XN5O

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/Y3F6XN5OJBDA3JYGVFKBVB6K6R \
  | 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: c6cbebb7ae48460da706a9541a87caf47bd8f3003eba5eedf64aeded4908404e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "850f5fe49ff786397e9281c1dd374ac6b01cc3fa9a8f212413e725c1b053bd99",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-08-30T18:06:08Z",
    "title_canon_sha256": "b0daca41934812b879b37e9a99db68147c9087aa271e8056a4f21a18eec1aa63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.6813",
    "kind": "arxiv",
    "version": 1
  }
}