Pith Number

pith:GZY2CIMU

pith:2017:GZY2CIMUFTEF4D6BGAXMYTKBVO

not attested not anchored not stored refs pending

Bounce statistics for rational lattice paths

Daniel Birmajer, Juan B. Gil, Michael D. Weiner

arxiv:1707.09918 v1 · 2017-07-31 · 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{GZY2CIMUFTEF4D6BGAXMYTKBVO}

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	2026-05-18T00:39:07.761983Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3671a121942cc85e0fc1302ecc4d41abb5908980e3040589130e932a0991cb8f

Aliases

arxiv: 1707.09918 · arxiv_version: 1707.09918v1 · doi: 10.48550/arxiv.1707.09918 · pith_short_12: GZY2CIMUFTEF · pith_short_16: GZY2CIMUFTEF4D6B · pith_short_8: GZY2CIMU

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/GZY2CIMUFTEF4D6BGAXMYTKBVO \
  | 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: 3671a121942cc85e0fc1302ecc4d41abb5908980e3040589130e932a0991cb8f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "afcf7ad85cc7e3270f0c093f4bb8a41838f76aeabd33b8a352025246eedb1af5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-07-31T15:27:31Z",
    "title_canon_sha256": "8cc38d908fd8980c1a9845c3a66ba8cdd42a5d0610e6737913c8fbfc229ab08c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1707.09918",
    "kind": "arxiv",
    "version": 1
  }
}