Pith Number

pith:GTDV7AGG

pith:2016:GTDV7AGG3JKX672ZE5XTD2CGKN

not attested not anchored not stored refs pending

A short conceptual proof of Narayana's path-counting formula

Mihai Ciucu

arxiv:1602.02085 v1 · 2016-02-05 · 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{GTDV7AGG3JKX672ZE5XTD2CGKN}

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	2026-05-18T01:21:14.560755Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34c75f80c6da557f7f59276f31e8465364836e1f393530f33795d575f87e5551

Aliases

arxiv: 1602.02085 · arxiv_version: 1602.02085v1 · doi: 10.48550/arxiv.1602.02085 · pith_short_12: GTDV7AGG3JKX · pith_short_16: GTDV7AGG3JKX672Z · pith_short_8: GTDV7AGG

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/GTDV7AGG3JKX672ZE5XTD2CGKN \
  | 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: 34c75f80c6da557f7f59276f31e8465364836e1f393530f33795d575f87e5551

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "38cf00a4c01885e84295e414a4040bcd14899bf49adb93129fbe853e2e34ca88",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-02-05T16:29:26Z",
    "title_canon_sha256": "9943055a6f15898c838429eccf006cd19f28154d1312960551e5f4d5e804c2d5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.02085",
    "kind": "arxiv",
    "version": 1
  }
}