Pith Number

pith:MNGW4LUW

pith:2017:MNGW4LUWQQOUCI3OAMN536FO6I

not attested not anchored not stored refs pending

The Undirected Optical Indices of Complete $m$-ary Trees

Hung-Lin Fu, Wing Shing Wong, Yijin Zhang, Yuan-Hsun Lo

arxiv:1707.09745 v2 · 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{MNGW4LUWQQOUCI3OAMN536FO6I}

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	2026-05-18T00:08:03.431471Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

634d6e2e96841d41236e031bddf8aef22d59a1bb6424be3bacdb3150b414b33c

Aliases

arxiv: 1707.09745 · arxiv_version: 1707.09745v2 · doi: 10.48550/arxiv.1707.09745 · pith_short_12: MNGW4LUWQQOU · pith_short_16: MNGW4LUWQQOUCI3O · pith_short_8: MNGW4LUW

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/MNGW4LUWQQOUCI3OAMN536FO6I \
  | 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: 634d6e2e96841d41236e031bddf8aef22d59a1bb6424be3bacdb3150b414b33c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a59b06bb7da68540df4196c8ce38954a990ffd488cd448b062bfefb272595961",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-07-31T07:48:10Z",
    "title_canon_sha256": "78d45b1a30cab779e3a446dc81af294db4d405ae1108401439aa853949e2a75b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1707.09745",
    "kind": "arxiv",
    "version": 2
  }
}