Pith Number

pith:N4DV24HG

pith:2016:N4DV24HGVWN27WV2FIUSJ2XZ3P

not attested not anchored not stored refs pending

Constructions of graphs and trees with partially prescribed spectrum

Ivan Gutman, Wasin So, Xueliang Li

arxiv:1611.01938 v4 · 2016-11-07 · 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{N4DV24HGVWN27WV2FIUSJ2XZ3P}

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	2026-05-18T00:53:20.543123Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f075d70e6ad9bafdaba2a2924eaf9dbd94bbba930ad0fcdb8bc86b0df6d4b6f

Aliases

arxiv: 1611.01938 · arxiv_version: 1611.01938v4 · doi: 10.48550/arxiv.1611.01938 · pith_short_12: N4DV24HGVWN2 · pith_short_16: N4DV24HGVWN27WV2 · pith_short_8: N4DV24HG

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/N4DV24HGVWN27WV2FIUSJ2XZ3P \
  | 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: 6f075d70e6ad9bafdaba2a2924eaf9dbd94bbba930ad0fcdb8bc86b0df6d4b6f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "902011fd7053aab3c141d1d9a4f4f8ed9656756f57cdf381fab53b946644c3f9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-11-07T08:55:28Z",
    "title_canon_sha256": "470ab447d30b1bc940f250757713dc5a9d411e2d2667e5a62f2e78bae0d2e9e8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.01938",
    "kind": "arxiv",
    "version": 4
  }
}