Pith Number

pith:NNUKWGU7

pith:2015:NNUKWGU7NZ7WRVWWCW3OHGMYVK

not attested not anchored not stored refs pending

On Tree Representations of Relations and Graphs: Symbolic Ultrametrics and Cograph Edge Decompositions

Marc Hellmuth, Nicolas Wieseke

arxiv:1509.05069 v1 · 2015-09-16 · cs.DM

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NNUKWGU7NZ7WRVWWCW3OHGMYVK}

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	2026-05-18T01:32:49.993516Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6b68ab1a9f6e7f68d6d615b6e39998aa9eb4b8d3b2f8856339377e44363954c2

Aliases

arxiv: 1509.05069 · arxiv_version: 1509.05069v1 · doi: 10.48550/arxiv.1509.05069 · pith_short_12: NNUKWGU7NZ7W · pith_short_16: NNUKWGU7NZ7WRVWW · pith_short_8: NNUKWGU7

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/NNUKWGU7NZ7WRVWWCW3OHGMYVK \
  | 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: 6b68ab1a9f6e7f68d6d615b6e39998aa9eb4b8d3b2f8856339377e44363954c2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "96b9634589625f6bbd188ea98de501080c322beaaa7ece250d84fe955875f6d2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2015-09-16T21:38:32Z",
    "title_canon_sha256": "aced92ab1960ec3739c3cecd736dae9d9df531c9ceed88627d1c65c364362317"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.05069",
    "kind": "arxiv",
    "version": 1
  }
}