Pith Number

pith:6QG72NF5

pith:2015:6QG72NF5H5N4T6PM4EHRRO7WKJ

not attested not anchored not stored refs pending

A short proof that every finite graph has a tree-decomposition displaying its tangles

Johannes Carmesin

arxiv:1511.02734 v2 · 2015-11-09 · 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{6QG72NF5H5N4T6PM4EHRRO7WKJ}

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	2026-05-18T01:13:16.347283Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f40dfd34bd3f5bc9f9ece10f18bbf6526c73d647677fe33e8a2637f4db4a2685

Aliases

arxiv: 1511.02734 · arxiv_version: 1511.02734v2 · doi: 10.48550/arxiv.1511.02734 · pith_short_12: 6QG72NF5H5N4 · pith_short_16: 6QG72NF5H5N4T6PM · pith_short_8: 6QG72NF5

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/6QG72NF5H5N4T6PM4EHRRO7WKJ \
  | 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: f40dfd34bd3f5bc9f9ece10f18bbf6526c73d647677fe33e8a2637f4db4a2685

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eb47cb0f4ca9f98a00e4aeb7f822a83b04bf255c24893474478c49b33bcf3025",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-11-09T16:10:00Z",
    "title_canon_sha256": "47187376cafb731227b9cb8598d0d323b0396738c76663bc511fb72e33c1a899"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.02734",
    "kind": "arxiv",
    "version": 2
  }
}