Pith Number

pith:4J4GUPJE

pith:2015:4J4GUPJEZEPGAF2UNRN3KD456W

not attested not anchored not stored refs pending

On the Existence of Tree Backbones that Realize the Chromatic Number on a Backbone Coloring

Alexandre A. Cezar, Ana Silva, Julio Araujo

arxiv:1511.05398 v1 · 2015-11-17 · cs.DM · 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{4J4GUPJEZEPGAF2UNRN3KD456W}

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	2026-05-18T01:26:40.354857Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e2786a3d24c91e6017546c5bb50f9df5b4eb8c26fa0e7d706a40e5f1ad710a03

Aliases

arxiv: 1511.05398 · arxiv_version: 1511.05398v1 · doi: 10.48550/arxiv.1511.05398 · pith_short_12: 4J4GUPJEZEPG · pith_short_16: 4J4GUPJEZEPGAF2U · pith_short_8: 4J4GUPJE

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/4J4GUPJEZEPGAF2UNRN3KD456W \
  | 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: e2786a3d24c91e6017546c5bb50f9df5b4eb8c26fa0e7d706a40e5f1ad710a03

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce318b126e7b5982e902743cd960f63835a6b28814bafe8ccddc991770b5c466",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2015-11-17T13:45:14Z",
    "title_canon_sha256": "e44bcb205562078abb3304d15d1c13d85e9e2f0dd3ebd713c4f52030fe80593a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.05398",
    "kind": "arxiv",
    "version": 1
  }
}