Pith Number

pith:KQO6ARSG

pith:2012:KQO6ARSGQPIVKW5NQQDTL2ZQLR

not attested not anchored not stored refs pending

A sufficient condition for the existence of plane spanning trees on geometric graphs

Eduardo Rivera-Campo, Virginia Urrutia-Galicia

arxiv:1202.3385 v1 · 2012-02-15 · math.CO · cs.CG · 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{KQO6ARSGQPIVKW5NQQDTL2ZQLR}

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	2026-05-18T01:27:55.113925Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

541de0464683d1555bad840735eb305c5fb44c571ec5be171ce2f499b6d9172d

Aliases

arxiv: 1202.3385 · arxiv_version: 1202.3385v1 · doi: 10.48550/arxiv.1202.3385 · pith_short_12: KQO6ARSGQPIV · pith_short_16: KQO6ARSGQPIVKW5N · pith_short_8: KQO6ARSG

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/KQO6ARSGQPIVKW5NQQDTL2ZQLR \
  | 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: 541de0464683d1555bad840735eb305c5fb44c571ec5be171ce2f499b6d9172d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1386c5ca563cc9c695366b91056b6af701df1cf3bc6bf0360df3f6f8954958be",
    "cross_cats_sorted": [
      "cs.CG",
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-02-15T17:43:06Z",
    "title_canon_sha256": "c0f686ece9d22bf9746096426ee4a45c1c0f8d5a07bba343c09b8ffaa26cc241"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.3385",
    "kind": "arxiv",
    "version": 1
  }
}