Pith Number

pith:M5CVK62Y

pith:2012:M5CVK62YHD6X4OEO2LAR43DPW6

not attested not anchored not stored refs pending

Spanning trees and even integer eigenvalues of graphs

Ebrahim Ghorbani

arxiv:1201.3221 v4 · 2012-01-16 · 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{M5CVK62YHD6X4OEO2LAR43DPW6}

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	2026-05-18T03:00:50.019115Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6745557b5838fd7e388ed2c11e6c6fb78e322085ad085777be790039ec887d21

Aliases

arxiv: 1201.3221 · arxiv_version: 1201.3221v4 · doi: 10.48550/arxiv.1201.3221 · pith_short_12: M5CVK62YHD6X · pith_short_16: M5CVK62YHD6X4OEO · pith_short_8: M5CVK62Y

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/M5CVK62YHD6X4OEO2LAR43DPW6 \
  | 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: 6745557b5838fd7e388ed2c11e6c6fb78e322085ad085777be790039ec887d21

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c80de11950ae477e583e71dbf519231fc717dc8270bf9371d9dc559e6cbec622",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-01-16T11:36:47Z",
    "title_canon_sha256": "472a00bde673a211be3b39d865d0df244ffcd1cafcb86220ccc76d9e65bd4428"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.3221",
    "kind": "arxiv",
    "version": 4
  }
}