Pith Number

pith:QWB365N3

pith:2009:QWB365N3SMIMR3ASXR6UEX4GFB

not attested not anchored not stored refs pending

Minimum congestion spanning trees in planar graphs

M.I. Ostrovskii

arxiv:0909.3903 v1 · 2009-09-22 · 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{QWB365N3SMIMR3ASXR6UEX4GFB}

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	2026-05-18T04:41:25.257415Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8583bf75bb9310c8ec12bc7d425f8628707d8202a97a2a11e0bd78856cf52ed5

Aliases

arxiv: 0909.3903 · arxiv_version: 0909.3903v1 · doi: 10.48550/arxiv.0909.3903 · pith_short_12: QWB365N3SMIM · pith_short_16: QWB365N3SMIMR3AS · pith_short_8: QWB365N3

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/QWB365N3SMIMR3ASXR6UEX4GFB \
  | 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: 8583bf75bb9310c8ec12bc7d425f8628707d8202a97a2a11e0bd78856cf52ed5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7e952d7d93a73cb59a663a0fc7386c0ea25998f7c5061189e8a1c8cd5570f99d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-09-22T03:48:18Z",
    "title_canon_sha256": "5e4ea2c0e36eb20ec0816191589eca5d6b2e2860baf43212ef849bbb1c77a7e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.3903",
    "kind": "arxiv",
    "version": 1
  }
}