Pith Number

pith:VK4THMXH

pith:2013:VK4THMXH3XZDI3ZQ7DXU5YXCSY

not attested not anchored not stored refs pending

Rotor-routing and spanning trees on planar graphs

Joshua A. Grochow, Melody Chan, Thomas Church

arxiv:1308.2677 v2 · 2013-08-12 · 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{VK4THMXH3XZDI3ZQ7DXU5YXCSY}

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	2026-05-18T01:36:04.210359Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aab933b2e7ddf2346f30f8ef4ee2e296172ff9cb0329b625985099247d1237f0

Aliases

arxiv: 1308.2677 · arxiv_version: 1308.2677v2 · doi: 10.48550/arxiv.1308.2677 · pith_short_12: VK4THMXH3XZD · pith_short_16: VK4THMXH3XZDI3ZQ · pith_short_8: VK4THMXH

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/VK4THMXH3XZDI3ZQ7DXU5YXCSY \
  | 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: aab933b2e7ddf2346f30f8ef4ee2e296172ff9cb0329b625985099247d1237f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf42add598b623e83bd308e7ac6079503f3cee383e7e1c73b22b9cd77ab19278",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-08-12T20:00:08Z",
    "title_canon_sha256": "84699e94af35b0b1d0df7fc9be3ffee49eafca31a40981391e3ce1ac65c861f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.2677",
    "kind": "arxiv",
    "version": 2
  }
}