Pith Number

pith:6425NSXH

pith:2014:6425NSXHEVKXZ2BGJYY7EWVZJX

not attested not anchored not stored refs pending

There exist no Minimally Knotted Planar Spatial Graphs on the Torus

Senja Barthel

arxiv:1411.7734 v3 · 2014-11-28 · math.GT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6425NSXHEVKXZ2BGJYY7EWVZJX}

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	2026-05-17T23:47:08.923779Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f735d6cae725557ce8264e31f25ab94de03f1a6d0c923d471e57316809d8534b

Aliases

arxiv: 1411.7734 · arxiv_version: 1411.7734v3 · doi: 10.48550/arxiv.1411.7734 · pith_short_12: 6425NSXHEVKX · pith_short_16: 6425NSXHEVKXZ2BG · pith_short_8: 6425NSXH

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/6425NSXHEVKXZ2BGJYY7EWVZJX \
  | 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: f735d6cae725557ce8264e31f25ab94de03f1a6d0c923d471e57316809d8534b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0885422a349a9740ad966f9c350de386f97423262ddafad903f6b1b362384ef3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2014-11-28T01:37:48Z",
    "title_canon_sha256": "627a58802e14faf3aa1205a44f1e86ce094877416b03e3fb848cf0a1e429e489"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.7734",
    "kind": "arxiv",
    "version": 3
  }
}