Pith Number

pith:ADOSQ4SH

pith:2015:ADOSQ4SH6HMY7ZRDENQBJC6W3S

not attested not anchored not stored refs pending

Toroidal embeddings of abstractly planar graphs are knotted or linked

Dorothy Buck, Senja Barthel

arxiv:1505.05696 v2 · 2015-05-21 · 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{ADOSQ4SH6HMY7ZRDENQBJC6W3S}

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	2026-05-17T23:46:46.721506Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

00dd287247f1d98fe6232360148bd6dc9b7ab2fba73e7db5d50c9fee8ed88be6

Aliases

arxiv: 1505.05696 · arxiv_version: 1505.05696v2 · doi: 10.48550/arxiv.1505.05696 · pith_short_12: ADOSQ4SH6HMY · pith_short_16: ADOSQ4SH6HMY7ZRD · pith_short_8: ADOSQ4SH

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/ADOSQ4SH6HMY7ZRDENQBJC6W3S \
  | 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: 00dd287247f1d98fe6232360148bd6dc9b7ab2fba73e7db5d50c9fee8ed88be6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "121b878cb5c5ab5da4fd51e44a8dac11271482c3fd866b25b7569aba1ad4d9a1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-05-21T12:21:19Z",
    "title_canon_sha256": "d944fa55933c53eb1fb2b4783aa97eaa7096396b9128db72062c8b07422c830d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.05696",
    "kind": "arxiv",
    "version": 2
  }
}