Pith Number

pith:AGLSOBRB

pith:2015:AGLSOBRBSF34QHFYIRHKPXH2YH

not attested not anchored not stored refs pending

A knot without a nonorientable essential spanning surface

Nathan M. Dunfield

arxiv:1509.06653 v2 · 2015-09-22 · 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{AGLSOBRBSF34QHFYIRHKPXH2YH}

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	2026-05-18T00:35:10.803105Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

01972706219177c81cb8444ea7dcfac1e7b827085d74d368de18e4eb9a1f1eb8

Aliases

arxiv: 1509.06653 · arxiv_version: 1509.06653v2 · doi: 10.48550/arxiv.1509.06653 · pith_short_12: AGLSOBRBSF34 · pith_short_16: AGLSOBRBSF34QHFY · pith_short_8: AGLSOBRB

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/AGLSOBRBSF34QHFYIRHKPXH2YH \
  | 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: 01972706219177c81cb8444ea7dcfac1e7b827085d74d368de18e4eb9a1f1eb8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb44e8e482f30aaf0ab0925917e3e22f9f9f270b497f19796de773f2722f3c9e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-09-22T15:47:28Z",
    "title_canon_sha256": "ae235582ba46af75c9d270bca9b6ba682e696b7087b1f53365b6182087891884"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.06653",
    "kind": "arxiv",
    "version": 2
  }
}