Pith Number

pith:B2WTFVAY

pith:2015:B2WTFVAYG57TTRSTHTVASQ2DJ5

not attested not anchored not stored refs pending

Geometric criteria for overtwistedness

Emmy Murphy, Francisco Presas, Roger Casals

arxiv:1503.06221 v2 · 2015-03-20 · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B2WTFVAYG57TTRSTHTVASQ2DJ5}

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	2026-05-18T00:00:13.884976Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0ead32d418377f39c6533cea0943434f7d41fec92d034cc3a70123f8c849e288

Aliases

arxiv: 1503.06221 · arxiv_version: 1503.06221v2 · doi: 10.48550/arxiv.1503.06221 · pith_short_12: B2WTFVAYG57T · pith_short_16: B2WTFVAYG57TTRST · pith_short_8: B2WTFVAY

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/B2WTFVAYG57TTRSTHTVASQ2DJ5 \
  | 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: 0ead32d418377f39c6533cea0943434f7d41fec92d034cc3a70123f8c849e288

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "739ed14c105bb19ed2740c55e8eb90c6ec7775f6474b5011def38ca2689fabe7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2015-03-20T20:08:37Z",
    "title_canon_sha256": "4ed7dfe5ff91140c5e41aad5498610d164e39d11d856927187877bd95204305b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.06221",
    "kind": "arxiv",
    "version": 2
  }
}