Pith Number

pith:K45CWOQE

pith:2013:K45CWOQEZ42HOMA7UTYVHNAISU

not attested not anchored not stored refs pending

Framing functions and strengthened version of Dehn's lemma

Tetsuya Ito

arxiv:1307.5115 v3 · 2013-07-19 · 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{K45CWOQEZ42HOMA7UTYVHNAISU}

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	2026-05-18T02:41:42.297358Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

573a2b3a04cf3477301fa4f153b408950f431df3ae809da0ed4a78c2ff74e51f

Aliases

arxiv: 1307.5115 · arxiv_version: 1307.5115v3 · doi: 10.48550/arxiv.1307.5115 · pith_short_12: K45CWOQEZ42H · pith_short_16: K45CWOQEZ42HOMA7 · pith_short_8: K45CWOQE

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/K45CWOQEZ42HOMA7UTYVHNAISU \
  | 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: 573a2b3a04cf3477301fa4f153b408950f431df3ae809da0ed4a78c2ff74e51f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ac4176abcb8593ea49f65ff24e5e0d8971793b908bac567c64ac145382d6c29",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-07-19T02:21:07Z",
    "title_canon_sha256": "6b827f78dd2833cf58d9bfa212835ac9d54bcfb585b188e59778064fce2c7b64"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.5115",
    "kind": "arxiv",
    "version": 3
  }
}