Pith Number

pith:54CF5CI2

pith:1997:54CF5CI2SUFLMXHGQ7LAQJWMDO

not attested not anchored not stored refs pending

Extension of incompressible surfaces on the boundary of 3-manifolds

Hugh Howards, Michael Freedman, Ying-Qing Wu

arxiv:math/9706222 v1 · 1997-06-30 · 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{54CF5CI2SUFLMXHGQ7LAQJWMDO}

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	2026-05-18T01:05:35.138097Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef045e891a950ab65ce687d60826cc1b83d9b1fea2bde8a610dcba5b793f472d

Aliases

arxiv: math/9706222 · arxiv_version: math/9706222v1 · doi: 10.48550/arxiv.math/9706222 · pith_short_12: 54CF5CI2SUFL · pith_short_16: 54CF5CI2SUFLMXHG · pith_short_8: 54CF5CI2

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/54CF5CI2SUFLMXHGQ7LAQJWMDO \
  | 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: ef045e891a950ab65ce687d60826cc1b83d9b1fea2bde8a610dcba5b793f472d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c08566e13d3404fb8aef87f4956f72b8269d4cc80bdce2f82cdc4de56abeb564",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "1997-06-30T00:00:00Z",
    "title_canon_sha256": "07cfb1fc03a0942e432cf2faba7c8a747dd574c6955477adf8ea06ed8e909638"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9706222",
    "kind": "arxiv",
    "version": 1
  }
}