Pith Number

pith:6ZP25OQA

pith:2011:6ZP25OQASPMBVQPPNIDRW6KOZX

not attested not anchored not stored refs pending

Surgery on Nullhomologous Tori

Ronald Fintushel, Ronald J. Stern

arxiv:1111.4509 v2 · 2011-11-18 · math.GT · math.AG · 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{6ZP25OQASPMBVQPPNIDRW6KOZX}

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	2026-05-18T02:58:00.157699Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f65faeba0093d81ac1ef6a071b794ecdea282b618f52f44417acfe85a46964d2

Aliases

arxiv: 1111.4509 · arxiv_version: 1111.4509v2 · doi: 10.48550/arxiv.1111.4509 · pith_short_12: 6ZP25OQASPMB · pith_short_16: 6ZP25OQASPMBVQPP · pith_short_8: 6ZP25OQA

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/6ZP25OQASPMBVQPPNIDRW6KOZX \
  | 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: f65faeba0093d81ac1ef6a071b794ecdea282b618f52f44417acfe85a46964d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b7fc473c972aeda90e84bd0e5c90fc6a4a2857bcc664835f33056615b711e294",
    "cross_cats_sorted": [
      "math.AG",
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-11-18T22:31:01Z",
    "title_canon_sha256": "50e55fe844be53040594d0555d29d9969f640e9f01859d11a36840a6a83d5a2d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.4509",
    "kind": "arxiv",
    "version": 2
  }
}