Pith Number

pith:ZD4KXEU4

pith:2011:ZD4KXEU47KFXZAPP7GE2PETR2J

not attested not anchored not stored refs pending

Incompressibility criteria for spun-normal surfaces

Nathan M. Dunfield, Stavros Garoufalidis

arxiv:1102.4588 v3 · 2011-02-22 · 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{ZD4KXEU47KFXZAPP7GE2PETR2J}

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	2026-05-18T02:46:15.316731Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c8f8ab929cfa8b7c81eff989a79271d26a2e0d13a36389d615fb13d366b5c1d2

Aliases

arxiv: 1102.4588 · arxiv_version: 1102.4588v3 · doi: 10.48550/arxiv.1102.4588 · pith_short_12: ZD4KXEU47KFX · pith_short_16: ZD4KXEU47KFXZAPP · pith_short_8: ZD4KXEU4

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/ZD4KXEU47KFXZAPP7GE2PETR2J \
  | 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: c8f8ab929cfa8b7c81eff989a79271d26a2e0d13a36389d615fb13d366b5c1d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4a6ca5b1fbaee49ddd2b4ab8d723086eb5b839617457e05635b115b97303eed9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-02-22T19:31:30Z",
    "title_canon_sha256": "37912c647cf0344cea6dd0a1ef61585818a235a61ce02bbed350b18d2814b385"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.4588",
    "kind": "arxiv",
    "version": 3
  }
}