Pith Number

pith:VF4VI5AK

pith:2011:VF4VI5AKDEAEQ5JGX5QKI5EQJN

not attested not anchored not stored refs pending

Invariants of Handlebody-Knots via Yokota's Invariants

Atsuhiko Mizusawa, Jun Murakami

arxiv:1112.2719 v4 · 2011-12-09 · 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{VF4VI5AKDEAEQ5JGX5QKI5EQJN}

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	2026-05-18T02:21:27.282474Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a97954740a1900487526bf60a474904b780b8442599e75c2bd30f898cd15dfd6

Aliases

arxiv: 1112.2719 · arxiv_version: 1112.2719v4 · doi: 10.48550/arxiv.1112.2719 · pith_short_12: VF4VI5AKDEAE · pith_short_16: VF4VI5AKDEAEQ5JG · pith_short_8: VF4VI5AK

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/VF4VI5AKDEAEQ5JGX5QKI5EQJN \
  | 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: a97954740a1900487526bf60a474904b780b8442599e75c2bd30f898cd15dfd6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0495a410c3053f8e8e9ebccbfbf98f9e798900f0a523d8fbb1777006ab73cf4c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-12-09T20:50:39Z",
    "title_canon_sha256": "0f7f0499c099ad00c0ccff53e8708a7e8bb5f60ad1917c52059290c88721fa63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.2719",
    "kind": "arxiv",
    "version": 4
  }
}