Pith Number

pith:ZOJ3A5UI

pith:2021:ZOJ3A5UIEQA5YGMTWNNE2LMF42

not attested not anchored not stored refs pending

Milnor-type invariants for surface-links and cut-diagrams

Akira Yasuhara, Benjamin Audoux, Jean-Baptiste Meilhan

arxiv:2109.14578 v5 · 2021-09-29 · 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{ZOJ3A5UIEQA5YGMTWNNE2LMF42}

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	2026-06-19T16:12:43.535751Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb93b076882401dc1993b35a4d2d85e6a7b0dabd076c42a7979bd1217a0fe38e

Aliases

arxiv: 2109.14578 · arxiv_version: 2109.14578v5 · doi: 10.48550/arxiv.2109.14578 · pith_short_12: ZOJ3A5UIEQA5 · pith_short_16: ZOJ3A5UIEQA5YGMT · pith_short_8: ZOJ3A5UI

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/ZOJ3A5UIEQA5YGMTWNNE2LMF42 \
  | 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: cb93b076882401dc1993b35a4d2d85e6a7b0dabd076c42a7979bd1217a0fe38e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e467f37fa7676e9942c72035a1f48025ee73a4271cbbcc8f524fe61c35582a6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2021-09-29T17:15:37Z",
    "title_canon_sha256": "0a563b058cbc71e512829b08c4fdfd552eed67051aa288b64bc2eeb117c8868c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.14578",
    "kind": "arxiv",
    "version": 5
  }
}