Pith Number

pith:4ET7IKNS

pith:2019:4ET7IKNSSQOZUGOYYN5PV7NH2U

not attested not anchored not stored refs pending

Link concordances as surfaces in 4-space and the 4-dimensional Milnor invariants

Akira Yasuhara, Jean-Baptiste Meilhan

arxiv:1910.06214 v4 · 2019-10-14 · 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{4ET7IKNSSQOZUGOYYN5PV7NH2U}

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	2026-07-05T02:37:40.159958Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e127f429b2941d9a19d8c37afafda7d51d46c6d5ee7ee7d70e02b069e5947c52

Aliases

arxiv: 1910.06214 · arxiv_version: 1910.06214v4 · doi: 10.48550/arxiv.1910.06214 · pith_short_12: 4ET7IKNSSQOZ · pith_short_16: 4ET7IKNSSQOZUGOY · pith_short_8: 4ET7IKNS

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/4ET7IKNSSQOZUGOYYN5PV7NH2U \
  | 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: e127f429b2941d9a19d8c37afafda7d51d46c6d5ee7ee7d70e02b069e5947c52

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b44c07334e54eaa7836d99dd173d1042c66e7e89031c16ce89dfa40bc13c70d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2019-10-14T15:39:13Z",
    "title_canon_sha256": "311a6134d3942dec7b7c49727650c727b7f9475f47e673ef3df12a1775707334"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1910.06214",
    "kind": "arxiv",
    "version": 4
  }
}