Pith Number

pith:QNEWHDWA

pith:2013:QNEWHDWAGKGAQ7WXR7T4CXIJBG

not attested not anchored not stored refs pending

Milnor invariants of length $2k+2$ for links with vanishing Milnor invariants of length $\leq k$

Akira Yasuhara, Yuka Kotorii

arxiv:1304.1870 v1 · 2013-04-06 · 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{QNEWHDWAGKGAQ7WXR7T4CXIJBG}

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	2026-05-18T03:28:44.904443Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8349638ec0328c087ed78fe7c15d0909ab7e09a7d268cb401a5bf09974b3c8e5

Aliases

arxiv: 1304.1870 · arxiv_version: 1304.1870v1 · doi: 10.48550/arxiv.1304.1870 · pith_short_12: QNEWHDWAGKGA · pith_short_16: QNEWHDWAGKGAQ7WX · pith_short_8: QNEWHDWA

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/QNEWHDWAGKGAQ7WXR7T4CXIJBG \
  | 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: 8349638ec0328c087ed78fe7c15d0909ab7e09a7d268cb401a5bf09974b3c8e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07f9d7f15b154a1757c02397cc2d70d5aa5ec3853267e063cfbf280feee34820",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-04-06T09:57:41Z",
    "title_canon_sha256": "2df921a95e01b08bb98ce37d3e0350f2cddb7fcd0a461eaa449e73e98368182a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.1870",
    "kind": "arxiv",
    "version": 1
  }
}