Pith Number

pith:FO32WKG6

pith:2026:FO32WKG62E5DLQEI2QWTQ7SIYZ

not attested not anchored not stored refs pending

Implementation of the Habegger--Lin decision algorithm

Atsuhiko Mizusawa, Yuka Kotorii

Implementation of the Habegger-Lin algorithm decides link-homotopy for four- and five-component links and finds new examples beyond Milnor invariants.

arxiv:2605.04433 v2 · 2026-05-06 · 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{FO32WKG62E5DLQEI2QWTQ7SIYZ}

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.

Claims

C1strongest claim

we present an implementation of this algorithm, which is available at [KMcode], and exhibit new pairs of links that are not link-homotopic yet cannot be distinguished by Milnor's link-homotopy invariants, called μ-bar-invariants.

C2weakest assumption

The explicit computations of the group actions on string links for the 4- and 5-component cases, reported in the authors' prior paper [KM4], are correct and complete.

C3one line summary

Implementation of the Habegger-Lin decision algorithm for link-homotopy of 4- and 5-component links, together with new pairs not distinguished by Milnor invariants.

Receipt and verification

First computed	2026-05-20T00:03:13.988262Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2bb7ab28ded13a35c088d42d387e48c6545804906d49f276e711bd80b4dec3fe

Aliases

arxiv: 2605.04433 · arxiv_version: 2605.04433v2 · doi: 10.48550/arxiv.2605.04433 · pith_short_12: FO32WKG62E5D · pith_short_16: FO32WKG62E5DLQEI · pith_short_8: FO32WKG6

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/FO32WKG62E5DLQEI2QWTQ7SIYZ \
  | 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: 2bb7ab28ded13a35c088d42d387e48c6545804906d49f276e711bd80b4dec3fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "230c3b91cc5bfc9541920ff25e62519d70f6cc93fdd4eae10a5e16c97f0ba0f7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-05-06T02:53:44Z",
    "title_canon_sha256": "13bc2b904219cadab444bd5a0920392d9086d3c76e683d2495f66a54206ff79c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.04433",
    "kind": "arxiv",
    "version": 2
  }
}