Pith Number

pith:6ZUZP6Z7

pith:2022:6ZUZP6Z77R2U767G23UM7KJKE4

not attested not anchored not stored refs pending

k-reduced groups and Milnor invariants

Akira Yasuhara, Benjamin Audoux, Jean-Baptiste Meilhan

arxiv:2205.04768 v1 · 2022-05-10 · 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{6ZUZP6Z77R2U767G23UM7KJKE4}

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	2026-07-05T04:22:10.425636Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f66997fb3ffc754ffbe6d6e8cfa92a272c86760b57c698baca81a4ab7dc1bbd6

Aliases

arxiv: 2205.04768 · arxiv_version: 2205.04768v1 · doi: 10.48550/arxiv.2205.04768 · pith_short_12: 6ZUZP6Z77R2U · pith_short_16: 6ZUZP6Z77R2U767G · pith_short_8: 6ZUZP6Z7

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/6ZUZP6Z77R2U767G23UM7KJKE4 \
  | 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: f66997fb3ffc754ffbe6d6e8cfa92a272c86760b57c698baca81a4ab7dc1bbd6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "981045e462000675adc195b7b6986c1f77765ca55680d0ec4e2c96c3af2108c8",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2022-05-10T09:44:08Z",
    "title_canon_sha256": "359d2e312fc1f927e0976307574e9748559e03a55fa38f5d7bf265c8507bbf55"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2205.04768",
    "kind": "arxiv",
    "version": 1
  }
}