Pith Number

pith:6XRK6FLE

pith:2024:6XRK6FLEUJDBUHXJOLCHIFJ3NO

not attested not anchored not stored refs pending

Embedding groups into boundedly acyclic groups

Fan Wu, Mengfei Zhao, Xiaolei Wu, Zixiang Zhou

arxiv:2407.07703 v4 · 2024-07-10 · math.GR · math.KT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6XRK6FLEUJDBUHXJOLCHIFJ3NO}

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	2026-07-05T10:48:17.422349Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f5e2af1564a2461a1ee972c474153b6bbce5262f1f36d13c9632ae90d846a12f

Aliases

arxiv: 2407.07703 · arxiv_version: 2407.07703v4 · doi: 10.48550/arxiv.2407.07703 · pith_short_12: 6XRK6FLEUJDB · pith_short_16: 6XRK6FLEUJDBUHXJ · pith_short_8: 6XRK6FLE

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/6XRK6FLEUJDBUHXJOLCHIFJ3NO \
  | 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: f5e2af1564a2461a1ee972c474153b6bbce5262f1f36d13c9632ae90d846a12f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "667ce20fe07e29d315567f79810a8919f63f85a3655705a1fcceef0f06c16b42",
    "cross_cats_sorted": [
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2024-07-10T14:34:45Z",
    "title_canon_sha256": "b3fb4835b7bedffb78a27f7d885daa692f8300e249374a7e33cd29a96ac93092"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2407.07703",
    "kind": "arxiv",
    "version": 4
  }
}