Pith Number

pith:KNFOXOIU

pith:2026:KNFOXOIUGXFW4LU6F6KRCVWTVY

not attested not anchored not stored refs pending

Abelianizations of finite-index subgroups of the handlebody group

Annie Holden

arxiv:2607.07587 v1 · 2026-07-08 · math.GT · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KNFOXOIUGXFW4LU6F6KRCVWTVY}

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	2026-07-09T01:20:30.281869Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

534aebb91435cb6e2e9e2f951156d3ae12294429dd41f9392887fa9ddcb0ba3d

Aliases

arxiv: 2607.07587 · arxiv_version: 2607.07587v1 · doi: 10.48550/arxiv.2607.07587 · pith_short_12: KNFOXOIUGXFW · pith_short_16: KNFOXOIUGXFW4LU6 · pith_short_8: KNFOXOIU

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/KNFOXOIUGXFW4LU6F6KRCVWTVY \
  | 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: 534aebb91435cb6e2e9e2f951156d3ae12294429dd41f9392887fa9ddcb0ba3d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "feec3f8869490c280cc1e515a953dbba877ac4f4a2bf4336e6baf879e95ba287",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-07-08T16:11:11Z",
    "title_canon_sha256": "07c2bd5b1f85d7a0ea1c09a263f192fb975689309c4d2e9fe14aad2de91f20fb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.07587",
    "kind": "arxiv",
    "version": 1
  }
}