Pith Number

pith:XK3XUJFN

pith:2014:XK3XUJFN7HJBYFGQKCECYK2UVL

not attested not anchored not stored refs pending

On computing homology gradients over finite fields

{\L}ukasz Grabowski, Thomas Schick

arxiv:1410.1693 v3 · 2014-10-07 · math.GT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XK3XUJFN7HJBYFGQKCECYK2UVL}

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	2026-05-18T01:09:37.372380Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bab77a24adf9d21c14d050882c2b54aac315cf81202720fe8fd7a44fdf43e9bb

Aliases

arxiv: 1410.1693 · arxiv_version: 1410.1693v3 · doi: 10.48550/arxiv.1410.1693 · pith_short_12: XK3XUJFN7HJB · pith_short_16: XK3XUJFN7HJBYFGQ · pith_short_8: XK3XUJFN

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/XK3XUJFN7HJBYFGQKCECYK2UVL \
  | 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: bab77a24adf9d21c14d050882c2b54aac315cf81202720fe8fd7a44fdf43e9bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b9f2bd96b3fee607e14659de78ecaa11d30958726827dccfc5ccb423c41210dc",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2014-10-07T11:40:17Z",
    "title_canon_sha256": "574d5cf067fc7b55655d96e01faf442140e7740bda6cdc96b33271fb5d6941fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1410.1693",
    "kind": "arxiv",
    "version": 3
  }
}