Pith Number

pith:XBU75EUM

pith:2017:XBU75EUMA7IZ5A7VG3OVYDL6HC

not attested not anchored not stored refs pending

On finitely generated submonoids of virtually free groups

Alexander Zakharov, Pedro V. Silva

arxiv:1712.07746 v2 · 2017-12-20 · math.GR · cs.FL

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XBU75EUMA7IZ5A7VG3OVYDL6HC}

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	2026-05-18T00:15:36.882512Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b869fe928c07d19e83f536dd5c0d7e388b65deb7c1b9ce9717875e92aaab0bc6

Aliases

arxiv: 1712.07746 · arxiv_version: 1712.07746v2 · doi: 10.48550/arxiv.1712.07746 · pith_short_12: XBU75EUMA7IZ · pith_short_16: XBU75EUMA7IZ5A7V · pith_short_8: XBU75EUM

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/XBU75EUMA7IZ5A7VG3OVYDL6HC \
  | 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: b869fe928c07d19e83f536dd5c0d7e388b65deb7c1b9ce9717875e92aaab0bc6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2cd473ab6d95e03dfc1e34f26a003d23db3c591a0e3ef066d34cc2e54b4f16d0",
    "cross_cats_sorted": [
      "cs.FL"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2017-12-20T23:11:53Z",
    "title_canon_sha256": "de5d7861ec7448955868bad81e443dcccd94fe565db6cb6cbfa00664140c775b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.07746",
    "kind": "arxiv",
    "version": 2
  }
}