Pith Number

pith:X4ZBFESV

pith:2016:X4ZBFESV5VNNY27DSRACKD6R7L

not attested not anchored not stored refs pending

Metabelian groups with large return probability

Lison Jacoboni

arxiv:1611.08026 v2 · 2016-11-23 · math.GR · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X4ZBFESV5VNNY27DSRACKD6R7L}

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	2026-05-18T00:39:56.849309Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf32129255ed5adc6be39440250fd1faf8b462fe3881d973b8d97846646c3a8c

Aliases

arxiv: 1611.08026 · arxiv_version: 1611.08026v2 · doi: 10.48550/arxiv.1611.08026 · pith_short_12: X4ZBFESV5VNN · pith_short_16: X4ZBFESV5VNNY27D · pith_short_8: X4ZBFESV

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/X4ZBFESV5VNNY27DSRACKD6R7L \
  | 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: bf32129255ed5adc6be39440250fd1faf8b462fe3881d973b8d97846646c3a8c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2c6bd328f0bf865739ec45bc85d603b35baa57ec2fab80952aefc13de2fa42db",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-11-23T22:45:16Z",
    "title_canon_sha256": "bad7ad62c74235722e0434deaade803b316b39dd1e04221ad4997c60f5536475"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.08026",
    "kind": "arxiv",
    "version": 2
  }
}