Pith Number

pith:VZ75BYMG

pith:2012:VZ75BYMGPTF4M3QBFO2WJ56XES

not attested not anchored not stored refs pending

A note on ampleness in the theory of non abelian free groups

Rizos Sklinos

arxiv:1205.4662 v2 · 2012-05-21 · math.LO · 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{VZ75BYMGPTF4M3QBFO2WJ56XES}

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	2026-05-18T03:53:43.469427Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae7fd0e1867ccbc66e012bb564f7d7248308547b184c1bcbc76a8ab8ee8f4021

Aliases

arxiv: 1205.4662 · arxiv_version: 1205.4662v2 · doi: 10.48550/arxiv.1205.4662 · pith_short_12: VZ75BYMGPTF4 · pith_short_16: VZ75BYMGPTF4M3QB · pith_short_8: VZ75BYMG

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/VZ75BYMGPTF4M3QBFO2WJ56XES \
  | 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: ae7fd0e1867ccbc66e012bb564f7d7248308547b184c1bcbc76a8ab8ee8f4021

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c188b7a7de6074b67c075e12943ecfa8f32ac23fdc4607e72f34d73083c046d",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2012-05-21T18:01:28Z",
    "title_canon_sha256": "f47313090082f2115ceab81278d64e3e30a587fe4627521a79941eae83e4a1f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.4662",
    "kind": "arxiv",
    "version": 2
  }
}