Pith Number

pith:CL7B56EG

pith:2019:CL7B56EG3ZR5SYTU5PR7TMGMIZ

not attested not anchored not stored refs pending

On Products of Closed Subsets in Free Groups

Eliyahu Rips, Rita Gitik

arxiv:1906.07275 v1 · 2019-06-11 · 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{CL7B56EG3ZR5SYTU5PR7TMGMIZ}

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	2026-05-17T23:43:08.328996Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12fe1ef886de63d96274ebe3f9b0cc465d08bae2a4a674a66d6151c51718f233

Aliases

arxiv: 1906.07275 · arxiv_version: 1906.07275v1 · doi: 10.48550/arxiv.1906.07275 · pith_short_12: CL7B56EG3ZR5 · pith_short_16: CL7B56EG3ZR5SYTU · pith_short_8: CL7B56EG

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/CL7B56EG3ZR5SYTU5PR7TMGMIZ \
  | 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: 12fe1ef886de63d96274ebe3f9b0cc465d08bae2a4a674a66d6151c51718f233

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "589c1c41a98e904924d40ff253ac970b329fb6a64f69a453ddf6f8b5b1aae9d8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2019-06-11T18:41:08Z",
    "title_canon_sha256": "0921a38253416759acfb6ed4670205a09ab1a7d2a793e76fb1fc4d464e62a3cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.07275",
    "kind": "arxiv",
    "version": 1
  }
}