Pith Number

pith:MDOXQI4C

pith:2013:MDOXQI4CHHN26M3A77TKARWE6O

not attested not anchored not stored refs pending

On double cosets in free groups

Eliyahu Rips, Rita Gitik

arxiv:1306.0033 v1 · 2013-05-31 · 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{MDOXQI4CHHN26M3A77TKARWE6O}

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	2026-05-18T03:22:04.810602Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60dd78238239dbaf3360ffe6a046c4f3b7eb6b31439f022bf090ada97e43d603

Aliases

arxiv: 1306.0033 · arxiv_version: 1306.0033v1 · doi: 10.48550/arxiv.1306.0033 · pith_short_12: MDOXQI4CHHN2 · pith_short_16: MDOXQI4CHHN26M3A · pith_short_8: MDOXQI4C

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/MDOXQI4CHHN26M3A77TKARWE6O \
  | 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: 60dd78238239dbaf3360ffe6a046c4f3b7eb6b31439f022bf090ada97e43d603

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b592be86acc7744036fb322d7805955311831c4f250fb803e84f360d5d7e37a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-05-31T21:38:39Z",
    "title_canon_sha256": "77e4a9c9ac4bb74c85fc033fa6d53c3a25a3f43621fe476d174224ab981b0a7c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.0033",
    "kind": "arxiv",
    "version": 1
  }
}