Pith Number

pith:M7Q3VMJI

pith:2011:M7Q3VMJICQNGL3HFILXIYPGESF

not attested not anchored not stored refs pending

Subset currents on free groups

Ilya Kapovich, Tatiana Nagnibeda

arxiv:1105.5742 v5 · 2011-05-28 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M7Q3VMJICQNGL3HFILXIYPGESF}

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	2026-05-18T03:13:32.281563Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67e1bab128141a65ece542ee8c3cc4916daf0e20da033d0f613f40172488993c

Aliases

arxiv: 1105.5742 · arxiv_version: 1105.5742v5 · doi: 10.48550/arxiv.1105.5742 · pith_short_12: M7Q3VMJICQNG · pith_short_16: M7Q3VMJICQNGL3HF · pith_short_8: M7Q3VMJI

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/M7Q3VMJICQNGL3HFILXIYPGESF \
  | 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: 67e1bab128141a65ece542ee8c3cc4916daf0e20da033d0f613f40172488993c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c676e1184348bd75e6509d4a9c63d0bdf3668d1a7774ed9433553429b2cbea5",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-05-28T22:23:02Z",
    "title_canon_sha256": "1c1ea50fb9659235cf48f47d2b7d3cd956b0889a27089fb25a0bf3a53c03193a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.5742",
    "kind": "arxiv",
    "version": 5
  }
}