Pith Number

pith:42IZVQTG

pith:2014:42IZVQTGSGNSAV6VSYGH2KJI7C

not attested not anchored not stored refs pending

The Tits alternative for non-spherical triangles of groups

Johannes Cuno, J\"org Lehnert

arxiv:1405.3433 v2 · 2014-05-14 · 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{42IZVQTGSGNSAV6VSYGH2KJI7C}

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	2026-05-18T00:44:29.021704Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6919ac266919b2057d5960c7d2928f8a299c1fd0566d80029aca1bffd48932d

Aliases

arxiv: 1405.3433 · arxiv_version: 1405.3433v2 · doi: 10.48550/arxiv.1405.3433 · pith_short_12: 42IZVQTGSGNS · pith_short_16: 42IZVQTGSGNSAV6V · pith_short_8: 42IZVQTG

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/42IZVQTGSGNSAV6VSYGH2KJI7C \
  | 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: e6919ac266919b2057d5960c7d2928f8a299c1fd0566d80029aca1bffd48932d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e806a20b7fdc48194556a6e5cdd26fa656d5da8a1c3976085722ca9b35137063",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-05-14T10:04:42Z",
    "title_canon_sha256": "888c1d4f5d3d88edfdac64f414dc11fa84da7643330464224bfbbb5bf6f18691"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1405.3433",
    "kind": "arxiv",
    "version": 2
  }
}