Pith Number

pith:KTW22AXX

pith:2017:KTW22AXXFXP3MT7LE62ZZF5H2A

not attested not anchored not stored refs pending

Elementary equivalence vs commensurability for hyperbolic groups

Gilbert Levitt, Rizos Sklinos, Vincent Guirardel

arxiv:1701.08853 v1 · 2017-01-30 · math.GR · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KTW22AXXFXP3MT7LE62ZZF5H2A}

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	2026-05-17T23:44:04.926844Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

54edad02f72ddfb64feb27b59c97a7d00d55c0f76893caba160a4d09caaff794

Aliases

arxiv: 1701.08853 · arxiv_version: 1701.08853v1 · doi: 10.48550/arxiv.1701.08853 · pith_short_12: KTW22AXXFXP3 · pith_short_16: KTW22AXXFXP3MT7L · pith_short_8: KTW22AXX

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/KTW22AXXFXP3MT7LE62ZZF5H2A \
  | 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: 54edad02f72ddfb64feb27b59c97a7d00d55c0f76893caba160a4d09caaff794

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b980321096049382680d8f4a5ead513690ef82700e5ddf83843ee311c63fcbc5",
    "cross_cats_sorted": [
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2017-01-30T22:12:55Z",
    "title_canon_sha256": "802fef3234491d67aad0242948e8ae8a06b1a76d9f0b3fc63d88bb08d24b5c55"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1701.08853",
    "kind": "arxiv",
    "version": 1
  }
}