Pith Number

pith:BYYL6QWF

pith:2007:BYYL6QWFSE5M22F2BUUVURFM7L

not attested not anchored not stored refs pending

Conjugacy classes of solutions to equations and inequations over hyperbolic groups

Daniel Groves, Henry Wilton

arxiv:0710.1892 v2 · 2007-10-09 · 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{BYYL6QWFSE5M22F2BUUVURFM7L}

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	2026-05-18T02:58:12.208111Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e30bf42c5913acd68ba0d295a44acfaf2117d6a606d20b7909620858851952a

Aliases

arxiv: 0710.1892 · arxiv_version: 0710.1892v2 · doi: 10.48550/arxiv.0710.1892 · pith_short_12: BYYL6QWFSE5M · pith_short_16: BYYL6QWFSE5M22F2 · pith_short_8: BYYL6QWF

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/BYYL6QWFSE5M22F2BUUVURFM7L \
  | 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: 0e30bf42c5913acd68ba0d295a44acfaf2117d6a606d20b7909620858851952a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7628a19db1f169bf69261abfa35717d4bd63a1d07f42a4f380e4ee3e764034d7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2007-10-09T23:21:51Z",
    "title_canon_sha256": "ea5b1d4fcb75136111112eab408ba354396da3705f15ab46c1c36f36d9fa9b84"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0710.1892",
    "kind": "arxiv",
    "version": 2
  }
}