Pith Number

pith:CHMZPY4H

pith:2005:CHMZPY4HQYXUTUFD5TWB3VTENG

not attested not anchored not stored refs pending

Subgroups of direct products of elementarily free groups

James Howie, Martin R Bridson

arxiv:math/0506482 v1 · 2005-06-23 · 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{CHMZPY4HQYXUTUFD5TWB3VTENG}

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	2026-05-18T04:33:27.533097Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

11d997e387862f49d0a3ecec1dd66469bc04972c1457276438be51e38ebf8aa1

Aliases

arxiv: math/0506482 · arxiv_version: math/0506482v1 · doi: 10.48550/arxiv.math/0506482 · pith_short_12: CHMZPY4HQYXU · pith_short_16: CHMZPY4HQYXUTUFD · pith_short_8: CHMZPY4H

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/CHMZPY4HQYXUTUFD5TWB3VTENG \
  | 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: 11d997e387862f49d0a3ecec1dd66469bc04972c1457276438be51e38ebf8aa1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "96d25888d7b6e37926ee633cd3552d746bf04237d973a83748a3634d03a67e43",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2005-06-23T17:14:34Z",
    "title_canon_sha256": "280cdbb739fee90fb2ed23367534c2667f8e3e8880c472463169af530ef9db60"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0506482",
    "kind": "arxiv",
    "version": 1
  }
}