Pith Number

pith:45ELXQNM

pith:2010:45ELXQNMY7TARHNI4WCJCHCPM7

not attested not anchored not stored refs pending

Examples of amalgamated free products and coupling rigidity

Yoshikata Kida

arxiv:1007.1529 v3 · 2010-07-09 · 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{45ELXQNMY7TARHNI4WCJCHCPM7}

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	2026-05-18T03:12:35.429117Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e748bbc1acc7e6089da8e584911c4f67f6781e649c866c326429e82f496debce

Aliases

arxiv: 1007.1529 · arxiv_version: 1007.1529v3 · doi: 10.48550/arxiv.1007.1529 · pith_short_12: 45ELXQNMY7TA · pith_short_16: 45ELXQNMY7TARHNI · pith_short_8: 45ELXQNM

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/45ELXQNMY7TARHNI4WCJCHCPM7 \
  | 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: e748bbc1acc7e6089da8e584911c4f67f6781e649c866c326429e82f496debce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "901a81ab173431fb493de8799c79a9751de377a717e8414a5d033cd4eaa3e9ab",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-07-09T08:23:32Z",
    "title_canon_sha256": "bccf595613d751643d937953060049f3a2f9babc9fc4014a462741a81d75c732"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.1529",
    "kind": "arxiv",
    "version": 3
  }
}