Pith Number

pith:3WQCDE2R

pith:2014:3WQCDE2RC45X7AY3TFFZ5L3I63

not attested not anchored not stored refs pending

The boundary of the outer space of a free product

Camille Horbez

arxiv:1408.0543 v3 · 2014-08-03 · 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{3WQCDE2RC45X7AY3TFFZ5L3I63}

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	2026-05-18T01:16:26.745814Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dda0219351173b7f831b994b9eaf68f6e567e9150c1e3eb092620d00194cf7e7

Aliases

arxiv: 1408.0543 · arxiv_version: 1408.0543v3 · doi: 10.48550/arxiv.1408.0543 · pith_short_12: 3WQCDE2RC45X · pith_short_16: 3WQCDE2RC45X7AY3 · pith_short_8: 3WQCDE2R

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/3WQCDE2RC45X7AY3TFFZ5L3I63 \
  | 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: dda0219351173b7f831b994b9eaf68f6e567e9150c1e3eb092620d00194cf7e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6156ce39d7507c0e62d805f28913f48b85af73110c55ba51d704e5ad442b4933",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-08-03T21:00:28Z",
    "title_canon_sha256": "7e08d99631dbb8c2c11e95b41d92250793a5b72ae95a9d410a5ce0ddf7906150"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1408.0543",
    "kind": "arxiv",
    "version": 3
  }
}