Pith Number

pith:TI3DC7YX

pith:2021:TI3DC7YX4YWJSRBKK6Q7I2P7UP

not attested not anchored not stored refs pending

A strong Schottky lemma on $n$ generators for $\mathrm{CAT}(0)$ spaces

Jeroen Schillewaert, Matthew J. Conder

arxiv:2103.15257 v2 · 2021-03-29 · math.GR · math.GT · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TI3DC7YX4YWJSRBKK6Q7I2P7UP}

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	2026-07-05T03:50:48.185137Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a36317f17e62c99442a57a1f469ffa3e10ff24558416ab57edbfa78d82ff984

Aliases

arxiv: 2103.15257 · arxiv_version: 2103.15257v2 · doi: 10.48550/arxiv.2103.15257 · pith_short_12: TI3DC7YX4YWJ · pith_short_16: TI3DC7YX4YWJSRBK · pith_short_8: TI3DC7YX

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/TI3DC7YX4YWJSRBKK6Q7I2P7UP \
  | 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: 9a36317f17e62c99442a57a1f469ffa3e10ff24558416ab57edbfa78d82ff984

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9368b760d52a60ee7dfb4587875af7ceeaf3f7c23f56797659564ff3ccc8582b",
    "cross_cats_sorted": [
      "math.GT",
      "math.MG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2021-03-29T00:58:00Z",
    "title_canon_sha256": "eac2379662c3c4fe106a302b00d67da18ce661d094efee6c102deaa2c0b1ae64"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2103.15257",
    "kind": "arxiv",
    "version": 2
  }
}