Pith Number

pith:HWS4N2WJ

pith:2013:HWS4N2WJNMWNCS2VL3JUMKCGBI

not attested not anchored not stored refs pending

Thickness, relative hyperbolicity, and randomness in Coxeter groups

Alessandro Sisto, Jason Behrstock, Mark F. Hagen, Pierre-Emmanuel Caprace

arxiv:1312.4789 v1 · 2013-12-17 · math.GR · math.CO · 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{HWS4N2WJNMWNCS2VL3JUMKCGBI}

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	2026-05-18T00:48:10.478571Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3da5c6eac96b2cd14b555ed34628460a05e3580f390430af881f19063cbb0cf1

Aliases

arxiv: 1312.4789 · arxiv_version: 1312.4789v1 · doi: 10.48550/arxiv.1312.4789 · pith_short_12: HWS4N2WJNMWN · pith_short_16: HWS4N2WJNMWNCS2V · pith_short_8: HWS4N2WJ

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/HWS4N2WJNMWNCS2VL3JUMKCGBI \
  | 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: 3da5c6eac96b2cd14b555ed34628460a05e3580f390430af881f19063cbb0cf1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "456f4f5e0de5e6dc2ea9daf6deceb57e9165449f5b42c48b7b392d4588528158",
    "cross_cats_sorted": [
      "math.CO",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-12-17T13:49:59Z",
    "title_canon_sha256": "e1ebea37ddbff57b3fbc9f134c3019b300ed5d6357e6ea0e6c1b9e7953a218af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.4789",
    "kind": "arxiv",
    "version": 1
  }
}