Pith Number

pith:ZBSOUFIO

pith:2025:ZBSOUFIOMS7IWRMQ5K77NLHMZ2

not attested not anchored not stored refs pending

Groups admitting Wirtinger presentations and Gromov hyperbolic groups

Toshiyuki Akita

arxiv:2506.07143 v3 · 2025-06-08 · 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{ZBSOUFIOMS7IWRMQ5K77NLHMZ2}

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	2026-07-17T00:20:38.977053Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c864ea150e64be8b4590eabff6acecce9e7c24b315fe3606cf113c586ecc19ae

Aliases

arxiv: 2506.07143 · arxiv_version: 2506.07143v3 · doi: 10.48550/arxiv.2506.07143 · pith_short_12: ZBSOUFIOMS7I · pith_short_16: ZBSOUFIOMS7IWRMQ · pith_short_8: ZBSOUFIO

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/ZBSOUFIOMS7IWRMQ5K77NLHMZ2 \
  | 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: c864ea150e64be8b4590eabff6acecce9e7c24b315fe3606cf113c586ecc19ae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "170aa75fb32089d5480026c7714efa893fcb9786770cb0d249b6f54e16c6375d",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2025-06-08T13:43:58Z",
    "title_canon_sha256": "6ef9cb883833658071a82931afb201c3a248680e3d3afdc7357fe4482c00042c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.07143",
    "kind": "arxiv",
    "version": 3
  }
}