Pith Number

pith:GFTRG4PN

pith:2016:GFTRG4PNXIU4LEU63J3IQB2SGL

not attested not anchored not stored refs pending

Computing JSJ decompositions of hyperbolic groups

Benjamin Barrett

arxiv:1611.00652 v4 · 2016-11-02 · math.GT · 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{GFTRG4PNXIU4LEU63J3IQB2SGL}

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	2026-05-18T00:16:45.652586Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31671371edba29c5929eda7688075232c81dd5cdc54046c68d61e6d44b46ade9

Aliases

arxiv: 1611.00652 · arxiv_version: 1611.00652v4 · doi: 10.48550/arxiv.1611.00652 · pith_short_12: GFTRG4PNXIU4 · pith_short_16: GFTRG4PNXIU4LEU6 · pith_short_8: GFTRG4PN

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/GFTRG4PNXIU4LEU63J3IQB2SGL \
  | 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: 31671371edba29c5929eda7688075232c81dd5cdc54046c68d61e6d44b46ade9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b365fb23db9cb03a5530f652a2ab1aa1a90c0a801210c2954805127281b9f27f",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-11-02T15:27:17Z",
    "title_canon_sha256": "362e8df6b1090dd7efcc7d6dff523ae02c71d9a493d49f5e8392bf7f88278d2d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.00652",
    "kind": "arxiv",
    "version": 4
  }
}