Pith Number

pith:JT3GPNQL

pith:2016:JT3GPNQLKAJB54DPBI74HSAPNA

not attested not anchored not stored refs pending

Alexander and Thurston norms, and the Bieri-Neumann-Strebel invariants for free-by-cyclic groups

Dawid Kielak, Florian Funke

arxiv:1605.09067 v3 · 2016-05-29 · 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{JT3GPNQLKAJB54DPBI74HSAPNA}

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	2026-05-17T23:52:56.400556Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4cf667b60b50121ef06f0a3fc3c80f68078543591e9fdb1da7a273174c51421d

Aliases

arxiv: 1605.09067 · arxiv_version: 1605.09067v3 · doi: 10.48550/arxiv.1605.09067 · pith_short_12: JT3GPNQLKAJB · pith_short_16: JT3GPNQLKAJB54DP · pith_short_8: JT3GPNQL

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/JT3GPNQLKAJB54DPBI74HSAPNA \
  | 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: 4cf667b60b50121ef06f0a3fc3c80f68078543591e9fdb1da7a273174c51421d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9f6c44caa95a66e8f093a62e563805557edbeeb5b9513df8f1ba7db451b6ce17",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-05-29T21:33:28Z",
    "title_canon_sha256": "52f32b786332d831e07d8f900f5010019f23dbe9ea90c4a696f6f5660c2fb133"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.09067",
    "kind": "arxiv",
    "version": 3
  }
}