Pith Number

pith:NWYDZDII

pith:2013:NWYDZDIIDCWCKS7AQHIG4FO7Y2

not attested not anchored not stored refs pending

Dynamics on free-by-cyclic groups

Christopher J. Leininger, Ilya Kapovich, Spencer Dowdall

arxiv:1301.7739 v7 · 2013-01-31 · math.GT · math.DS · 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{NWYDZDIIDCWCKS7AQHIG4FO7Y2}

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	2026-05-18T01:29:11.881548Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6db03c8d0818ac254be081d06e15dfc69d9c5e81d6f277ea3e4ad00295f78cc9

Aliases

arxiv: 1301.7739 · arxiv_version: 1301.7739v7 · doi: 10.48550/arxiv.1301.7739 · pith_short_12: NWYDZDIIDCWC · pith_short_16: NWYDZDIIDCWCKS7A · pith_short_8: NWYDZDII

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/NWYDZDIIDCWCKS7AQHIG4FO7Y2 \
  | 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: 6db03c8d0818ac254be081d06e15dfc69d9c5e81d6f277ea3e4ad00295f78cc9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "934a5238b4099982499b63ab4d5c738e0c6a8c60894a08180504ab9b89de4200",
    "cross_cats_sorted": [
      "math.DS",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-01-31T20:30:55Z",
    "title_canon_sha256": "e3794195fa5f1bfa0605bb4ba2005f3f485df819f1baca0b3d540dd6bcadb1e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.7739",
    "kind": "arxiv",
    "version": 7
  }
}