Pith Number

pith:EJURQKKW

pith:2013:EJURQKKWBOSBOBXLEFKFFYT6EC

not attested not anchored not stored refs pending

McMullen polynomials and Lipschitz flows for free-by-cyclic groups

Christopher J. Leininger, Ilya Kapovich, Spencer Dowdall

arxiv:1310.7481 v6 · 2013-10-28 · 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{EJURQKKWBOSBOBXLEFKFFYT6EC}

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	2026-05-18T01:06:23.256334Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

22691829560ba41706eb215452e27e20a4c03b67f96e5f367abd0ef61fd56791

Aliases

arxiv: 1310.7481 · arxiv_version: 1310.7481v6 · doi: 10.48550/arxiv.1310.7481 · pith_short_12: EJURQKKWBOSB · pith_short_16: EJURQKKWBOSBOBXL · pith_short_8: EJURQKKW

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/EJURQKKWBOSBOBXLEFKFFYT6EC \
  | 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: 22691829560ba41706eb215452e27e20a4c03b67f96e5f367abd0ef61fd56791

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7ec2349f7b1a277527df240d800a704d014b7112bc2c4ce8e2ce3aa6e8581ca9",
    "cross_cats_sorted": [
      "math.DS",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-10-28T16:26:07Z",
    "title_canon_sha256": "97f270d53e786a6030c92d34960f1c363aeab68f501dda157d788be1bdc7a329"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.7481",
    "kind": "arxiv",
    "version": 6
  }
}