Pith Number

pith:6NJYDK5U

pith:2016:6NJYDK5UPB7XSZYM3NAPTMKXC7

not attested not anchored not stored refs pending

The cycle structure of a Markoff automorphism over finite fields

Alois Cerbu, Elijah Gunther, Luke Peilen, Michael Magee

arxiv:1610.07077 v2 · 2016-10-22 · math.NT · math.AG · 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{6NJYDK5UPB7XSZYM3NAPTMKXC7}

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	2026-05-18T00:20:57.083664Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f35381abb4787f79670cdb40f9b15717d7de103dc63eeb66da4c2cdfbea312de

Aliases

arxiv: 1610.07077 · arxiv_version: 1610.07077v2 · doi: 10.48550/arxiv.1610.07077 · pith_short_12: 6NJYDK5UPB7X · pith_short_16: 6NJYDK5UPB7XSZYM · pith_short_8: 6NJYDK5U

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/6NJYDK5UPB7XSZYM3NAPTMKXC7 \
  | 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: f35381abb4787f79670cdb40f9b15717d7de103dc63eeb66da4c2cdfbea312de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2a4057480b217e847cb4914f8a7d5ff3941b75c0f53f0491a44b3e3ea2ffb44d",
    "cross_cats_sorted": [
      "math.AG",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-10-22T17:07:42Z",
    "title_canon_sha256": "01160b9d4ac1e68b9657d094ccc804e974ee11fae7722e023e2f47d764261842"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.07077",
    "kind": "arxiv",
    "version": 2
  }
}