Pith Number

pith:CJX2VGMC

pith:2015:CJX2VGMCNKVLULVOZUKMVJZBUJ

not attested not anchored not stored refs pending

Endomorphisms, train track maps, and fully irreducible monodromies

Christopher J. Leininger, Ilya Kapovich, Spencer Dowdall

arxiv:1507.03028 v2 · 2015-07-10 · math.GR · math.DS · 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{CJX2VGMCNKVLULVOZUKMVJZBUJ}

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	2026-05-18T00:36:24.970064Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

126faa99826aaaba2eaecd14caa721a2645dce61c1a000b374650e7d92daa007

Aliases

arxiv: 1507.03028 · arxiv_version: 1507.03028v2 · doi: 10.48550/arxiv.1507.03028 · pith_short_12: CJX2VGMCNKVL · pith_short_16: CJX2VGMCNKVLULVO · pith_short_8: CJX2VGMC

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/CJX2VGMCNKVLULVOZUKMVJZBUJ \
  | 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: 126faa99826aaaba2eaecd14caa721a2645dce61c1a000b374650e7d92daa007

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "501fcb2ef990263332362cc870cd38f706b4d975f49256957ad9cea0f264abe9",
    "cross_cats_sorted": [
      "math.DS",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-07-10T20:30:51Z",
    "title_canon_sha256": "bbe29d55d0a0dbd4c272370e2396a90c467c115cac6604bd8c060f4516e61cb5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.03028",
    "kind": "arxiv",
    "version": 2
  }
}