Pith Number

pith:42ZZNAQA

pith:2013:42ZZNAQAUS3DRIGGOPVHBSFYCU

not attested not anchored not stored refs pending

Density of orbits of semigroups of endomorphisms acting on the Adeles

Alan Haynes, Sara Munday

arxiv:1303.1661 v1 · 2013-03-07 · math.NT · math.DS

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{42ZZNAQAUS3DRIGGOPVHBSFYCU}

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	2026-05-18T03:31:33.544612Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6b3968200a4b638a0c673ea70c8b81509948ea92d882240fcf0441069aebe81

Aliases

arxiv: 1303.1661 · arxiv_version: 1303.1661v1 · doi: 10.48550/arxiv.1303.1661 · pith_short_12: 42ZZNAQAUS3D · pith_short_16: 42ZZNAQAUS3DRIGG · pith_short_8: 42ZZNAQA

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/42ZZNAQAUS3DRIGGOPVHBSFYCU \
  | 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: e6b3968200a4b638a0c673ea70c8b81509948ea92d882240fcf0441069aebe81

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "51af5ff326b7dff2aa8966397f24aaafc48b416648cdf3c6c585fb86a3477ff9",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-03-07T12:25:10Z",
    "title_canon_sha256": "e3d609bbed3ace901dd3e15bfc36e7052ffc4245d3992d324c437a06ad32061f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.1661",
    "kind": "arxiv",
    "version": 1
  }
}