Pith Number

pith:4ZGJQBPK

pith:2012:4ZGJQBPKNI5U4M7GTLO26GCQ2P

not attested not anchored not stored refs pending

Limit Points Badly Approximable by Horoballs

Dustin Mayeda, Keith Merrill

arxiv:1201.4505 v2 · 2012-01-21 · math.MG · math.DS · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4ZGJQBPKNI5U4M7GTLO26GCQ2P}

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	2026-05-18T03:29:40.833235Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e64c9805ea6a3b4e33e69addaf1850d3faeb3edd27b9c3d6f1a8255018c23121

Aliases

arxiv: 1201.4505 · arxiv_version: 1201.4505v2 · doi: 10.48550/arxiv.1201.4505 · pith_short_12: 4ZGJQBPKNI5U · pith_short_16: 4ZGJQBPKNI5U4M7G · pith_short_8: 4ZGJQBPK

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/4ZGJQBPKNI5U4M7GTLO26GCQ2P \
  | 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: e64c9805ea6a3b4e33e69addaf1850d3faeb3edd27b9c3d6f1a8255018c23121

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7925adb14f68fe6041b329ffc5dd26168a054f6472df333233496678a0f4c730",
    "cross_cats_sorted": [
      "math.DS",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2012-01-21T20:08:40Z",
    "title_canon_sha256": "e7b893f42536443ebf320a2ee303196836c2d2b8e9fa1059b3cb5c388f560766"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.4505",
    "kind": "arxiv",
    "version": 2
  }
}