Pith Number

pith:WXAXY5AF

pith:2011:WXAXY5AFZTLBAM4WKZUHHIVM2M

not attested not anchored not stored refs pending

Algebraic Numbers, Hyperbolicity, and Density Modulo One

Alexander Gorodnik, Shirali Kadyrov

arxiv:1109.0183 v1 · 2011-09-01 · 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{WXAXY5AFZTLBAM4WKZUHHIVM2M}

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	2026-05-18T04:14:17.173710Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5c17c7405ccd6103396566873a2acd30cca5f77aa63d7fbd425d435319c6fc9

Aliases

arxiv: 1109.0183 · arxiv_version: 1109.0183v1 · doi: 10.48550/arxiv.1109.0183 · pith_short_12: WXAXY5AFZTLB · pith_short_16: WXAXY5AFZTLBAM4W · pith_short_8: WXAXY5AF

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/WXAXY5AFZTLBAM4WKZUHHIVM2M \
  | 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: b5c17c7405ccd6103396566873a2acd30cca5f77aa63d7fbd425d435319c6fc9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5d810d50b924b1002300a066cbb8fbc85d3d2cbfbc47a805507974d353a233cb",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-09-01T13:18:29Z",
    "title_canon_sha256": "48a521d4767cf0b232abb930fcfd7312cae5485bc8b19172c178094c4d1f9b0a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.0183",
    "kind": "arxiv",
    "version": 1
  }
}