Pith Number

pith:3XMFY5H4

pith:2013:3XMFY5H4FV7CLT2ZN3RLGLSE2O

not attested not anchored not stored refs pending

Liouville numbers, Liouville sets and Liouville fields

K. Senthil Kumar, M. Waldschmidt, R. Thangadurai

arxiv:1312.7151 v1 · 2013-12-26 · 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{3XMFY5H4FV7CLT2ZN3RLGLSE2O}

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	2026-05-18T03:03:45.681815Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ddd85c74fc2d7e25cf596ee2b32e44d3960520ff4be0357c4158e30f1ee1ff76

Aliases

arxiv: 1312.7151 · arxiv_version: 1312.7151v1 · doi: 10.48550/arxiv.1312.7151 · pith_short_12: 3XMFY5H4FV7C · pith_short_16: 3XMFY5H4FV7CLT2Z · pith_short_8: 3XMFY5H4

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/3XMFY5H4FV7CLT2ZN3RLGLSE2O \
  | 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: ddd85c74fc2d7e25cf596ee2b32e44d3960520ff4be0357c4158e30f1ee1ff76

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7fea72cf7226373de546493c5b9ae90047b8a296cde18ae2468d1f7890009611",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-12-26T21:59:25Z",
    "title_canon_sha256": "2280d7953d59c45249e8a505272241a1c1f5c36ada1bdd95b72d87ce52be69ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.7151",
    "kind": "arxiv",
    "version": 1
  }
}