Pith Number

pith:WJJLHVRA

pith:2011:WJJLHVRAAOV4GDAJUXTJ3X2NJO

not attested not anchored not stored refs pending

Entropy and Escape of Mass for Hilbert Modular Spaces

Shirali Kadyrov

arxiv:1101.4658 v2 · 2011-01-24 · 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{WJJLHVRAAOV4GDAJUXTJ3X2NJO}

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	2026-05-18T04:07:32.407426Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b252b3d62003abc30c09a5e69ddf4d4bae5e57c957b936ade60038816b6c886f

Aliases

arxiv: 1101.4658 · arxiv_version: 1101.4658v2 · doi: 10.48550/arxiv.1101.4658 · pith_short_12: WJJLHVRAAOV4 · pith_short_16: WJJLHVRAAOV4GDAJ · pith_short_8: WJJLHVRA

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/WJJLHVRAAOV4GDAJUXTJ3X2NJO \
  | 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: b252b3d62003abc30c09a5e69ddf4d4bae5e57c957b936ade60038816b6c886f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc0ab89d622180d488a649f1705382c547e992a77a04ba37a161a334257649e7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-01-24T21:03:51Z",
    "title_canon_sha256": "038cd96a19fa9a135676e010df9918af0f25b565daaa51d708f46f66a62f815b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.4658",
    "kind": "arxiv",
    "version": 2
  }
}