Pith Number

pith:5TW5EIEZ

pith:2016:5TW5EIEZPLL5ESXGG2DBUGTIZH

not attested not anchored not stored refs pending

Entropy bounds and quantum unique ergodicity for Hecke eigenfunctions on division algebras

Akshay Venkatesh, Lior Silberman

arxiv:1606.02267 v1 · 2016-06-07 · 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{5TW5EIEZPLL5ESXGG2DBUGTIZH}

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	2026-05-18T01:12:44.352887Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ecedd220997ad7d24ae636861a1a68c9e7ec46b44915f274ebdbe3cb352bff96

Aliases

arxiv: 1606.02267 · arxiv_version: 1606.02267v1 · doi: 10.48550/arxiv.1606.02267 · pith_short_12: 5TW5EIEZPLL5 · pith_short_16: 5TW5EIEZPLL5ESXG · pith_short_8: 5TW5EIEZ

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/5TW5EIEZPLL5ESXGG2DBUGTIZH \
  | 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: ecedd220997ad7d24ae636861a1a68c9e7ec46b44915f274ebdbe3cb352bff96

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87e8d114b72c9032186685e084cdfa5442135f988ab3a81af669ed7f21e1ed85",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-06-07T19:05:52Z",
    "title_canon_sha256": "2844dfd7c839ab951f708d5202dd61f9599b6594ae702b075c95dec138c6b087"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.02267",
    "kind": "arxiv",
    "version": 1
  }
}