Pith Number

pith:LU5L6AZH

pith:2017:LU5L6AZHPOH76OSF3KGW6N427O

not attested not anchored not stored refs pending

Fourier dimension and spectral gaps for hyperbolic surfaces

Jean Bourgain, Semyon Dyatlov

arxiv:1704.02909 v2 · 2017-04-10 · math.CA · math.AP · math.CO · 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{LU5L6AZHPOH76OSF3KGW6N427O}

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	2026-05-18T00:32:55.217893Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5d3abf03277b8fff3a45da8d6f379afbb2e1ce4bdc86be65b46883ff92c86b4c

Aliases

arxiv: 1704.02909 · arxiv_version: 1704.02909v2 · doi: 10.48550/arxiv.1704.02909 · pith_short_12: LU5L6AZHPOH7 · pith_short_16: LU5L6AZHPOH76OSF · pith_short_8: LU5L6AZH

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/LU5L6AZHPOH76OSF3KGW6N427O \
  | 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: 5d3abf03277b8fff3a45da8d6f379afbb2e1ce4bdc86be65b46883ff92c86b4c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "63ed88a5f0dd6e2b820371d7115c4c378aa27091e02de7ff8dfe856448967e12",
    "cross_cats_sorted": [
      "math.AP",
      "math.CO",
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2017-04-10T15:35:10Z",
    "title_canon_sha256": "b4dc9830b36dcde07e60479fc3b42ea94b87c3561b6facb2a012b6be55a03c20"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1704.02909",
    "kind": "arxiv",
    "version": 2
  }
}