Pith Number

pith:OB2BXJ3W

pith:2018:OB2BXJ3WHUHMHVSVAVUKVNGMQN

not attested not anchored not stored refs pending

A microlocal approach to eigenfunction concentration

Jeffrey Galkowski

arxiv:1809.08677 v2 · 2018-09-23 · math.AP · math.SP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OB2BXJ3WHUHMHVSVAVUKVNGMQN}

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	2026-05-17T23:56:33.517451Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

70741ba7763d0ec3d6550568aab4cc8371ec9bf62152d8a7a6ec49b23eff9c46

Aliases

arxiv: 1809.08677 · arxiv_version: 1809.08677v2 · doi: 10.48550/arxiv.1809.08677 · pith_short_12: OB2BXJ3WHUHM · pith_short_16: OB2BXJ3WHUHMHVSV · pith_short_8: OB2BXJ3W

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/OB2BXJ3WHUHMHVSVAVUKVNGMQN \
  | 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: 70741ba7763d0ec3d6550568aab4cc8371ec9bf62152d8a7a6ec49b23eff9c46

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a9f87db75340e8e057fca75529e89ac29d113353e6c728a277448010c6c8845",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-09-23T20:56:18Z",
    "title_canon_sha256": "4cf807f33338d62a5371c42be70475aaa98dcde832f38121700d31d30d1cfd0c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.08677",
    "kind": "arxiv",
    "version": 2
  }
}