Pith Number

pith:JF23BHR2

pith:2015:JF23BHR2XEEP6DNS5LTM5JO4WQ

not attested not anchored not stored refs pending

Bounds on eigenfunctions of semiclassical operators with double characteristics

Gunther Uhlmann, Katya Krupchyk

arxiv:1504.01069 v2 · 2015-04-05 · 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{JF23BHR2XEEP6DNS5LTM5JO4WQ}

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	2026-05-18T00:40:52.025391Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4975b09e3ab908ff0db2eae6cea5dcb41a834081bc9544b57aff609faa6b7c83

Aliases

arxiv: 1504.01069 · arxiv_version: 1504.01069v2 · doi: 10.48550/arxiv.1504.01069 · pith_short_12: JF23BHR2XEEP · pith_short_16: JF23BHR2XEEP6DNS · pith_short_8: JF23BHR2

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/JF23BHR2XEEP6DNS5LTM5JO4WQ \
  | 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: 4975b09e3ab908ff0db2eae6cea5dcb41a834081bc9544b57aff609faa6b7c83

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "39a24453e0cc7491ba67330ff4bec358e2e51b35aeec1261e16a7798532ff4d9",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-04-05T00:01:28Z",
    "title_canon_sha256": "f617b618c1d9585c5daaa17494f10fa527afe177f1845bbf646085aaaf45603b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.01069",
    "kind": "arxiv",
    "version": 2
  }
}