Pith Number

pith:KVZDBX3O

pith:2016:KVZDBX3OGGYXO2H4IJFJKEVRXA

not attested not anchored not stored refs pending

$L^p$ concentration estimates for the Laplacian eigenfunctions near submanifolds

Katya Krupchyk

arxiv:1604.05769 v2 · 2016-04-19 · 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{KVZDBX3OGGYXO2H4IJFJKEVRXA}

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	2026-05-18T01:14:52.236000Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

557230df6e31b17768fc424a9512b1b811e433f0bf20ca0e7d2aa7290a13a44e

Aliases

arxiv: 1604.05769 · arxiv_version: 1604.05769v2 · doi: 10.48550/arxiv.1604.05769 · pith_short_12: KVZDBX3OGGYX · pith_short_16: KVZDBX3OGGYXO2H4 · pith_short_8: KVZDBX3O

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/KVZDBX3OGGYXO2H4IJFJKEVRXA \
  | 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: 557230df6e31b17768fc424a9512b1b811e433f0bf20ca0e7d2aa7290a13a44e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c76ff0fb2eb9c27ceb75dade3d91a64e4e3bad2b3bb3600c66e1e754c1d02846",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-04-19T22:43:46Z",
    "title_canon_sha256": "a0113e988d47bc18448a4875e1fde1eaf493761ea22b82158695fd9da5730db1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.05769",
    "kind": "arxiv",
    "version": 2
  }
}