Pith Number

pith:42KDB6O7

pith:2012:42KDB6O737DIJBWHNADY4J3U4N

not attested not anchored not stored refs pending

Localization and Schr\"odinger perturbations of kernels

Krzysztof Bogdan, Tomasz Jakubowski, Wolfhard Hansen

arxiv:1201.4530 v2 · 2012-01-22 · math.FA · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{42KDB6O737DIJBWHNADY4J3U4N}

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	2026-05-18T03:48:44.992193Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e69430f9dfdfc68486c768078e2774e363619812ff3dff9f2388b9c652e151cf

Aliases

arxiv: 1201.4530 · arxiv_version: 1201.4530v2 · doi: 10.48550/arxiv.1201.4530 · pith_short_12: 42KDB6O737DI · pith_short_16: 42KDB6O737DIJBWH · pith_short_8: 42KDB6O7

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/42KDB6O737DIJBWHNADY4J3U4N \
  | 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: e69430f9dfdfc68486c768078e2774e363619812ff3dff9f2388b9c652e151cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d411254d00b8526b70afeaf90da284e939fd23cdc34f4c811d03846c20185be2",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-01-22T06:08:42Z",
    "title_canon_sha256": "00e5b350ea5945b8c71e2c970f7a341a64f4f0b0346cbf1ba768db97affa076f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.4530",
    "kind": "arxiv",
    "version": 2
  }
}