Pith Number

pith:HJD6PZ4H

pith:2014:HJD6PZ4HYCNKSWBTHRF3W4YG5X

not attested not anchored not stored refs pending

Liouville transformation, analytic approximation of transmutation operators and solution of spectral problems

Samy Morelos, Sergii M. Torba, Vladislav V. Kravchenko

arxiv:1412.5237 v1 · 2014-12-17 · math.CA · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HJD6PZ4HYCNKSWBTHRF3W4YG5X}

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	2026-05-18T01:27:05.471335Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a47e7e787c09aa958333c4bbb7306edfc6358191c8b4050d6796a5a7aa3bc2c

Aliases

arxiv: 1412.5237 · arxiv_version: 1412.5237v1 · doi: 10.48550/arxiv.1412.5237 · pith_short_12: HJD6PZ4HYCNK · pith_short_16: HJD6PZ4HYCNKSWBT · pith_short_8: HJD6PZ4H

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/HJD6PZ4HYCNKSWBTHRF3W4YG5X \
  | 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: 3a47e7e787c09aa958333c4bbb7306edfc6358191c8b4050d6796a5a7aa3bc2c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de8b5f24b50febc76554a965c6c76bfb45ea7b52cf4836f09b1d09ba075993c4",
    "cross_cats_sorted": [
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2014-12-17T01:23:45Z",
    "title_canon_sha256": "bb4847bc99d2a7580bbd2eaf9a03e0dd9fac445d746b78616301947e3f3262f2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.5237",
    "kind": "arxiv",
    "version": 1
  }
}