Pith Number

pith:GRPAIDXT

pith:2015:GRPAIDXTN2ISB56D5HBNPLAVMS

not attested not anchored not stored refs pending

Representation of solutions to the one-dimensional Schr\"odinger equation in terms of Neumann series of Bessel functions

Luis J. Navarro, Sergii M. Torba, Vladislav V. Kravchenko

arxiv:1508.02738 v3 · 2015-08-11 · 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{GRPAIDXTN2ISB56D5HBNPLAVMS}

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	2026-05-18T00:39:57.122382Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

345e040ef36e9120f7c3e9c2d7ac1564a5474deafd50053bfc8bba2dbaff0dc2

Aliases

arxiv: 1508.02738 · arxiv_version: 1508.02738v3 · doi: 10.48550/arxiv.1508.02738 · pith_short_12: GRPAIDXTN2IS · pith_short_16: GRPAIDXTN2ISB56D · pith_short_8: GRPAIDXT

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/GRPAIDXTN2ISB56D5HBNPLAVMS \
  | 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: 345e040ef36e9120f7c3e9c2d7ac1564a5474deafd50053bfc8bba2dbaff0dc2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c2be1c6c2e59543e053eeed356e40df42cfb3d1a21384c35a2421f6dd2aeede",
    "cross_cats_sorted": [
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-08-11T20:46:34Z",
    "title_canon_sha256": "8f1ed0fa288e022e62ce496e6e51d7abd525f9713ae473e8ca1f547ec99dfc27"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.02738",
    "kind": "arxiv",
    "version": 3
  }
}