Pith Number

pith:HTS6KGM5

pith:1998:HTS6KGM5VQLWHP6SG2EZJ7IGLY

not attested not anchored not stored refs pending

Extension Of Bertrand's Theorem And Factorization Of The Radial Schr\"odinger Equation

Jin-Yan Zeng (Department of Physics, Peking University), Zuo-Bing Wu

arxiv:quant-ph/9812077 v1 · 1998-12-27 · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HTS6KGM5VQLWHP6SG2EZJ7IGLY}

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	2026-07-04T16:11:03.257696Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3ce5e5199dac1763bfd2368994fd065e374140c1c8167cf6d3ed41945563d658

Aliases

arxiv: quant-ph/9812077 · arxiv_version: quant-ph/9812077v1 · doi: 10.48550/arxiv.quant-ph/9812077 · pith_short_12: HTS6KGM5VQLW · pith_short_16: HTS6KGM5VQLWHP6S · pith_short_8: HTS6KGM5

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/HTS6KGM5VQLWHP6SG2EZJ7IGLY \
  | 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: 3ce5e5199dac1763bfd2368994fd065e374140c1c8167cf6d3ed41945563d658

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2124fb20fe2a6b35da4a4b8799b894811221bc0c0c7ae8f1151a2716413d803c",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "1998-12-27T10:13:45Z",
    "title_canon_sha256": "ac4359fb07c7c7ee91b0c5c18e71f6561ef42755151df1395e80a5f33a944ce3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/9812077",
    "kind": "arxiv",
    "version": 1
  }
}