Pith Number

pith:TO7NGNFW

pith:2012:TO7NGNFWXPV52VVPFPJQ2GN4DQ

not attested not anchored not stored refs pending

Solutions of Helmholtz and Schr\"odinger Equations with Side Condition and Nonregular Separation of Variables

Claudia M. Chanu, Philip Broadbridge, Willard Miller Jr

arxiv:1209.2019 v2 · 2012-09-10 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TO7NGNFWXPV52VVPFPJQ2GN4DQ}

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	2026-05-18T03:40:02.755462Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9bbed334b6bbebdd56af2bd30d19bc1c12a168008a144a44544092f9541fbc55

Aliases

arxiv: 1209.2019 · arxiv_version: 1209.2019v2 · doi: 10.48550/arxiv.1209.2019 · pith_short_12: TO7NGNFWXPV5 · pith_short_16: TO7NGNFWXPV52VVP · pith_short_8: TO7NGNFW

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/TO7NGNFWXPV52VVPFPJQ2GN4DQ \
  | 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: 9bbed334b6bbebdd56af2bd30d19bc1c12a168008a144a44544092f9541fbc55

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "056acc0fe1f1cf556ddc92be0f12dc71c60fa9882b574f65ec32ad45eb7bee04",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/3.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-09-10T15:02:42Z",
    "title_canon_sha256": "9a52aab7c947c32fa5eaf179b693aa7bd232d5f7cc7ed6afff0d5c310b6556e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.2019",
    "kind": "arxiv",
    "version": 2
  }
}