Pith Number

pith:VX4XD2TP

pith:2012:VX4XD2TPN6V7CLFL4UC2JFGMAS

not attested not anchored not stored refs pending

Explicit formulas for the Schroedinger wave operators in R^2

R. Tiedra de Aldecoa, S. Richard

arxiv:1212.2230 v1 · 2012-12-10 · math-ph · math.MP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VX4XD2TPN6V7CLFL4UC2JFGMAS}

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	2026-05-18T03:38:45.619704Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

adf971ea6f6fabf12cabe505a494cc04992ba0f21e375c966e97b22962300123

Aliases

arxiv: 1212.2230 · arxiv_version: 1212.2230v1 · doi: 10.48550/arxiv.1212.2230 · pith_short_12: VX4XD2TPN6V7 · pith_short_16: VX4XD2TPN6V7CLFL · pith_short_8: VX4XD2TP

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/VX4XD2TPN6V7CLFL4UC2JFGMAS \
  | 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: adf971ea6f6fabf12cabe505a494cc04992ba0f21e375c966e97b22962300123

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c7ef399fe11748d74ce41ec6ffaf03414aa66746cbdbf1226d14f98c1e2ae236",
    "cross_cats_sorted": [
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-12-10T22:02:52Z",
    "title_canon_sha256": "d44a8add0e4b95ec1bee6ae7494bcad4443706580a69a1714ad7025a55596823"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.2230",
    "kind": "arxiv",
    "version": 1
  }
}