Pith Number

pith:WI5C6IQX

pith:2012:WI5C6IQXGDSBNURELCCSVTWC3C

not attested not anchored not stored refs pending

On the negative spectrum of the hierarchical Schr\"{o}dinger operator

B. Vainberg, S. Molchanov

arxiv:1206.4019 v1 · 2012-06-18 · 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{WI5C6IQXGDSBNURELCCSVTWC3C}

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	2026-05-18T01:17:57.628409Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b23a2f221730e416d22458852acec2d8b98657836cc6a8adae53d8834787ee65

Aliases

arxiv: 1206.4019 · arxiv_version: 1206.4019v1 · doi: 10.48550/arxiv.1206.4019 · pith_short_12: WI5C6IQXGDSB · pith_short_16: WI5C6IQXGDSBNURE · pith_short_8: WI5C6IQX

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/WI5C6IQXGDSBNURELCCSVTWC3C \
  | 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: b23a2f221730e416d22458852acec2d8b98657836cc6a8adae53d8834787ee65

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4a60e20798d7faf5dfece6c8c7215b58415936259058505785baee478dae3de",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-06-18T19:17:27Z",
    "title_canon_sha256": "fe2b48da38f94ab5fe64319597d1f638092175ed79f7410b593641a51aedf123"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.4019",
    "kind": "arxiv",
    "version": 1
  }
}