Pith Number

pith:YIHGYJDR

pith:2012:YIHGYJDRZMZPWFB4L7JR7XRCCU

not attested not anchored not stored refs pending

Spectral properties of Schr\"{o}dinger-type operators and large-time behavior of the solutions to the corresponding wave equation

A. G. Ramm

arxiv:1206.5990 v1 · 2012-06-26 · math.AP · 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{YIHGYJDRZMZPWFB4L7JR7XRCCU}

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	2026-05-18T03:52:37.412373Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c20e6c2471cb32fb143c5fd31fde22150b29c50de99bc818ed0b3b3566ee2012

Aliases

arxiv: 1206.5990 · arxiv_version: 1206.5990v1 · doi: 10.48550/arxiv.1206.5990 · pith_short_12: YIHGYJDRZMZP · pith_short_16: YIHGYJDRZMZPWFB4 · pith_short_8: YIHGYJDR

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/YIHGYJDRZMZPWFB4L7JR7XRCCU \
  | 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: c20e6c2471cb32fb143c5fd31fde22150b29c50de99bc818ed0b3b3566ee2012

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be42f40f145a239124d715fd60ff61edb32cee994208a17284d66ed84ce97b9a",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-06-26T13:57:48Z",
    "title_canon_sha256": "63c591501cad660f8aae285a06be367506dc1e35f695ff0714ba4dc548859dd1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.5990",
    "kind": "arxiv",
    "version": 1
  }
}