Pith Number

pith:HT73EIAN

pith:2012:HT73EIANXNKPDGPFBO4IP5XHLT

not attested not anchored not stored refs pending

Eigenvalue estimates for a three-dimensional magnetic Schr\"odinger operator

Bernard Helffer, Yuri A. Kordyukov

arxiv:1203.4021 v1 · 2012-03-19 · math.SP · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HT73EIANXNKPDGPFBO4IP5XHLT}

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	2026-05-18T03:59:48.448331Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3cffb2200dbb54f199e50bb887f6e75cc9305386b1b6b1a60c1a78c6a621a91b

Aliases

arxiv: 1203.4021 · arxiv_version: 1203.4021v1 · doi: 10.48550/arxiv.1203.4021 · pith_short_12: HT73EIANXNKP · pith_short_16: HT73EIANXNKPDGPF · pith_short_8: HT73EIAN

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/HT73EIANXNKPDGPFBO4IP5XHLT \
  | 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: 3cffb2200dbb54f199e50bb887f6e75cc9305386b1b6b1a60c1a78c6a621a91b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a434de0a1c8c1dd0920eaeaa34042b1b103ae1aec837615c5f0a6553ae2900ae",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2012-03-19T02:36:43Z",
    "title_canon_sha256": "898ea4713757ae50617157fc974df703cfa7870f6a0eb819ea633debac76d79e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.4021",
    "kind": "arxiv",
    "version": 1
  }
}