Pith Number

pith:HFPCDWNB

pith:2025:HFPCDWNBK5HAZC6FY5X2Q7S4NK

not attested not anchored not stored refs pending

The distribution of negative eigenvalues of Schr\"odinger operators on asymptotically hyperbolic manifolds

Ant\^onio S\'a Barreto, Yiran Wang

arxiv:2501.12606 v1 · 2025-01-22 · 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{HFPCDWNBK5HAZC6FY5X2Q7S4NK}

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	2026-07-05T10:03:55.606397Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

395e21d9a1574e0c8bc5c76fa87e5c6a869b651312dcd79821f261a231879134

Aliases

arxiv: 2501.12606 · arxiv_version: 2501.12606v1 · doi: 10.48550/arxiv.2501.12606 · pith_short_12: HFPCDWNBK5HA · pith_short_16: HFPCDWNBK5HAZC6F · pith_short_8: HFPCDWNB

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/HFPCDWNBK5HAZC6FY5X2Q7S4NK \
  | 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: 395e21d9a1574e0c8bc5c76fa87e5c6a869b651312dcd79821f261a231879134

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a31ef764f0812b759a3daf1bcefe1cd3a269b77cec24e2397983ff5f1ef04722",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2025-01-22T03:17:07Z",
    "title_canon_sha256": "54d595c5ead2fcf82a1701b7fa42bd459967614c13a9cb2a30753c1ebc31ac24"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.12606",
    "kind": "arxiv",
    "version": 1
  }
}