Pith Number

pith:GPYV7TKX

pith:2019:GPYV7TKXZEKTMLBJQ4L4YK7TWI

not attested not anchored not stored refs pending

Noncompact complete Riemannian manifolds with singular continuous spectrum embedded into the essential spectrum of the Laplacian, I. The hyperbolic case

Svetlana Jitomirskaya, Wencai Liu

arxiv:1908.03808 v1 · 2019-08-10 · math.SP · math-ph · math.DG · 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{GPYV7TKXZEKTMLBJQ4L4YK7TWI}

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	2026-07-05T03:28:08.891719Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

33f15fcd57c915362c298717cc2bf3b234dd5fd74ba6776ae79b1175be2ae7c8

Aliases

arxiv: 1908.03808 · arxiv_version: 1908.03808v1 · doi: 10.48550/arxiv.1908.03808 · pith_short_12: GPYV7TKXZEKT · pith_short_16: GPYV7TKXZEKTMLBJ · pith_short_8: GPYV7TKX

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/GPYV7TKXZEKTMLBJQ4L4YK7TWI \
  | 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: 33f15fcd57c915362c298717cc2bf3b234dd5fd74ba6776ae79b1175be2ae7c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "28bc8891b0465d456b552c17450976266a19d44a58e5413f49825d4a80a5c236",
    "cross_cats_sorted": [
      "math-ph",
      "math.DG",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2019-08-10T21:14:03Z",
    "title_canon_sha256": "dae38e6b72c95cc1c9909c501a67d9836de9332a0008cd9926c6e98cfb8bf6c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.03808",
    "kind": "arxiv",
    "version": 1
  }
}