Pith Number

pith:3WIEG4TL

pith:2018:3WIEG4TLIPIIXV5I32Q64BKKQM

not attested not anchored not stored refs pending

Discreteness of spectrum for the $\overline\partial$-Neumann Laplacian on manifolds of bounded geometry

Franz Berger

arxiv:1808.02730 v1 · 2018-08-08 · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3WIEG4TLIPIIXV5I32Q64BKKQM}

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	2026-05-18T00:08:32.350813Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd9043726b43d08bd7a8dea1ee054a833c4b52e7b741d8ce9d00919025a89ebb

Aliases

arxiv: 1808.02730 · arxiv_version: 1808.02730v1 · doi: 10.48550/arxiv.1808.02730 · pith_short_12: 3WIEG4TLIPII · pith_short_16: 3WIEG4TLIPIIXV5I · pith_short_8: 3WIEG4TL

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/3WIEG4TLIPIIXV5I32Q64BKKQM \
  | 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: dd9043726b43d08bd7a8dea1ee054a833c4b52e7b741d8ce9d00919025a89ebb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c6fcd631807f0d01e321ba5c254df05ebf548fe04980b957b25e14e4b70dac64",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2018-08-08T11:42:54Z",
    "title_canon_sha256": "0389704bcde4ee330ea73c22eb717e39544259ad4f84d70cdce6b53346e6a3b1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.02730",
    "kind": "arxiv",
    "version": 1
  }
}