Pith Number

pith:4FZGTXGA

pith:2017:4FZGTXGANGUCI7R2JN5GRYVCPD

not attested not anchored not stored refs pending

Compactness of the resolvent for the Witten Laplacian

Wei-Xi Li

arxiv:1707.04745 v2 · 2017-07-15 · math.AP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4FZGTXGANGUCI7R2JN5GRYVCPD}

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	2026-05-18T00:19:27.627716Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e17269dcc069a8247e3a4b7a68e2a278f751980c374d5e00bf009c7434d1f7af

Aliases

arxiv: 1707.04745 · arxiv_version: 1707.04745v2 · doi: 10.48550/arxiv.1707.04745 · pith_short_12: 4FZGTXGANGUC · pith_short_16: 4FZGTXGANGUCI7R2 · pith_short_8: 4FZGTXGA

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/4FZGTXGANGUCI7R2JN5GRYVCPD \
  | 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: e17269dcc069a8247e3a4b7a68e2a278f751980c374d5e00bf009c7434d1f7af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e24a61c7cdc2f9d52baddb6f14d168c2b14d82cd4ade9d1993005c6fbee52ec6",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-07-15T14:46:26Z",
    "title_canon_sha256": "8a392473ad79b01b3129c327b51c238a17348f9f0d885b8455ae7ecb80f5f2bc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1707.04745",
    "kind": "arxiv",
    "version": 2
  }
}