Pith Number

pith:I7X4CRZU

pith:2017:I7X4CRZUHPQQZWDDTE3NMC7TXK

not attested not anchored not stored refs pending

On concrete spectral properties of a twisted-Laplacian associated to a central extension of the real Heisenberg group

Ahmed Intissar, Allal Ghanmi, Aymane EL Fardi

arxiv:1705.04920 v1 · 2017-05-14 · 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{I7X4CRZUHPQQZWDDTE3NMC7TXK}

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	2026-05-18T00:44:34.343184Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

47efc147343be10cd8639936d60bf3ba86938878820518aa851f61a6a30282a3

Aliases

arxiv: 1705.04920 · arxiv_version: 1705.04920v1 · doi: 10.48550/arxiv.1705.04920 · pith_short_12: I7X4CRZUHPQQ · pith_short_16: I7X4CRZUHPQQZWDD · pith_short_8: I7X4CRZU

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/I7X4CRZUHPQQZWDDTE3NMC7TXK \
  | 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: 47efc147343be10cd8639936d60bf3ba86938878820518aa851f61a6a30282a3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b86ee925f768262e788327b2c3463fb6c2d62370ea5e299f4b9e173413d1d2ab",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2017-05-14T06:34:03Z",
    "title_canon_sha256": "40b34bfc36fdcbad89ce19aaa03f87d783e43919e576dbaa9a6e976260ccab49"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.04920",
    "kind": "arxiv",
    "version": 1
  }
}