Pith Number

pith:WG4EJ3FU

pith:2022:WG4EJ3FUIWCZRZKELRCG6U3UBX

not attested not anchored not stored refs pending

Matrix representation of Magnetic pseudo-differential operators via tight Gabor frames

Bernard Helffer, Horia D. Cornean, Radu Purice

arxiv:2212.12229 v3 · 2022-12-23 · math.AP · math-ph · 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{WG4EJ3FUIWCZRZKELRCG6U3UBX}

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	2026-05-20T00:02:44.706103Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b1b844ecb4458598e5445c446f53740df695cc8bff219492c1b7881e5e3e4f80

Aliases

arxiv: 2212.12229 · arxiv_version: 2212.12229v3 · doi: 10.48550/arxiv.2212.12229 · pith_short_12: WG4EJ3FUIWCZ · pith_short_16: WG4EJ3FUIWCZRZKE · pith_short_8: WG4EJ3FU

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/WG4EJ3FUIWCZRZKELRCG6U3UBX \
  | 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: b1b844ecb4458598e5445c446f53740df695cc8bff219492c1b7881e5e3e4f80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c7407975ebbb5a9568a0fa3b6d6e3d2f4adb94d1e8fbff628e1e85af5c74ccce",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2022-12-23T09:55:09Z",
    "title_canon_sha256": "8fb8113fd31fd20deb9175bcf8f7f53bc146ab17578ab98852723acf61b5ecef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2212.12229",
    "kind": "arxiv",
    "version": 3
  }
}