Pith Number

pith:QLNG3O4H

pith:2012:QLNG3O4HOYVWTMPDDCVMUXGO2O

not attested not anchored not stored refs pending

A pseudo-differential calculus on non-standard symplectic space; spectral and regularity results in modulation spaces

Franz Luef, Jo\~ao Nuno Prata, Maurice de Gosson, Nuno Costa Dias

arxiv:1209.1849 v1 · 2012-09-09 · math.FA · math-ph · math.MP · math.SP · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QLNG3O4HOYVWTMPDDCVMUXGO2O}

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	2026-05-18T03:45:54.187352Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82da6dbb87762b69b1e318aaca5cced3ac421398758eb5c3bbdc12d1a2f1d9fc

Aliases

arxiv: 1209.1849 · arxiv_version: 1209.1849v1 · doi: 10.48550/arxiv.1209.1849 · pith_short_12: QLNG3O4HOYVW · pith_short_16: QLNG3O4HOYVWTMPD · pith_short_8: QLNG3O4H

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/QLNG3O4HOYVWTMPDDCVMUXGO2O \
  | 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: 82da6dbb87762b69b1e318aaca5cced3ac421398758eb5c3bbdc12d1a2f1d9fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8bf17cb778b78ef7bb3ddaaa35d4ad7fc5c5e30fff01e8ddd680b765272749f7",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.SP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-09-09T22:39:59Z",
    "title_canon_sha256": "1665069cb8bb433be176161c73b44a9827d658ffdc7da928ec58782b24d1a5a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.1849",
    "kind": "arxiv",
    "version": 1
  }
}