Pith Number

pith:G3FX4RK4

pith:2014:G3FX4RK466RRNQONUUVEA6KDK4

not attested not anchored not stored refs pending

The spectral density of a product of spectral projections

Alexander Pushnitski, Rupert L. Frank

arxiv:1409.1206 v2 · 2014-09-03 · math.SP · math-ph · math.FA · 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{G3FX4RK466RRNQONUUVEA6KDK4}

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	2026-05-18T02:25:18.719964Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

36cb7e455cf7a316c1cda52a40794357153215884c8cdadbb42d74ba4775c32c

Aliases

arxiv: 1409.1206 · arxiv_version: 1409.1206v2 · doi: 10.48550/arxiv.1409.1206 · pith_short_12: G3FX4RK466RR · pith_short_16: G3FX4RK466RRNQON · pith_short_8: G3FX4RK4

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/G3FX4RK466RRNQONUUVEA6KDK4 \
  | 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: 36cb7e455cf7a316c1cda52a40794357153215884c8cdadbb42d74ba4775c32c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1d16f0be3ce842b0e346eaf0860b5ec0de85ac9870989243cc227a74eaf7b1ee",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2014-09-03T19:40:55Z",
    "title_canon_sha256": "51d21bd7872afdf569bef591239bc3ac623ca1725accff61f5b176d68716c337"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.1206",
    "kind": "arxiv",
    "version": 2
  }
}