Pith Number

pith:QGNY6KQG

pith:2009:QGNY6KQGKVFY3SVZK6QEIMJM6V

not attested not anchored not stored refs pending

Spectral density and Sobolev inequalities for pure and mixed states

Michel Rumin

arxiv:0906.2902 v1 · 2009-06-16 · math.FA · 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{QGNY6KQGKVFY3SVZK6QEIMJM6V}

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	2026-05-18T04:29:42.722222Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

819b8f2a06554b8dcab957a044312cf562e445f64893f160329cb817d1055c31

Aliases

arxiv: 0906.2902 · arxiv_version: 0906.2902v1 · doi: 10.48550/arxiv.0906.2902 · pith_short_12: QGNY6KQGKVFY · pith_short_16: QGNY6KQGKVFY3SVZ · pith_short_8: QGNY6KQG

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/QGNY6KQGKVFY3SVZK6QEIMJM6V \
  | 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: 819b8f2a06554b8dcab957a044312cf562e445f64893f160329cb817d1055c31

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea6a6a177ff2800ca1e2b86c7fd88c79e90d6bc12f663241645370a8d85937ce",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2009-06-16T11:46:03Z",
    "title_canon_sha256": "b5ed3388074455bf04915783982a57add6f230ed9cf4d03235b0c17f2b96f21d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.2902",
    "kind": "arxiv",
    "version": 1
  }
}