Pith Number

pith:2LTRXLYO

pith:2008:2LTRXLYO72IP3UYWQKXHZ5GVPC

not attested not anchored not stored refs pending

Operator theoretic methods for the eigenvalue counting function in spectral gaps

Alexander Pushnitski

arxiv:0809.4365 v1 · 2008-09-25 · 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{2LTRXLYO72IP3UYWQKXHZ5GVPC}

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	2026-05-18T02:15:33.629665Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d2e71baf0efe90fdd31682ae7cf4d578a7d6a7631b413775f8f2eadc1e87ab89

Aliases

arxiv: 0809.4365 · arxiv_version: 0809.4365v1 · doi: 10.48550/arxiv.0809.4365 · pith_short_12: 2LTRXLYO72IP · pith_short_16: 2LTRXLYO72IP3UYW · pith_short_8: 2LTRXLYO

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/2LTRXLYO72IP3UYWQKXHZ5GVPC \
  | 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: d2e71baf0efe90fdd31682ae7cf4d578a7d6a7631b413775f8f2eadc1e87ab89

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "407c1003b62a0ebbb0fc3ddc6718257bd729a553825173ef24c4ab99bbeccaae",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2008-09-25T10:59:15Z",
    "title_canon_sha256": "412c110746b317b7d978ee508166b58beba8c6a375bd863b3a1881a33471d217"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0809.4365",
    "kind": "arxiv",
    "version": 1
  }
}