Pith Number

pith:7H2BLZS7

pith:2010:7H2BLZS7PFBPNI5D7YX6NWCIZ2

not attested not anchored not stored refs pending

Spectral gaps for self-adjoint second order operators

Denis Borisov, Ivan Veselic'

arxiv:1010.0314 v2 · 2010-10-02 · math.SP · 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{7H2BLZS7PFBPNI5D7YX6NWCIZ2}

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	2026-05-18T00:04:42.349111Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9f415e65f7942f6a3a3fe2fe6d848ce87bc2eadd1e101191ab0fecbbab13c74

Aliases

arxiv: 1010.0314 · arxiv_version: 1010.0314v2 · doi: 10.48550/arxiv.1010.0314 · pith_short_12: 7H2BLZS7PFBP · pith_short_16: 7H2BLZS7PFBPNI5D · pith_short_8: 7H2BLZS7

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/7H2BLZS7PFBPNI5D7YX6NWCIZ2 \
  | 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: f9f415e65f7942f6a3a3fe2fe6d848ce87bc2eadd1e101191ab0fecbbab13c74

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "80680afda04708cc75a679d27276a268e1b885985f1d42ccc4b07db67621fa82",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2010-10-02T09:08:07Z",
    "title_canon_sha256": "abdbcf63ac8724124ca3979072165e8b9e9a9947175ad5675c9741b2452e2aee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.0314",
    "kind": "arxiv",
    "version": 2
  }
}