Pith Number

pith:ODLQT2P2

pith:2015:ODLQT2P22FR3FOH7O3ELKHTMKC

not attested not anchored not stored refs pending

Essential Spectral Singularities and the Spectral Expansion for the Hill Operator

O. A. Veliev

arxiv:1512.04473 v2 · 2015-12-14 · 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{ODLQT2P22FR3FOH7O3ELKHTMKC}

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	2026-05-18T01:24:13.966771Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

70d709e9fad163b2b8ff76c8b51e6c5095b2eb9ce626f84c6cedbe1d22ac4b3f

Aliases

arxiv: 1512.04473 · arxiv_version: 1512.04473v2 · doi: 10.48550/arxiv.1512.04473 · pith_short_12: ODLQT2P22FR3 · pith_short_16: ODLQT2P22FR3FOH7 · pith_short_8: ODLQT2P2

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/ODLQT2P22FR3FOH7O3ELKHTMKC \
  | 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: 70d709e9fad163b2b8ff76c8b51e6c5095b2eb9ce626f84c6cedbe1d22ac4b3f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5668bb5e8659494173e3445927c58b9ae149066e0fbeeed086cf9b46915a7c52",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2015-12-14T19:19:15Z",
    "title_canon_sha256": "e814489dea931363193a8b723f3b4e9c9fe9fdebe024b62a6c373da4a973b4f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.04473",
    "kind": "arxiv",
    "version": 2
  }
}