Pith Number

pith:F42Y6X35

pith:2015:F42Y6X35LHDZSQ4O2YA5IGEERC

not attested not anchored not stored refs pending

Criterion for $\mathbb{Z}_d$--symmetry of a Spectrum of a Compact Operator

Boris S. Mityagin

arxiv:1504.05242 v1 · 2015-04-20 · 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{F42Y6X35LHDZSQ4O2YA5IGEERC}

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	2026-05-18T02:18:14.769186Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f358f5f7d59c799438ed601d41884889c62eb63527695f8f962100216b052ce

Aliases

arxiv: 1504.05242 · arxiv_version: 1504.05242v1 · doi: 10.48550/arxiv.1504.05242 · pith_short_12: F42Y6X35LHDZ · pith_short_16: F42Y6X35LHDZSQ4O · pith_short_8: F42Y6X35

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/F42Y6X35LHDZSQ4O2YA5IGEERC \
  | 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: 2f358f5f7d59c799438ed601d41884889c62eb63527695f8f962100216b052ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "91fcb0449085e7a9bb507917425300d79b4c9347e4a044bf75189ecdc6011859",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-04-20T21:43:57Z",
    "title_canon_sha256": "eb76d697f19e4b4ddd75d18b5de73b43550b817d463b48bf973ccc09037bad64"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.05242",
    "kind": "arxiv",
    "version": 1
  }
}