Pith Number

pith:PT26T2DH

pith:2013:PT26T2DHDANJCIPP2TT7EEWORC

not attested not anchored not stored refs pending

Criteria of Spectral Gap for Markov Operators

Feng-Yu Wang

arxiv:1305.4460 v6 · 2013-05-20 · math.FA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PT26T2DHDANJCIPP2TT7EEWORC}

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	2026-05-18T03:07:01.786543Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7cf5e9e867181a9121efd4e7f212ce88853284452a1ca13a68fb07273bf86ac3

Aliases

arxiv: 1305.4460 · arxiv_version: 1305.4460v6 · doi: 10.48550/arxiv.1305.4460 · pith_short_12: PT26T2DHDANJ · pith_short_16: PT26T2DHDANJCIPP · pith_short_8: PT26T2DH

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/PT26T2DHDANJCIPP2TT7EEWORC \
  | 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: 7cf5e9e867181a9121efd4e7f212ce88853284452a1ca13a68fb07273bf86ac3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a6a10b56661007af428fd9db83fc23212ce8e66cb1a6c3cd8529a4d6cc68b01f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-05-20T08:10:53Z",
    "title_canon_sha256": "97ed25b499e58887d8444a3f0459820f449cf48ed073242669ed0541f19dbbf3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.4460",
    "kind": "arxiv",
    "version": 6
  }
}