Pith Number

pith:NLDUEM5E

pith:2013:NLDUEM5EGRXXV5LBSEBJI6SZ4H

not attested not anchored not stored refs pending

The Spectrum of an Adelic Markov Operator

Andreas Knauf

arxiv:1305.6410 v1 · 2013-05-28 · math.SP · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NLDUEM5EGRXXV5LBSEBJI6SZ4H}

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	2026-05-18T03:24:40.812264Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6ac74233a4346f7af5619102947a59e1ecb2d4b5d9d23374212efc509f69f620

Aliases

arxiv: 1305.6410 · arxiv_version: 1305.6410v1 · doi: 10.48550/arxiv.1305.6410 · pith_short_12: NLDUEM5EGRXX · pith_short_16: NLDUEM5EGRXXV5LB · pith_short_8: NLDUEM5E

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/NLDUEM5EGRXXV5LBSEBJI6SZ4H \
  | 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: 6ac74233a4346f7af5619102947a59e1ecb2d4b5d9d23374212efc509f69f620

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe35a88c670f369425f2848396a9f2451eac89bff4baedffe1058157c4ed96b3",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2013-05-28T08:36:18Z",
    "title_canon_sha256": "bc0a1311dbe79e7417493161a6789726c1672ace6f1910d66273dd7a60000854"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.6410",
    "kind": "arxiv",
    "version": 1
  }
}