Pith Number

pith:JTZPA7EO

pith:2000:JTZPA7EOP4DCKZQBHIXH2Q6CAO

not attested not anchored not stored refs pending

Perron-Frobenius Theory for Positive Maps on Trace Ideals

Robert Schrader

arxiv:math-ph/0007020 v1 · 2000-07-14 · 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{JTZPA7EOP4DCKZQBHIXH2Q6CAO}

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.

Cited by

1 paper in Pith

Periodicity in Ergodic Quantum Processes

Receipt and verification

First computed	2026-07-04T14:33:35.983230Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4cf2f07c8e7f062566013a2e7d43c203a67608d4721a0e8bfc54cfbb601f28e7

Aliases

arxiv: math-ph/0007020 · arxiv_version: math-ph/0007020v1 · doi: 10.48550/arxiv.math-ph/0007020 · pith_short_12: JTZPA7EOP4DC · pith_short_16: JTZPA7EOP4DCKZQB · pith_short_8: JTZPA7EO

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/JTZPA7EOP4DCKZQBHIXH2Q6CAO \
  | 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: 4cf2f07c8e7f062566013a2e7d43c203a67608d4721a0e8bfc54cfbb601f28e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "56557952ecd49e63ae235f3e3063db2d581dcdb38dcf42b7981478350cba2e77",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2000-07-14T13:41:27Z",
    "title_canon_sha256": "a993a4e7ff8205060672b78ce0f7a6044f5f5c10f4686dba0c898d739148f618"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0007020",
    "kind": "arxiv",
    "version": 1
  }
}