Pith Number

pith:QL5MQI5M

pith:2025:QL5MQI5MSRFNT27QLIRUU7MSEP

not attested not anchored not stored refs pending

Unitary causal decompositions: a combinatorial characterisation via lattice theory

Robin Lorenz, Tein van der Lugt

arxiv:2508.11762 v1 · 2025-08-15 · quant-ph · math.CO · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QL5MQI5MSRFNT27QLIRUU7MSEP}

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	2026-07-05T11:54:54.012960Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82fac823ac944ad9ebf05a234a7d9223d359bfaff17925e2752210024143e589

Aliases

arxiv: 2508.11762 · arxiv_version: 2508.11762v1 · doi: 10.48550/arxiv.2508.11762 · pith_short_12: QL5MQI5MSRFN · pith_short_16: QL5MQI5MSRFNT27Q · pith_short_8: QL5MQI5M

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/QL5MQI5MSRFNT27QLIRUU7MSEP \
  | 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: 82fac823ac944ad9ebf05a234a7d9223d359bfaff17925e2752210024143e589

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b1dbb669024205986204959c77254292e105b2b57b3bfc966af052c64b5bc39",
    "cross_cats_sorted": [
      "math.CO",
      "math.RA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2025-08-15T18:22:29Z",
    "title_canon_sha256": "765db4e21775d1ee521452e3967f4bc67117b792d7af38bf8392be274087c886"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.11762",
    "kind": "arxiv",
    "version": 1
  }
}