Pith Number

pith:VONKHSYJ

pith:2026:VONKHSYJZ35SJCEC5RVBBH5ZTI

not attested not anchored not stored refs pending

Contraction and Expansion Values of Quantum Channels

Mikel Sanz, Ruben Ibarrondo

arxiv:2607.04950 v1 · 2026-07-06 · quant-ph · 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{VONKHSYJZ35SJCEC5RVBBH5ZTI}

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	2026-07-07T02:20:14.993982Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab9aa3cb09cefb248882ec6a109fb99a0df03ff5ab954347e2727086f780c45c

Aliases

arxiv: 2607.04950 · arxiv_version: 2607.04950v1 · doi: 10.48550/arxiv.2607.04950 · pith_short_12: VONKHSYJZ35S · pith_short_16: VONKHSYJZ35SJCEC · pith_short_8: VONKHSYJ

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/VONKHSYJZ35SJCEC5RVBBH5ZTI \
  | 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: ab9aa3cb09cefb248882ec6a109fb99a0df03ff5ab954347e2727086f780c45c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a3ebc7e104b151b9c9427264cb505badb65a85c0459551a7db189d1dd3a1d7cb",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-07-06T11:25:19Z",
    "title_canon_sha256": "51321d25bc4739ee31d922b16622bf44e8166dae931892c9d16d1383dcc664a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.04950",
    "kind": "arxiv",
    "version": 1
  }
}