Pith Number

pith:V4IYL7M2

pith:2007:V4IYL7M2MIJHAE5W3WSCK7Y4CR

not attested not anchored not stored refs pending

Higher rank numerical ranges and low rank perturbations of quantum channels

Chi-Kwong Li, Nung-sing Sze, Yiu-Tung Poon

arxiv:0710.2898 v2 · 2007-10-15 · math.FA · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{V4IYL7M2MIJHAE5W3WSCK7Y4CR}

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	2026-05-18T04:29:44.725649Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

af1185fd9a62127013b6dda4257f1c14400557ab467a946ff71ec0ed6215c245

Aliases

arxiv: 0710.2898 · arxiv_version: 0710.2898v2 · doi: 10.48550/arxiv.0710.2898 · pith_short_12: V4IYL7M2MIJH · pith_short_16: V4IYL7M2MIJHAE5W · pith_short_8: V4IYL7M2

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/V4IYL7M2MIJHAE5W3WSCK7Y4CR \
  | 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: af1185fd9a62127013b6dda4257f1c14400557ab467a946ff71ec0ed6215c245

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "071b1ce2d10ef1d80527273bf7180fc0be6e1ff11178c13dbe472e1d7c7555b7",
    "cross_cats_sorted": [
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2007-10-15T19:49:33Z",
    "title_canon_sha256": "f862b0bf8c4a51364c7db24e3f34fd58d21a06a38b9048390b2d6d69bef8481d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0710.2898",
    "kind": "arxiv",
    "version": 2
  }
}