Pith Number

pith:IJ27HICT

pith:2007:IJ27HICTF5AOLTTENSW7DXFCNQ

not attested not anchored not stored refs pending

Condition for the higher rank numerical range to be non-empty

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

arxiv:0706.1540 v2 · 2007-06-11 · 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{IJ27HICTF5AOLTTENSW7DXFCNQ}

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	2026-05-18T04:29:44.732360Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4275f3a0532f40e5ce646cadf1dca26c361641e8561cddbeaa66cd8c8fab5d60

Aliases

arxiv: 0706.1540 · arxiv_version: 0706.1540v2 · doi: 10.48550/arxiv.0706.1540 · pith_short_12: IJ27HICTF5AO · pith_short_16: IJ27HICTF5AOLTTE · pith_short_8: IJ27HICT

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/IJ27HICTF5AOLTTENSW7DXFCNQ \
  | 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: 4275f3a0532f40e5ce646cadf1dca26c361641e8561cddbeaa66cd8c8fab5d60

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1d6edce8e5a025dcb9bf4b2beaa918925036713b46f0dccd572cf04092099d13",
    "cross_cats_sorted": [
      "quant-ph"
    ],
    "license": "",
    "primary_cat": "math.FA",
    "submitted_at": "2007-06-11T18:36:26Z",
    "title_canon_sha256": "4d1ed834912b7430db5f1595bfcf0205503827d876b1d7b40ea082f0216fb6dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0706.1540",
    "kind": "arxiv",
    "version": 2
  }
}