Pith Number

pith:LXSYKJ3W

pith:2007:LXSYKJ3W6BTETZ4P6XLUSR5SL3

not attested not anchored not stored refs pending

Catalytic majorization and $\ell_p$ norms

Guillaume Aubrun (ICJ), Ion Nechita (ICJ)

arxiv:quant-ph/0702153 v2 · 2007-02-15 · 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{LXSYKJ3W6BTETZ4P6XLUSR5SL3}

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	2026-05-18T03:12:58.365610Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5de5852776f06649e78ff5d74947b25ed47088f0913800d875adc4edfb4554dc

Aliases

arxiv: quant-ph/0702153 · arxiv_version: quant-ph/0702153v2 · doi: 10.48550/arxiv.quant-ph/0702153 · pith_short_12: LXSYKJ3W6BTE · pith_short_16: LXSYKJ3W6BTETZ4P · pith_short_8: LXSYKJ3W

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/LXSYKJ3W6BTETZ4P6XLUSR5SL3 \
  | 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: 5de5852776f06649e78ff5d74947b25ed47088f0913800d875adc4edfb4554dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d48e2aaf63a3adf15cde97ec46b428c3452cc1ef1a05f732a87d5bedf994a1f1",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "2007-02-15T12:48:57Z",
    "title_canon_sha256": "296e1a6d46a491cea612198ad8f7f17c7afca1d91f8a10d3f0ccd8d7f58f8b38"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/0702153",
    "kind": "arxiv",
    "version": 2
  }
}