Pith Number

pith:QW6LWVF2

pith:1996:QW6LWVF2HEGZSUABEVEDCAUHLU

not attested not anchored not stored refs pending

Quantum MacWilliams Identities

Peter Shor, Raymond Laflamme

arxiv:quant-ph/9610040 v1 · 1996-10-25 · 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{QW6LWVF2HEGZSUABEVEDCAUHLU}

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.

Cited by

1 paper in Pith

Convergence rates of Sum-of-Hermitian-Squares Hierarchies for the Pauli algebra

Receipt and verification

First computed	2026-07-04T14:47:05.635722Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

85bcbb54ba390d99500125483102875d10badbda05ac57f0e8e133db4c5d9361

Aliases

arxiv: quant-ph/9610040 · arxiv_version: quant-ph/9610040v1 · doi: 10.48550/arxiv.quant-ph/9610040 · pith_short_12: QW6LWVF2HEGZ · pith_short_16: QW6LWVF2HEGZSUAB · pith_short_8: QW6LWVF2

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/QW6LWVF2HEGZSUABEVEDCAUHLU \
  | 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: 85bcbb54ba390d99500125483102875d10badbda05ac57f0e8e133db4c5d9361

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "12df8876a2098effbd4c21abcf4625490e65dac9877e0817f2f67f3ae58d2571",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "1996-10-25T21:32:14Z",
    "title_canon_sha256": "2de63f420bc2f64927df6bfd13d9a980ae576ee108dfe7508a5d731dc8ad383c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/9610040",
    "kind": "arxiv",
    "version": 1
  }
}