Pith Number

pith:O4PUNMCW

pith:2026:O4PUNMCWLLKEYZ5C62TRMHUSII

not attested not anchored not stored refs pending

Logical Spectroscopy: Lifted-Product Codes with Addressable Bases

Jong Yeon Lee

arxiv:2607.05386 v1 · 2026-07-06 · 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{O4PUNMCWLLKEYZ5C62TRMHUSII}

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	2026-07-07T03:19:25.669043Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

771f46b0565ad44c67a2f6a7161e9242181a25fcef5341d9ab98160626fd3517

Aliases

arxiv: 2607.05386 · arxiv_version: 2607.05386v1 · doi: 10.48550/arxiv.2607.05386 · pith_short_12: O4PUNMCWLLKE · pith_short_16: O4PUNMCWLLKEYZ5C · pith_short_8: O4PUNMCW

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/O4PUNMCWLLKEYZ5C62TRMHUSII \
  | 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: 771f46b0565ad44c67a2f6a7161e9242181a25fcef5341d9ab98160626fd3517

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "30d8088e5c7efd49f968ad3fd9988e0d6d80f3bdca676a6498423c81916a3231",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-07-06T17:56:55Z",
    "title_canon_sha256": "7bbb2f93b1a42f35573a3ef111365ff5e700cd5d151e879dd77372f6bd1ee6da"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.05386",
    "kind": "arxiv",
    "version": 1
  }
}