Pith Number

pith:ZNUBRIYR

pith:2015:ZNUBRIYR4GV4RKQHVH2RXOZM7X

not attested not anchored not stored refs pending

New self-dual additive $\mathbb{F}_4$-codes constructed from circulant graphs

Markus Grassl, Masaaki Harada

arxiv:1509.04846 v2 · 2015-09-16 · math.CO · cs.IT · math.IT · 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{ZNUBRIYR4GV4RKQHVH2RXOZM7X}

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	2026-05-18T00:58:55.470270Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb6818a311e1abc8aa07a9f51bbb2cfdff0d96d9cc37b9a4a358298e8d7b571e

Aliases

arxiv: 1509.04846 · arxiv_version: 1509.04846v2 · doi: 10.48550/arxiv.1509.04846 · pith_short_12: ZNUBRIYR4GV4 · pith_short_16: ZNUBRIYR4GV4RKQH · pith_short_8: ZNUBRIYR

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/ZNUBRIYR4GV4RKQHVH2RXOZM7X \
  | 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: cb6818a311e1abc8aa07a9f51bbb2cfdff0d96d9cc37b9a4a358298e8d7b571e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "658770a6159e59d41579085195f43ceeeb7aaf32d91c55d3324617b307726703",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-09-16T08:12:11Z",
    "title_canon_sha256": "ea93dd786c03a09acfc2b6dd8b9367b4fda58f33636110ffccb028e7448290cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.04846",
    "kind": "arxiv",
    "version": 2
  }
}