Pith Number

pith:KRJHC6NF

pith:2016:KRJHC6NFKM7STSLC67Z7476ZMU

not attested not anchored not stored refs pending

MacWilliams type identities on the Lee and Euclidean weights for linear codes over $\mathbb{Z}_{\ell}$

Shixin Zhu, Xiaoshan Kai, Yongsheng Tang

arxiv:1605.08994 v4 · 2016-05-29 · cs.IT · math.IT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KRJHC6NFKM7STSLC67Z7476ZMU}

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	2026-05-18T01:11:04.665757Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

54527179a5533f29c962f7f3fe7fd9650a996137c3bab5cf824c7608a923232d

Aliases

arxiv: 1605.08994 · arxiv_version: 1605.08994v4 · doi: 10.48550/arxiv.1605.08994 · pith_short_12: KRJHC6NFKM7S · pith_short_16: KRJHC6NFKM7STSLC · pith_short_8: KRJHC6NF

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/KRJHC6NFKM7STSLC67Z7476ZMU \
  | 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: 54527179a5533f29c962f7f3fe7fd9650a996137c3bab5cf824c7608a923232d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "158c9a99d51c9022654bb5d65c05382ba4842766a83191cc8402c7d5892b65b0",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2016-05-29T12:01:44Z",
    "title_canon_sha256": "616c51bd56dd558bfbfcfabdce08678b5d51e722dcbf522958060732435e08b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.08994",
    "kind": "arxiv",
    "version": 4
  }
}