Pith Number

pith:7BECGKVL

pith:2013:7BECGKVLRB3CZBEPPIHCNSA6Q4

not attested not anchored not stored refs pending

MacWilliams Extension Theorems and the Local-Global Property for Codes over Rings

Aleams Barra, Heide Gluesing-Luerssen

arxiv:1307.7159 v2 · 2013-07-26 · cs.IT · math.IT · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7BECGKVLRB3CZBEPPIHCNSA6Q4}

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	2026-05-18T02:55:36.273346Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f848232aab88762c848f7a0e26c81e87233614e0603957057e4ce05435aa7d01

Aliases

arxiv: 1307.7159 · arxiv_version: 1307.7159v2 · doi: 10.48550/arxiv.1307.7159 · pith_short_12: 7BECGKVLRB3C · pith_short_16: 7BECGKVLRB3CZBEP · pith_short_8: 7BECGKVL

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/7BECGKVLRB3CZBEPPIHCNSA6Q4 \
  | 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: f848232aab88762c848f7a0e26c81e87233614e0603957057e4ce05435aa7d01

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e866be113ec5833b12553f98177a46fc80bb9bfdda9e87415afa0c5d8147d2d0",
    "cross_cats_sorted": [
      "math.IT",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2013-07-26T20:23:15Z",
    "title_canon_sha256": "dde34c3e11fe1a8a455146a14c2199c94b98d53772cc81df01bc625981fc4241"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.7159",
    "kind": "arxiv",
    "version": 2
  }
}