Pith Number

pith:SSNWQUVN

pith:2013:SSNWQUVNSTJP5F5ZKGLTPRG65F

not attested not anchored not stored refs pending

MacWilliams' Extension Theorem for Bi-Invariant Weights over Finite Principal Ideal Rings

Cathy Mc Fadden, Jay A. Wood, Jens Zumbr\"agel, Marcus Greferath, Thomas Honold

arxiv:1309.3292 v1 · 2013-09-12 · math.RA · 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{SSNWQUVNSTJP5F5ZKGLTPRG65F}

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	2026-05-18T03:13:23.027345Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

949b6852ad94d2fe97b9519737c4dee942053bffa010319c3387f070d2f3bf80

Aliases

arxiv: 1309.3292 · arxiv_version: 1309.3292v1 · doi: 10.48550/arxiv.1309.3292 · pith_short_12: SSNWQUVNSTJP · pith_short_16: SSNWQUVNSTJP5F5Z · pith_short_8: SSNWQUVN

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/SSNWQUVNSTJP5F5ZKGLTPRG65F \
  | 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: 949b6852ad94d2fe97b9519737c4dee942053bffa010319c3387f070d2f3bf80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e5095620d452da0f89cf1dcf855437bbcda7d5ef716f6f74241a3ee47e61dda",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2013-09-12T20:22:50Z",
    "title_canon_sha256": "7d27008e7c9b26c4fe288d669e53dbad07a8e5cd3e7b974bc46f3208d5e06bbb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.3292",
    "kind": "arxiv",
    "version": 1
  }
}