Pith Number

pith:UWQ5WOZO

pith:2015:UWQ5WOZOFG47XIP6G4NIQJIWKD

not attested not anchored not stored refs pending

Geometric approach to the MacWilliams Extension Theorem for codes over modules

Serhii Dyshko

arxiv:1507.05212 v1 · 2015-07-18 · cs.IT · math.CO · 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{UWQ5WOZOFG47XIP6G4NIQJIWKD}

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	2026-05-18T00:43:39.874114Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a5a1db3b2e29b9fba1fe371a88251650e3ac2637112bfe3faec766505bb4fb11

Aliases

arxiv: 1507.05212 · arxiv_version: 1507.05212v1 · doi: 10.48550/arxiv.1507.05212 · pith_short_12: UWQ5WOZOFG47 · pith_short_16: UWQ5WOZOFG47XIP6 · pith_short_8: UWQ5WOZO

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/UWQ5WOZOFG47XIP6G4NIQJIWKD \
  | 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: a5a1db3b2e29b9fba1fe371a88251650e3ac2637112bfe3faec766505bb4fb11

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1771860131637e9a6669edd73f289deb02ecf72df84e5966bde01173df045cda",
    "cross_cats_sorted": [
      "math.CO",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2015-07-18T18:15:04Z",
    "title_canon_sha256": "e7ce0ef6aca4a13a294f08cef2ed6b8495513426495ac9fe7c3c666234408ddf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.05212",
    "kind": "arxiv",
    "version": 1
  }
}