Pith Number

pith:ZGG524XP

pith:2015:ZGG524XPPOBAYPRV4JZYEOSX23

not attested not anchored not stored refs pending

On the Symmetry of Polar Codes for Symmetric Binary-Input Discrete Memoryless Channels

Liping Li, Qiming Wang

arxiv:1504.04934 v1 · 2015-04-20 · 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{ZGG524XPPOBAYPRV4JZYEOSX23}

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	2026-05-18T02:18:24.304377Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c98ddd72ef7b820c3e35e273823a57d6c565899a6ba3263ab9a0d7c9b4e6c121

Aliases

arxiv: 1504.04934 · arxiv_version: 1504.04934v1 · doi: 10.48550/arxiv.1504.04934 · pith_short_12: ZGG524XPPOBA · pith_short_16: ZGG524XPPOBAYPRV · pith_short_8: ZGG524XP

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/ZGG524XPPOBAYPRV4JZYEOSX23 \
  | 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: c98ddd72ef7b820c3e35e273823a57d6c565899a6ba3263ab9a0d7c9b4e6c121

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "634d971f917ba865a64fcb27fb232fa26e0721ae2d6601a1806a23c697b5f815",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2015-04-20T04:19:03Z",
    "title_canon_sha256": "24ce1aa8fe1a8e3fdc08147f98cab4841854dbdd1e8ca457b7834891e50faae8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.04934",
    "kind": "arxiv",
    "version": 1
  }
}