Pith Number

pith:TEN3WSPH

pith:2011:TEN3WSPHEIJN5V4HBZWMKMR5DC

not attested not anchored not stored refs pending

Multilevel Polarization of Polar Codes Over Arbitrary Discrete Memoryless Channels

Aria G. Sahebi, S. Sandeep Pradhan

arxiv:1107.1535 v3 · 2011-07-07 · 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{TEN3WSPHEIJN5V4HBZWMKMR5DC}

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	2026-05-18T02:21:43.318657Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

991bbb49e72212ded7870e6cc5323d18aedc80009071fb61fc79dcfd3b8dd601

Aliases

arxiv: 1107.1535 · arxiv_version: 1107.1535v3 · doi: 10.48550/arxiv.1107.1535 · pith_short_12: TEN3WSPHEIJN · pith_short_16: TEN3WSPHEIJN5V4H · pith_short_8: TEN3WSPH

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/TEN3WSPHEIJN5V4HBZWMKMR5DC \
  | 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: 991bbb49e72212ded7870e6cc5323d18aedc80009071fb61fc79dcfd3b8dd601

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe5d50921255b01ee4885a225e8a4c66b709e4ed446d1d83f3a344ac1f7d68eb",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2011-07-07T23:41:33Z",
    "title_canon_sha256": "363427ce5e21e66be6f82f3bbda3c9f7c81f4c5742de77a9e1872410efec871d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.1535",
    "kind": "arxiv",
    "version": 3
  }
}