Pith Number

pith:WK5J2PBF

pith:2015:WK5J2PBFTSKYCBO4YWWF2UCNTM

not attested not anchored not stored refs pending

Lattice Codes Achieve the Capacity of Common Message Gaussian Broadcast Channels with Coded Side Information

Emanuele Viterbo, Lakshmi Natarajan, Yi Hong

arxiv:1509.01332 v3 · 2015-09-04 · 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{WK5J2PBFTSKYCBO4YWWF2UCNTM}

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	2026-05-18T00:27:55.444557Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2ba9d3c259c958105dcc5ac5d504d9b2959a7439a3ff9125a8357af7fee4bdf

Aliases

arxiv: 1509.01332 · arxiv_version: 1509.01332v3 · doi: 10.48550/arxiv.1509.01332 · pith_short_12: WK5J2PBFTSKY · pith_short_16: WK5J2PBFTSKYCBO4 · pith_short_8: WK5J2PBF

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/WK5J2PBFTSKYCBO4YWWF2UCNTM \
  | 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: b2ba9d3c259c958105dcc5ac5d504d9b2959a7439a3ff9125a8357af7fee4bdf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b943045f9b87f4815fb0a2afdadff25b28d3ab15ed4e3eb52a246d8baf1a89a0",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2015-09-04T02:38:22Z",
    "title_canon_sha256": "739b745446cb4e5394446432d1e14f070abb4e0f2662ab8e9fb2dc3420e64417"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.01332",
    "kind": "arxiv",
    "version": 3
  }
}