Pith Number

pith:K3DDZ5AJ

pith:2012:K3DDZ5AJVN2JDD76PCD5PHLORJ

not attested not anchored not stored refs pending

High-SNR Asymptotics of Mutual Information for Discrete Constellations with Applications to BICM

Alex Alvarado, Erik Agrell, Fredrik Brannstrom, Tobias Koch

arxiv:1212.6526 v4 · 2012-12-28 · 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{K3DDZ5AJVN2JDD76PCD5PHLORJ}

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	2026-05-18T02:53:41.684425Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

56c63cf409ab74918ffe7887d79d6e8a6510c28e8be4268b93426357728ae49d

Aliases

arxiv: 1212.6526 · arxiv_version: 1212.6526v4 · doi: 10.48550/arxiv.1212.6526 · pith_short_12: K3DDZ5AJVN2J · pith_short_16: K3DDZ5AJVN2JDD76 · pith_short_8: K3DDZ5AJ

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/K3DDZ5AJVN2JDD76PCD5PHLORJ \
  | 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: 56c63cf409ab74918ffe7887d79d6e8a6510c28e8be4268b93426357728ae49d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "25b5da47ef6e8c4eb9fa86de7252f4bb5c8c6096eaa414a0f38877eacfe11f21",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2012-12-28T15:17:25Z",
    "title_canon_sha256": "727154b0c268c18715b9eb309e45d5076a8ba726eb4cdf445b42a2cabc06cb7c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.6526",
    "kind": "arxiv",
    "version": 4
  }
}