Pith Number

pith:4UNG5Y32

pith:2016:4UNG5Y32HR2X55LYB6KQJQ4DBD

not attested not anchored not stored refs pending

Capacity Achieving Distributions & Information Lossless Randomized Strategies for Feedback Channels with Memory: The LQG Theory of Directed Information-Part II

Charalambos D. Charalambous, Christos K. Kourtellaris, Sergey Loyka

arxiv:1604.01056 v1 · 2016-04-04 · 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{4UNG5Y32HR2X55LYB6KQJQ4DBD}

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	2026-05-18T01:17:46.636598Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e51a6ee37a3c757ef5780f9504c38308de5b2f78a01d3e9af3a8dc07ae8e904c

Aliases

arxiv: 1604.01056 · arxiv_version: 1604.01056v1 · doi: 10.48550/arxiv.1604.01056 · pith_short_12: 4UNG5Y32HR2X · pith_short_16: 4UNG5Y32HR2X55LY · pith_short_8: 4UNG5Y32

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/4UNG5Y32HR2X55LYB6KQJQ4DBD \
  | 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: e51a6ee37a3c757ef5780f9504c38308de5b2f78a01d3e9af3a8dc07ae8e904c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "99aec909ea2937044e0300b6906a2cc9a353550238b510322caef3b97ece892b",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2016-04-04T20:53:08Z",
    "title_canon_sha256": "fb7f7dac900004aeee31c2b9dee25d66837807f084f559ffb60d9636360c0b49"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.01056",
    "kind": "arxiv",
    "version": 1
  }
}