Pith Number

pith:7WK2U5EB

pith:2026:7WK2U5EBNXBYC74RCGD2G3IZPK

not attested not anchored not stored refs pending

Mutual Information Optimization via K-Recursion and Automatic Differentiation for Linear Gaussian Wireless Networks

Na Siqi, Tadashi Wadayama

arxiv:2606.06982 v1 · 2026-06-05 · 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{7WK2U5EBNXBYC74RCGD2G3IZPK}

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	2026-06-08T01:04:39.414520Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd95aa74816dc3817f911187a36d197a845a1871db07d13903a2dd944f5efb69

Aliases

arxiv: 2606.06982 · arxiv_version: 2606.06982v1 · doi: 10.48550/arxiv.2606.06982 · pith_short_12: 7WK2U5EBNXBY · pith_short_16: 7WK2U5EBNXBYC74R · pith_short_8: 7WK2U5EB

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/7WK2U5EBNXBYC74RCGD2G3IZPK \
  | 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: fd95aa74816dc3817f911187a36d197a845a1871db07d13903a2dd944f5efb69

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "84ce29487239a5157ff590ee7fc8132f3e37b90898b54158f14bbc4a44660c99",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-06-05T07:18:12Z",
    "title_canon_sha256": "9aaa4cfd771ec83bf1f3215ec70361a5478c5eac3ed464f8f19870fb0fd201cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.06982",
    "kind": "arxiv",
    "version": 1
  }
}