Pith Number

pith:WIGZK5QE

pith:2015:WIGZK5QEE6PCVX6IJAAGXE2IWI

not attested not anchored not stored refs pending

Entropies of weighted sums in cyclic groups and an application to polar codes

Emmanuel Abbe, Jiange Li, Mokshay Madiman

arxiv:1512.00135 v4 · 2015-12-01 · 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{WIGZK5QEE6PCVX6IJAAGXE2IWI}

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	2026-05-18T00:16:34.141198Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b20d957604279e2adfc848006b9348b23d19ace2ca09c3ee09d255411f9faaf2

Aliases

arxiv: 1512.00135 · arxiv_version: 1512.00135v4 · doi: 10.48550/arxiv.1512.00135 · pith_short_12: WIGZK5QEE6PC · pith_short_16: WIGZK5QEE6PCVX6I · pith_short_8: WIGZK5QE

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/WIGZK5QEE6PCVX6IJAAGXE2IWI \
  | 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: b20d957604279e2adfc848006b9348b23d19ace2ca09c3ee09d255411f9faaf2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "080eda6d75738c266eef55e5a519a460ff8623cc366eb81529d8c82c9576a774",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2015-12-01T04:12:28Z",
    "title_canon_sha256": "5820b7a20a89c67ba09cdd279cf1dfe5a444bbfbc527cf8fd26720fa6d224941"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.00135",
    "kind": "arxiv",
    "version": 4
  }
}