Pith Number

pith:HOYWPGCF

pith:2019:HOYWPGCFQ4G52VI7PQLD2WAVSX

not attested not anchored not stored refs pending

Subadditivity Beyond Trees and the Chi-Squared Mutual Information

Emmanuel Abbe, Enric Boix-Adser\`a

arxiv:1902.02431 v1 · 2019-02-06 · math.PR · 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{HOYWPGCFQ4G52VI7PQLD2WAVSX}

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	2026-05-17T23:54:33.343214Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3bb1679845870ddd551f7c163d581595ca34c3df38811ad8517ebe507fe0c7f3

Aliases

arxiv: 1902.02431 · arxiv_version: 1902.02431v1 · doi: 10.48550/arxiv.1902.02431 · pith_short_12: HOYWPGCFQ4G5 · pith_short_16: HOYWPGCFQ4G52VI7 · pith_short_8: HOYWPGCF

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/HOYWPGCFQ4G52VI7PQLD2WAVSX \
  | 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: 3bb1679845870ddd551f7c163d581595ca34c3df38811ad8517ebe507fe0c7f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a4b0a143bdac886dbfa4c26d9c069531c1115cf10ae5eda55563773ee83310b5",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-02-06T23:37:20Z",
    "title_canon_sha256": "19a7006a05db2c7b645a94b595b1b6efaecfdafca67377bb2893f0692d19107b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1902.02431",
    "kind": "arxiv",
    "version": 1
  }
}