Pith Number

pith:47RH3N3G

pith:2025:47RH3N3GKL5UZYYOP4HQ2AJJ5U

not attested not anchored not stored refs pending

Entropic additive energy and entropy inequalities for sums and products

Ioannis Kontoyiannis, Lampros Gavalakis, Rupert Li

arxiv:2506.20813 v2 · 2025-06-25 · cs.IT · math.CO · math.IT · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{47RH3N3GKL5UZYYOP4HQ2AJJ5U}

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	2026-07-01T01:17:10.134208Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e7e27db76652fb4ce30e7f0f0d0129ed1397bd48e5cc1a96f952912ef6e2e98d

Aliases

arxiv: 2506.20813 · arxiv_version: 2506.20813v2 · doi: 10.48550/arxiv.2506.20813 · pith_short_12: 47RH3N3GKL5U · pith_short_16: 47RH3N3GKL5UZYYO · pith_short_8: 47RH3N3G

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/47RH3N3GKL5UZYYOP4HQ2AJJ5U \
  | 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: e7e27db76652fb4ce30e7f0f0d0129ed1397bd48e5cc1a96f952912ef6e2e98d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "00ed801da5c4b6556f2d52d78574248e83422158bac6d5092dd83b8617c87ae1",
    "cross_cats_sorted": [
      "math.CO",
      "math.IT",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2025-06-25T20:22:12Z",
    "title_canon_sha256": "c962543a695b0c1327e8ba0d1c616c2d5b390fb35533d0576eea08cb76fc5b02"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.20813",
    "kind": "arxiv",
    "version": 2
  }
}